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  • 1995-1999  (851)
  • 1980-1984  (2,019)
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  • 1
    Electronic Resource
    Electronic Resource
    Minimum Time Control of Flexible Spacecraft by Hamilton's Principle (1997)
    Springer
    Meccanica 32 (1997), S. 555-565 
    Details
    ISSN: 1572-9648
    Keywords: Spacecraft dynamics ; Optimal control ; Hamilton principle ; Vibrations (structures)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Modern space vehicles structure requisites are getting more and more stringent and complex as mission tasks become more sophisticated. This leads to the necessity of developing analysis methods that take into account structure flexibility and the need of reducing manoeuvre time as much as possible. In this work, a method based on the Hamilton Principle in its weak mixed form is developed, in which co-ordinates derivatives do not appear, but only their virtual variations. The proposed formulation is able to take into account system flexibility and saturation constraints on control torques and forces. A non-linear variational condition is obtained, which can be solved by means of a time-finite-element technique to give the minimum-time solutions of the control problem. The solutions for slewing manoeuvres are given, along with a new solution of the distributed optimal control problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004204510722
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  • 2
    Electronic Resource
    Electronic Resource
    Animals as indicators of ecosystem responses to air emissions (1984)
    Springer
    Environmental management 8 (1984), S. 309-324 
    Details
    ISSN: 1432-1009
    Keywords: Animals ; Indicators ; Air pollution ; Ecosystem responses
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract With existing and proposed air-quality regulations, ecological disasters resulting from air emissions such as those observed at Copperhill, Tennessee, and Sudbury, Ontario, are unlikely. Current air-quality standards, however, may not protect ecosystems from subacute and chronic exposure to air emissions. The encouragement of the use of coal for energy production and the development of the fossil-fuel industries, including oil shales, tar sands, and coal liquification, point to an increase and spread of fossil-fuel emissions and the potential to influence a number of natural ecosystems. This paper reviews the reported responses of ecosystems to air-borne pollutants and discusses the use of animals as indicators of ecosystem responses to these pollutants. Animal species and populations can act as important indicators of biotic and abiotic responses of aquatic and terrestrial ecosystems. These responses can indicate long-term trends in ecosystem health and productivity, chemical cycling, genetics, and regulation. For short-term trends, fish and wildlife also serve as monitors of changes in community structure, signaling food-web contamination, as well as providing a measure of ecosystem vitality. Information is presented to show not only the importance of animals as indicators of ecosystem responses to air-quality degradation, but also their value as air-pollution indices, that is, as air-quality-related values (AQRV), required in current air-pollution regulation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01868030
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  • 3
    Electronic Resource
    Electronic Resource
    Optimal control of the chemotherapy of HIV (1997)
    Springer
    Journal of mathematical biology 35 (1997), S. 775-792 
    Details
    ISSN: 1432-1416
    Keywords: Key words: Chemotherapy ; HIV ; Optimal control ; Ordinary differential equation system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract.  Using an existing ordinary differential equation model which describes the interaction of the immune system with the human immunodeficiency virus (HIV), we introduce chemotherapy in an early treatment setting through a dynamic treatment and then solve for an optimal chemotherapy strategy. The control represents the percentage of effect the chemotherapy has on the viral production. Using an objective function based on a combination of maximizing benefit based on T cell counts and minimizing the systemic cost of chemotherapy (based on high drug dose/strength), we solve for the optimal control in the optimality system composed of four ordinary differential equations and four adjoint ordinary differential equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002850050076
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  • 4
    Electronic Resource
    Electronic Resource
    The ultrastructure, catecholamine, and prolactin contents of the rostral pars distalis of the fish Mugil platanus after reserpine or 6-hydroxydopamine administration (1975)
    Springer
    Cell & tissue research 162 (1975), S. 551-563 
    Details
    ISSN: 1432-0878
    Keywords: Hypophysis ; Rostral pars distalis ; Mugil platanus ; Animals ; Prolactin hormone secretion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Medicine
    Notes: Summary The rostral pars distalis (RPD) of the teleost Mugil platanus from animals pretreated with reserpine or 6-hydroxydopamine (6-HODA) were assayed for dopamine (DA) or noradrenaline (NA) or for prolactin hormone. Such determinations were coupled with electron microscopy. It was found that reserpine and 6-HODA produced a significant decrease in the content of DA, NA, and prolactin. Electron microscope studies revealed that prolactin cells became activated as judged by ultrastructural criteria. After 6-HODA treatment type “B” neurosecretory fibers entering the RPD became selectively destroyed. These observations lead us to suggest that prolactin secretion is under inhibitory control by type “B” neurosecretory fibers of adrenergic nature.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00209354
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  • 5
    Electronic Resource
    Electronic Resource
    Optimal control for a tandem network of queues with blocking (1997)
    Springer
    Acta mathematicae applicatae sinica 13 (1997), S. 425-437 
    Details
    ISSN: 1618-3932
    Keywords: Optimal control ; tandem queueing system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a two-station tandem queue with no intermediate buffer. Jobs at the first station may be blocked when the following station is occupied by another job. The objective is to control the arrival and departure processes, subject to some capacity limits, so that an expected discounted profit function is maximized. We prove that the optimal control policy is of a threshold type, and the characterization of the threshold is provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02009552
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  • 6
    Electronic Resource
    Electronic Resource
    The linear quadratic optimal control problem for linear descriptor systems with variable coefficients (1997)
    Springer
    Mathematics of control, signals, and systems 10 (1997), S. 247-264 
    Details
    ISSN: 1435-568X
    Keywords: Descriptor systems ; Differential algebraic equations ; Optimal control ; Strangeness index ; Riccati differential-algebraic equations ; Euler-Lagrange equations ; Linear feedback
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics , Technology
    Notes: Abstract We study linear quadratic optimal control problems for linear variable coefficient descriptor systems. Generalization from the case of standard control problems leads to several difficulties. We discuss a behavioral approach that solves some of these difficulties. Furthermore, an analysis of general rectangular systems is given and generalized Euler-Lagrange equations and Riccati differential algebraic equations are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01211506
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  • 7
    Electronic Resource
    Electronic Resource
    Animal Consciousness and Ethics in Asia and the Pacific (1997)
    Springer
    Journal of agricultural and environmental ethics 10 (1997), S. 249-267 
    Details
    ISSN: 1573-322X
    Keywords: Animals ; Asia ; consciousness ; Australia ; Hong Kong ; India ; Israel ; Japan ; New Zealand ; The Philippines ; Russia ; Singapore ; Thailand
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering , Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition , Philosophy
    Notes: Abstract The interactions between humans, animals and the environment have shaped human values and ethics, not only the genes that we are made of. The animal rights movement challenges human beings to reconsider interactions between humans and other animals, and maybe connected to the environmental movement that begs us to recognize the fact that there are symbiotic relationships between humans and all other organisms. The first part of this paper looks at types of bioethics, the implications of autonomy and the value of being alive. Then the level of consciousness of these relationships are explored in survey results from Asia and the Pacific, especially in the 1993 International Bioethics Survey conducted in Australia, Hong Kong, India, Israel, Japan, New Zealand, The Philippines, Russia, Singapore and Thailand. Very few mentioned animal consciousness in the survey, but there were more biocentric comments in Australia and Japan; and more comments with the idea of harmony including humans in Thailand. Comparisons between questions and surveys will also be made, in an attempt to describe what people imagine animal consciousness to be, and whether this relates to human ethics of the relationships.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007774409131
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  • 8
    Electronic Resource
    Electronic Resource
    Quadratic control problems (1975)
    Springer
    Journal of optimization theory and applications 17 (1975), S. 1-42 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; calculus of variations ; quadratic control problems ; linear spaces ; conjugate points ; focal points ; Bolza problem ; Hilbert space techniques
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The present paper is concerned with the study of quadratic control problems on linear spaces. In particular, we are concerned with the conditions under which a quadratic criterion function is positive on certain linear spaces. This involves the elementary theory of conjugate and focal points, the existence of a conjugate system with a nonvanishing determinant, and the existence of extremal fields. The results given are in part a translation into control language of known theory for the problem of Bolza. The method used is based on the Hilbert space techniques developed earlier by the author.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933915
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  • 9
    Electronic Resource
    Electronic Resource
    On the existence of optimal controls (1975)
    Springer
    Journal of optimization theory and applications 17 (1975), S. 273-278 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; existence theorems ; control theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Using a recent result due to Berkovitz, we prove the existence of an optimal control in a broad class of problems, under relatively mild conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933880
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  • 10
    Electronic Resource
    Electronic Resource
    Remarks on bang-bang control in a Hilbert space (1977)
    Springer
    Journal of optimization theory and applications 21 (1977), S. 51-57 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; linear systems ; linear-quadratic problems ; bang-bang control ; Hilbert spaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The control of a linear system, whose performance index is the sum of a linear term and a quadratic term, is considered. A necessary and sufficient condition is given for the optimal control to be bang-bang, and this is used to extend and clarify the results of Refs. 1–2. As an illustration, an application to an elliptic boundary-value problem is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932543
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  • 11
    Electronic Resource
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    Forward differential dynamic programming (1977)
    Springer
    Journal of optimization theory and applications 21 (1977), S. 487-504 
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    ISSN: 1573-2878
    Keywords: Optimal control ; forward dynamic programming ; differential dynamic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The dynamic programming formulation of the forward principle of optimality in the solution of optimal control problems results in a partial differential equation with initial boundary condition whose solution is independent of terminal cost and terminal constraints. Based on this property, two computational algorithms are described. The first-order algorithm with minimum computer storage requirements uses only integration of a system of differential equations with specified initial conditions and numerical minimization in finite-dimensional space. The second-order algorithm is based on the differential dynamic programming approach. Either of the two algorithms may be used for problems with nondifferentiable terminal cost or terminal constraints, and the solution of problems with complicated terminal conditions (e.g., with free terminal time) is greatly simplified.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933093
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  • 12
    Electronic Resource
    Electronic Resource
    On the optimal control of a single-server queueing system: Reply (1978)
    Springer
    Journal of optimization theory and applications 26 (1978), S. 463-464 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; queueing systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This comment replies to a criticism due to Klein and Gruver (Ref. 1) of our earlier paper (Ref. 2) on the application of control theory to a queueing system. The criticism concerns the state-space diagram and the table which we inadvertently gave for the terminal-reward problem, albeit incorrectly labeled, rather than for the free-endpoint problem considered in our paper. We show that the solution given by Klein and Gruver is itself incorrect and nonoptimal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933467
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  • 13
    Electronic Resource
    Electronic Resource
    Sequential gradient-restoration algorithm for optimal control problems with general boundary conditions (1978)
    Springer
    Journal of optimization theory and applications 26 (1978), S. 395-425 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; numerical methods ; computing methods ; gradient methods ; gradient-restoration algorithms ; sequential gradient-restoration algorithms ; general boundary conditions ; nondifferential constraints ; bounded control ; bounded state
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper considers the numerical solution of two classes of optimal control problems, called Problem P1 and Problem P2 for easy identification. Problem P1 involves a functionalI subject to differential constraints and general boundary conditions. It consists of finding the statex(t), the controlu(t), and the parameter π so that the functionalI is minimized, while the constraints and the boundary conditions are satisfied to a predetermined accuracy. Problem P2 extends Problem P1 to include nondifferential constraints to be satisfied everywhere along the interval of integration. Algorithms are developed for both Problem P1 and Problem P2. The approach taken is a sequence of two-phase cycles, composed of a gradient phase and a restoration phase. The gradient phase involves one iteration and is designed to decrease the value of the functional, while the constraints are satisfied to first order. The restoration phase involves one or more iterations and is designed to force constraint satisfaction to a predetermined accuracy, while the norm squared of the variations of the control, the parameter, and the missing components of the initial state is minimized. The principal property of both algorithms is that they produce a sequence of feasible suboptimal solutions: the functions obtained at the end of each cycle satisfy the constraints to a predetermined accuracy. Therefore, the values of the functionalI corresponding to any two elements of the sequence are comparable. The stepsize of the gradient phase is determined by a one-dimensional search on the augmented functionalJ, while the stepsize of the restoration phase is obtained by a one-dimensional search on the constraint errorP. The gradient stepsize and the restoration stepsize are chosen so that the restoration phase preserves the descent property of the gradient phase. Therefore, the value of the functionalI at the end of any complete gradient-restoration cycle is smaller than the value of the same functional at the beginning of that cycle. The algorithms presented here differ from those of Refs. 1 and 2, in that it is not required that the state vector be given at the initial point. Instead, the initial conditions can be absolutely general. In analogy with Refs. 1 and 2, the present algorithms are capable of handling general final conditions; therefore, they are suited for the solution of optimal control problems with general boundary conditions. Their importance lies in the fact that many optimal control problems involve initial conditions of the type considered here. Six numerical examples are presented in order to illustrate the performance of the algorithms associated with Problem P1 and Problem P2. The numerical results show the feasibility as well as the convergence characteristics of these algorithms.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933463
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  • 14
    Electronic Resource
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    On the optimal control problem of a single-server queueing system (1983)
    Springer
    Journal of optimization theory and applications 41 (1983), S. 317-325 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; queueing theory ; phase type distributions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a single-server queueing system (with a finite waiting room) with phase type arrivals and exponential service times, an optimal control for the service rate is derived. This generalizes the result of Scott and Jefferson for theM/M/1/1 queueing model.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935227
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  • 15
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    Realistic feedback control of two interconnected turbogenerators (1984)
    Springer
    Journal of optimization theory and applications 42 (1984), S. 103-141 
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    ISSN: 1573-2878
    Keywords: Optimal control ; realistic feedback control ; interconnected turbogenerators ; torque and voltage control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the optimal control of a system with two identical interconnected turbogenerators, which are connected to an infinite bus, is considered. The alternators are controlled through a linear feedback of the state variables. The feedback parameters are obtained by solving a nonlinear, two-point boundary-value problem. The values obtained for these parameters depend on the strength and duration of the disturbance, since the model is nonlinear, contrary to the usual feedback control of a linear model. In contrast to the model used in Ref. 1, the model used here includes the transfer function of the governors, the turbines, and the voltage regulators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934135
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  • 16
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    Convergence of a strong variational algorithm for relaxed controls involving a class of hyperbolic systems (1984)
    Springer
    Journal of optimization theory and applications 42 (1984), S. 467-485 
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    ISSN: 1573-2878
    Keywords: Optimal control ; hyperbolic partial differential equations ; Darboux boundary conditions ; strong variational algorithm ; convergence ; relaxed control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a class of optimal control problems involving linear hyperbolic partial differential equations with Darboux boundary conditions. A strong variational algorithm has been obtained for solving this class of optimal control problems in a previous paper by the third and the first authors. It was also shown that anyL ∞ accumulation points of control sequences generated by the algorithm satisfy a necessary condition for optimality. Since such accumulation points need not exist, it is shown in this paper that the control sequences generated by the algorithm always have accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed control problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935327
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  • 17
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    Necessary and sufficient conditions for optimal control of quasilinear partial differential systems (1984)
    Springer
    Journal of optimization theory and applications 43 (1984), S. 89-101 
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    ISSN: 1573-2878
    Keywords: Optimal control ; distributed-parameter systems ; control of partial differential equations ; sufficiency conditions ; Green's formula
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract First-order necessary and sufficient conditions are obtained for the following quasilinear distributed-parameter optimal control problem: $$max\left\{ {J(u) = \int_\Omega {F(x,u,t) d\omega + } \int_{\partial \Omega } {G(x,t) \cdot d\sigma } } \right\},$$ subject to the partial differential equation $$A(t)x = f(x,u,t),$$ wheret,u,G are vectors andx,F are scalars. Use is made of then-dimensional Green's theorem and the adjoint problem of the equation. The second integral in the objective function is a generalized surface integral. Use of then-dimensional Green's theorem allows simple generalization of single-parameter methods. Sufficiency is proved under a concavity assumption for the maximized Hamiltonian $$H^\circ (x,\lambda ,t) = \max \{ H(x,u,\lambda ,t):u\varepsilon K\} $$ .
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    URL: http://dx.doi.org/10.1007/BF00934748
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  • 18
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    Use of Augmented Lagrangian Methods for the Optimal Control of Obstacle Problems (1997)
    Springer
    Journal of optimization theory and applications 95 (1997), S. 101-126 
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    ISSN: 1573-2878
    Keywords: Optimal control ; Lagrange multipliers ; augmented Lagrangians ; variational inequalities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate optimal control problems governed by variational inequalities involving constraints on the control, and more precisely the example of the obstacle problem. In this paper, we discuss some augmented Lagrangian algorithms to compute the solution.
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    URL: http://dx.doi.org/10.1023/A:1022635428708
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  • 19
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    The sommerfeld half-plane problem revisited, II the factoring of a matrix of analytic functionsThese results were announced at the XXth General Assembly of the U.R.S.I. held in Washington, D.C., August 1981. (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 14-21 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A half-plane under plane wave excitation obeys a Dirichlet boundary condition on one side and a Neumann boundary condition on the other. These boundary conditions contrast the ones used by A. Sommerfeld in his classical paper. The present problem leads to a system of integral equations of the Wiener-Hopf type which may be solved by a matrix factoring method suggested by A. E. Heins in 1950.
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    URL: http://dx.doi.org/10.1002/mma.1670050103
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  • 20
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    Asymptotic equipartition of energy for equations of elasticity (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 186-194 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we give a review of the equipartition of energy results of Goldstein and Sandefur [3], [4], [5] as well as proving a new result in the case of a particular fourth order equation. These results are then applied to the equations of elasticity to give a weak asymptotic orthogonality for the shear and pressure waves. In the case of boundary value problems in the interior of a bounded domain we get weak asymptotic orthogonality in the average.
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    URL: http://dx.doi.org/10.1002/mma.1670050114
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  • 21
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    Variational derivatives and p-gradients of functionals on spaces of continuously differentiable functions (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 530-543 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The purpose of this paper is to introduce and study a new type of derivative - the variational gradient - for a functional on Cn[a, b]. Local and global versions of this concept are analyzed. This notion provides a natural approach to variational derivatives on Cn[a, b] under rather mild smoothness assumptions on the functional. When applied in the context of the Calculus of Variations, the notion of the variational gradient captures the natural boundary conditions (as well as the Euler-Lagrange equations) under weaker smoothness assumptions than those usually required using Gǎteaux variations.Conditions are established for the existence of the variational derivative and an integral representation for the Gǎteaux variation in terms of the variational derivative is derived. Conditions for the variational derivative to be differentiable are also established.
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    URL: http://dx.doi.org/10.1002/mma.1670050132
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  • 22
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    Masthead (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    URL: http://dx.doi.org/10.1002/mma.1670050101
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  • 23
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    Half-stable solution branches for ordinary bifurcation problemsThis paper is an extended version of a part of the author's work [2]. (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 1-13 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: It is shown that second order bifurcation problems with a positive, autonomous nonlinearity have a smooth branch of positive solutions which tends to infinity. Moreover, this branch satisfies a stability rule saying that the solutions are stable if the branch turns to the right and unstable if it turns to the left.
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    URL: http://dx.doi.org/10.1002/mma.1670050102
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    A critical case for the solvability of stefan-like problemsWork performed under the auspices of the Italian C.N.R., G.N.F.M. (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 84-96 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider a one-phase one-dimensional Stefan problem with general data with the aim to investigate some open questions on existence of classical solutions. We show how existence and nonexistence are discriminated by the behavior of the initial datum in the neighborhood of the starting point of the free boundary.
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    URL: http://dx.doi.org/10.1002/mma.1670050107
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  • 25
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    Periodic solutions of u'(t) = -f(u(t - 1)): Multiplicity results and small period solutions (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 162-175 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we are concerned with the differential delay equationFor odd and continuous nonlinearities f: R → R. We want to prove existence and multiplicity criteria for so called “slowly oscillating” periodic solutions of (A).The oddness condition is of course a rather restrictive one, but due to results of Nussbaum [9], [10] and Peters [13],[14] and numerical studies of Jürgens, Peitgen and Saupe [7] and Hadeler [6] we know that even for odd nonlinearities f (A) may display a complicated dynamical behaviour. On the other hand the oddness condition allows a classification of symmetry properties of periodic solutions of (A).
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    Lösungen der poissongleichung und harmonische vektorfelder in unbeschränkten gebieten (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 233-255 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In the first part of this paper we consider generalised solutions of the Poisson equation Δ U = F in open subsets of Rn(n ≥ 3) with Dirichlet or Neumann boundary data. We prove existence and uniqueness theorems, not only for the corresponding interior and exterior problems, but also for domains with boundaries extending to infinity. In the second part we discuss generalised harmonic fields in open subsets of R3 with vanishing Dirichlet or Neumann boundary condition.
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    Gruppentheoretische aspekte der signalübertragung und der kardinalen interpolationssplines I (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 195-215 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: As is well known the real Heisenberg nilpotent group A(R) constitutes the group-theoretic embodiment of the Heisenberg canonical commutation relations (CCR) of classical quantum mechanics. In this connection, quantum mechanics stands for the quantum-mechanical description, at a given instant of time, of a non-relativistic microparticle moving in the one-dimensional configuration space R and having the plane R2 as its (flat) phase space. In fact, the (nilpotent) Lie algebra n of Ã(R) reflects the Weyl equations which are global versions of the Heisenberg CCR. Unfortunately, the subject of Heisenberg nilpotent groups is outside quantum mechanics and all the more outside mathematical physics not as commonly known as it should be considering its wide range of applications in a variety of different fields. The present paper which has two parts aims to develop a central topic of nilpotent harmonic analysis, to wit, the microparticle model, the lattice model which will be realized on the Heisenberg compact nilmanifold, and the complex wave model (or Bargmann-Fock-Segal model) of the linear Schrödinger representation of Ã(R) in order to examine geometrically several applications which are governed by the real Heisenberg nilpotent group Ã(R). These applications are in Part I the classical Whittaker-Shannon sampling theorem which is of basic importance in signal processing, to wit, for the transmission of digital signals as well as analog signals, and in Part II the Subbotin-Schoenberg existence and uniqueness theorem of cardinal spline interpolation. Moreover, Part II indicates briefly some connections of the aforementioned models to the Wigner phase-space quasiprobability density function of quantum statistical mechanics via the Schwartz kernels theory on unimodular Lie groups, an approach to the cross- and autoambiguity functions of radar synthesis, and to the Zak transform of solid state physics. The second part also points out some relations of harmonic analysis of the finite nilpotent group A(Z/NZ) to periodic spline interpolants admitting N equidistant knots on the one-dimensional compact torus group T. These last examples should serve mainly as hints for some further lines of investigations in the field of applications of nilpotent harmonic analysis.
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    Das asymptotische verhalten der greenschen funktion N-irregulaärer eigenwertprobleme mit zerfallenden randbedingungen (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 331-345 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We prove asymptotic estimates for the Green's function of N-irregular eigenvalue problems My = λNγ with splitting boundary conditions.In contrast to the N-regular case the Green's function G(x,ζ,λ) grows exponentially for |λ| → ∞ if x 〉 ζ.These estimates are fundamental for the expansion of functions into a series of eigenfunctions of N-irregular eigenvalue problems. In a subsequent paper it will be shown that this irregular behavior of G(x,ζ,λ) implies that only a very small class of functions can be expanded into a series of eigenfunctions of such problems.
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    URL: http://dx.doi.org/10.1002/mma.1670050122
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    Approximation of the signorini problem with friction, obeying the coulomb law (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 422-437 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The approximation of the Signorini problem with friction by mixed finite element method is studied. The relation between the continuous case and its finite dimensional discretization is analyzed.
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    URL: http://dx.doi.org/10.1002/mma.1670050127
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    Free boundary problem for a two-layer inviscid incompressible fluid (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 476-490 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The existence of a local (in time) classical solution of a free boundary problem for a two-layer inviscid incompressible fluid is shown. The method of successive approximations and the novel approach to Lagrangian coordinates of Solonnikov are used.
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    Masthead (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984) 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    Solvability of an initial boundary value problem for the euler equations in twodimensional domain with corners (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 1-22 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The aim of this paper is to prove the existence and uniqueness of local solutions of some initial boundary value problems for the Euler equations of an incompressible fluid in a bounded domain Ω ⊂ R2 with corners. We consider two cases of a nonvanishing normal component of velocity on the boundary. In three-dimensional case such problems have been considered in papers [12], [13], [14]. Similar problems in domains without corners have been considered in [2]-[6], [11]. In this paper the relation between the maximal corner angle of the boundary and the smoothness of the solutions is shown. The paper consists of four sections. In section 1 two initial boundary value problems for the Euler equations are formulated. In section 2 the existence and uniqueness of solutions of the Laplace equation in twodimensional domain with corners for the Dirichlet and Neumann problems is proved in the Sobolev spaces. In sections 3 and 4 we prove the existence and uniqueness of solutions of problems formulated in section 1, using the method of successive approximations.
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    Faedo-galerkin approximations in equations of evolution (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 41-54 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the evolution equation u' = Au + Nu u(0) = φu is a function on a real interval [0, T] with values in a Hilbert space H, A is a linear operator in H generating a continuous semigroup eAt and N is a nonlinear operator in H.We show that 1Existence of the exact solution implies existence of the Faedo-Galerkin Approximations.2Existence of the Faedo-Galerkin Approximations implies existence of the exact solution.3Uniform convergence of the Faedo-Galerkin Approximations to the exact solution.The Paper consists of two parts. In the first five sections we require that A possesses a complete orthonormal system of eigenfunctions, in section 6 we drop this requirement.
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    Functional differential equations with certain monotonicity properties (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 97-103 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: The present paper is concerned with the study of retarded differential equations in n-space, which satisfy some monotonicity properties. Sufficient conditions are given guaranteeing that solutions are contained in the probability (n - 1)-simplex. Existence and uniqueness of constant solutions are proved. It is also shown that every solution converges to a constant as t → ∞.
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    On the transmission problem of the helmholtz equation for quadrantsHerrn Prof. Dr. K. Nickel zum 60. Geburtstag am 9. 2. 1984 gewidmet (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 129-157 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The plane transmission problem of the Helmholtz equation for quadrants is characterized by a one-dimensional singular integral equation, which refers to the Fourier transform of the normal derivative of the solution along the x-axis. It is derived by solving the transmission problem for the upper and the lower half-plane involving a Neumann condition at y = 0. This is done by a two-dimensional Laplace transform technique. The inverse Laplace transform with respect to the second cartesian coordinate and the restriction of this one to y = 0 then lead to the integral equation. Thereby the transmission conditions of the original problem at y = 0 have to be taken into account. The resulting integral equation is of generalized Wiener-Hopf-type. It is solved via the contraction theorem imposing restricting conditions on the wave numbers.
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    Bifurcation of periodic solutions for wave equations with scalar nonlinearities (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 206-214 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We treat wave equations with “scalar nonlinearities” and demonstrate the connection between the bifurcation theory of an associated system of Hammerstein integral equations and the existence of periodic solutions of the nonlinear wave equation.
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    Weak solutions of the initial value problem for the unmodified non-linear vlasov equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 262-279 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
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    Notes: The existence of weak LL-solutions of the initial value problem for Vlasov's equation is proved under rather general assumptions. In the three-dimensional case the solutions exist on the entire time axis.
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    A generalized jacobi theta function (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 327-344 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: The delta function initial condition solution v*(x,t;y) at x = y ≥ 0 of the generalized Feller equation is used to define a generalized Jacobi Theta function \documentclass{article}\pagestyle{empty}\begin{document}$ \Theta (x,t) = \upsilon *(x,t;0) + 2\sum\limits_{n = 1}^\infty {v*(x,t;y_n)} $\end{document} for a sufficiently rapidly increasing and unbounded positive sequence {yy}. It is shown that Θ(x,t) is analytic in each variable in certain regions of the complex x and t planes and that it is a solution of the generalized Feller equation. For those parameters for which this equation reduces to the heat equation, Θ(x,t) reduces to the third Jacobi Theta function.
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    Applications of convex analysis and comparison functionals to extremum principles (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 353-370 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In many areas of applied mathematics, the govering equations can be expressed as dual equations which are elements in two vector spaces where a given functional defined on a cartesian product space has zero gradients. If this functional has a global saddle structure then the variational principle can be replaced by dual extremum principles of the Noble and Sewell type. The purpose of the present paper is to investigate how comparison functional which have convex, concave or saddle structure can be used to generate upper and lower bounding principles and critical sequences. The methods are illustrated by applications to the periodic solutions of a non-linear differential equation and the Fredholm integral equation.
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    Continuous dependence on geometry for the backward heat equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 433-448 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we are concerned with the development of criteria for stabilizing inherently unstable initial-boundary value problems under small errors in the geometry of the underlying domain. We consider in particular the initial-boundary-value problem for the backward heat equation assuming that some error has been made in characterizing the geometry of the domain under consideration. It is shown that solutions which belong to an appropriately defined constraint set depend continuously in L2 on errors in the geometry.
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    Transmutation via the momentum plane (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 467-495 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Notes: Transmutation methods are developed for equations of the form x2 ϕ“ + x2(k2” - q̃(x)) ϕ = (v2 - (1/4)) ϕ, with v as spectral variable, which correspond to problems in quantum scattering theory at fixed energy k2 (here v ˜ l + (1/2) with l complex angular momentum). Spectral formulas for transmutation kernels are constructed and the machinery of transmutation theory developed by the author for spectral variable k is shown to have a version here. General Kontrorovič-Lebedev theorems are also proved.
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    Two remarks on continuation procedures for solving some nonlinear equations (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 512-514 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    Notes: Let F be a mapping from Rn+1 into Rn, x(t) be a parametrization for ∣t - t0 ∣ 〈 c, of a smooth solution branch of the equation F(x) = 0, A(t) be the jacobian (n + 1) associated to a standard continuation method used for computing the solution branch. We study for a class of singularities at x(t0) the behaviour, near t = t0, of the determinant of A(t).
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    On the Vlasov-Fokker-Planck equation (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 527-538 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We study a modification of the Vlasov-Poisson equation, obtained by adding a diffusion term with respect to velocity. It describes, from a physical point of view, a plasma in thermal equilibrium, in a mean field limit situation. We find that the already known results concerning existence and uniqueness of the solutions for the ordinary Vlasov equation (constructive results and counterexamples) translate to our case.
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    A trace theorem for solutions of the wave equation, and the remote determination of acoustic sources (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 131-152 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The determination of sources of acoustic wave motion in several dimensions from remote measurements is of considerable interest in many applications, and the underlying mathematical problem is quite ill-posed. We separate the source determination problem into a control problem for the wave equation and an inverse mixed initial-boundary value problem, and concentrate on the latter, in which the initial data for a solution of the wave equation are to be determined from its trace on a time-like hyperplane. Though the geometry of this problem is simple, it exhibits some of the central analytic difficulties of more complex problems. We prove a uniqueness theorem, give examples of instability, establish regularity properties of the trace, and locate noncompact classes of stable functionals. The existence of these noncompact classes shows that the problem is “partially well-posed”, i.e. that smoothing in all directions is not required to regularize the problem, and distinguishes it from most other ill-posed problems, such as backwards diffusion and analytic continuation.
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    Bifurcation of periodic orbits in coupled chemical reactors II (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 216-232 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this part of the paper we deal with computational aspects of the bifurcation problem introduced in Part I, cf. [1]. It follows from Section 3 that the bifurcation behaviour is essentially determined by the expression KP(Ω) - ∧β, where β is some constant which was assumed to be nonzero, while P(Ω) is some 2π-periodic function which was implicitly defined in Section 2. In Section 4 we first derive easily computable expressions for P(Ω) and β from the definitions of Section 2. Secondly we offer a direct, although formal, derivation for these quantities. In Section 5 we briefly show how P(Ω). β can actually be computed by means of a high speed computer and discuss a number of examples. In Section 6 finally we give some asymptotic results for systems depending on an additional parameter.
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    Interactions of fast and slow waves in hyperbolic systems with two time scales (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 292-307 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider certain symmetric hyperbolic systems of nonlinear partial differential equations whose solutions vary on two time scales. The large part of the spatial operator is assumed to have constant coefficients, but a nonlinear term multiplying the time derivatives is allowed. We show that if the initial data are not prepared correctly for the suppression of the fast scale motion, but contain errors of amplitude O(∊), then the perturbation in the solution will also be of amplitude O(∊). Further, if the large part of the spatial operator is nonsingular, we show that the error introduced in the slow scale motion will be of amplitude O(∊2), even though fast scale waves of amplitude O(∊) will be present in the solution.
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    The coupling of boundary integral and finite element methods for the bidimensional exterior steady stokes problem (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 356-375 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper, we represent a new numerical method for solving the steady-state Stokes equations in an unbounded plane domain. The technique consists in coupling the boundary integral and the finite element methods. An artificial smooth boundary is introduced separating an interior inhomogeneous region from an exterior one. The solution in the exterior domain is represented by an integral equation over the artificial boundary. This integral equation is incorporated into a velocitypressure formulation for the interior region, and a finite element method is used to approximate the resulting variational problem. This is studied by means of an abstract framework, well adapted to the model problem, in which convergence results and optimal error estimates are derived. Computer results will be discussed in a forthcoming paper.
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    Ein resonanzphänomen in der theorie akustischer und elektromagnetischer wellenHerrn Professor Karl Nickel zum 60. Geburtstag am 9. 2. 1984 gewidmet (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 104-128 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We discuss the asymptotic behaviour of acoustic and electromagnetic waves, generated by given time-harmonic exterior forces with frequency ω, in the unbounded region between the parallel planes X3 = 0 and X3 = 1, and show that the principle of limiting amplitude is violated if ω = πn(n = 1, 2,…). For these values of the frequency, forces with compact support can be chosen such that the amplitudes of the waves increase with a logarithmic rate as t → ∞.
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    Thin elastic and periodic plates (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 159-191 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: This paper is devoted to the study of a three dimensional model of elastic periodic plate when the thickness e of the plate and the size ω of the periods are small. In the three studied limits (e → 0 then ω → 0), (ω → 0 then e → 0) and lately (e and ω → 0 together) the three dimensional equation of elasticity are approached by the two dimensional general equations of a linear anisotropic plate, the stretching and bending being coupled. This study points out the importance of the ratio of the two small parameters, indeed the moduli occuring in the two dimensional equations are different in the three limits. In each case a convergence proof is carried out.
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    Bifurcation phenomena in a free boundary problem for a circulating flow with surface tension (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 215-233 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A free boundary problem for a flow around a circle is analyzed. We find and mathematically prove that bifurcations from the trivial flow actually take place. Golubitsky-Schaeffer theory, together with a formula concerning variations of domains, enables us to clarify the behaviors of the branches of nontrivial solutions.
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    Truncated random variables with application to random surfaces (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 248-261 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: There has been considerable interest in obtaining discrete results for random surfaces. Standard results have been published in journals of physics or engineering which have emphasised the applications. This paper gives a detailed background of the mathematical methods needed so that the central connection, namely truncated random variables, between these standard results can be understood. Distributions of discrete peak measures are obtained from the distributions of discrete profile measures of a random Gaussian surface by applying results for the distributions of truncated random variables. This enable the moments to be obtained from known results for the truncated distributions.
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    Asymptotic behavior of a nonhomogeneous predator-prey system with one diffusing and one sedentary species (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 40-67 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In general the predator-prey system studied will have many equilibrium states with different “patches”, i.e. regions where the sedentary species vanishes. If one equilibrium is given, a Ljapunov functional can be constructed for a set of initial data with patches satisfying a certain compatibility condition. By the methods of Alikakos [1] and Rothe [28] this implies uniform bounds for the diffusing species in a Hölder space and the sedentary species in a Lp-space. Considering pieces of the trajectory for time in some bounded interval and using the weak*-topology for the sedentary species, one defines an ω-limit set which is compact and nonvoid. Using the Ljapunov functional an asymptotic version of the differential equations is derived. It turns out that they admit only constant solutions except for a very special case. Thus convergence to the equilibrium follows.
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    Local existence and uniqueness theorems for a free boundary problem (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 308-330 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Free boundary problems are considered, where the tangential and normal components ut and un of an otherwise unknown plane harmonic vector field are prescribed along the unknown boundary curve as a function of the coordinates x, y and the tangent angle θ. The vector field is required to exist either in the interior region G+ or in the exterior G-. In each case the free boundary is characterized by a nonlinear integral equation. A linearised version of this equation is a one-dimensional singular integral equation. Under rather general hypotheses which are easy to check, the properties of the linear equation are described by Noether's theorems. The regularity of the solution is studied and the effect of the nonlinear terms is estimated. A variant of the Nash-Moser implicit-function theorem can be applied. This yields local existence and uniqueness theorems for the free boundary problem in Hölder-classes H2+μ. The boundary curve depends continuously on the defining data. Finally some examples are given, where the linearised equation can be completely discussed.
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    Layer potentials and boundary value problems for the helmholtz equation in the complement of a thin obstacle (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 389-421 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Our purpose is to show in a precise manner the mathematical approach of the problem of the acoustic diffraction by an infinitely thin screen. The classical equations of acoustics are transformed into integral equations. The sound field diffracted by the obstacle is described by a double layer potential, the density of which is equal to the step of the potential across the screen. To avoid the mathematical difficulties, the infinitely thin screen will be considered as the limit of a sequence of obstacles with finite thickness. On such obstacles, the operators can be defined, thanks to the theory of Pseudo-differential operators and Pseudo-Poisson kernels. Then a limiting process is used and gives existence and unicity of the desired solutions in Sobolev spaces.
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    On turning points (1983)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 5 (1983), S. 491-515 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: For a family {T + Nλ: λ ∊ [a, b]} of semilinear operators T + Nλ in L2(Ω) the solution set {(λ, uλ) ∊ J × D(T): Tuλ + Nλuλ = h} is investigated with respect to turning points. By Ljapunov-Schmidt-reduction and calculation of the derivatives of the bifurcation equation a class of turning points is characterized by properties of these derivatives.
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    Forward speed motions of a submerged body. The cauchy problem (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 371-392 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We consider the linearized problem for the ideal fluid flow induced by the horizontal motion of a fully immersed body. The system of equations is made up of an elliptic problem (P) and an initialvalue problem (R) which are coupled by a pseudo-differential operator T.We define a regularized Cauchy problem (R∊) using the Yosida approximation of T; we give energy and wave resistance estimates and finally we obtain existence uniqueness and regularity of the weak solution of (R) by taking the limit when ∊ goes to zero.
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    Half- and finite-range completeness for the equation of transfer of polarized light (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 393-416 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: On neglecting reflection by the surface the existence and uniqueness are proved for the solution of the equation of transfer of polarized light in a homogeneous semi-infinite or finite plane-parallel medium. A general LL-space formulation, where 1 ≤ p 〈 ∞, is adopted. The analysis concerns a vector-valued convolution equation, which is an equivalent form of the equation of radiative transfer and is solved with the help of Wiener-Hopf factorization, Fredholm index and cone preservation methods. The results are also proved for the equations obtained from the full equation of transfer by means of Fourier expansion and symmetry relations.
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    Exact bounds for the radially symmetric shape of confined plasma in the unit circle (1984)
    Chichester, West Sussex : Wiley-Blackwell
    Mathematical Methods in the Applied Sciences 6 (1984), S. 496-511 
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    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The method of “cone iteration”; is used to obtain exact bounds for the solutions of a class of nonlinear operator equations. The general theory is applied to the problem of finding radially symmetric solutions of the plasma problem in the unit circle. Existence and uniqueness results are obtained at the same time. Some numerical examples demonstrate the method's high degree of accuracy.
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    Optimal control in light traffic Markov decision processes (1997)
    Springer
    Mathematical methods of operations research 45 (1997), S. 63-79 
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    ISSN: 1432-5217
    Keywords: Optimal control ; Markov decision processes ; light traffic ; discounted cost ; average cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider Markov Decision Processes under light traffic conditions. We develop an algorithm to obtain asymptotically optimal policies for both the total discounted and the average cost criterion. This gives a general framework for several light traffic results in the literature. We illustrate the method by deriving the asymptotically optimal control of a simple ATM network.
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    A new augmented penalty function technique for optimal control problems (1977)
    Springer
    Journal of optimization theory and applications 21 (1977), S. 39-49 
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    ISSN: 1573-2878
    Keywords: Optimal control ; augmented penalty function ; terminal constraints ; gradient methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This note presents an extension of the Miele—Cragg-Iyer-Levy augmented function method for finite-dimensional optimization problems to optimal control problems. A numerical study is provided.
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    Existence of optimal controls for the diffusion equation (1977)
    Springer
    Journal of optimization theory and applications 22 (1977), S. 91-101 
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    ISSN: 1573-2878
    Keywords: Optimal control ; Radon measures ; existence theory ; diffusion equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The existence is considered of a boundary control which drives a system governed by the one-dimensional diffusion equation from the zero state to a given final state, and at the same time minimizes a given functional. The problem is first modified to one in which the minimum is sought of a functional defined on a set of Radon measures. The existence of a minimizing measure is demonstrated, and it is shown that this measure may be approximated by a piecewise constant control. Finally, conditions are given under which a minimizing measurable control exists for the unmodified problem.
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    On the optimal control for variational inequalities (1977)
    Springer
    Journal of optimization theory and applications 22 (1977), S. 373-388 
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    ISSN: 1573-2878
    Keywords: Optimal control ; variational inequalities ; existence theorems ; sensitivity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove an existence theorem for the optimal control of variational inequalities governed by a pseudomonotone operator: the cost is assumed to be quadratic. Then, we give an extension of the theorem to more general costs (assuming the operator to be monotone); we also give a result on a perturbation problem.
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    Nearest feasible paths in optimal control problems: Theory, examples, and counterexamples (1977)
    Springer
    Journal of optimization theory and applications 23 (1977), S. 563-579 
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    ISSN: 1573-2878
    Keywords: Optimal control ; Green's theorem ; infinite horizon ; multiplicative problems ; optimal stationary equilibrium ; economic applications
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Many infinite-horizon optimal control problems in management science and economics have optimal paths that approach some stationary level. Often, this path has the property of being the nearest feasible path to the stationary equilibrium. This paper obtains a simple multiplicative characterization for a single-state single-control problem to have this property. By using Green's theorem it is shown that the property is observed as long as the stationary level is sustainable by a feasible control. If not, the property is, in general, shown to be false. The paper concludes with an important theorem which states that even in the case of multiple equilibria, the optimal path is a nearest feasible path to one of them.
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    Optimal control of systems governed by a class of nonlinear evolution equations in a reflexive Banach space (1978)
    Springer
    Journal of optimization theory and applications 25 (1978), S. 57-81 
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    ISSN: 1573-2878
    Keywords: Optimal control ; nonlinear evolution equations ; reflexive Banach spaces ; existence theorems ; time-optimal control ; Bolza problem ; terminal control ; velocity field ; set-valued map ; weak Cesari property
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The paper presents a closure theorem for the attainable trajectories of a class of control systems governed by a large class of nonlinear evolution equations in reflexive Banach spaces. Several existence theorems for optimal controls are proven that include a terminal control problem, a time-optimal control problem, and a special Bolza problem. Some results of independent interest are also presented.
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    An interaction-coordination algorithm with modified performance index for nonlinear optimal control problems (1978)
    Springer
    Journal of optimization theory and applications 25 (1978), S. 229-245 
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    ISSN: 1573-2878
    Keywords: Optimal control ; nonlinear large systems ; decomposition and coordination ; modification of performance index ; improvement of convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper proposes a coordination algorithm for multilevel control of a nonlinear dynamical system. The overall system under consideration is composed of subsystems with relatively strong interactions or relatively strong nonlinearities, or both. The objective is to minimize a performance index of quadratic type. The idea of the present algorithm is to replace the system variables associated with interactions and nonlinearities by artificially introducedinteraction variables and to decompose the overall problem into a number of smaller and simpler subproblems. At the same time, the appearance of the performance index is modified by using the interaction variables. Parameters, called weights, are introduced into the modified performance index. Choice of the values of these parameters has significant influence on the convergence rate of the algorithm, and hence is one of the major factors determining the total computing time. The interaction variables are adjusted directly by a nearly steepest-descent algorithm, without using Jacobian matrix, until the interactions attain consistency. In the paper, some sufficient conditions for convergence of the iterative algorithm are discussed in detail, and several features of the present algorithm are illustrated by examining an example.
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    Necessary and sufficient conditions for bang-bang control (1978)
    Springer
    Journal of optimization theory and applications 25 (1978), S. 549-554 
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    ISSN: 1573-2878
    Keywords: Optimal control ; nonlinear operators ; Frechet differentiability ; Hilbert spaces ; bang-bang control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Necessary and sufficient conditions for the optimal control to be bang-bang are presented for a nonlinear system. The payoff, which is not necessarily quadratic, is assumed to be described by a Hilbert-space norm and to be differentiable and convex. The results are extensions of Ref. 1 to the case of nonlinear systems.
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    Second-order necessary conditions in optimal control: Accessory-problem results without normality conditions (1983)
    Springer
    Journal of optimization theory and applications 41 (1983), S. 75-106 
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    ISSN: 1573-2878
    Keywords: Optimal control ; second-order necessary conditions ; accessory problem ; control constraints ; normality condition
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An optimal control problem, which includes restrictions on the controls and equality/inequality constraints on the terminal states, is formulated. Second-order necessary conditions of the accessory-problem type are obtained in the absence of normality conditions. It is shown that the necessary conditions generalize and simplify prior results due to Hestenes (Ref. 5) and Warga (Refs. 6 and 7).
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    Homogenization of Optimal Control Problems for Functional Differential Equations (1997)
    Springer
    Journal of optimization theory and applications 93 (1997), S. 103-119 
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    ISSN: 1573-2878
    Keywords: Optimal control ; variational convergence ; functional differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The paper deals with the variational convergence of a sequence of optimal control problems for functional differential state equations with deviating argument. Variational limit problems are found under various conditions of convergence of the input data. It is shown that, upon sufficiently weak assumptions on convergence of the argument deviations, the limit problem can assume a form different from that of the whole sequence. In particular, it can be either an optimal control problem for an integro-differential equation or a purely variational problem. Conditions are found under which the limit problem preserves the form of the original sequence.
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    New Algorithm for Computing LQ Suboptimal Output Feedback Gains of Decentralized Control Systems (1997)
    Springer
    Journal of optimization theory and applications 93 (1997), S. 597-607 
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    ISSN: 1573-2878
    Keywords: Optimal control ; gradient flows ; optimization ; decentralized systems ; performance index
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the problem of computing the suboptimal output feedback gains of decentralized control systems is investigated. First, the problem is formulated. Then, the gradient matrices based on the index function are derived and a new algorithm is established based on some nice properties. This algorithm shows that a suboptimal gain can be computed by solving several ordinary differential equations (ODEs). In order to find an initial condition for the ODEs, an algorithm for finding a stabilizing output feedback gain is exploited, and the convergence of this algorithm is discussed. Finally, an example is given to illustrate the proposed algorithm.
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    Optimal control of two interconnected turbogenerators (1983)
    Springer
    Journal of optimization theory and applications 40 (1983), S. 255-291 
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    ISSN: 1573-2878
    Keywords: Optimal control ; two interconnected turbogenerators ; torque control ; voltage control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the optimal control of a system with two identical interconnected turbogenerators, which are connected to an infinite bus, is considered. Control of the generators is effected through control of field voltages and turbine torques. The alternators are controlled through a linear feedback of the state variables. The feedback parameters are obtained by solving a nonlinear, two-point boundary-value problem. The values obtained for these parameters depend on the strength and duration of the disturbance, since the model is nonlinear, in contrast to the usual feedback control of a linear model. The numerical values used are indicated in the Appendix.
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    An Optimal Control Problem for Flows with Discontinuities (1997)
    Springer
    Journal of optimization theory and applications 94 (1997), S. 273-309 
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    ISSN: 1573-2878
    Keywords: Optimal control ; Euler flow equations ; sequential quadratic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we study a design problem for a duct flow with a shock. The presence of the shock causes numerical difficulties. Good shock-capturing schemes with low continuity properties often cannot be combined successfully with efficient optimization methods requiring smooth functions. A remedy studied in this paper is to introduce the shock location as an explicit variable. This allows one to fit the shock and yields a problem with sufficiently smooth functions. We prove the existence of optimal solutions, Fréchet differentiability, and the existence of Lagrange multipliers. In the second part, we introduce and investigate the discrete problem and study the relations between the optimality conditions for the infinite-dimensional problem and the discretized one. This reveals important information for the numerical solution of the problem. Numerical examples are given to demonstrate the theoretical findings.
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    Properties of the Bellman Function in Time-Optimal Control Problems (1997)
    Springer
    Journal of optimization theory and applications 94 (1997), S. 155-168 
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    ISSN: 1573-2878
    Keywords: Optimal control ; Bellman function ; value function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, time-optimal control problems with closed terminal sets are considered. We give conditions which guarantee the Bellman function to be Hölder and Lipschitz continuous. We then prove that the condition for Lipschitz continuity is also necessary.
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    Efficient Sequential Quadratic Programming Implementations for Equality-Constrained Discrete-Time Optimal Control (1997)
    Springer
    Journal of optimization theory and applications 95 (1997), S. 323-346 
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    ISSN: 1573-2878
    Keywords: Optimal control ; sequential quadratic programming ; dynamic programming ; Newton method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Efficient sequential quadratic programming (SQP) implementations are presented for equality-constrained, discrete-time, optimal control problems. The algorithm developed calculates the search direction for the equality-based variant of SQP and is applicable to problems with either fixed or free final time. Problem solutions are obtained by solving iteratively a series of constrained quadratic programs. The number of mathematical operations required for each iteration is proportional to the number of discrete times N. This is contrasted by conventional methods in which this number is proportional to N 3. The algorithm results in quadratic convergence of the iterates under the same conditions as those for SQP and simplifies to an existing dynamic programming approach when there are no constraints and the final time is fixed. A simple test problem and two application problems are presented. The application examples include a satellite dynamics problem and a set of brachistochrone problems involving viscous friction.
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    Dual-mode free volume model for diffusion of gas molecules in glassy polymers (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1737-1746 
    Details
    ISSN: 0887-6266
    Keywords: free volume ; dual mode ; diffusion ; glassy polymer ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The development of a new model for the diffusion of gas molecules in glassy polymers is presented which utilizes concepts from free volume theory and relies on a dual-mode interpretation of sorptive dilation in glassy polymers. Three assumptions are made in the development of the model. First, the free volume available for molecular transport processes is taken as constant below the glass transition temperature. Second, two populations of gas molecules are assumed to exist - one which contributes to the maintenance of an iso-free volume state upon sorptive dilation and one which does not contribute owing to sorption into regions of unrelaxed volume. Third, the former population is assumed to be mobile while the latter is not. The resulting model predicts, at constant temperature, a diffusion coefficient that is independent of solute volume fraction. This is in contrast to the widely used dual-mode sorption model with partial immobilization for gas transport in glassy polymers which leads to a diffusion coefficient that is dependent on solute mole fraction through the molar gas concentration. The new model is used to interpret gas transport data from permeation experiments for carbon dioxide, methane, and ethylene in three polycarbonates. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1737-1746, 1997
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    Surface modification strategies for multicomponent polymer systems, Part I: Use of diblock copolymers as surface modifiers of rutile (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1793-1805 
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    ISSN: 0887-6266
    Keywords: rutile ; surface modification ; diblock copolymer ; inverse gas chromatography ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Various functional diblock copolymers have been used as surface modifiers for rutile pigment in an effort to condition the solid for eventual use in multicomponent polymer systems. Coated surfaces were analyzed by inverse gas chromatography at infinite and finite dilution of the vapor phase, and by XPS. At high coverages (about 10% by weight of the pigment), the diblocks were randomly oriented at the air interface, effectively masking the surface of the rutile. At low diblock concentrations acid/base interactions dominated the orientation of the adsorbed molecule at the rutile interface, thereby also affecting the orientational states at the air interface. In this condition, the performance of the pigment in specified host polymer systems may be expected to vary with the selection of the diblock copolymer modifier. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1793-1805, 1997
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    The phase morphology and crystal growth habits of DNA fractions. Optical microscopy and light scattering (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1843-1854 
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    ISSN: 0887-6266
    Keywords: crystallization ; DNA ; fractionation ; gel-electrophoresis ; morphology ; phase transition ; SALLS ; sonication ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Polydisperse DNA of reasonable molecular weights was prepared from a mammalian source via sonication and fractionation. A method for characterizing the molecular weight using gel electrophoresis is described. Quiescent crystallization was studied in thin films of one of the fractions induced by rapidly changing the hydration state isothermally. We report the occurrence of the semicrystalline nature of DNA. The crystal growth occurring via aggregates is best described as sheaves and spherulites from DNA gels in the relative humidity range (RH) corresponding to A-DNA. These habits exhibit primary nucleation and secondary growth, which closely resemble those of melt-crystallized, synthetic macromolecules and, in a follow-up report, will be shown to be lamellar in nature. Small, needle-like crystals are observed for B-DNA hydration levels, and are unstable at lower hydration levels. A transformation from needle to lamellar crystals can occur, even when the primary nucleation of lamellar forms is otherwise absent at that hydration level, through a cylindrical phase exhibiting selective reflection of colored bands. The hydration level plays, in part, the role of the supercooling in this system and the long-known hysteresis in the formation and dissolution of the A-DNA (crystals) can now be viewed in light of those factors known to operate in semicrystalline systems. A morphological phase diagram is developed and is in accord with the known physical evidence. Because this preparation and these morphological observations are without precedence, substantial detail into methodology is included for this first article in the series. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1843-1854, 1997
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    The first 85% kraft lignin-based thermoplasticsPaper No. 22,538 of the Scientific Journal Series of the Minnesota Agricultural Experiment Station, funded through Minnesota Agricultural Experiment Station Project No. 43-68, supported by Hatch Funds. (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1899-1910 
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    ISSN: 0887-6266
    Keywords: kraft lignin ; thermoplastics ; polymer association ; poly(vinyl acetate) ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Interest in the development of lignin-containing polymeric materials has been upheld more or less continuously for the past 20 years. Tendencies toward high moduli and poorly defined thermal transitions have been regarded as imposing inevitable limitations upon the use of lignin derivatives for such purposes. Incorporation of more than 25-40% (w/w) lignin had usually resulted in materials that were brittle and weak. For the first time, however, from homogeneous blends containing 85% (w/w) underivatized industrial kraft lignin with poly(vinyl acetate) and two plasticizers, a series of thermoplastics has been fabricated with promising mechanical properties. The tensile behavior of these new polymeric materials depends directly upon the degree of association between the intrinsic kraft lignin components. In extending to values about 25 MPa and 1.5 GPa, respectively, the tensile strengths and Young's moduli vary linearly with the effective M̄w for the kraft lignin species, under conditions where the proportions of the individual molecular components, both associated and discrete, do not change. Moreover, melt-flow index measurements indicate that these polymeric materials are amenable to thermal processing by extrusion molding. Thus a significant step has been taken toward developing a new generation of thermoplastics that are lignin-based in a very fundamental way. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1899-1910, 1997
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    Viscoelasticity and self-diffusion in melts of entangled linear polymers (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1933-1942 
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    ISSN: 0887-6266
    Keywords: self-diffusion ; viscosity ; polymer melt ; entanglement ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Dynamic properties in the melt state for two saturated hydrocarbon polymers, poly(ethylene-alt-propylene) (PEP) and head-to-head polypropylene (HHPP), were investigated by viscoelastic and diffusion measurements. Several nearly monodisperse linear samples of each species were used. Zero-shear viscosity η0 and self-diffusion coefficient D varied with temperature in accord with the WLF equation, and they also varied with molecular weight M in a manner that was consistent with the behavior of other species. The product η0D was of particular interest because extensive previous results for two other species, polystyrene and polyethylene, had led Pearson et al. to suggest that η0D/(η0D)Rouse is a universal function of the number of entanglements per molecule M/Me. With values for the Rouse model product for each species calculated from chain dimensions, and entanglement molecular weight from the plateau modulus, we show that the data for PEP and HHPP also support the Pearson universal form. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1933-1942, 1997
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    Dynamic mechanical behavior of fluorinated aromatic poly(ethers) (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1963-1971 
    Details
    ISSN: 0887-6266
    Keywords: dynamic mechanical analysis ; fluorinated poly(ethers) ; intermolecular cooperativity ; relaxation behavior ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The relaxation behavior of six fluorinated aromatic poly(ethers) was investigated using dynamic mechanical analysis. The glass transition temperature was found to increase as the size and rigidity of linking groups increased and varied between 168°C for a dimethyl linking group and 300°C for a bicyclic benzoate ether-linking group. For the α-relaxation the steepness of time/temperature plots and broadness of the loss curves could be qualitatively correlated with chemical structure in a manner predicted by the coupling model of relaxation. Well-separated sub-Tg transitions were also observed, as a shoulder on the low temperature side of the α-peak, and as a broad, low loss transition around -100°C. The higher temperature process was similar to the structural relaxation often found in quenched glassy polymers, while the position, intensity, and breadth of the subambient process was sensitive to chemical structure. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1963-1971, 1997
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    FTIR studies of conformational energies of poly(acrylic acid) in cast films (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 507-515 
    Details
    ISSN: 0887-6266
    Keywords: poly(acrylic acid) ; FTIR ; polyelectrolyte ; conformation ; conformers ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Fourier transform infrared (FTIR) spectroscopic measurements have been undertaken to estimate the conformational energies of poly(acrylic acid) (PAA) cast films in the temperature range of 40-130°C. The temperature dependence of the IR spectra in the C=O stretching region has been analyzed to yield the side-chain and backbone conformational energies. The estimated energies are close to those previously obtained by polarized Raman spectroscopic measurements for PAA solutions. Combining the FTIR value of conformational energy with the simplified rotational isomeric state (RIS) model proposed in the Raman analysis provides a persistence length in accordance with earlier SAXS experiments. The data also agree with the Gibbs-DiMarzio predictions, further substantiating the validity of the analysis. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 507-515, 1997
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    Computer-simulation analysis of the ESR spectra of mechanoradicals in PMMA (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 2195-2200 
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    ISSN: 0887-6266
    Keywords: ESR ; mechanoradicals ; PMMA ; drilling apparatus ; computer simulation ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: In this study, initially, we tried to obtain the mechanoradicals of PMMA (poly(methyl methacrylate)). For this purpose, we designed a simple drilling apparatus. Using this apparatus, we prepared some PMMA samples at 77 K in vacuum. Later, by using an ESR (electron spin resonance spectrometer), we observed ESR signals for these samples at 77 K. This means that mechanoradicals have been successfully produced by mechanical fracture in PMMA using our drilling apparatus. Secondly, we tried to identify the radicals from these spectra through using theoretical analyses and, some computer simulations have been done by suggesting two different theoretical models for these ESR signals. Finally, by using experimental and theoretical data, we showed that our simple apparatus could be used to obtain mechanoradicals from polymers. Results were seen to be in very good agreement with the literature. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2195-2200, 1997
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    Measurement of crystalline index in nylons by DSC: Complexities and recommendations (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 2219-2231 
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    ISSN: 0887-6266
    Keywords: nylons ; crystallinity ; DSC ; x-ray diffraction ; complications ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Differential scanning calorimetry (DSC) is one of the most widely used technique for measuring crystallinity in the polymer industry. The major source of error in the crystalline index (CIDSC) of low crystallinity polymeric articles, is the development of further crystallinity during the DSC scan. Although, this type of cold crystallization is obvious, and thus accounted for in polymers like polyethylene terephthalate, nylons are a difficult class of materials in that respect. The major contributing factors to the failure of DSC in measuring low levels of crystallinity in nylons are identified to be (1) silent crystallization between the glass (Tg) and melting (Tm) transitions, (2) extreme difficulties in packing a moisture-free nylon in the sample pan (the response due to traces of moisture being a broad endotherm competing with a broad exothermic crystallization), and (3) a sub-Tm exotherm, especially in low crystallinity nylons, due to relaxation of the processing-induced stresses. These factors, specific to nylons, mask the observation of cold crystallization and lead to substantially higher than real crystallinities. This manuscript deals with such complications and corrective actions using commercial nylon 6 films of CIDSC = 0-40%. X-ray diffraction measurements have been included to support the validity of our improved DSC methodology. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2219-2231, 1997
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    Heat capacity and phonon dispersion in poly(L-methionine) (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 2281-2292 
    Details
    ISSN: 0887-6266
    Keywords: conformation ; phonon dispersion ; α-helix ; normal modes ; poly(L-leucine) ; density of states ; heat capacity ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Poly(L-methionine) (PMet) is one of the two sulfur containing polyamino acids. Raman, FTIR spectra, and heat capacity measurements of PMet have been well interpreted through the normal mode analysis and the density of states derived therefrom. Earlier interpretation of heat capacity data is limited because it is based on the Tarasov model, wherein the concept of group frequency and skeletal similarity are used. A special feature of some dispersion curves is their tendency to bunch in the neighborhood of the helix angle. This has been attributed to the presence of strong intramolecular interactions. Repulsion between the dispersion curves is also observed. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2281-2292, 1997
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    Use of “living” radical polymerizations to study the structural evolution and properties of highly crosslinked polymer networks (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 2297-2307 
    Details
    ISSN: 0887-6266
    Keywords: crosslinked polymers ; photopolymerizations ; living radical polymerizations ; mechanical properties ; dynamic mechanical analysis ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Crosslinked polymer networks are used in a wide variety of applications. To use these materials effectively, a fundamental understanding of their structural evolution and the relationship between material properties and structure is essential. In this article, a novel technique employing “iniferters,” i.e., living radical polymerizations, to photopolymerize these networks is utilized to study the property and structural evolution of these highly desirable materials. Living radical polymerizations are used in this work since this technique avoids the problem of carbon radical trapping encountered while using conventional initiators. Dynamic mechanical measurements are performed on highly crosslinked methacrylate networks to glean information regarding their structural heterogeneity. By performing these measurements on homopolymerized samples at various stages of the reaction and on copolymerized samples of multifunctional methacrylates, the mechanical properties are characterized as a function of double bond conversion and comonomer composition. From such analyses, with respect to both temperature and frequency, quantitative conclusions regarding the structure of the networks are drawn. This effort is aimed at exploiting the living radical polymerizations initiated by p-xylylene bis(N,N-diethyl dithiocarbamate) (XDT), to study the mechanical property evolution and structural heterogeneity of crosslinked polymers which is nearly impossible otherwise. Polymers examined in this study include networks formed by homopolymerization of diethylene glycol dimethacrylate (DEGDMA) and polyethylene glycol 600 dimethacrylate (PEG600DMA) as well as copolymers of DEGDMA and PEG600DMA. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2297-2307, 1997
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    Probing the microstructure of Nafion-117 using positron annihilation spectroscopy (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 771-776 
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    ISSN: 0887-6266
    Keywords: Nafion ; positron annihilation ; free volume ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: We report a new result on positron annihilation studies in acid- and cation-neutralized (Li+, Na+, K+, Rb+, Cs+, UO22+, Ni2+) Nafion membranes using positron lifetime and Doppler-broadened annihilation radiation (DBAR) measurements. The free-volume structure is characterized using a simple quantum mechanical model of positronium (Ps) in a spherical well. Our studies indicate that formation and expansion of clusters is always associated with a change in free-volume structure resulting in smaller free-volume holes. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 771-776, 1997
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    Blends of bisphenol-A polycarbonate and acrylic polymers: III. Effect of imide concentration on compatibility (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 749-761 
    Details
    ISSN: 0887-6266
    Keywords: polycarbonate ; polyglutanimide ; polymer blends ; copolymer ; compatibilization ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Imide units copolymerized with MMA units have been selected in order to improve compatibility between PC and acrylics through specific interaction or internal repulsion. Good dispersion of acrylic inside a PC matrix has been observed upon melt mixing, which can be partially explained by the good rheological agreement between these two polymers. Transmission electron microscopy has shown that the system remains phase separated from 5 to 95 wt % of PC. Phase diagrams for three different imide concentrations have been drawn. Results obtained by DSC (conventional and with enthalpy relaxation) are similar to those obtained by optical cloud point detection. The phase diagrams show the raise of the PC/PMMA demixtion curve (LCST type) when percentage of imide increases in the acrylic phase. Theoretical calculations on binary interaction energy density show a slight improvement of the interaction between acrylic and PC when imide percentage increases. Cloud point measurements on 50/50 PC/acrylic blends varying the imide concentration show that the improvement of compatibility deduced from the raise of the demixtion curve (LCST type) is more related to a kinetic effect (the high Tg of imidized samples is reducing macromolecule mobility) than specific interactions. The calculated favorable interactions are probably too weak to be detected with cloud point measurements. The microstructures obtained after crystallization of the PC phase under solvent vapors in phase separated PC/acrylics blends can also be explained by Tg effects. Moreover, solvent vapor exposure could be a powerful tool to determine the real thermodynamic behavior of the blends at room temperature. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 749-761, 1997
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    A process-structure-property study of anisotropic PMDA-ODA films (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 777-788 
    Details
    ISSN: 0887-6266
    Keywords: PMDA-ODA polyimide ; intrinsic molecular properties ; sheet mapping ; fabrication processes ; three-dimensional orientation functions ; anisotropic coefficient of thermal expansion (CTE) ; anisotropic mechanical moduli ; anisotropic compliances ; anisotropic dielectric constants ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A practical methodology for the correlation and prediction of the process-property performance of advanced materials is developed. The model polymer studied is PMDA-ODA polyimide. The connecting link between the process and the properties is the structural state of the polymer. An essential ingredient for a quantitative characterization of the system is a knowledge of its phase state and intrinsic molecular properties. The intrinsic molecular properties define the limiting performance properties available to the polymer. Anisotropic films and sheets produced by five different fabrication processes are examined. Maps of the molecular symmetry axis, the orientation function, and the thickness distributions of two 50-in.-wide sheets fabricated differently are measured nondestructively for process comparison. Four other film fabrication processes are examined and their three-dimensional orientation states determined and correlated. A three-dimensional orientation function triangular plot permits simultaneous representation of the different fabrication processes on the same figure and allows the investigator to choose the most economic and efficient fabrication route. The structure-property study includes the structural correlation and intrinsic molecular property determination of the anisotropic coefficient of thermal expansion (CTE), the anisotropic mechanical moduli and compliances, and the anisotropic dielectric constants. 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 777-788, 1997
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    Polymer-polymer interactions via analog calorimetry. 3. Interaction between styrene and acrylonitrile repeat units (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 831-839 
    Details
    ISSN: 0887-6266
    Keywords: polymer blends ; analog calorimetry ; heat of mixing ; mean-field binary interaction model ; polystyrene ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Analog calorimetry is used to study the interaction between styrene and acrylonitrile repeat units. Electrostatic charge calculations were used as a guide to divide the polymer repeat units and analogs into groups. A mean-field binary interaction model was used to evaluate group interaction energies. The enthalpic interaction energy for the styrene-acrylonitrile pair from this study is 7.63 ± 0.12 cal/cm3 which is consistent with values obtained from phase behavior studies of poly(styrene-co-acrylonitrile) blends. The cyano group, C(TRIPLE BOND)N, of the acrylonitrile repeat unit has a permanent dipole. The results of this study suggest that the orientation of this dipole with respect to the backbone of the acrylonitrile unit strongly affects its interaction with styrene repeat unit. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 831-839, 1997
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    Architectural effects on the stability limits of ABC block copolymers (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 849-864 
    Details
    ISSN: 0887-6266
    Keywords: ABC block copolymers ; self-assembly ; microphases ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The random phase approximation has been used to extend the Leibler theory for the stability limit of a homogeneous melt of A-B diblock copolymers to examine the onset of microphase and macrophase separation in a variety of ABC block copolymer systems. The stability limit is located by the divergence of the collective structure factor of the melt. We introduce and analyze three models for ABC block copolymers: linear triblocks, random comb copolymers where a fixed number of A and B teeth are placed randomly along a C backbone, and statistical comb copolymers, with A or B teeth spaced regularly, but with sequences constructed using a two parameter Markov process. We compute order-disorder stability boundaries for the segregation strength parameter χABN at threshold as a function of χACN, χBCN, composition, and other model parameters, and compare the results for the three different architectural models. An interesting “reentrant order-disorder transition” is located in several model phase diagrams, and is associated with a peculiar situation in which more incompatibility causes less segregation. In the case of statistical combs, macrophase separation into two liquid phases can be favored over microphase separation. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 849-864, 1997
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    Effect of droplet size on the dielectric properties of PDLC films (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1373-1381 
    Details
    ISSN: 0887-6266
    Keywords: PDLC ; LC droplet ; LC configuration ; electro-optical response ; conductance ; dielectric constant ; dielectric loss ; switching voltage ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Polymer dispersed liquid crystal (PDLC) films (5CB/PMMA, 60/40) of different droplet size were prepared by a solvent-induced phase separation method under different N2 flow speeds. The effects of droplet size on the thermal transitions of the LC and various dielectric properties such as dielectric constant, conductance, dielectric loss, and the electric field induced in a droplet were examined. The configuration of the LC in the film with smaller droplets can be identified by comparing the dielectric constant of the film with the one predicted by Boettcher's mixture formula. In addition, the effect of droplet size on the electro-optical response of the PDLC film was investigated. Variations of the conductance and the dielectric constant of the film were analyzed under various AC frequencies, with the purpose of elucidating the polarization mechanism of the LC molecules in the droplet. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1373-1381, 1997
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    Epitaxial recrystallization of HDPE-quenched ultrathin films on oriented iPP substrates (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1415-1421 
    Details
    ISSN: 0887-6266
    Keywords: epitaxy ; recrystallization ; high-density polyethylene ; isotactic polypropylene ; morphology ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The recrystallization behavior of high-density polyethylene (HDPE) on the highly oriented isotactic polypropylene (iPP) substrates at temperatures below the melting temperature of HDPE has been investigated by means of transmission electron microscopy. The results obtained by the bright-field observation and the electron diffraction show that upon annealing the HDPE-quenched films on the oriented iPP substrates at temperatures below 125°C, only a small amount of HDPE recrystallizes on the iPP substrate with [001]HDPE//[001]iPP, while annealing the HDPE-quenched films at temperatures above 125°C, all of the HDPE crystallites recrystallize epitaxially on the iPP substrate with [001]HDPE//[101]iPP. © 1997 John Wiley & Sons, Inc. J Polym Sci B: 35: 1415-1421, 1997
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    Viscosity behavior of polyelectrolyte copolymers containing sulfonate groups in mixed organic solvents (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1433-1438 
    Details
    ISSN: 0887-6266
    Keywords: polyelectrolyte gel ; reduced viscosity ; dipole-dipole attraction ; medium polarity ; copolymerization ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Copolymerization of 2-acrylamido-2-methylpropane sulfonic acid (AMPS, monomer 1) with 2-hydropropyl methacrylate (HPM, monomer 2) was conducted in ethylene glycol/water (1 : 1 in weight) at 70°C. The reactivity ratios estimated from the copolymer composition at low conversion are r1 = 2.31 ± 0.25 and r2 = 11.70 ± 1.05. The azeotropic composition was found at the monomer mole ratio AMPS/HPM equal to 8/2. Viscosity of these copolymers was measured in dimethyl sulfoxide (DMSO) and DMSO/tetrahydrofuran (THF) mixed solvent at 25 ± 0.05°C. Polyelectrolyte behavior was observed for all the copolymers, even in the mixed solvent containing 65 wt % of THF. The reduced viscosity at constant polymer concentration decreased with increasing THF content in the mixed solvent. The copolymers having AMPS repeat units more than 42 mol % precipitated in the mixed solvent when the THF was beyond 68 wt %. The viscosity reduction and precipitation in the copolymer solutions with increasing THF can be attributed to the dipole-dipole attraction between ion-pairs formed in less-polar medium. This is helpful in understanding the volume phase transition in highly charged hydrogels caused by mixing solvents. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1433-1438, 1997
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    Diffusion of methyl ethyl ketone in polyisobutylene: Comparison of spectroscopic and gravimetric techniques (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1261-1267 
    Details
    ISSN: 0887-6266
    Keywords: FTIR-ATR spectroscopy ; gravimetric sorption ; diffusion ; polymer ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: In this study, vapor sorption FTIR-ATR (Fourier Transform Infrared Attenuated Total Reflectance) spectroscopy was combined with a conventional gravimetric sorption balance to examine diffusion in polymers. Mutual diffusion coefficients of methyl ethyl ketone in polyisobutylene were measured using both methods at various penetrant activities and temperatures in the range 40-60°C. Actual penetrant concentrations were determined from the sorption balance. The diffusion coefficients from the two techniques agree very well with each other. In addition, the diffusivity data from both techniques could be correlated successfully as a function of temperature and concentration with the Vrentas and Duda free-volume model. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1261-1267, 1997
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    Poly(4-methylpentene-1)/hydrogenated oligo (cyclopentadiene) blends: Miscibility, tensile stress-strain, and dynamic mechanical behaviors (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1269-1277 
    Details
    ISSN: 0887-6266
    Keywords: poly(4-methylpentene-1) ; hydrogenated oligo (cyclopentadiene) ; blends ; miscibility ; mechanical properties ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: This article discusses the influence of the oligomeric resin, hydrogenated oligo(cyclopentadiene) (HOCP), on the morphology, and thermal and tensile mechanical properties of its blends with isotactic poly(4-methylpentene-1) (P4MP1). The P4MP1 and HOCP are found not miscible in the melt state. P4MP1/HOCP blends after solidification contain three phases: the crystalline phase of P4MP1, an amorphous phase of P4MP1, and an amorphous phase of HOCP. From optical micrographs obtained at 150°C, it is found that the solidified blends show a morphology constituted by P4MP1 microspherulites and small HOCP domains homogeneously distributed in intraspherulitic regions. DSC and DMTA results show that the blends present two glass transition temperatures (Tg) equal to the Tgs of the pure components. The tensile mechanical properties have been investigated at 20, 60, and 120°C. At 20°C both the HOCP oligomer and the amorphous P4MP1 are glassy, and it is found that all the blends are brittle and the stress-strain curves have equal trends. At 60°C the HOCP oligomer is glassy, whereas the amorphous P4MP1 is rubbery. The tensile mechanical properties at 60°C are found to depend on blend composition. It is found that the Young's modulus, the stresses at yielding and break points slightly decrease with HOCP content in the blends and these results are related to the decrease of blend crystallinity. The decrease of the elongation at break is accounted for by the presence of glassy HOCP domains that act as defects in the P4MP1 matrix, hampering the drawing. At 120°C both the amorphous phases are rubbery. It is found decreases of Young's modulus, stresses at yielding and break points. These results have been related to the decrease of blend crystallinity and to the increase of the total rubbery amorphous phase. Moreover, it is found that the blends present elongations at break equal to that of pure P4MP1. This constancy is attributed to: (a) at 120°C the HOCP domains are rubbery and their presence seems not to disturb the drawing of the samples; (b) a sufficient number of the tie-molecules and entanglements of P4MP1 present in the blends. In fact, although the numbers of tie-molecules and entanglements decrease in the blends, increasing the HOCP oligomer, they seem to be enough to keep the material interlaced and avoid earlier rupture. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1269-1277, 1997
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    Densely crosslinked polycarbosiloxanes. II: Thermal and mechanical properties (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1311-1331 
    Details
    ISSN: 0887-6266
    Keywords: branched prepolymers ; hydrosilylation cure ; densely crosslinked polymers ; thermal and mechanical properties ; tough-brittle transition ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The thermal and mechanical properties of two densely crosslinked polycarbosiloxane systems were investigated in relation to the molecular structure. The networks were prepared from functional branched prepolymers and crosslinked via a hydrosilylation curing reaction. The prepolymers having only vinyl functionalities (poly[phenylmethylvinyl]siloxanes) were crosslinked by using crosslinking agents with reactive silicon-hydrogen groups. In prepolymers having both silicon-vinyl and silicon-hydrogen groups (poly[phenylmethylvinylhydro)]siloxanes crosslinking took place intermolecularly. The thermal and mechanical properties of the polymer networks were found to be dependent on the phenyl —Si—O3/2 (branches) content in the prepolymer, the number of elastically effective crosslinks, the elastically effective network chain density and molecular weight between crosslinks, length of the chain segments introduced by the hydrosilylation crosslinking reaction, and the number of dangling ends. As a consequence of the dense crosslinking, the mechanical properties were also strongly dependent on the glass transition temperature. A tough-brittle transition was observed around the glass transition temperature of the polymer networks. The properties of the poly(phenylmethylvinylhydro)siloxane networks were found to be superior to those of the poly(phenylmethylvinyl)siloxane networks. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1311-1331, 1997
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    Infrared dichroism and polymer orientation in attenuated total reflection. Theoretical considerations (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1361-1372 
    Details
    ISSN: 0887-6266
    Keywords: polymer ; infrared ; attenuated total reflection (ATR) ; dichroism ; molecular orientation ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The orientation of molecular chains in polymers cannot be easily extracted from ATR spectra measurements. One can infer the orientation parameters by using plausible models that describe the type of the statistical distribution of the molecular chains in the sample. In this work, we are interested in the case of weakly aligned polymers. Therefore, we first adjusted the partial axial orientation model usually applied for strongly oriented polymers to the samples under our investigations and second, related the parameters describing the orientation configuration to the dichroic ratios in four particular molecular chain distributions: randomly, totally, partially, and elliptically oriented. A new method that leads to the determination of these dichroic ratios from ATR spectra is presented. This method is based only on the use of three distinct polarizations of the beam. Thus, all the practical difficulties usually encountered in the other methods are eliminated. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1361-1372, 1997
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    Hydrogen bonds in silk fibroin-poly(acrylonitrile-co-methyl acrylate) blends: FT-IR study (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1405-1414 
    Details
    ISSN: 0887-6266
    Keywords: silk fibroin ; FT-IR spectroscopy ; hydrogen bonds ; polyacrylonitrile ; poly(acrylonitrile-co-methyl acrylate) ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: FT-IR spectroscopy was used to study the specific interactions in polyacrylonitrile-silk fibroin (PAN-SF) and poly(acrylonitrile-co-methyl acrylate)-silk fibroin (PANMA-SF) blends. No specific interaction was found in PAN-SF blends. In PANMA-SF blends, however, a new 1703 cm-1 band, assigned to be hydrogen-bonded carbonyl groups of PANMA, appears, and its intensity depends on the compositions of the blends and the MA contents in PANMA. Furthermore, when the sample was heated, considerable changes in position and intensities of the hydrogen-bonded bands, in both stretching regions of the carbonyl group of PANMA and the hydroxl group of SF, were found, and these changes were irreversible on cooling. Finally, we suggested that the bands of hydrogen bonds in PANMA-SF blends may be the average result of several kinds of possible hydrogen bondings. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1405-1414, 1997
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    Moisture sorption mechanism of aromatic polyamide fibers. V: Growth of crystallites in as-spun wet poly(p-phenylene terephthalamide) fiber during dehydration (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1423-1432 
    Details
    ISSN: 0887-6266
    Keywords: crystallite ; Kevlar ; moisture sorption ; poly(p-phenylene terephthalamide) ; wide-angle x-ray diffraction ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Wide-angle x-ray diffraction studies were performed for as-spun wet poly(p-phenylene terephthalamide) fiber. The effects of sorbed water on the equatorial diffractions from the (110) and (200) crystal planes and on the meridional diffractions from the (002), (004), and (006) crystal planes were analyzed during desorption and absorption. There was no significant change in the d-spacing from the respective crystal plane irrespective of the moisture (water) regain. The ratio of the diffracted intensity from the (110) diffraction to that from the (200) diffraction remarkably increased by removing the sorbed water. The crystallite size estimated from the (110) diffraction, L110, also increased as the moisture regain decreased, while the L200 did not increase. The longitudinal size of paracrystallite, D001, also remarkably increased with the decrease in moisture regain with the lattice distortion factor, gII, kept unchanged. These results strongly suggested the growth of the crystallite via hydrogen bonds in the lateral (b-axis) direction. The growth of the lateral size of crystallite also accompanied the longitudinal growth of crystallite during desorption. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1423-1432, 1997
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    Adhesion of silicon oxide layers on poly(ethylene terephthalate). I: Effect of substrate properties on coating's fragmentation process (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1449-1461 
    Details
    ISSN: 0887-6266
    Keywords: adhesion ; oxide coating ; fragmentation test ; molecular orientation ; substrate temperature ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Fragmentation tests in the uniaxial mode were performed on poly(ethylene terephthalate) (PET) films coated with a 100 nm thin silicon oxide layer. The coating's fragmentation process was analyzed in light of the mechanical behavior of the polymer substrate. It was shown that, upon unloading samples strained to less than 4% nominal strain, strain recovery leads to the closure of coating cracks. The usual fragmentation diagram, which shows the crack density (CD) versus applied strain, was used to identify the various energy dissipation mechanisms controlling the fragmentation process. An alternative presentation of CD versus true stress provided accurate measurements of both fragmentation and saturation onsets. The interfacial strength was modeled from the CD at saturation according to the Kelly-Tyson approach, including a Weibull distribution of the coating strength. The prediction was compared to the substrate shear stress at saturation. Effects of substrate yield, temperature, and molecular orientation are discussed. It was shown that the coating deposition by evaporation on the PET substrate did not induce structural changes at the polymer interface, whereas heat treatments increased the polymer crystallinity in the interfacial zone, resulting in higher interfacial strength. © 1997 John Wiley & Sons, Inc. J. Polym Sci B: Polym Phys 35: 1449-1461, 1997
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    Crystalline structure of poly(methyl-n-propylsilane) (1997)
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part B: Polymer Physics 35 (1997), S. 1533-1543 
    Details
    ISSN: 0887-6266
    Keywords: polysilane ; lamellar microstructure ; crystal structure ; crystallization kinetics ; Physics ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The thermal behavior and physical structure of atactic poly(methyl-n-propylsilane) (PMPrS) have been investigated by complementary techniques. Temperature-dependent wide-angle X-ray scattering as well as thermal analysis clearly indicate that atactic PMPrS crystallizes below 40°C in a monoclinic lattice with PMPrS adopting an all-trans planar zigzag conformation. Above 40°C, the polymer is in the isotropic amorphous state. A restricted analysis of the structure factors of PMPrS has been performed, indicating that the zigzag planes most probably lie in (110) planes. The chains pack with little interpenetration, and the crystals may be considered as bundles of long, closely packed prisms. The restricted interlocking of neighboring chains results, in turn, in a poor register of the chains along the c-axis. Moreover, transmission electron microscopy reveals that the crystallized polymer adopts a lamellar microstructure, with parallel lamellae tending to form tight bundles. Both electron microscopy and small-angle X-ray scattering indicate crystal thicknesses of about 60 Å. Finally, PMPrS was found to crystallize with a nucleation-controlled type of kinetics. Avrami exponents were calculated as n ≈ 1, suggesting a fibrillar growth geometry compatible with the absence of spherulitic superstructure. A double-melting behavior is also observed for PMPrS. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1533-1543, 1997
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