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  • 1
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    Springer
    Meccanica 32 (1997), S. 555-565 
    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.
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  • 2
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    Journal of mathematical biology 35 (1997), S. 775-792 
    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.
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  • 3
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    Acta mathematicae applicatae sinica 13 (1997), S. 425-437 
    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.
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  • 4
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    Mathematics of control, signals, and systems 10 (1997), S. 247-264 
    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.
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  • 5
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    Journal of optimization theory and applications 17 (1975), S. 1-42 
    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.
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  • 6
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    Journal of optimization theory and applications 17 (1975), S. 273-278 
    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.
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  • 7
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    Journal of optimization theory and applications 21 (1977), S. 51-57 
    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.
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  • 8
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    Journal of optimization theory and applications 21 (1977), S. 487-504 
    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.
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  • 9
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    Journal of optimization theory and applications 26 (1978), S. 463-464 
    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.
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  • 10
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    Journal of optimization theory and applications 26 (1978), S. 395-425 
    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.
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  • 11
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    Journal of optimization theory and applications 41 (1983), S. 317-325 
    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.
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  • 12
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    Journal of optimization theory and applications 42 (1984), S. 103-141 
    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.
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  • 13
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    Journal of optimization theory and applications 42 (1984), S. 467-485 
    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.
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  • 14
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    Journal of optimization theory and applications 43 (1984), S. 89-101 
    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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  • 15
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    Journal of optimization theory and applications 95 (1997), S. 101-126 
    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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  • 16
    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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  • 17
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    Mathematical Methods in the Applied Sciences 5 (1983), S. 186-194 
    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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  • 18
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    Mathematical Methods in the Applied Sciences 5 (1983), S. 530-543 
    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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  • 19
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    Mathematical Methods in the Applied Sciences 5 (1983) 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
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  • 20
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    Mathematical Methods in the Applied Sciences 5 (1983), S. 1-13 
    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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  • 21
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    Mathematical Methods in the Applied Sciences 5 (1983), S. 84-96 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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  • 22
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    Mathematical Methods in the Applied Sciences 5 (1983), S. 162-175 
    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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  • 23
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    Mathematical Methods in the Applied Sciences 5 (1983), S. 233-255 
    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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  • 24
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    Mathematical Methods in the Applied Sciences 5 (1983), S. 195-215 
    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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    Mathematical Methods in the Applied Sciences 5 (1983), S. 331-345 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 5 (1983), S. 422-437 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 5 (1983), S. 476-490 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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  • 28
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    Mathematical Methods in the Applied Sciences 6 (1984) 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
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    Mathematical Methods in the Applied Sciences 6 (1984), S. 1-22 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 41-54 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 129-157 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 206-214 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 262-279 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 327-344 
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    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 353-370 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 433-448 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 467-495 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    Topics: Mathematics
    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 512-514 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 527-538 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 5 (1983), S. 131-152 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 5 (1983), S. 216-232 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 5 (1983), S. 292-307 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 5 (1983), S. 356-375 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 104-128 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 159-191 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 215-233 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 248-261 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 5 (1983), S. 40-67 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 5 (1983), S. 308-330 
    ISSN: 0170-4214
    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 5 (1983), S. 389-421 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 5 (1983), S. 491-515 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 371-392 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 393-416 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Mathematical Methods in the Applied Sciences 6 (1984), S. 496-511 
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    Keywords: Mathematics and Statistics ; Applied Mathematics
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    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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    Biotechnology and Bioengineering 55 (1997), S. 252-260 
    ISSN: 0006-3592
    Keywords: lipase ; chemical modification ; stability ; esterification ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Semipurified lipase of Candida rugosa (CRSL) was subjected to chemical modification, and the activities of the modified lipase, in hydrolysis and esterification reactions, were examined. The esterification reactions were carried out in the absence and presence of isooctane. When the enzyme was modified with polyethylene glycol (PEG), two methodologies were studied. The activation of PEG with p-NO2-phenylchloroformate gives better biocatalysts than those obtained with cyanuric chloride-PEG. The chemical modification with PEG increases the stability of pure lipases in isooctane at 50°C (extreme conditions). The chemically modified enzymes are useful for biotransformations in organic solvents. In addition the nitration of tyrosines with tetranitromethane was also studied. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 252-260, 1997.
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    Biotechnology and Bioengineering 55 (1997), S. 565-570 
    ISSN: 0006-3592
    Keywords: hybridoma ; hypoosmotic stress ; specific antibody productivity ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: To investigate the response of hybridoma cells to hypoosmotic stress, S3H5/γ2bA2 and DB9G8 hybridomas were cultivated in the hypoosmolar medium [Dulbecco's modified Eagle's medium (DMEM) supplemented with 10% serum] resulting from sodium chloride subtraction. Both hybridomas showed similar responses to hypoosmotic stress in regard to cell growth and antibody production. The cell growth and antibody production at 276 mOsm/kg were comparable to those at 329 mOsm/kg (standard DMEM). Both cells grew well at 219 mOsm/kg, though their growth and antibody production were slightly decreased. When the osmolality was further decreased to 168 mOsm/kg, the cell growth did not occur. When subjected to hyperosmotic stress, both cells displayed significantly enhanced specific antibody productivity (qAb). However, the cells subjected to hypoosmotic stress did not display enhanced qAb. Taken together, both hyperosmotic and hypoosmotic stresses depressed the growth of S3H5/γ2bA2 and DB9G8 hybridomas. However, their response to hypoosmotic stress in regard to qAb was different from that to hyperosmotic stress. © 1997 John Wiley & Sons, Inc. Biotechnol Biong 55: 565-570, 1997.
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    Biotechnology and Bioengineering 55 (1997), S. 547-555 
    ISSN: 0006-3592
    Keywords: ethanol ; cellulose ; hemicellulose ; endoglucanase ; cellulase ; lignocellulose ; biomass ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: This study demonstrates a new approach to reduce the amount of fungal cellulase required for the conversion of cellulose into ethanol. Escherichia coli KO11, a biocatalyst developed for the fermentation of hemicellulose syrups, was used to produce recombinant endoglucanase as a co-product with ethanol. Seven different bacterial genes were expressed from plasmids in KO11. All produced cell-associated endoglucanase activity. KO11(pLOI1620) containing Erwinia chrysanthemi celZ (EGZ) produced the highest activity, 3,200 IU endoglucanase/L fermentation broth (assayed at pH 5.2 and 35°C). Recombinant EGZ was solubilized from harvested cells by treatment with dilute sodium dodecyl sulfate (12.5 mg/ml, 10 min, 50°C) and tested in fermentation experiments with commercial fungal cellulase (5 filter paper units/g cellulose) and purified cellulose (100 g/L). Using Klebsiella oxytoca P2 as the biocatalyst, fermentations supplemented with EGZ as a detergent-lysate of KO11(pLOI1620) produced 14%-24% more ethanol than control fermentations supplemented with a detergent-lysate of KO11(pUC18). These results demonstrate that recombinant bacterial endoglucanase can function with fungal cellulase to increase ethanol yield during the simultaneous saccharification and fermentation of cellulose. © 1997 Wiley & Sons, Inc. Biotechnol Bioeng 55: 547-555, 1997.
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    Biotechnology and Bioengineering 55 (1997), S. 577-580 
    ISSN: 0006-3592
    Keywords: mRNA stability ; hairpins ; gene expression control ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An expression system has been developed for the introduction of DNA cassettes into the region between the transcription and translation start sites of a gene of interest. This cassette system was used to engineer mRNA stability through the introduction of hairpins at the 5′ end. A synthetic DNA cassette was designed so that the resulting mRNA hairpin would be positioned one nucleotide from the 5′ mRNA end. The hairpin-containing mRNA exhibited a half-life 3 times that of the mRNA with no hairpin, resulting in increases in both mRNA and protein levels. These results indicate that it is possible to engineer mRNA stability as an additional means of controlling gene expression. © 1997 John Wiley & Sons Inc. Biotechnol Bioeng 55: 557-580, 1997
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    Biotechnology and Bioengineering 55 (1997), S. 581-591 
    ISSN: 0006-3592
    Keywords: adsorptive membranes ; oscillatory flow ; integrated processes ; in situ product recovery ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Preferential transport in adsorptive membranes can be used to selectively remove biochemicals directly from fermentation broths. During preferential transport, an adsorbing solute is selectively transported across the membrane while nonadsorbing solutes and cells are retained by the membrane. This technique was used to separate lysozyme directly from a feed containing lysozyme, myoglobin, and yeast cells. We found that because the oscillatory flows used in preferential transport involve strokes that are close to symmetric, they are very efficient in alleviating cake formation due to cell deposition on the membrane surface. Theoretical results suggest that, by optimizing process variables, preferential transport can lead to a continuous concentrated stream of the adsorbing protein. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 54: 581-591, 1997.
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    Biotechnology and Bioengineering 55 (1997), S. 592-608 
    ISSN: 0006-3592
    Keywords: Saccharomyces cerevisiae ; metabolic modeling ; sensitivity analysis ; glycolysis ; compartmentation ; transient response ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A mathematical model of glycolysis in Saccharomyces cerevisiae is presented. The model is based on rate equations for the individual reactions and aims to predict changes in the levels of intra- and extracellular metabolites after a glucose pulse, as described in part I of this study. Kinetic analysis focuses on a time scale of seconds, thereby neglecting biosynthesis of new enzymes. The model structure and experimental observations are related to the aerobic growth of the yeast. The model is based on material balance equations of the key metabolites in the extracellular environment, the cytoplasm and the mitochondria, and includes mechanistically based, experimentally matched rate equations for the individual enzymes. The model includes removal of metabolites from glycolysis and TCC for biosynthesis, and also compartmentation and translocation of adenine nucleotides. The model was verified by in vivo diagnosis of intracellular enzymes, which includes the decomposition of the network of reactions to reduce the number of parameters to be estimated simultaneously. Additionally, sensitivity analysis guarantees that only those parameters are estimated that contribute to systems trajectory with reasonable sensitivity. The model predictions and experimental observations agree reasonably well for most of the metabolites, except for pyruvate and adenine nucleotides. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 592-608, 1997.
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    Biotechnology and Bioengineering 55 (1997), S. 609-615 
    ISSN: 0006-3592
    Keywords: interacting populations ; membrane reactor ; induced metabolic changes ; elicitation ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The design of a reactor in which two interacting cell populations (microorganisms and plants) could grow under controlled conditions was considered. In this reactor, the cell populations are separated by a membrane which permits semi-in vivo study of induced interaction-specific changes in metabolism. In this paper, the interaction of suspension culture of Nicotiana tabacum (tobacco) and the Oomycete, Phytophthora nicotiana was simulated. The results of the computer simulation show the induced metabolic changes as a consequence of the biological interaction. The paper introduces a novel approach in the strategy for the study of interacting population in suspension cultures. This type of system has potential applications in studies of the regulation of secondary metabolism and for the production of high values pharmaceuticals. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 609-615, 1997.
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    Biotechnology and Bioengineering 55 (1997), S. 616-629 
    ISSN: 0006-3592
    Keywords: cell adhesion ; radial-flow chamber ; hydrodynamic shear ; detachment kinetics ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The strength of adhesion and dynamics of detachment of murine 3T3 fibroblasts from self-assembled monolayers were measured in a radial-flow chamber (RFC) by applying models for fluid mechanics, adhesion strength probability distributions, and detachment kinetics. Four models for predicting fluid mechanics in a RFC were compared to evaluate the accuracy of each model and the significance of inlet effects. Analysis of these models indicated an outer region at large radial positions consistent with creeping flow, an intermediate region influenced by inertial dampening, and an inner region dominated by entrance effects from the axially-oriented inlet. In accompanying experiments patterns of the fraction of cells resisting detachment were constructed for individual surfaces as a function of the applied shear stress and evaluated by comparison with integrals of both a normal and a log-normal distribution function. The two functions were equally appropriate, yielding similar estimates of the mean strength of adhesion. Further, varying the Reynolds number in the inlet, Red, between 630 and 1480 (corresponding to volumetric flow rates between 0.9 and 2.1 mL/s) did not affect the mean strength of adhesion. For these same experiments, analysis of the dynamics of detachment revealed three temporal phases: 1) rapid detachment of cells at the onset of flow, consistent with a first-order homogeneous kinetic model; 2) time-dependent rate of detachment during the first 30 sec. of exposure to hydrodynamic shear, consistent with the first-order heterogeneous kinetic model proposed by Dickinson and Cooper (1995); and 3) negligible detachment, indicative of pseudo-steady state after 60 sec. of flow. Our results provide rigorous guidelines for the measurement of adhesive interactions between mammalian cells and prospective biomaterial surfaces using a RFC. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 616-629, 1997.
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    Biotechnology and Bioengineering 55 (1997), S. 693-700 
    ISSN: 0006-3592
    Keywords: glucose ; lactate ; real-time determination ; hematopoietic cell culture ; colony-forming cells ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Glucose and lactate metabolic rates were evaluated for cultures of cord blood (CB) mononuclear cell (MNC), peripheral blood (PB) MNC, and PB CD34+ cell cultures carried out in spinner flasks and in T-flasks in both serum-containing and serum-free media. Specific glucose uptake rates (qgluc, in micromoles per cell per hour) and lactate generation rates (qlac) correlated with the percentage of colony-forming cells (CFC) present in the culture for a broad range of culture conditions. Specifically, the time of maximum CFC percentage in each culture coincided with the time of maximum qgluc and qlac in cultures with different seeding densities and cytokine combinations. A two-population model (Qlac = α[CFC] + β([TC] - [CFC]), where [TC] is total cell concentration; Qlac is volumetric lactate production rate in micromoles per milliliter per hour; α is qlac for an average CFC; and β is qlac for an average non-CFC) was developed to describe lactate production. The model described lactate production well for cultures carried out in both T-flasks and spinner flasks and inoculated with either PB or CB MNC or PB CD34+ cells. The values for α and β that were derived from the model varied with both the inoculum density and the cytokine combination. However, preliminary results indicate that cultures carried out under the same conditions from different samples with similar initial CD34+ cell content have similar values for β and β. These findings suggest that it should be possible to use lactate production data to predict the harvest time that corresponds to the maximum number of CFC in culture. The ability to harvest ex vivo hematopoietic cultures for transplantation when CFC are at a maximum has the potential to speed the rate at which immunocompromised patients recover. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 693-700, 1997.
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  • 65
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    Keywords: tubular photobioreactors ; light distribution ; average solar irradiance ; light attenuation ; microalgae mass culture ; Chemistry ; Biochemistry and Biotechnology
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    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A mathematical model to estimate the solar irradiance profile and average light intensity inside a tubular photobioreactor under outdoor conditions is proposed, requiring only geographic, geometric, and solar position parameters. First, the length of the path into the culture traveled by any direct or disperse ray of light was calculated as the function of three variables: day of year, solar hour, and geographic latitude. Then, the phenomenon of light attenuation by biomass was studied considering Lambert-Beer's law (only considering absorption) and the monodimensional model of Cornet et al. (1900) (considering absorption and scattering phenomena). Due to the existence of differential wavelength absorption, none of the literature models are useful for explaining light attenuation by the biomass. Therefore, an empirical hyperbolic expression is proposed. The equations to calculate light path length were substituted in the proposed hyperbolic expression, reproducing light intensity data obtained in the center of the loop tubes. The proposed model was also likely to estimate the irradiance accurately at any point inside the culture. Calculation of the local intensity was thus extended to the full culture volume in order to obtain the average irradiance, showing how the higher biomass productivities in a Phaeodactylum tricornutum UTEX 640 outdoor chemostat culture could be maintained by delaying light limitation. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 701-714, 1997.
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    Biotechnology and Bioengineering 55 (1997), S. 715-726 
    ISSN: 0006-3592
    Keywords: fungal morphology ; pellets ; hyphae ; hair of pellets ; agitation intensity ; fermentation ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Both parallel fermentations with Aspergillus awamori (CBS 115.52) and a literature study on several fungi have been carried out to determine a relation between fungal morphology and agitation intensity. The studied parameters include hyphal length, pellet size, surface structure or so-called hairy length of pellets, and dry mass per-wet-pellet volume at different specific energy dissipation rates. The literature data from different strains, different fermenters, and different cultivation conditions can be summarized to say that the main mean hyphal length is proportional to the specific energy dissipation rate according to a power function with an exponent of -0.25 ± 0.08. Fermentations with identical inocula showed that pellet size was also a function of the specific energy dissipation rate and proportional to the specific energy dissipation rate to an exponent of -0.16 ± 0.03. Based on the experimental observations, we propose the following mechanism of pellet damage during submerged cultivation in stirred fermenters. Interaction between mechanical forces and pellets results in the hyphal chip-off from the pellet outer zone instead of the breakup of pellets. By this mechanism, the extension of the hyphae or hair from pellets is restricted so that the size of pellets is related to the specific energy dissipation rate. Hyphae chipped off from pellets contribute free filamentous mycelia and reseed their growth. So the fraction of filamentous mycelial mass in the total biomass is related to the specific energy dissipation rate as well.To describe the surface morphology of pellets, the hyphal length in the outer zone of pellets or the so-called hairy length was measured in this study. A theoretical relation of the hairy length with the specific energy dissipation rate was derived. This relation matched the measured data well. It was found that the porosity of pellets showed an inverse relationship with the specific energy dissipation rate and that the dry biomass per-wet-pellet volume increased with the specific energy dissipation rates. This means that the tensile strength of pellets increased with the increase of specific energy dissipation rate. The assumption of a constant tensile strength, which is often used in literature, is then not valid for the derivation of the relation between pellet size and specific energy dissipation rate. The fraction of free filamentous mycelia in the total biomass appeared to be a function of the specific energy dissipation in stirred bioreactors. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 715-726, 1997.
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    Biotechnology and Bioengineering 55 (1997), S. 921-926 
    ISSN: 0006-3592
    Keywords: green fluorescent protein ; sensor ; on-line monitoring ; quantitation ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: We present an intensity based sensor designed for on-line monitoring of green fluorescent protein, a revolutionary marker of protein expression. The device consisted of a blue light emitting diode as the excitation source. A band pass excitation filter cut off light longer than 490 nm. The light was directed into a bifurcated optical fiber bundle with the common end inserted into a stainless steel housing equipped with a quartz window. The fiber bundle and stainless steel housing are steam sterilizable. The emission radiation was collected through a long wave pass filter to reject the excitation light shorter than 505 nm and was detected by a photomultiplier tube. The signal was amplified and sent to a computer for recording time course data. The sensor was tested in an Escherichia coli fermentation of JM105 transformed with pBAD-GFP. The on-line signal was compared to off-line fluorescence spectrophotometer measurements. The on-line profile closely followed the off-line. Western blot data showed that with a time shift, the sensor was able to both continuously and quantitatively monitor expression of green fluorescent protein on-line in real time. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55:921-926, 1997.
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    Biotechnology and Bioengineering 55 (1997), S. 909-920 
    ISSN: 0006-3592
    Keywords: baculovirus ; insect cells ; metabolism ; Sf-9; high five™ ; Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Nutrient utilization and byproduct accumulation were monitored in Spodoptera frugiperda Sf-9 and Trichoplusia ni BTI-Tn-5B1-4 (High Five™) cell lines during growth and following viral infection in suspension cultures in order to develop a better understanding of cell metabolism and to acquire information relevant to large scale fed-batch bioreactors. The utilization of glucose, dissolved oxygen, and amino acids were monitored in Sf-9 cell cultures grown in Sf-900 II serum-free medium (SFM) and in High Five™ cell cultures grown in both Sf-900 II and Express Five SFM. Using the optimal medium for each cell line, i.e., Sf-900 II SFM for Sf-9 cells and Express Five SFM for High Five™ cells, the cell growth rate, maximum cell density, specific glucose and glutamine utilization rates, and specific alanine production rate were comparable during cell growth. In addition, the expression level of recombinant human tissue plasminogen activator was comparable in the two cell lines on a per cell basis. It was found, however, that lactate and ammonia accumulated in High Five™ cell cultures, but not in Sf-9 cell cultures. In addition, High Five™ cells utilized asparagine more rapidly than glutamine, whereas Sf-9 cells consumed only minimal asparagine, and the oxygen utilization rate was significantly higher in High Five™ cell cultures. It was also found that the medium had a significant effect on High Five™ cell metabolism, e.g., the specific glucose utilization rate and the specific lactate and alanine production rates were significantly higher in Sf-900 II SFM than in Express Five SFM. In addition, the maximum cell density and specific asparagine utilization rate were significantly higher in Express Five SFM. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55:909-920, 1997.
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    Biotechnology and Bioengineering 55 (1997), S. 940-940 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
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    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: No abstract.
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    Biotechnology and Bioengineering 56 (1997), S. 1-8 
    ISSN: 0006-3592
    Keywords: transesterification ; hydrolysis ; water activity ; cutinase ; gas ; bioreactor ; Chemistry ; Biochemistry and Biotechnology
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    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Fusarium solani cutinase supported onto Chromosorb P was used to catalyze transesterification (alcoholysis) and hydrolysis on short volatile alcohols and esters in a continuous gas/solid bioreactor. In this system, a solid phase composed of a packed enzymatic preparation was continuously percolated with carrier gas which fed substrates and removed reaction products simultaneously. A kinetic study was performed under differential operating conditions in order to get initial reaction rates. The effect of the hydration state of the biocatalyst on the kinetics was studied for 3 conditions of hydration (aw = 0.2, aw = 0.4 and aw = 0.6), the alcoholysis of propionic acid methyl ester with n-propanol, and for 5 hydration levels (from aw = 0.2 to aw = 0.6) for the hydrolysis of propionic acid methyl, ethyl or propyl esters. F. solani cutinase was found to have an unusual kinetic behavior. A sigmoid relationship between the rate of transesterification and the activity of methyl propionate was observed, suggesting some form of cooperative activation of the enzyme by one of its substrate. For the hydrolysis of short volatile propionic acid alkyl esters, threshold effects on the reaction rate, highly depending on the water activity and the substrate polarity, are reported. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 1-8, 1997.
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    Biotechnology and Bioengineering 56 (1997), S. 9-22 
    ISSN: 0006-3592
    Keywords: condensation reactions ; disaccharides ; equilibria ; glucoamylase ; kinetics ; monosaccharides ; Chemistry ; Biochemistry and Biotechnology
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    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Arabinose, fructose, galactose, myo-inositol, lyxose, mannose, ribose, and xylose were incubated individually and with glucose in the presence of Aspergillus niger glucoamylase at pH 4.5 and 45°C. Glucoamylase condenses galactose, glucose, and mannose individually into disaccharides. It also produces mixed disaccharides when each of the eight carbohydrates is incubated with glucose. Many products were identified by gas chromatography of the derivatized reaction mixtures followed by mass spectroscopy of the individual chromatographic peaks. Galacto-, gluco-, or mannopyranosyl rings appear to be present at the nonreducing ends of all the disaccharides produced. Molecules linked through primary hydroxyl groups have the highest equilibrium constants of all products formed, since these bonds are thermodynamically favored. However, glucoamylase is capable of forming bonds with many available hydroxyl groups, as previously demonstrated when it was incubated with glucose alone. Formation rates of different bonds linking different residues vary widely. These results demonstrate that glucoamylase has a wide selectivity toward residues it will condense into disaccharides and toward bonds it will form between them. © 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 9-22, 1997.
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    Mathematical methods of operations research 45 (1997), S. 63-79 
    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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    Journal of optimization theory and applications 21 (1977), S. 39-49 
    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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    Journal of optimization theory and applications 22 (1977), S. 91-101 
    ISSN: 1573-2878
    Keywords: Optimal control ; Radon measures ; existence theory ; diffusion equation
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    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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    Journal of optimization theory and applications 22 (1977), S. 373-388 
    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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    Journal of optimization theory and applications 23 (1977), S. 563-579 
    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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    Journal of optimization theory and applications 25 (1978), S. 57-81 
    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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    Journal of optimization theory and applications 25 (1978), S. 229-245 
    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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    Journal of optimization theory and applications 25 (1978), S. 549-554 
    ISSN: 1573-2878
    Keywords: Optimal control ; nonlinear operators ; Frechet differentiability ; Hilbert spaces ; bang-bang control
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    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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    Journal of optimization theory and applications 41 (1983), S. 75-106 
    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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    Journal of optimization theory and applications 93 (1997), S. 103-119 
    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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    Journal of optimization theory and applications 93 (1997), S. 597-607 
    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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    Journal of optimization theory and applications 40 (1983), S. 255-291 
    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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    Journal of optimization theory and applications 94 (1997), S. 273-309 
    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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    Journal of optimization theory and applications 94 (1997), S. 155-168 
    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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    Journal of optimization theory and applications 95 (1997), S. 323-346 
    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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  • 87
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    Biotechnology and Bioengineering 17 (1975), S. 541-556 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A nondimensionalized plot, obtained by normalizing the drop-size distribution in the hydrocarbon phase using the Sauter mean diameter, shows a tendency towards self-preservation of the distribution. Changes of distribution in time during the course of fermentation, initial dispersed phase fraction, speed of rotation, and reactor size were taken into account. Using this self-preserving property, an empirical (single parameter) equation has been proposed for drop-size distribution. Data, available from the literature, are presented for non-biological and biological systems (gas-oil, n-hexadecane, and n-hexadecane dissolved in dewaxed gas oil as dispersed phases). The parameter, Sauter mean diameter, has been correlated with the operating conditions, and a critical review presented. Cell density was found to have significant effect on Sauter mean diameter. This effect has also been empirically explained. The possibilities of using generalized distribution in predicting the performance of fermenters is outlined.
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  • 88
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    Biotechnology and Bioengineering 17 (1975), S. 279-283 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
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  • 89
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    Biotechnology and Bioengineering 17 (1975), S. 291-293 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
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  • 90
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    Biotechnology and Bioengineering 17 (1975), S. 305-314 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: A potent inhibitory agent against human plasmin, fibrinolytic proteinase, has been found in the extracts of callus tissue of Scopolia japonica. Effects of cultural conditions on cell growth and production of the plasmin inhibitory substance by this cell line in suspension cultures were examined in MurashigeSkoog's medium. More than l.5 mg of the inhibitor, as t-amino cyclohexane carboxylic acid, a synthetic plasmin inhibitor, were observed to accumulate per ml of medium containing 0.83 g of NH4NO3 and 7.6 g of KNO3 per liter as well as suitable levels of growth hormones.Addiction of antibiotics and deformers were examined in preliminary tests for large scale cultivation. Semicontinuous culture on a small scale in a glass cylinder, was also tested and growth rate of 1.29 g/liter/day (by dry wt) was obtained. Plasmin inhibitory activities in the extracts of the results intact plant and in cultured cells of S. japonica were compared and the results indicated that cell suspension culture was superior to extraction the natural plant for inhibitor production.
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  • 91
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    Biotechnology and Bioengineering 17 (1975), S. 361-374 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The cellulase production by two strains of the cellulolytic fungus Trichoderma viride was examined. The fungi were grown on different preparations of barley straw pretreated with NaOH under high pressure. The production of cellulases and microbial protein by the better strain (QM 9123) was investigated in an aerated 5-liter fermenter under varying stirring rates (200-350 rpm) and straw concentrations (1-2%). The pH was kept between 3.5 and 4.5. The growth of the fungus was followed by measuring the quantity of CO2 produced and the cell protein. After 2-6 days growth ceased, the lag phases lasting 0-2 days, increasing with increasing straw concentrations. The maximum enzyme yields were reached after 4-10 days. The protein content of the product was 21-26% and up to 70% of the straw was utilized. The yield constants were calculated to be 0.40-0.56; of the same order as those which can be obtained by growing the fungus on glucose.
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  • 92
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    Biotechnology and Bioengineering 17 (1975), S. 441-444 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
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  • 93
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    Biotechnology and Bioengineering 17 (1975), S. 451-453 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
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  • 94
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    Biotechnology and Bioengineering 17 (1975), S. 461-462 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
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  • 95
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    Biotechnology and Bioengineering 17 (1975), S. 985-995 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An apparatus for the cultivation of microorganism under controlled conditions is described. This apparatus is basically a turbidostat improved with automatic devices for sample withdrawal and tube cleaning. The results of experiments, using Euglena gracilis to check the constancy of some physiological parameters (in particular phototactic reactivity), are reported.
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  • 96
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    Biotechnology and Bioengineering 17 (1975), S. 675-694 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: An automated system for cell cycle analysis is described in which synchronous populations of greater than 95% mitotic cells can be selected and subcultured without resorting to inhibitors or altered media. Selection of mitotic cells from roller bottle cultures generates synchronous populations of up to 5 × 107 cells, as often as every 30 min, under conditions of constant temperature. A detailed analysis of the temporal pattern of DNA synthesis in the S phase of several Chinese hamster cells is presented. Several potential artefacts and uncertainties regarding the cell cycle blockage point in S phase synchronization are discussed.
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  • 97
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    Biotechnology and Bioengineering 17 (1975), S. 703-712 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Unbalanced growth has been studied in HeLa cell cultures maintained in perpetual division synchrony by periodic inhibition of DNA synthesis. Observation of eight independent cellular parameters indicates that once synchrony has been established the degree of unbalanced growth in later cycles is not as great as is observed with the conventional “double-block” technique. This significant diminution of unbalanced growth appears to be related to the significantly shorter periods of inhibition of DNA synthesis used in the resynchronization process.
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  • 98
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    Biotechnology and Bioengineering 17 (1975), S. 1083-1098 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Values of the enhancement factor for oxygen absorption into fermentation broth, i.e., the ratio of the liquid phase mass transfer coefficients for oxygen absorption for both cases with and without respiration of microorganisms were predicted theoretically on the assumption of various cell concentration distributions. Calculations indicate that in the usual case the enhancement factor is only slightly or negligibly larger than unity, even when accumulation of microorganisms at or near the gas-liquid interface is assumed. Results of experiments with sparged-stirred fermentors on oxygen absorption into fermentation broths containing resting and growing cells of Candida tropicalis confirmed the theoretical prediction. Except for extreme cases, the effect of respiration of microorganisms on kLa, values can practically be ignored.
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  • 99
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    Biotechnology and Bioengineering 17 (1975), S. 1119-1135 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: Anaerobic digestion offers a potential means of converting organic solid waste into fuel gas and thereby provide a supplemental and readily utilizable source of energy. We are particularly interested in the use of thermophilic digestion over a mesophilic operation for it can achieve higher rates of digestion, greater conversion of waste organics to gas, faster solid-liquid separation, and minimization of bacterial and viral pathogen accumulation. Our results comparing mesophilic (37°C) and thermophilic (65°C) anaerobic digestion of domestic solid waste confirm the increased rate and conversion of waste to methane. In addition, utilizing radioactive labeling of glucose and acetic acid, we have measured the volumetric rates of volatile acid production and disappearance under both mesophilic and thermophilic conditions.
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  • 100
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    Biotechnology and Bioengineering 17 (1975), S. 1183-1197 
    ISSN: 0006-3592
    Keywords: Chemistry ; Biochemistry and Biotechnology
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Biology , Process Engineering, Biotechnology, Nutrition Technology
    Notes: The imperfect state, Sporotrichum pulverulentum, of thecellulolytic basidiomycete Phanerochaete chrysosporiumhas been grown on barley flour and other agricultural products in shake cultures, in an air-lift fermentor, and in stirred fermentors. The growth morphology varied with cultivation conditions, but it was possible to maintain heavy suspensions of loosely associated mycelia in fermentors. The fungus can grow in temperatures up to 40°C and use ammonium salts or organic nitrogen sources to convert sugars, starch, pectin, and various seed residues to a biomass containing 30-40% protein with a favorable amino acid composition. Serial cultures were grown on flours under conditions where the larger part of the culture was withdrawn and replaced with new medium every, or every other, day. The mycelia are easy to harvest by filtration and have several properties which make the product attractive as a potential food ingredient.
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