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  • mathematical programming  (13)
  • kinetics
  • Springer  (18)
  • Public Library of Science (PLoS)
  • 1975-1979  (18)
  • 1975  (18)
Collection
Publisher
  • Springer  (18)
  • Public Library of Science (PLoS)
Years
  • 1975-1979  (18)
Year
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Oxidation of metals 9 (1975), S. 459-472 
    ISSN: 1573-4889
    Keywords: Cr ; oxidation ; kinetics ; Cr2O3 grain size ; short-circuit diffusion ; surface ; preparation ; Fe-Cr
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract Cr was oxidized in 1 aim O2 at 980, 1090, and 1200°C. ElectropolishedCr and some orientations of etched Cr oxidize rapidly and develop compressive stress in the growing Cr2O3; other orientations oxidize slowly, apparently free of stress. SEM examination of fracture sections shows that the thick oxide is polycrystalline whereas the thin oxide on etched Cr is monocrystalline. It is deduced that the monocrystalline oxide grows by lattice diffusion of cations outward, and the polycrystalline layer by the two-way transport of cation diffusion outward and anion diffusion inward along oxide grain boundaries. The consequent formation of oxide within the body of the polycrystalline layer generates compressive stress and leads to wrinkling by plastic deformation. The activation energy for oxidation of Cr by cation lattice transport is 58 kcal/mole. Polycrystalline Cr2O3 forms on Fe-26Cr alloy, whether electropolished or etched; oxidation is accordingly rapid and accompanied by compressive stress.
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  • 2
    Electronic Resource
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    Oxidation of metals 9 (1975), S. 357-365 
    ISSN: 1573-4889
    Keywords: kinetics ; zirconia ; defect structure ; ionic conductivity ; yttria dopant
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A Zr-0.5 Y alloy was found to oxidize about 6 times faster than pure zirconium over the temperature range of 400 to 565°C. The activation energies were nearly identical (∼32 kcal/mole). The activation energies correspond to grain boundary diffusion of oxygen through the scale. The higher oxidation rate of the alloy was attributed to a higher anion vacancy concentration and the assumption that diffusion sites in the lattice and boundaries were in local equilibrium. Measurements on yttria-doped zirconia showed that ionic conductivity was increased markedly by yttrium and extended over a wide range of oxygen pressure. The defect structure of the doped oxide was changed to one of oxygen vacancies, even at the high end of the oxygen pressure range, 10−8 to 0.2 atm, over which pure ziconia contains oxygen interstitials. The doped oxide was found to be extrinsic over the entire range of oxygen pressure and, although ionic conductivity predominated, electronic conductivity was still appreciable. The electronic conductivity, however, was still sufficiently high so that electron transport was not rate-controlling in the predominantly ionic-conducting scale.
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  • 3
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    Oxidation of metals 9 (1975), S. 99-116 
    ISSN: 1573-4889
    Keywords: oxidation ; kinetics ; ilmenite ; rutile ; pseudobrookite
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The oxidation of ilmenite (FeTiO3) in air and dry oxygen was investigated over the temperature interval 600 to 970°C. Dense platelets of ilmenite crystals as well as powder samples of ilmenite were oxidized. The weight data were recorded employing a thermobalance. The oxidation kinetics of ilmenite platelets were parabolic except for the initial stages during which logarithmic kinetics were observed. For powder samples the logarithmic rate law was followed primarily. The logarithmic rate law was attributed to free penetration of oxygen through cracks and short-circuit paths. The activation energies associated with the logarithmic rate law were nearly one-half of those obtained from parabolic oxidation. The growth morphology of the products of oxidation of ilmenite was observed with a scanning electron microscope. The effect of growth morphology on the kinetics is discussed, and a probable reaction mechanism is suggested for the oxidation of ilmenite.
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  • 4
    ISSN: 1573-4889
    Keywords: kinetics ; cobalt and nickel oxidation ; parabolic rate constant
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract A new fast method is proposed for the determination of parabolic rate constants of metal oxidation as a function of pressure and temperature. The method consists of determining rate constants by oxidation of a single metal sample in a continuous manner, periodically changing the oxidant pressure or temperature. This method eliminates a number of errors inherent in the classical method which involves the use of a new metal specimen in each experiment and it further shortens the time of evaluating the functions k p '' = f (p, T). The method is particularly suitable for the determination of rate constants of slow processes. To verify the proposed method measurements of the kinetics of oxidation of cobalt and nickel at different oxygen pressures over the temperature range 1000–1300° C were carried out.
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  • 5
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    Journal of pharmacokinetics and pharmacodynamics 3 (1975), S. 277-290 
    ISSN: 1573-8744
    Keywords: sulfobromophthalein (BSP) ; kinetics ; BSP disposition ; mathematical model ; flow-limited
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract A linear, flow-limited mathematical model of drug kinetics was used to simulate total sulfobromophthalein (BSP) kinetics in normal anesthetized rats during intravenous infusions and following rapid intravenous injections. Four parameters were used to characterize the distribution and biliary and urinary excretion of BSP: liver- to- plasma concentration ratio, extrahepatic tissue- to- plasma concentration ratio, liver clearance rate constant, and renal plasma clearance rate constant. The same parameters appear to characterize the kinetics of BSP in man through the successful application of “scale- up” techniques utilizing data from experiments in rats. Plasma levels of BSP corresponding to intravenous infusions and rapid intravenous injections in man are approximated by computer simulation.
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  • 6
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    Journal of optimization theory and applications 15 (1975), S. 285-309 
    ISSN: 1573-2878
    Keywords: Decomposition methods ; duality theory ; engineering design ; method of multipliers ; nonconvex programming ; mathematical programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For nonconvex problems, the saddle point equivalence of the Lagrangian approach need not hold. The nonexistence of a saddle point causes the generation of a dual gap at the solution point, and the Lagrangian approach then fails to give the solution to the original problem. Unfortunately, dual gaps are a fairly common phenomenon for engineering system design problems. Methods which are available to resolve the dual gaps destroy the separability of separable systems. The present work employs the method of multipliers by Hestenes to resolve the dual gaps of engineering system design problems; it then develops an algorithmic procedure which preserves the separability characteristics of the system. The theoretical foundations of the proposed algorithm are developed, and examples are provided to clarify the approach taken.
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  • 7
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    Journal of optimization theory and applications 15 (1975), S. 549-564 
    ISSN: 1573-2878
    Keywords: Nonconvex programming ; mathematical programming ; operations research ; sufficiency conditions ; necessary conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A nonconvex programming problem, which arises in the context of application of Benders' decomposition procedure to a class of network optimization problems, is considered. Conditions which are both necessary and sufficient for a local maximum are derived. The concept of a basic local maximum is introduced, and it is shown that there is a finite number of basic local maxima and at least one such local maximum is optimal.
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  • 8
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    Journal of optimization theory and applications 15 (1975), S. 667-684 
    ISSN: 1573-2878
    Keywords: Necessary conditions ; mathematical programming ; Banach spaces ; optimization theorems ; nonlinear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, necessary optimality conditions for nonlinear programs in Banach spaces and constraint qualifications for their applicability are considered. A new optimality condition is introduced, and a constraint qualification ensuring the validity of this condition is given. When the domain space is a reflexive space, it is shown that the qualification is the weakest possible. If a certain convexity assumption is made, then this optimality condition is shown to reduce to the well-known extension of the Kuhn-Tucker conditions to Banach spaces. In this case, the constraint qualification is weaker than those previously given.
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  • 9
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    Journal of optimization theory and applications 17 (1975), S. 337-342 
    ISSN: 1573-2878
    Keywords: Bounds on cost functionals ; engineering design ; inequality constraints ; mathematical programming ; penalty-function methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper describes a new algorithm for solving constrained optimization problems, based on a method proposed by Chattopadhyay. The proposed algorithm replaces the original problem withm constraints,m〉1, by a sequence of optimization problems, with one constraint. Here, we modify the algorithm given by Chattopadhyay in order to make it applicable for a larger class of optimization problems and to improve its convergence characteristics.
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  • 10
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    Journal of optimization theory and applications 16 (1975), S. 207-220 
    ISSN: 1573-2878
    Keywords: Duality theory ; nonlinear programming ; mathematical programming ; convex programming ; optimization theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Duality relations for the programming problem of a special class where the objective function is a sum of positive-semidefinite quadratic forms, and a sum of square roots of positive-semidefinite quadratic forms, over a convex polyhedral cone in complex space are considered. The duality relations between the primal problem and its dual are established.
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  • 11
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    Journal of optimization theory and applications 15 (1975), S. 565-586 
    ISSN: 1573-2878
    Keywords: Nonconvex programming ; network flows ; mathematical programming ; network synthesis ; operations research
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The problem of optimally allocating a fixed budget to the various arcs of a single-source, single-sink network for the purpose of maximizing network flow capacity is considered. The initial vector of arc capacities is given, and the cost function, associated with each arc, for incrementing capacity is concave; therefore, the feasible region is nonconvex. The problem is approached by Benders' decomposition procedure, and a finite algorithm is developed for solving the nonconvex relaxed master problems. A numerical example of optimizing network flow capacity, under economies of scale, is included.
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  • 12
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    Journal of optimization theory and applications 16 (1975), S. 49-66 
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; penalty-function methods ; Lagrange multipliers ; mathematical programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract As an approach to solving nonlinear programs, we study a class of functions known to be exact penalty functions for a proper choice of the parameters. The goal is to iteratively determine the correct parameters. A basic algorithm has been developed. We have proved that this algorithm converges to a global solution for concave programs and, in the limited computational tests performed to date, it has always converged to at least a local solution for nonconcave programs also.
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  • 13
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    Journal of optimization theory and applications 16 (1975), S. 1-24 
    ISSN: 1573-2878
    Keywords: Penalty-function methods ; mathematical programming ; nonlinear programming ; pseudo Newton-Raphson methods ; parameter optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An effective algorithm is described for solving the general constrained parameter optimization problem. The method is quasi-second-order and requires only function and gradient information. An exterior point penalty function method is used to transform the constrained problem into a sequence of unconstrained problems. The penalty weightr is chosen as a function of the pointx such that the sequence of optimization problems is computationally easy. A rank-one optimization algorithm is developed that takes advantage of the special properties of the augmented performance index. The optimization algorithm accounts for the usual difficulties associated with discontinuous second derivatives of the augmented index. Finite convergence is exhibited for a quadratic performance index with linear constraints; accelerated convergence is demonstrated for nonquadratic indices and nonlinear constraints. A computer program has been written to implement the algorithm and its performance is illustrated in fourteen test problems.
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  • 14
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    Journal of optimization theory and applications 16 (1975), S. 245-254 
    ISSN: 1573-2878
    Keywords: Two-point boundary-value problems ; approximation methods ; spline functions ; mathematical programming ; gradient projection methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper describes a technique for computing spline function approximations to the solution of two-point boundary-value problems. A performance index that measures the meansquare error in the differential system is employed, and this yields a mathematical programming problem in the parameters characterizing the spline function. The gradients of the performance index and constraint functions with respect to these parameters are evaluated, and a numerical solution is then obtained using standard gradient projection algorithms. Computational results confirm the feasibility of this approach and show that good approximations are obtained with spline functions having relatively few knots. It appears that this new technique is very competitive with existing algorithms, especially for problems where the differential system is nonlinear but the boundary restraints are linear.
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  • 15
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    Journal of optimization theory and applications 16 (1975), S. 447-485 
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; mathematical programming ; quadratically convergent algorithms ; conjugate-gradient methods ; variable-metric methods ; computing methods ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The problem of minimizing a functionf(x) subject to the constraint ϕ(x)=0 is considered. Here,f is a scalar,x is ann-vector, and ϕ is anm-vector, wherem 〈n. A general quadratically convergent algorithm is presented. The conjugate-gradient algorithm and the variable-metric algorithms for constrained function minimization can be obtained as particular cases of the general algorithm. It is shown that, for a quadratic function subject to a linear constraint, all the particular algorithms behave identically if the one-dimensional search for the stepsize is exact. Specifically, they all produce the same sequence of points and lead to the constrained minimal point in no more thann −r descent steps, wherer is the number of linearly independent constraints. The algorithms are then modified so that they can also be employed for a nonquadratic function subject to a nonlinear constraint. Some particular algorithms are tested through several numerical examples.
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  • 16
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    Journal of optimization theory and applications 16 (1975), S. 183-190 
    ISSN: 1573-2878
    Keywords: Global optimality ; nonconvex programming ; point-to-set maps ; mathematical programming ; nonlinear optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, necessary and sufficient conditions for a local minimum to be global are derived. The main result is that a real function, defined on a subset ofR n, has the property that every local minimum is global if, and only if, its level sets are lower-semicontinuous point-to-set mappings.
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  • 17
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    Journal of optimization theory and applications 16 (1975), S. 565-569 
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; function maximization ; mathematical programming ; quasiconcave functions ; global maximality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is shown that the class of weakly nonconstant functions possesses the property that every local maximum is global. This is also a necessary condition.
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  • 18
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    Journal of optimization theory and applications 16 (1975), S. 571-571 
    ISSN: 1573-2878
    Keywords: Newton-Raphson method ; quasilinearization method ; mathematical programming ; nonlinear programming ; quadratically convergent algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A modification to the algorithm of Ref. 1 is given.
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