A novel type of matrix multidimensional singular linear integral equation
Matrix multidimensional singular linear integral equation applied to electromagnetic radiation transfer through stratified atmosphere
Abhyankar, K. D.↗
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Approximate solutions of systems of singular integral equations
Simultaneous singular integral equations approximate solution in orthogonal polynomials
Erdogan, F.↗
Foundations of computer-aided circuit design by singular imbedding
Computer-aided circuit design by imbedding singular elements to transform network synthesis into analysis problem
Kozemchak, E. B.↗
Computation of optimal singular controls
Optimal singular controls made nonsingular for decreasing epsilon values by adding integral quadratic functional of control to cost functional
Gershwin, S. B.↗
Singular solutions to the shallow shell equations
Singular solutions to concentrated loads on shallow shell equations with quadratic middle surface
Sanders, J. L., Jr.↗
New Jacobi-type necessary and sufficient conditions for singular optimization problems
Jacobi-type conditions for singular optimization problems obtained by transformation to nonsingular form adaptable to linear quadratic optimal control theory
Mcdanell, J. P.↗
Sufficient conditions for nonnegativity of the second variation in singular and nonsingular control problems
Singular and nonsingular optimal control problems, deriving sufficient conditions for nonnegativity of second variation
Jacobson, D. H.↗
Numerical analysis of a pair of singular integral equations with a principal value
Numerical analysis of pair of singular integral equations with principal value - Volterra and Fredholm equations
Clerkin, R. C.↗
The real singularities of the N-body problem in celestial mechanics
N-body problem real singularities in celestial mechanics, considering present status and holomorphic motion
Sperling, H. J.↗
Application of singular eigenfunction expansions to the propagation of periodic disturbances in a radiating grey gas
Periodic disturbances propagation in radiating gray gas, using singular eigenfunction expansions
Cheng, P.↗
Smoothness of solutions of Volterra integral equations with weakly singular kernels
Differentiability of nonlinear Volterra integral equations of second kind with convolutional weakly singular kernels
Feldstein, A.↗
Necessary conditions for joining optimal singular and nonsingular subarcs
Continuity and smoothness properties of piecewise optimal control at junction between singular and nonsingular subarcs, developing necessary conditions
Mcdanell, J. P.↗
A numerical method for solving Fredholm integral equations of the first kind using singular values
First kind Fredholm integral equation approximation by numerical quadrature formulas plus collocation, using singular value decomposition for solution
Hanson, R. J.↗
Multiple scattering theory of radiative transfer in the light of singular modes
Multiple scattering theory of radiative transfer boundary value problems, showing Neumann intensity expansion coefficients relation to singular normal modes
Kanal, M.↗
Singular perturbation methods and the warm plasma model
The application of techniques of the singular perturbation theory to the analysis of warm plasma is discussed. Typically, the cold plasma model can be applied over wide ranges of parameters and only over narrow ranges forming so-called boundary layers is the warm plasma model used. Simplified equations can be used and the solutions matched on both sides of the layer's boundary. Simple examples to illustrate the solution are presented. The analysis confirms that some results are highly sensitive to the values of: (1) wire radius or gap size for an antenna, (2) temperature of the medium, and (3) incident angle of a plane wave.
Lee, S. W.↗
Evaluation of the use of a singularity element in finite element analysis of center-cracked plates
Two different methods are applied to the analyses of finite width linear elastic plates with central cracks. Both methods give displacements as a primary part of the solution. One method makes use of Fourier transforms. The second method employs a coarse mesh of triangular second-order finite elements in conjunction with a single singularity element subjected to appropriate additional constraints. The displacements obtained by these two methods are in very good agreement. The results suggest considerable potential for the use of a cracked element for related crack problems, particularly in connection with the extension to nonlinear material behavior.
Mendelson, A.↗
Singular perturbations in the state regulator problem
Most of the results of singular perturbation theory have been concerned with initial value problems whereas optimal control problems are of two-point boundary value type. The portions of this theory applicable to the open loop state regulator problem are reviewed. For obtaining approximate solutions to the state regulator problem the method of matched asymptotic expansions is employed. This method has been developed in connection with certain fluid mechanics problems and is applicable to nonlinear as well as linear problems. It has been found in the past to be advantageous not to formulate this method generally but to apply it to each individual problem and this approach is adopted here. A general recipe for the method is given and its application is illustrated by using the method to obtain an approximate solution to a simple, specific state regulator problem.
Ardema, M. D.↗
Singular perturbation of absolute stability.
The influence of a small parameter at the higher derivatives in the differential equations describing nonlinear systems of the Lur'e-Postnikov class on absolute stability in the parameter space is investigated. The conditions leading to singular perturbations of absolute stability are examined.
Siljak, D. D.↗