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1970

Volume 19, Issue 4, pp. 637-777


Reliability of Two-Unit Redundant Repairable Systems When Failures are Revealed by Inspections

M. Mazumdar

SIAM J. Appl. Math. 19, pp. 637-647 (11 pages) | Cited 4 times

Online Publication Date: July 12, 2006

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Abstract Unavailable

A Continuous Right Inverse for Second Order Differential Operators with Variable Coefficients

D. K. Cohoon

SIAM J. Appl. Math. 19, pp. 648-657 (10 pages)

Online Publication Date: July 12, 2006

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A continuous right inverse $R$ for the second order linear differential operator \[ L = D_x^2 + p(x)D_x + q(x) \] with variable coefficients $p(x)$ and $q(x)$ is given. Moreover, there is a function $E(x,y)$ depending only on $p(x)$ and $q(x)$ such that\[ Rf(x) = \int_0^\pi {E(x,z)} \left( {\int_0^z {f(y)dy} } \right)dz \] for all $f$ in the space on which $L$ operates. Explicit formulas for $E(x,y)$ and moduli of continuity of $R$ are given for various spaces of functions.

On Some Applications of Mellin Transforms to Statistics: Dependent Random Variables

K. Subrahmaniam

SIAM J. Appl. Math. 19, pp. 658-662 (5 pages) | Cited 3 times

Online Publication Date: July 12, 2006

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This paper deals with the distribution of the statistics $Y = X_1 X_2 $ and $Z = X_1 /X_2 $, where $(X_1 ,X_2 )$ are jointly distributed random variables. The results are applied to the cases where (i) $X_1 ,X_2 $ are the $r$th and $s$th order statistics from the uniform and negative exponential populations and (ii) $(X_1 ,X_2 )$ have the bivariate normal distribution.

Probability Representations with Right-Cauchy Integrals

James D. Baker

SIAM J. Appl. Math. 19, pp. 663-667 (5 pages)

Online Publication Date: July 12, 2006

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Abstract Unavailable

On the Penultimate Remainder Algorithm and the Catalytic Multiplier

Alston S. Householder

SIAM J. Appl. Math. 19, pp. 668-671 (4 pages)

Online Publication Date: July 12, 2006

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Abstract Unavailable

A Generalization of the Albert-Nelson Counter with Semi-Markov Input

Georges Vandewiele

SIAM J. Appl. Math. 19, pp. 672-678 (7 pages)

Online Publication Date: July 12, 2006

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A new general counter model is presented. It is shown that conventional counters are particular cases of this model and that semi-Markov processes and simple semi-Markov processes are preserved by such a general counter transformation. Equations are obtained for output process characteristics when the input is a semi-Markov process for a counter which is sufficiently general to contain the Albert-Nelson counter and consequently type I and type II counters.

Some Inequalities for Positive Definite Symmetric Matrices

F. T. Man

SIAM J. Appl. Math. 19, pp. 679-681 (3 pages) | Cited 3 times

Online Publication Date: July 12, 2006

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Abstract Unavailable

An Extension of the Generalized Inverse of a Matrix

Randall E. Cline and T. N. E. Greville

SIAM J. Appl. Math. 19, pp. 682-688 (7 pages) | Cited 6 times

Online Publication Date: July 12, 2006

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Abstract Unavailable

The Shortest Hamiltonian Chain of a Graph

Nicos Christofides

SIAM J. Appl. Math. 19, pp. 689-696 (8 pages) | Cited 13 times

Online Publication Date: July 12, 2006

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Given a graph $G$ with weighted links, the problems considered in this paper are the following: (i) Find the shortest possible Hamiltonian chain (HC) of the graph $G$ when the end vertices are not specified.(ii) Find the shortest possible HC of $G$ when the end vertices are specified.
Two basic algorithms are given each of which can solve both of the above problems with only slight modification. The first algorithm, A, is based on a decision-tree search with lower bounds used to limit the search. The second algorithm, B, is a fast iterative procedure which is based on simple transformations of the cost matrix of the graph $G$, ensuring at each step that the relative cost of all Hamiltonian chains stay unchanged.
Both algorithms ensure the optimality of the final answer, but whereas the convergence of Algorithm A is self-evident, no proof of convergence has been obtained for Algorithm B. However, tests of Algorithm B (which is both simpler and computationally superior to Algorithm A) on a number of sample problems have not produced any difficulties with convergence. Two examples are given to illustrate the two methods.

Curvature and Arclength

H. G. Robertson

SIAM J. Appl. Math. 19, pp. 697-699 (3 pages) | Cited 1 time

Online Publication Date: July 12, 2006

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Upper and lower approximations on certain definite integrals are used in this paper to obtain the maximum length of a smooth curve satisfying certain side conditions, including specified minimum radius of curvature. The question has appeared (and was unresolved) in at least two previous research publications.

Optimal Cannibalization Policies for Multicomponent Systems

R. M. Simon

SIAM J. Appl. Math. 19, pp. 700-711 (12 pages) | Cited 4 times

Online Publication Date: July 12, 2006

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A reliability model for multicomponent multistate systems first described by Hirsch, Meisner, and Boll and later generalized by Simon is considered. Part failures are serviced either by spare replacements or by cannibalizing the locations to allocate shortages to positions least detrimental to system performance. An “admissible” cannibalization policy allocates shortages to maximize the system state following each failure. It is shown that not all admissible policies are equally good. An admissible policy which also looks ahead to future possible failures is characterized and in a certain sense is shown to be uniformly better than any other admissible policy.

The Semi-Infinite Elastic Cylinder Under Self-Equilibrated End Loading

James L. Klemm and Robert Wm. Little

SIAM J. Appl. Math. 19, pp. 712-729 (18 pages) | Cited 20 times

Online Publication Date: July 12, 2006

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This paper presents a practical formulation for the solution of the elastostatic problem of a semi-infinite solid cylinder with the long sides free from stress and self-equilibrated tractions applied on the end. The formulation is entirely in terms of stresses and displacement related auxiliary variables of the same differential order as the stresses. The equilibrium equations, the Beltrami-Michell equations of compatibility and the definitions of the auxiliary variables are used to write a first order matrix differential equation. The solution of this non-self adjoint equation yields a series of non-orthogonal vector eigenfunctions. The coefficients of this series are chosen by use of a generalized biorthogonality condition. Numerical solutions of trial problems are presented as an indication of the rate of convergence of this series.

On Quadrics in Finite Euclidean Geometries and Application to Construction of Balanced Incomplete Block Designs

Sakti P. Ghosh

SIAM J. Appl. Math. 19, pp. 730-740 (11 pages)

Online Publication Date: July 12, 2006

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Nondegenerate quadrics in finite Euclidean geometry are defined and a method of obtaining these from nondegenerate quadrics in finite projective geometry is outlined. It is shown that nondegenerate quadrics of particular types in finite Euclidean geometry can be used to construct balanced incomplete block designs. Seven new series of balanced incomplete block designs are obtained by this technique.

Generalized Inverses of Block Triangular Matrices

Carl D. Meyer, Jr.

SIAM J. Appl. Math. 19, pp. 741-750 (10 pages)

Online Publication Date: July 12, 2006

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Abstract Unavailable

Relation Between Boundary Value Problems in a Half-Space and the Whole Space

N. L. Maria

SIAM J. Appl. Math. 19, pp. 751-768 (18 pages)

Online Publication Date: July 12, 2006

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Abstract Unavailable

An Efficiency Property of the Exponentially Weighted Least Squares Estimators

Charlie H. Cooke

SIAM J. Appl. Math. 19, pp. 769-777 (9 pages) | Cited 1 time

Online Publication Date: July 12, 2006

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Abstract Unavailable
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