Showing papers in "Applications of Mathematics in 1973"
TL;DR: In this paper, a chain of inequalities for probabilities in some types of multivariate distributions is proved, and the inequalities embrace a large number of interesting special cases, such as normal and rank statistics for comparing many treatments with one control, order statistics used in estimating quantiles, and characteristic roots of covariance matrices in certain multiple sampling.
Abstract: Generalizing the result by Y. L. Tong, a chain of inequalities for probabilities in some types of multivariate distributions is proved. These inequalities embrace a large number of interesting special cases. Nine illustrations are given: cases of multivariate equicorrelated normal, $t,\chi^2$, Poisson, exponential distributions, normal and rank statistics for comparing many treatments with one control, order statistics used in estimating quantiles, and characteristic roots of covariance matrices in certain multiple sampling.
17 citations
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7 citations
TL;DR: In this paper, a new class of methods called overimplicit multistep methods is introduced for numerical solution of ordinary differential equations by a new set of methods, called over-implicit multi-step methods.
Abstract: The paper is concerned with the numerical solution of ordinary differential equations by a new class of methods called overimplicit multistep methods. The effort is devoted to the study of the convergence and $A$-stability of the introduced methods. $A$-stable formulae of arbitrarily high orders are shown to exist in this new class. This implies the efficiency of using these methods for stiff problems.
6 citations
6 citations
5 citations
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5 citations
TL;DR: In this paper, an algorithm for the Hermite-Birkhoff interpolation is presented, which reduces the problem to the problem of Hermite interpolation, and the missing values and derivatives are expressed by some of the given values and calculated from a system of linear equations.
Abstract: An algorithm for the Hermite-Birkhoff interpolation is presented, which reduces the problem to the Hermite interpolation. The missing values and derivatives are expressed by some of the given values and calculated from a system of linear equations. The system itself and its right-hand sides are computed from a set of Hermite interpolation problems. The needed values and derivatives of the Hermite interpolation polynomial can be computed using the algorithm given in the Appendix.
4 citations
4 citations
TL;DR: In this paper, the heat conduction problem is formulated in terms of the heat flux vector and a particular case of a general parabolic equation with positive definite and positive semi-definite operator coefficients is obtained.
Abstract: Formulating the heat conduction problem in terms of the heat flux vector, a particular case of a general parabolic equation with positive definite and positive semi-definite operator coef ficients is obtained. To such problem, the so-called semi-variational method can be applied, yielding a sequence of approximations with an inc reasing accuracy. Even the first approximation shows favourable numerical results in comparison with the corresponding procedure for the original problem.
TL;DR: In this paper, the problem of bending by a transverse load of orthotropic cylindrical beam is solved by reducing it to Almansi's problem, which allows some generalizations.
Abstract: The problem of bending by a transverse load of orthotropic cylindrical beam is solved by reducing it to Almansi's problem. The present method is much simpler then those already known and allows some generalizations.