Showing papers in "Applications of Mathematics in 1977"

Qualitative analysis of basic notions in parametric convex programming. II. Parameters in the objective function

Abstract: The paper presents a qualitative analysis of basic notions in parametric convex programming for convex programs with parameters in the objective function. These notions are the set of feasible parameters, the solvability set and the stability sets of the first and of the second kind. The functions encountered in the paper are assumed to possess first order partial continuous derivatives on $R^n$, the parameters assume arbitrary nonnegative real values and therefore the results obtained in the paper can be used for a wide class of convex programs.

Qualitative analysis of basic notions in parametric convex programming. I. Parameters in the constraints

Abstract: The paper presents a qualitative analysis of basic notions in parametric convex programming for convex programs with parameters in the righthand sides of the constraints. These notions are the set of feasible parameters, the solvability set and the stability sets of the first and of the second kind. The functions encountered in the paper are assumed to possess first order partial continuous derivatives on $R^n$, the parameters assume arbitrary real values and therefore the results obtained in the paper can be used for a wide class of convex programs.

Tables for the two-sample location $E$-test based on exceeding observations

Abstract: The rank statistic $E$, based on the minimum number of exceeding observations in two samples, gives rise to a quick and easy $E$-test, which is suitable for the two-sample location problem. The paper contains tables of the one-sided significance levels $P\left\{E\geq k\right\}$ for $2\leq k\leq 6$ for sizes $m,n$ of the two samples satisfying $3\leq m\leq n\leq 25$.

Inflated truncated negative binomial acceptance sampling plan

Abstract: This paper gives the maximum likelihood estimations of the process (or lot) average proportion $p$ of defectives and the proportion $(\alpha)$ of the population which follows a negative binomial distribution based on attribute samples that have been curtailed either with the rejection of a lot on finding the $k$th defective or with the acceptance of it on finding the $K$th nondefective. These estimates are based on inspection from a sequence of $m$ lots of inspected items. Moreover, the linear estimates of $p$ and $\alpha$ and the asymptotic variance and covariance of considered estimators are given.

Some methods of numerical integration over a semi-infinite interval

Abstract: The authors utilize some methods of numerical integration over a finite interval (Clenshaw and Curtic 1960, Filippi 1964, Basu 1971) to solve the quadrature problems over a semi-infinite interval. Technique similar to that presented in the authors' previous paper (Appl. mat. 20 (1975), pp. 216 to 221) has been adopted.

Solution of the first problem of plane elasticity for multiply connected regions by the method of least squares on the boundary. II

Abstract: For a simly connected region, the solution of the first problem of plane elasticity can be reduced - roughly speaking - to the solution of a biharmonic problem. This problem can then be solved approximately by the method of least squares on the boundary, developed by K. Rektorys and V. Zahradnik in Apl. mat. 19 (1974), 101-131. The present paper gives a generalization of this method for multiply connected regions. Two fundamental questions which arise in this case are answered, namely: (i) How to formulate the problem in order that it correspond to the reality. (ii) How to modify the method and prove the convergence.