On a generalization of the Dvoretzky–Wald–Wolfowitz theorem with an application to a robust optimization problem

A generalization of the Dvoretzky–Wald–Wolfowitz theorem to the case of conditional expectations is provided assuming that the σ-field on the state space has no conditional atoms. Neither continuity nor compactness assumptions are made on the model. An application to a robust (maxmin) optimization problem is given.     

An application of a qd-type discrete hungry Lotka–Volterra equation over finite fields to a decoding problem

In this paper, the decoding problem for multiple Bose–Chaudhuri–Hocquenghem (BCH)-Goppa codes over the same finite field is investigated. A new iterative decoding algorithm is proposed based on the quotient difference (qd)-type discrete hungry Lotka–Volterra equation over finite fields. Compared with certain existing algorithms, the proposed algorithm manifests its advantage in computational complexity. A few of examples are presented to demonstrate its efficiency.     

An application of the fixed point theorem to the inverse sturm–liouville problem

The Sturm–Liouville operators −y″ + v(x)y on [0, 1] with Dirichlet boundary conditions y(0) = y(1) = 0 are considered. For any 1 ≤ p < ∞, a short proof of the characterization theorem for the spectral data corresponding to v ∈ L^p(0, 1) is given. Bibliography: 10 titles.     

Performance evaluation of evolutionary class of algorithms—An application to 0–1 knapsack problem

The 0–1 knapsack [1] problem is a well-known NP-complete problem. There are different algorithms in the literature to attack this problem, two of them being of specific interest. One is a pseudo polynomial algorithm of order O(nK), K being the target of the problem. This algorithm works unsatisfactorily, as the given target becomes high. In fact, the complexity might become exponential in that case. The other scheme is a fully polynomial time approximation scheme (FPTAS) whose complexity is also polynomial time. The present paper suggests a probabilistic heuristic which is an evolutionary scheme accompanied by the necessary statistical formulation and its theoretical justification. We have identified parameters responsible for the performance of our evolutionary scheme which in turn would keep the option open for improving the scheme.     

A Chebyshev spectral method for solving Korteweg–de Vries equation with hydrodynamical application

It is well known that many hydrodynamical problems appearing in the study of shallow water theory or the theory of rotating fluids, can be reduced to Korteweg–de Vries equation subject to certain initial and boundary conditions. In this work, a Chebyshev spectral method for obtaining a semi-analytical solution to such equation is presented. One numerical application is considered to show how we can apply the presented proposed method. A comparison between our results and the numerical results obtained by the Hopscotch method are made.     

An extension of a data assimilation method based on the application of the Fokker–Planck equation

A data assimilation method based on the Kalman filter theory and on the Fokker–Planck equation is extended to assimilate Atlantic Ocean data into a new version of the well-known Modular Ocean Model (MOM_3) from NOAA/GFDL. This extension enables assimilation of non-uniformly distributed data in space and time. Numerical experiments with Levitus atlas data are carried out with the ocean model configured at a low resolution. Some results of these experiments as well as other possible expansions are discussed.     

Optimization of chance constraint programming with sum-of-fractional objectives – An application to assembled printed circuit board problem

This paper presents a procedure to solve a chance constraint programming problem with sum-of-fractional objectives. The problem and the solution procedure are described with the help of a practical problem – assembled printed circuit boards (PCBs). Errors occurring during assembling PCBs are in general classified into three kinds, viz. machine errors, manual errors and other errors. These errors may lead to the rejection of the major portion of the production and hence result the manufacturer a huge loss. The problem is decomposed to have two objective functions; one is a sum-of-fractional objectives and the other is a non-linear objective with bounded constraints. The interest is to maximize the sum-of-fractional objectives and to minimize the non-linear objective, subject to stochastic and non-stochastic bounded environment. The first problem deals with the maximization of the profit (maximizing sum-of-fractional objectives) and the second deals with the minimization of the loss (errors), so as to obtain the maximum profit after removing the number of defective PCBs.     

An existence theorem of a positive solution to a semipositone Sturm–Liouville boundary value problem

We study a positive solution of the semipositone Sturm-Liouville boundary value problem in which the nonlinear term has no numerical lower bound. By considering the integration of certain limit growth functions and applying the Krasnosel’skii fixed point theorem on a cone, an existence theorem is proved, and a classical existence result is extended by this theorem.