• Bulletin of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.977-992
• /
• 2019

Mittag-Leffler stability of nonlinear fractional nabla difference systems is defined and the Lyapunov direct method is employed to provide sufficient conditions for Mittag-Leffler stability of, and in some cases the stability of, the zero solution of a system nonlinear fractional nabla difference equations. For this purpose, we obtain several properties of the exponential and one parameter Mittag-Leffler functions of fractional nabla calculus. Two examples are provided to illustrate the applicability of established results.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.3
• /
• pp.611-628
• /
• 2021

In this paper, we propose a new branch-reduction-and-bound algorithm to solve the nonlinear knapsack problems by using general discrete monotonic optimization techniques. The specific properties of the problem are exploited to increase the efficiency of the algorithm. Computational experiments of the algorithm on problems with up to 30 variables and 5 different constraints are reported.

• 제어로봇시스템학회:학술대회논문집
• /
• 1994.10a
• /
• pp.753-757
• /
• 1994

In control system design, whether the various subsystems are in discrete time or continuous time, the state space is usually regarded as a continuum. However, when the system is implemented, some subsystems may have a state space which is a subset of finite computer arithmetic. This is an important concern if a subsystem has chaotic behaviour, because it is theoretically possible for rich and varied motions in a continuum to collapse to trivial and degenerate behaviour in a finite and discrete state space [5]. This paper discusses new ways to describe these effects and reports on computer experiments which document and illustrate such collapsing behaviour.

• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.399-409
• /
• 2007

In this paper we use iterative dynamic programming in the discrete case to solve a wide range of the nonlinear equations systems. First, by defining an error function, we transform the problem to an optimal control problem in discrete case. In using iterative dynamic programming to solve optimal control problems up to now, we have broken up the problem into a number of stages and assumed that the performance index could always be expressed explicitly in terms of the state variables at the last stage. This provided a scheme where we could proceed backwards in a systematic way, carrying out optimization at each stage. Suppose that the performance index can not be expressed in terms of the variables at the last stage only. In other words, suppose the performance index is also a function of controls and variables at the other stages. Then we have a nonseparable optimal control problem. Furthermore, we obtain the path from the initial point up to the approximate solution.

• Korean Journal of Mathematics
• /
• v.29 no.2
• /
• pp.371-386
• /
• 2021

This paper investigates two discrete time queueing inventory models with positive service time and lead time. Customers arrive according to a Bernoulli process and service time and lead time follow geometric distributions. The first model under discussion based on replenishment of order upto S policy where as the second model is based on order placement by a fixed quantity Q, where Q = S - s, whenever the inventory level falls to s. We analyse this queueing systems using the matrix geometric method and derive an explicit expression for the stability condition. We obtain the steady-state behaviour of these systems and several system performance measures. The influence of various parameters on the systems performance measures and comparison on the cost analysis are also discussed through numerical example.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
• /
• 2002.09a
• /
• pp.17.2-17
• /
• 2002

• Kyungpook Mathematical Journal
• /
• v.11 no.1
• /
• pp.21-24
• /
• 1971

• Kyungpook Mathematical Journal
• /
• v.18 no.1
• /
• pp.91-91
• /
• 1978

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.4
• /
• pp.449-455
• /
• 2007

We obtain a discrete version of a fundamental result by Yoshizawa related to the existence of almost periodic solutions of functional differential equations with finite delay.

• Journal of applied mathematics & informatics
• /
• v.4 no.2
• /
• pp.397-406
• /
• 1997

In this paper we introduce GESS method and show that dynamics of the system ｙ＇=A(s,t,y) ｙ is more faithfully approxi-mated by GESS method that by Euler method. Numerical experiments are given for the comparison of GESS method with Euler method.