• Korean Journal of Mathematics
• /
• 제14권1호
• /
• pp.35-46
• /
• 2006

The concept of convolution is a fundamental mathematical concept in a wide variety of disciplines and applications including probability, image processing, physics, and many more. The visualization of convolution for the continuous case is generally predetermined. On the other hand, the convolution structure embedded in the discrete case is often subtle and its visualization is non- trivial. This paper purports to develop the CAS techniques in visualizing the logical structure in the concept of a discrete convolution.

• Kyungpook Mathematical Journal
• /
• 제56권1호
• /
• pp.47-55
• /
• 2016

In this paper, we consider a discrete predator-prey system obtained from a continuous Beddington-DeAngelis type predator-prey system by using the method in [9]. In order to investigate dynamical behaviors of this discrete system, we find out all equilibrium points of the system and study their stability by using eigenvalues of a Jacobian matrix for each equilibrium points. In addition, we illustrate some numerical examples in order to substantiate theoretical results.

• Journal of applied mathematics & informatics
• /
• 제28권5_6호
• /
• pp.1379-1393
• /
• 2010

In this paper, a stage-structured predator prey model (stage structure on prey) with two discrete time delays has been discussed. The two discrete time delays occur due to maturation delay and gestation delay. Linear stability analysis for both non-delay as well as with delays reveals that certain thresholds have to be maintained for coexistence. Numerical simulation shows that the system exhibits Hopf bifurcation, resulting in a stable limit cycle.

• 호남수학학술지
• /
• 제45권3호
• /
• pp.457-470
• /
• 2023

In this study, we set a boundary value problem (BVP) consisting of a discrete Sturm-Liouville equation with transmission condition and boundary conditions depending on generalized eigenvalue parameter. Discussing the Jost and scattering solutions of this BVP, we present scattering function and find some properties of this function. Furthermore, we obtain resolvent operator, continuous and discrete spectrum of this problem and we give an valuable asymptotic equation to get the properties of eigenvalues. Finally, we give an example to compare our results with other studies.

• Advances in nano research
• /
• 제15권1호
• /
• pp.25-34
• /
• 2023

This paper investigates the dynamics and stability of steady states in a continuous and discrete-time single-mode laser system. By using an explicit criteria we explored the Neimark-Sacker bifurcation of the single mode continuous and discrete-time laser model at its positive equilibrium points. Moreover, we discussed the parametric conditions for the existence of period-doubling bifurcations at their positive steady states for the discrete time system. Both types of bifurcations are verified by the Lyapunov exponents, while the maximum Lyapunov ensures chaotic and complex behaviour. Furthermore, in a three-dimensional discrete-time laser model, we used a hybrid control method to control period-doubling and Neimark-Sacker bifurcation. To validate our theoretical discussion, we provide some numerical simulations.

• Korean Journal of Mathematics
• /
• 제21권2호
• /
• pp.125-150
• /
• 2013

The stabilized Gauge-Uzawa method (SGUM), which is a second order projection type algorithm to solve the time-dependent Navier-Stokes equations, has been newly constructed in 2013 Pyo's paper. The accuracy of SGUM has been proved only for time discrete scheme in the same paper, but it is crucial to study for fully discrete scheme, because the numerical errors depend on discretizations for both space and time, and because discrete spaces between velocity and pressure can not be chosen arbitrary. In this paper, we find out properties of the fully discrete SGUM and estimate its errors and stability to solve the evolution Navier-Stokes equations. The main difficulty in this estimation arises from losing some cancellation laws due to failing divergence free condition of the discrete velocity function. This result will be extended to Boussinesq equations in the continuous research (part II) and is essential in the study of part II.

• 한국학교수학회논문집
• /
• 제13권1호
• /
• pp.125-141
• /
• 2010

본 연구의 목적은 컴퓨터대수시스템(CAS)를 활용하여 개인 적응용 이산수학 학습을 가능케하는 웹기반 가상 학습용 콘텐츠를 개발하는 것이다. 중등과정과 대학과정의 이산수학에서 공통적으로 등장하는 집합, 관계, 행렬, 그래프 등의 내용 요목을 중심으로 콘텐츠를 구성하였다. 이산수학의 특성상 컴퓨터를 사용한 이산구조를 즉각적으로 처리하여 그 결과를 시각적으로 제시하는 가상 학습용 콘텐츠 제작 환경을 제시하였다. 각 단원마다 동영상 기반의 강의 콘텐츠를 제공하였으며 강의 기반의 개념을 구체화할 수 있는 Mathematica 기반의 실습하기 기능을 추가하였다. 특히 행렬 단원 학습에서 학습구조도식을 이용한 콘텐츠 설계와 이에 따른 내용 요소별 베이지언 추론망 기반의 진단학습 모듈을 추가함으로써 구체적인 피드백을 통한 개인 적응형 학습이 가능하도록 설계하였다. 개발된 행렬 학습용 콘텐츠 중심으로 10명의 이공계 대학생이 실제 사용해 본 반응을 형성평가의 일환으로 분석하여 향후 수정 방향을 도출하였다.

• Journal of applied mathematics & informatics
• /
• 제28권1_2호
• /
• pp.275-282
• /
• 2010

This paper analyzes a discrete-time bulk-service queue with probabilistic bulk size, where the service process is interrupted by a Markov chain. We study the joint probability generating function of system occupancy and the state of the Markov chain. We derive several performance measures of interest, including average system occupancy and delay distribution.

• Journal of applied mathematics & informatics
• /
• 제22권1_2호
• /
• pp.453-460
• /
• 2006

A discrete-time priority queueing system with place reservation discipline is studied, in which two different types of packets arrive according to batch geometric streams. It is assumed that there is a reserved place in the queue. Whenever a high-priority packet enters the queue, it will seize the reserved place and make a new reservation at the end of the queue. Low-priority arrivals take place at the end of the queue in the usual way. Using the probability generating function method, the joint distribution of system state and the delay distribution for each type are obtained.

• 대한수학회보
• /
• 제46권1호
• /
• pp.125-134
• /
• 2009

In the present paper, we give several discrete results for the open problem posed in the article [Feng Qi, Several integral inequalities, J. Inequal. Pure and Appl. Math. 1(2000), no. 2, Art. 19].