• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.399-410
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• 2019

In the manuscript, we concern with the existence of solutions of boundary value problems for fourth order nonlinear discrete systems. Some criteria for the existence of at least one nontrivial solution of the problem are obtained. The proof is mainly based upon the variational method and critical point theory. An example is presented to illustrate the main result.

• Research in Mathematical Education
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• v.11 no.2
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• pp.143-151
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• 2007

Nowadays there are practically no mathematical courses in which Computer Algebra Systems (CAS) programs, such as MATHEMATlCA, Maple, and TI-89/92, are not used to some extent. However, generally the usage of these programs is reduced to illustration of computing processes: calculation of integrals, differentiation, solution of various equations, etc. This is obtained by usage of standard command of type: Solve [...] in MATHEMATICA. At the same time the main difficulties arise at teaching nonconventional mathematical courses such as coding theory, discrete mathematics, cryptography, Scientific computing, which are gaining the increasing popularity now. Now it is impossible to imagine a modern engineer not having basic knowledge in discrete mathematics, Cryptography, coding theory. Digital processing of signals (digital sound, digital TV) has been introduced in our lives.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.263-273
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• 2008

For the discrete version of an artificial neural network of two neurons with piecewise constant argument, we obtain some sufficient conditions that every solution is either periodic or convergent.

• The Mathematical Education
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• v.59 no.1
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• pp.47-62
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• 2020

Understanding the concept of probability distribution becomes more important. We considered probabilities defined in the sample space, the definition of discrete random variables, the probability of defined discrete probability distribution, and the relationship between them as knowledge of discrete probability distribution, and investigated the understanding degree of the mathematics preservice teachers. The results are as follows. Firstly, about 70% of preservice teachers who participated in this study expressed discrete probability distribution graphs in ordered pairs or continuous distribution. Secondly, with regard to the two factors for obtaining discrete probability distributions: probability for each element in the sample space and the concept of random variables that convert each element in the sample space into a real value, only 13% of the preservice teachers understood and addressed both factors. Thirdly, 39% of the preservice teachers correctly responded to whether different probability distributions can be defined for one sample space. Fourthly, when the probability of each fundamental event was determined to obtain the probability distribution of the discrete random variables defined in the undefined sample space, approximately 70% habitually calculated by the uniform probability. Finally, about 20% of preservice teachers understood the meaning and relationship of binomial distribution, discrete random variables, and sample space. In relation, clear definitions and full explanations of concept need to be provided from textbooks and a program to improve the understanding of preservice teachers need to be developed.

• The Journal of the Korea Contents Association
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• v.17 no.10
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• pp.472-482
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• 2017

In this study, discrete mathematical items were classified into analytical items and mathematical items were analyzed on the basis of analytic framework items of mathematics and the past items of mathematics subject contents of the period 2011-2017 school year. First, the discrete mathematics evaluation areas and evaluation contents proposed by the Korea Institute for Curriculum and Evaluation should be evenly distributed. Second, the items of measuring metacognitive knowledge as a strategic knowledge on the use of cognitive methods should be given. Third, the ratio of the number of items in discrete mathematics to the number of that was 3.8%~6.8%, and the ratio according to the item weighting was 2.2%~6.3%. Fourth, it is analyzed that all the items are suitable for the evaluation goal and the pre-service math teachers who have faithfully implemented the curriculum have maintained the appropriate level of difficulty to solve. Finally, the content items such as the method of counting the discrete mathematics curriculum, the Recurrence Relation, the generation function, and the graph are matched with the teacher certification examination and the mathematics education curriculum of each teachers college. By these reasons, we conclude that the contribution of pre-service teachers to the motivation of learning is obtained and implications.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1555-1565
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• 2013

In this paper, some new generalized discrete Halanay inequalities are established. On the basis of these new established inequalities, we obtain the attracting set and the global asymptotic stability of the nonlinear discrete systems. Our results established here extend the main results in [R. P. Agarwal, Y. H. Kim, and S. K. Sen, New discrete Halanay inequalities: stability of difference equations, Commun. Appl. Anal. 12 (2008), no. 1, 83-90] and [S. Udpin and P. Niamsup, New discrete type inequalities and global stability of nonlinear difference equations, Appl. Math. Lett. 22 (2009), no. 6, 856-859].

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1517-1533
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• 2015

In this paper, we prove the existence of at least three nontrivial solutions to nonlinear discrete boundary value problems $$\{^{-{\Delta}_{p,{\omega}}u(x)+V(x){\mid}u(x){\mid}^{q-2}u(x)=f(x,u(x)),x{\in}S,}_{u(x)=0,\;x{\in}{\partial}S}$$, involving the discrete p-Laplacian on simple, nite and connected graphs $\bar{S}(S{\cup}{\partial}S,E)$ with weight ${\omega}$, where 1 < q < p < ${\infty}$. The approach is based on a suitable combine of variational and truncations methods.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.1
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• pp.51-64
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• 2012

This paper provides an efficient dimension reduction algorithm of the positive realization of discrete phase type(DPH) distributions. The relationship between the representation of DPH distributions and the positive realization of the positive system is explained. The dimension of the positive realization of a discrete phase-type realization may be larger than its McMillan degree of probability generating functions. The positive realization with sufficient large dimension bound can be obtained easily but generally, the minimal positive realization problem is not solved yet. We propose an efficient dimension reduction algorithm to make the positive realization with tighter upper bound from a given probability generating functions in terms of convex cone problem and linear programming.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.519-548
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• 2022

In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual L² and discrete H¹ norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.285-295
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• 2001

We consider a queueing system under overload control to support bursty traffic. The queueing system under overload control is modelled by MMBP/D1/K queue with two thresholds on buffer. Arrival of customer is assumed to be a Markov-modulated Bernoulli process (MMBP) by considering burstiness of traffic. Analysis is done in discrete-time case. Using the generating function method, we obtain the stationary queue length distribution. Finally, the loss probability and the waiting time distribution of a customer are given.