• Journal of applied mathematics & informatics
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• v.35 no.5_6
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• pp.449-457
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• 2017

In this paper, we shall provide several properties of Dedekind sums with quasi-periodicity Euler functions. In particular, we present a representation of these Dedekind sums in terms of the Eulerian functions and the tangent functions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.25-33
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• 2001

Let G be a finite group with a probability measure. We investigate the random walks on G in terms of ergodicity of the associated skew product transformation.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.95-100
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• 2006

In this paper we give some new characterizations of the intra-regular ordered semigroups in terms of bi-ideals and quasi-ideals, bi-ideals and left ideals, bi-ideals and right ideals of ordered semigroups.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.1
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• pp.7-11
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• 2008

The energy of a graph is the sum of the absolute values of its eigen values. We obtain some bounds for the energy of planar graphs in terms of its vertices, edges and faces.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.341-346
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• 2011

We deal with a kind of impossible decomposition of some entire functions in terms of a certain form.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.405-417
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• 2021

The aim of this paper is to provide the residues of Euler polynomials modulo p² in terms of alternating sums of like powers of numbers in arithmetical progression. Also, we establish the analogue of a classical congruence of Lehmer.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.299-309
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• 2013

In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method (FChFD). The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. We tested this technique to solve numerically fractional BVPs. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The fractional derivatives are presented in terms of Caputo sense. The application of the method to fractional BVPs leads to algebraic systems which can be solved by an appropriate method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

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

• Journal for History of Mathematics
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• v.30 no.5
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• pp.289-304
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• 2017

The interdisciplinary study explores the discussion of actual infinity between Georg Cantor and Roman Catholic Church. Regarding the actual infinity, we first trace the theological background of Cantor by interpreting his correspondence and major works including ${\ddot{U}}ber$ die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche(1885) and Mitteilungen zur Lehre vom Transfiniten (1887), and then investigate his argumentation for two points at issue: (1) pantheism and (2) inconsistency of the necessity with freedom of God. In terms of mathematics and theology, Cantor defined the actual infinity(aphorismenon) as characterized by (1) the transfinite infinity(Transfinitum) and (2) the absolute infinity(Absolutum). Transfinitum is conceptualized here in mathematical terms as a multipliable actual infinity, whereas Absolutum is not as a multipliable actual infinity. The results imply that Cantor's own concept of Transfinitum and Absolutum is adequate for Roman Catholic theology as well as mathematics including the reflection principle.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.655-676
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• 2021

A parameter uniform numerical scheme is proposed for solving singularly perturbed parabolic partial differential-difference convection-diffusion equations with a small delay and advance parameters in reaction terms and spatial variable. Taylor's series expansion is applied to approximate problems with the delay and advance terms. The resulting singularly perturbed parabolic convection-diffusion equation is solved by utilizing the implicit Euler method for the temporal discretization and finite difference method for the spatial discretization on a uniform mesh. The proposed numerical scheme is shown to be an ε-uniformly convergent accurate of the first order in time and second-order in space directions. The efficiency of the scheme is proved by some numerical experiments and by comparing the results with other results. It has been found that the proposed numerical scheme gives a more accurate approximate solution than some available numerical methods in the literature.