• East Asian mathematical journal
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• 제16권2호
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• pp.401-407
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• 2000

We give a generalization of the Bateman's polynomial $F_n(x)$ and also give two generating functions for the generalized polynomial.

• 대한수학회지
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• 제50권5호
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• pp.1067-1082
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• 2013

In this paper, we will find some recurrence relations of classical multiple OPS between the same family with different parameters using the generating functions, which are useful to find structure relations and their connection coefficients. In particular, the differential-difference equations of Jacobi-Pineiro polynomials and multiple Bessel polynomials are given.

• 대한수학회논문집
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• 제28권1호
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• pp.87-105
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• 2013

The aim of the present paper is to study some generating functions of generalized Bateman's and Pasternak's polynomials of two variables.

• Journal of applied mathematics & informatics
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• 제38권3_4호
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• pp.291-300
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• 2020

This type of polynomial is a generating function that substitutes e^λt for e^t in the denominator of the generating function for the Bernoulli polynomial, but polynomials by using this generating function has interesting properties involving the location of the roots. We define these generation functions and observe the properties of the generation functions.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.417-423
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• 2019

In the paper, by virtue of the $Fa{\grave{a}}$ di Bruno formula, properties of the Bell polynomials of the second kind, and the Lah inversion formula, the author simplifies coefficients in a family of ordinary differential equations related to the generating function of the Mittag-Leffler polynomials.

• 대한수학회보
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• 제52권2호
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• pp.467-481
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• 2015

Choi and Park introduced an invariant of a finite simple graph, called signed a-number, arising from computing certain topological invariants of some specific kinds of real toric manifolds. They also found the signed a-numbers of path graphs, cycle graphs, complete graphs, and star graphs. We introduce a signed a-polynomial which is a generalization of the signed a-number and gives a-, b-, and c-numbers. The signed a-polynomial of a graph G is related to the $Poincar\acute{e}$ polynomial $P_{M(G)}(z)$, which is the generating function for the Betti numbers of the real toric manifold M(G). We give the generating functions for the signed a-polynomials of not only path graphs, cycle graphs, complete graphs, and star graphs, but also complete bipartite graphs and complete multipartite graphs. As a consequence, we find the Euler characteristic number and the Betti numbers of the real toric manifold M(G) for complete multipartite graphs G.

• Journal of information and communication convergence engineering
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• 제8권3호
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• pp.317-322
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• 2010

This paper presents an algorithm generating inverse element over finite fields GF($3^m$), and constructing method of inverse element generator based on inverse element generating algorithm. An inverse computing method of an element over GF($3^m$) which corresponds to a polynomial over GF($3^m$) with order less than equal to m-1. Here, the computation is based on multiplication, square and cube method derived from the mathematics properties over finite fields.

• 대한수학회지
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• 제54권5호
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• pp.1595-1604
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• 2017

We give a complete formula for the characteristic polynomial of hyperplane arrangements ${\mathcal{J}}_n$ consisting of the hyperplanes $x_i+x_j=1$, $x_k=0$, $x_l=1$, $1{\leq}i$, j, k, $l{\leq}n$. The formula is obtained by associating hyperplane arrangements with graphs, and then enumerating central graphs via generating functions for the number of bipartite graphs of given order, size and number of connected components.

• 정보기술응용연구
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• 제3권3호
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• pp.25-40
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• 2001

본 논문에서는 유전적 프로그래밍(Genetic Programing)을 이용하여 최적의 다항식을 생성하는 기법을 제시하고자 한다. 다항식은 비선형성이 큰 응답면을 모델링해야 하며, 이를 위하여 GP 트리 생성시 2-3차 오더의 Taylor Series를 사용하는 방법을 시도하였다. 아울러 생서되는 다항식의 크기를 제어하기 위해서 GP 트리가 표현할 수 있는 다항식의 최대 차수를 제한함과 동시에 하나의 주 트리와 보 트리로 구성되는 GAGPT(Group of Additive Genetic Programming Trees) 사용을 모색하였다. 마지막으로 두 개의 응용 예를 통하여 본 방법의 유용성을 검증하였다.

• 대한수학회보
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• 제41권3호
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• pp.521-540
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• 2004

In this paper, we give a sharp estimate on the cardinality of the set generating the convex hull containing the image of harmonic maps with polynomial growth rate on a certain class of manifolds into a Cartan-Hadamard manifold with sectional curvature bounded by two negative constants. We also describe the asymptotic behavior of harmonic maps on a complete Riemannian manifold into a regular ball in terms of massive subsets, in the case when the space of bounded harmonic functions on the manifold is finite dimensional.