• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.443-450
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• 2011

In this paper, we construct a Gorenstein Artinian algebra R/J with non-unimodal Hilbert function h = (1, 13, 12, 13, 1) to investigate the algebraic structure of the ideal J in a polynomial ring R. For this purpose, we use a software system Macaulay 2, which is devoted to supporting research in algebraic geometry and commutative algebra.

• 한국지능시스템학회논문지
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• 제20권4호
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• pp.592-595
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• 2010

The extended algebraic operations are defined by applying the extension principle to normal algebraic operations. And these operations are calculated for some kinds of fuzzy numbers. In this paper, we get exact membership function as a results of calculation of these operations for generalized quadratic fuzzy sets.

• 대한수학교육학회지:학교수학
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• 제10권1호
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• pp.1-22
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• 2008

본 연구의 목적은 엑셀의 활용이 '일차함수의 그래프와 연립방정식의 해의 관계'를 이해하는 데 어떤 영향을 미치는가를 알아보는데 있다. 엑셀을 활용한 교수실험은 학습 능력 수준이 다른 다섯 명의 학생을 선정하여 중학교 2학년 8-가에서 다루고 있는 내용 중 일차함수의 활용을 중심으로 이루어졌다. 교수실험에서 각 학생들 스스로 규칙을 정해 식을 만들고 표와 그래프를 나타내면서 그 변화를 상당히 흥미롭게 탐구하였다. 또한 엑셀을 통해 식과 표와 그래프를 동시에 관찰하는 것에 익숙해졌고, 귀납적인 관찰을 통해 일반적인 규칙을 발견하는 성향을 보여주었다. 엑셀환경에서 다양한 식을 표와 그래프로 나타내고, 스핀버튼을 활용해 그래프를 역동적으로 변화시키면서 탐구하는 것은 디너스(Dienes)가 주장하는 '수학적 다양성의 원리'와 부합한다고 할 수 있다. 엑셀을 활용한 탐구환경은 학생들의 일차함수 개념의 형성을 촉진하는 역할을 수행함으로써 지필환경을 보완할 수 있다는 시사점을 도출하였다.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2005년도 추계종합학술대회
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• pp.849-852
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• 2005

A factorization is an extremely important part of multi-level logic synthesis. The number of literals in a factored from is a good estimate of the complexity of a logic function, and can be translated directly into the number of transistors required for implementation. Factored forms are described as either algebraic or Boolean, according to the trade-off between run-time and optimization. A Boolean factored form contains fewer number of literals than an algebraic factored form. In this paper, we present a new method for a Boolean factorization. The key idea is to identify two-cube Boolean subexpression pairs from given expression. Experimental results on various benchmark circuits show the improvements in literal counts over the algebraic factorization based on Brayton's co-kernel cube matrix.

• 한국산업융합학회 논문집
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• 제3권1호
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• pp.17-27
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• 2000

A factorization is an extremely important part of multi-level logic synthesis. The number of literals in a factored form is a good estimate of the complexity of a logic function. and can be translated directly into the number of transistors required for implementation. Factored forms are described as either algebraic or Boolean, according to the trade-off between run-time and optimization. A Boolean factored form contains fewer number of literals than an algebraic factored form. In this paper, we present a new method for a Boolean factorization. The key idea is to build an extended co-kernel cube matrix using co-kernel/kernel pairs and kernel/kernel pairs together. The extended co-kernel cube matrix makes it possible to yield a Boolean factored form. We also propose a heuristic method for covering of the extended co-kernel cube matrix. Experimental results on various benchmark circuits show the improvements in literal counts over the algebraic factorization based on Brayton's co-kernel cube matrix.

• 한국컴퓨터산업학회논문지
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• 제7권4호
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• pp.293-298
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• 2006

본 논문에서는 부울 분해식을 산출하기 위한 방법을 제시한다. SIS 1.2에서 사용되는 코커널 큐브 행렬은 코커널/커널들로부터 만들어지며, 이 행렬은 단지 대수 분해식만을 산출한다. 제안한 방법은 2개의 항에서 공통인수를 추출하고, 이들로부터 분해식 산출 행렬을 만들고 이로부터 부울 분해식을 산출하는 방법을 제안한다.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.951-969
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• 2012

In this paper, we propose a class of meshless collocation approaches for the solution of time dependent partial differential algebraic equations (PDAEs) in terms of a radial basis function interpolation numerical scheme. Kansa's method and the Hermite collocation method (HCM) for PDAEs are given. A sensitivity analysis of the solutions from different shape parameter c is obtained by numerical experiments. With use of the random collocation points, we have obtain the more accurate solution by the methods than those by the finite difference method for the PDAEs with index-2, i.e, we avoid the influence from an index jump of PDAEs in some degree. Several numerical experiments show that the methods are efficient.

• 호남수학학술지
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• 제31권4호
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• pp.463-478
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• 2009

Let k be an imaginary quadratic field, ℌ the complex upper half plane, and let ${\tau}{\in}k{\cap}$ℌ, q = exp(${\pi}i{\tau}$). And let n, t be positive integers with $1{\leq}t{\leq}n-1$. Then $q^{{\frac{n}{12}}-{\frac{t}{2}}+{\frac{t^2}{2n}}}{\prod}^{\infty}_{m=1}(1-q^{nm-t})(1-q^{nm-(n-t)})$ is an algebraic number [10]. As a generalization of this result, we find several infinite series and products giving algebraic numbers using Ramanujan's $_{1{\psi}1}$ summation. These are also related to Rogers-Ramanujan continued fractions.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제2권2호
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• pp.115-121
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• 2002

This paper presents an evolutionary design of digital IIR filters using the genetic algorithm (GA) with modified genetic operators and real-valued encoding. Conventional digital IIR filter design methods involve algebraic transformations of the transfer function of an analog low-pass filter (LPF) that satisfies prescribed filter specifications. Other types of frequency-selective digital fillers as high-pass (HPF), band-pass (BPF), and band-stop (BSF) filters are obtained by appropriate transformations of a prototype low-pass filter. In the GA-based digital IIR filter design scheme, filter coefficients are represented as a set of real-valued genes in a chromosome. Each chromosome represents the structure and weights of an individual filter. GA directly finds the coefficients of the desired filter transfer function through genetic search fur given filter specifications of minimum filter order. Crossover and mutation operators are selected to ensure the stability of resulting IIR filters. Other types of filters can be found independently from the filter specifications, not from algebraic transformations.

• 한국소음진동공학회논문집
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• 제26권5호
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• pp.602-608
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• 2016

The paper proposes a practical meshless method for the free vibration analysis of clamped plates having arbitrary shapes by extending the non-dimensional dynamic influence function (NDIF) method, which was developed by the author in 1999. In the proposed method, the domain and boundary of the plate of interest are discretized using only nodes without elements unlike FEM and the system matrices are obtained by making domain nodes and boundary nodes satisfy the governing differential equation and boundary conditions, respectively. However, since the above system matrices are not square ones, the problem of free vibrations of clamped plates is not reduced to an algebraic eigenvalue problem. An additional theoretical treatment is considered to produce an algebraic eigenvalue problem. It is revealed from case studies that the proposed method is valid and accurate.