• 대한수학회보
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• 제57권2호
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• pp.295-309
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• 2020

Loop transversal codes take an alternative approach to the theory of error-correcting codes, placing emphasis on the set of errors that are to be corrected. Hitherto, the loop transversal code method has been restricted to linear codes. The goal of the current paper is to extend the conceptual framework of loop transversal codes to admit nonlinear codes. We present a natural example of this nonlinearity among perfect single-error correcting codes that exhibit efficient domination in a circulant graph, and contrast it with linear codes in a similar context.

• Structural Engineering and Mechanics
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• 제13권4호
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• pp.437-453
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• 2002

In this paper, dynamic stiffness and flexibility for circular membranes are analytically derived using an efficient mixed-part dual boundary element method (BEM). We employ three approaches, the complex-valued BEM, the real-part and imaginary-part BEM, to determine the dynamic stiffness and flexibility. In the analytical formulation, the continuous system for a circular membrane is transformed into a discrete system with a circulant matrix. Based on the properties of the circulant, the analytical solutions for the dynamic stiffness and flexibility are derived. In deriving the stiffness and flexibility, the spurious resonance is cancelled out. Numerical aspects are discussed and emphasized. The problem of numerical instability due to division by zero is avoided by choosing additional constraints from the information of real and imaginary parts in the dual formulation. For the overdetermined system, the least squares method is considered to determine the dynamic stiffness and flexibility. A general purpose program has been developed to test several examples including circular and square cases.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.489-506
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• 2020

The spatial fractional diffusion equation can be discretized by employing the implicit finite difference scheme using the shifted Grünwald formula. The discretized linear system is obtained, whose the coefficient matrix has a diagonal-plus-Toeplitz structure. In order to solve the diagonal-plus-Toeplitz linear system, on the basis of circulant and skew-circulant splitting (CSCS splitting), we construct a new and efficient iterative method, called DSCS iterative methods, which have two parameters. Than we prove the convergence of DSCS methods. As a focus, we derive the simple and effective values of two optimal parameters under some restrictions. Some numerical experiments are carried out to illustrate the validity and accuracy of the new methods.

• 통합자연과학논문집
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• 제13권2호
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• pp.69-75
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• 2020

Multiple Input Multiple Output (MIMO) is one of the important wireless communication technologies. This paper proposes MIMO system capacity enhancement by using convolution of periodic circulating vector signals. This signal represents statistical dependencies between transmission signal with discrete noise and receiver signal with the linear shifting of MIMO channel capacity by positive extents. We examine the channel capacity, outage probability and SNR of MIMO receiver by adding log determinant signal with validated in terms of numerical simulation.

• 정보처리학회논문지:컴퓨터 및 통신 시스템
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• 제4권2호
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• pp.37-40
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• 2015

본 논문에서는 이항트리의 2-에지번호매김에서 선형적 에지번호매김 방법, 변형된 에지번호매김 방법 그리고 혼합형 에지번호매김 방법들을 제안한다. 이러한 연구결과는 최대 연결도를 갖는 신뢰성이 높은 상호연결망의 일종인 원형군 그래프(circulant graph)의 점프열(jump sequence)로 에지번호들을 사용하면 이항트리를 스패닝 트리로 갖고 최적방송이 가능한 다양한 위상들을 설계할 수 있다.

• 대한수학회보
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• 제60권3호
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• pp.829-844
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• 2023

In this paper, we present a new construction for self-dual codes that uses the concept of double bordered construction, group rings, and reverse circulant matrices. Using groups of orders 2, 3, 4, and 5, and by applying the construction over the binary field and the ring F₂ + uF₂, we obtain extremal binary self-dual codes of various lengths: 12, 16, 20, 24, 32, 40, and 48. In particular, we show the significance of this new construction by constructing the unique Extended Binary Golay Code [24, 12, 8] and the unique Extended Quadratic Residue [48, 24, 12] Type II linear block code. Moreover, we strengthen the existing relationship between units and non-units with the self-dual codes presented in [10] by limiting the conditions given in the corollary. Additionally, we establish a relationship between idempotent and self-dual codes, which is done for the first time in the literature.

• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.173-183
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• 2015

A radio k-labeling f of a graph G is a function f from V (G) to $Z^+{\cup}\{0\}$ such that $d(x,y)+{\mid}f(x)-f(y){\mid}{\geq}k+1$ for every two distinct vertices x and y of G, where d(x, y) is the distance between any two vertices $x,y{\in}G$. The span of a radio k-labeling f is denoted by sp(f) and defined as max$\{{\mid}f(x)-f(y){\mid}:x,y{\in}V(G)\}$. The radio k-labeling is a radio labeling when k = diam(G). In other words, a radio labeling is an injective function $f:V(G){\rightarrow}Z^+{\cup}\{0\}$ such that $${\mid}f(x)=f(y){\mid}{\geq}diam(G)+1-d(x,y)$$ for any pair of vertices $x,y{\in}G$. The radio number of G denoted by rn(G), is the lowest span taken over all radio labelings of the graph. When k = diam(G) - 1, a radio k-labeling is called a radio antipodal labeling. An antipodal labeling for a graph G is a function $f:V(G){\rightarrow}\{0,1,2,{\ldots}\}$ such that $d(x,y)+{\mid}f(x)-f(y){\mid}{\geq}diam(G)$ holds for all $x,y{\in}G$. The radio antipodal number for G denoted by an(G), is the minimum span of an antipodal labeling admitted by G. In this paper, we investigate the exact value of the radio number and radio antipodal number for the circulant graphs G(4k + 2; {1, 2}).

• 공학교육연구
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• 제21권1호
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• pp.77-89
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• 2018

The chromosomes of all the world are the same in all 24 pairs, but the key, skin color and appearance are different. Also, it is the resistance of adult disease, diabetes, cancer. In 1953, Watson, Crick of Cambridge University experimentally discovered a DNA double helix structure, and in 1962, They laureates the Nobel Prize. In 1964, Temin, University of Wisconsin, USA, experimentally identified the ability to copy gene information from RNA to DNA and received the Nobel Prize in 1975. In this paper, we analyzed 24 pairs of DNA chromosomes using mathematical matrices based on the combination order sequence of four groups, and designed the Taegeuk pattern genetic code for the first time in the world. In the case of normal persons, the middle Yin-Yang taegeuk is designed as a block circulant Jacket matrix in DNA, and the left-right and upper-lower pairs of east-west and north-south rulings are designed as pair complementary matrices. If (C U: A G) chromosomes are unbalanced, that is, people with disease or inheritance become squashed squirming patterns. In 2017, Professor Michel Young was awarded a Nobel by presenting a biological clock and experimentally explained the bio-imbalance through a yellow fruit fly experiment.This study proved mathematical matrices for balanced and unbalanced RNA.

• 한국정보과학회논문지:시스템및이론
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• 제31권1_2호
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• pp.86-94
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• 2004

이 논문에서는 재귀원형군 $ G(2^m, 4), m{\geq}3$은 고장인 요소의 수가 m-2개 이하일 때, 임의의 1, 4 ${\leq}1{\leq}2^m-f_v$에 대하여 길이 1인 고장 없는 사이클을 가짐을 보인다. 여기서, f$_{v}$ 는 고장 정점의 수이다. 이를 위하여, ｜F｜$\leq$k인 임의의 고장 요소 집합 F에 대해서 G-F가 임의의 두 정점을 잇는 길이가 해밀톤 경로보다 하나 작은 경로를 가질 때, G를 k-고장 하이포해밀톤 연결된 그래프라고 정의하고, $ G(2^m, 4), m{\geq}3$은 m-3-고장 하이포해밀톤 연결된 그래프임을 보인다.

• 한국수학사학회지
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• 제19권2호
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• pp.125-140
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• 2006

군환의 특별한 부분환으로 정의된 수어환(Schur ring)은 치환군의 구조 연구를 위해 1933년 I.Schur에 의해 소개되었다. 그 후 30여 년 동안 군론과 표현론에서 응용되던 수어환은 1970년대에 이르러 획기적인 분기점을 맞이하게 된다. 조합론, 특별히 대수적 그래프에 관한 많은 연구 속에서, 그래프를 분류하기위해 수어환을 이용하려는 새로운 시도가 Klin과 Poschel에 의해 제안되었다. 이것은 당시 대수학에서 이룩해낸 유한단순군의 분류에 큰 도움을 받은 것이다. 이 논문에서는 수어환의 발생에 대한 역사적 배경과, 수어환이 군이론에서 어떻게 이용되었는지를 살펴보고, 또한 그래프이론에서의 역할을 조사한다.