• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.285-293
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• 2006

Let X be a n-set and let A = [aij] be a $n {\times} n$ matrix for which $aij {\subseteq} X$, for $1 {\le} i,\;j {\le} n$. A is called a generalized Latin square on X, if the following conditions is satisfied: $U^n_{i=1}\;aij = X = U^n_{j=1}\;aij$. In this paper, we prove that every generalized Latin square has an orthogonal mate and introduce a Hv-structure on a set of generalized Latin squares. Finally, we prove that every generalized Latin square of order n, has a transversal set.

• 한국수학사학회지
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• 제23권3호
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• pp.21-31
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• 2010

2006년 이전까지도 유럽의 오일러가 직교라틴방진의 첫 연구자로서 인정을 받아왔다. 그러나 오일러 이전에 조선의 최석정이 오일러 이전에 이미 9차의 직교라틴 방진을 만들었다는 사실이 2006년 출판된 '조합론 디자인 편람' 에 소개됨으로써 우리만 알고 있던 사실이 세계적으로 공인되었다. 본 논문에서는 최석정과 양휘산법의 마방진을 비교하고 세계최초로 만들어진 최석정의 직교라틴방진과 오일러 가설의 역사를 설명한다.

• 대한토목학회논문집
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• 제31권5D호
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• pp.623-631
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• 2011

본 연구에서는 단속류 도로에서의 유고상황을 감지할 수 있는 새로운 유고감지기법을 제시하였다. 유고감지를 위하여 적용된 방법은 교통특성들을 이용한 라틴방격(Latin Square)분석법이다. 라틴방격분석법을 이용하여 기존 연구사례에서 시도했던 방법과는 다르게 차로별, 시간대별 교통특성의 변화를 분석하여 유고상황을 감지하였다. 사용된 교통특성자료는 맑은 기상상태에서 정상운영시 또는 유고발생시 관측된 교통량, 속도, 점유율 자료이며, 유고시 자료는 2차로에서 10분간 유고가 발생했었던 자료이다. 정상운영시 및 유고발생시에 대한 교통상황을 감지하기 위하여 교통량, 속도 및 점유율 등을 기준으로 각각 라틴방격분석을 시행했다. 분석결과, 라틴방격분석을 이용하여 교통상황을 감지하는 경우, 교통량을 기준으로 교통상황을 감지하는 것이 다른 교통특성을 기준으로 교통상황을 감지하는 것보다 감지능력이 우수한 것으로 나타났다.

• 대한가정학회지
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• 제23권3호
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• pp.49-53
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• 1985

The typical texture profile analysis of acorn flour gel was investigated with Instron univ. testing machine by two experimental designs, 3$\times$3 latin square and $3^{3}$factorial experiment. As the result, it was revealed that Latin square is a useful method to reduce the number of experiments, in the case of a negligible interaction.

• Journal of Information Processing Systems
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• 제9권3호
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• pp.499-510
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• 2013

Hardware-Software co-simulation of a multiple image encryption technique shall be described in this paper. Our proposed multiple image encryption technique is based on the Latin Square Image Cipher (LSIC). First, a carrier image that is based on the Latin Square is generated by using 256-bits of length key. The XOR operation is applied between an input image and the Latin Square Image to generate an encrypted image. Then, the XOR operation is applied between the encrypted image and the second input image to encrypt the second image. This process is continues until the nth input image is encrypted. We achieved hardware co-simulation of the proposed multiple image encryption technique by using the Xilinx System Generator (XSG). This encryption technique is modeled using Simulink and XSG Block set and synthesized onto Virtex 2 pro FPGA device. We validated our proposed technique by using the hardware software co-simulation method.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제6권
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• pp.371-381
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• 1997

Let p be an odd prime number. We introduce simple and useful decoding algorithm for orthogonal Latin square codes of order p. Let H be the parity check matrix of orthogonal Latin square code. For any x ${\in}$ GF(p)$^{n}$, we call xH$^{T}$ the syndrome of x. This method is based on the syndrome decoding for linear codes. In L$_{p}$, we need to find the first and the second coordinates of codeword in order to correct the errored received vector.

• 대한수학회지
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• 제60권1호
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• pp.91-113
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• 2023

The polytope of tristochastic tensors of degree three, the Latin polytope, has two kinds of extreme points. Those that are at a maximum distance from the barycenter of the polytope correspond to Latin squares. The remaining extreme points are said to be short. The aim of the paper is to determine the geometry of these short extreme points, as they relate to the Latin squares. The paper adapts the Latin square notion of an intercalate to yield the new concept of a cross-intercalate between two Latin squares. Cross-intercalates of pairs of orthogonal Latin squares of degree three are used to produce the short extreme points of the degree three Latin polytope. The pairs of orthogonal Latin squares fall into two classes, described as parallel and reversed, each forming an orbit under the isotopy group. In the inverse direction, we show that each short extreme point of the Latin polytope determines four pairs of orthogonal Latin squares, two parallel and two reversed.

• 한국멀티미디어학회논문지
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• 제18권9호
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• pp.1083-1090
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• 2015

A generalized recursive circulant network(GR) is widely used in the design and implementation of local area networks and parallel processing architectures. In this paper, we investigate the routing of a message on this network, that is a key to the performance of this network. We would like to transmit maximum number of packets from a source node to a destination node simultaneously along paths on this network, where the i^th packet traverses along the i^th path. In order for all packets to arrive at the destination node securely, the i^th path must be node-disjoint from all other paths. For construction of these paths, employing the Hamiltonian Circuit Latin Square(HCLS), a special class of (n x n) matrices, we present O(n²) parallel routing algorithm on generalized recursive circulant networks.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 2004년도 추계학술대회 논문집
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• pp.433-438
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• 2004

The rapid machining of prototypes plays an important role in product process. Rapid Prototyping(RP) is the widespread technology to produce prototype. But, it have many problems such as shrinkage, deformation and formation occurred by hardening of resin and stair shaping, On the contrary, high speed machining(HSM) technology has many advantages such as good quality, low cost and rapid machining time. Moreover, it is possible to use the material of original product. This paper presents manufacture of trial product by HSM and optimization of machining condition for high productivity in the view of manufacturing time and average error. For example, propeller is machined by the surface machining of thin surface parts. Experiments are designed of machining conditions by Latin Square method and machining condition is optimized and selected by ANOVA

• 한국정밀공학회지
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• 제22권10호
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• pp.99-106
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• 2005

This paper presents manufacture of mock-up by HSM and optimization of machining condition for high productivity in the view of manufacturing time and accuracy. The rapid machining of prototypes plays an important role in building mock-up. Rapid Prototyping(RP) is a technology to make prototype. But, it have many problems such as shrinkage. deformation and formation occurred by hardening of resin and stair shaping. On the contrary, high speed machining(HSM) technology has many advantages such as good quality, low cost and rapid machining time. HSM and RP is compared for machining efficiency. Experiments are designed by Latin Square Method and machining condition is optimized and selected by ANOVA. For example, propeller is machined by the surface machining of thin surface parts.