• Title/Summary/Keyword: system of linear algebra

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THE SEMIGROUPS OF BINARY SYSTEMS AND SOME PERSPECTIVES

  • Kim, Hee-Sik;Neggers, Joseph
    • Bulletin of the Korean Mathematical Society
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    • v.45 no.4
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    • pp.651-661
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    • 2008
  • Given binary operations "*" and "$\circ$" on a set X, define a product binary operation "$\Box$" as follows: $x{\Box}y\;:=\;(x\;{\ast}\;y)\;{\circ}\;(y\;{\ast}\;x)$. This in turn yields a binary operation on Bin(X), the set of groupoids defined on X turning it into a semigroup (Bin(X), $\Box$)with identity (x * y = x) the left zero semigroup and an analog of negative one in the right zero semigroup (x * y = y). The composition $\Box$ is a generalization of the composition of functions, modelled here as leftoids (x * y = f(x)), permitting one to study the dynamics of binary systems as well as a variety of other perspectives also of interest.

Application of (Max, +)-algebra to the Waiting Times in Deterministic 2-node Tandem Queues with Blocking ((Max, +)-대수를 이용한 2-노드 유한 버퍼 일렬대기행렬에서의 대기시간 분석)

  • Seo Dong-Won
    • Journal of the Korean Operations Research and Management Science Society
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    • v.30 no.1
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    • pp.149-159
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    • 2005
  • In this study, we consider characteristics of stationary waiting times in single-server 2-node tandem queues with a finite buffer, a Poisson arrival process and deterministic service times. The system has two buffers: one at the first node is infinite and the other one at the second node is finite. We show that the sojourn time or departure process does not depend on the capacity of the finite buffer and on the order of nodes (service times), which are the same as the previous results. Furthermore, the explicit expressions of waiting times at the first node are given as a function of the capacity of the finite buffer and we are able to disclose a relationship of waiting times between under communication blocking and under manufacturing blocking. Some numerical examples are also given.

Construction of a macro plane stress triangle element with drilling d.o.f.'s (드릴링 자유도를 가진 매크로 삼각형 요소를 이용한 평면 응력 해석)

  • 엄재성;김영태;이병채
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 2004.10a
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    • pp.886-889
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    • 2004
  • A simple macro triangle with drilling d.o.f.'s is proposed for plane stress problems based on IET(Individual element test) and finite element template. Three-node triangular element has geometrical advantages in preprocessing but suffers from bad performance comparing to other shapes of elements -especially quadrilateral. Main purpose of this study is to construct a high-performance linear triangular element with limited supplementary d.o.f.'s. A triangle is divided by three sub-triangles with drilling d.o.f.'s. The sub-triangle stiffness come from IET passing force-lumping matrix, so this assures the consistency of the element. The macro element strategy takes care of the element‘s stability and accuracy like higher-order stiffness in the F.E. template. The resulting element fits on the uses of conventional three-node. Benchmark examples show proposed element in closed form stiffness from CAS (Computer algebra system) gives the improved results without more computational efforts than others.

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A mathematical theory of the AHP(Analytic Hierarchy Process) and its application to assess research proposals (계층분석적 의사결정(AHP)을 이용한 연구과제 선정방법에 관한 연구)

  • Yang, Jeong-Mo;Lee, Sang-Gu
    • Communications of Mathematical Education
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    • v.22 no.4
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    • pp.459-469
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    • 2008
  • We give a mathematical approach using Linear Algebra, especially largest eigenvalue and eigenvector on decision making support system. We find a mathematical modeling on decision making problem which could be solved by AHP(Analytic Hierarchy Process) method. Especially, we give a new approach to change evaluation indicator weight on assessing research proposals.

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Optimal Buffer Allocation in Tandem Queues with Communication Blocking

  • Seo, Dong-Won;Ko, Sung-Seok;Jung, Uk
    • ETRI Journal
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    • v.31 no.1
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    • pp.86-88
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    • 2009
  • In this letter, we consider an m-node tandem queue (queues in series) with a Poisson arrival process and either deterministic or non-overlapping service times. With the assumption that each node has a finite buffer except for the first node, we show the non-increasing convex property of stationary waiting time with respect to the finite buffer capacities. We apply it to an optimization problem which determines the smallest buffer capacities subject to probabilistic constraints on stationary waiting times.

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Stationary Waiting Times in Simple Fork-and-Join Queues with Finite Buffers and Communication Blocking (통신차단규칙을 따르는 유한버퍼 단순 조립형 대기행렬 망에서의 안정대기시간)

  • Seo, Dong-Won;Lee, Seung-Man
    • Journal of the Korea Society for Simulation
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    • v.19 no.3
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    • pp.109-117
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    • 2010
  • In this study, we consider stationary waiting times in a simple fork-and-join type queue which consists of three single-server machines, Machine 1, Machine 2, and Assembly Machine. We assume that the queue has a renewal arrival process and that independent service times at each node are either deterministic or non-overlapping. We also assume that the Machines 1 and 2 have an infinite buffer capacity whereas the Assembly Machine has two finite buffers, one for each machine. Services at each machine are given by FIFO service discipline and a communication blocking policy. We derive the explicit expressions for stationary waiting times at all nodes as a function of finite buffer capacities by using (max,+)-algebra. Various characteristics of stationary waiting times such as mean, higher moments, and tail probability can be computed from these expressions.

On freshmen's academic achievements of college mathematics and the efficient methods of education (이공계열 대학 신입생의 기초 수학분야 학업성취도 및 효율적인 교육 방안에 대한 연구)

  • Kim, Byung Hak;Kim, Jae Woong;Kim, Jiyun
    • Communications of Mathematical Education
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    • v.31 no.1
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    • pp.1-15
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    • 2017
  • The university entrance examination in deeply related to high school education, adaptation and study ability in university. In this point of view, we investigate the scholastic achievement to the Calculus 1,2, linear algebra and differential equation from academic year 2006 to 2016. The above four subjects contain elementary and essential contents to study for science and engineering major in university. We compare and analyse the data of scholastic achievement and system of various university entrance examination, and we discuss and propose the methods of improvements for adaptation to each major field and study ability.

Eye Gaze Tracking System Under Natural Head Movements (머리 움직임이 자유로운 안구 응시 추정 시스템)

  • ;Matthew, Sked;Qiang, Ji
    • Journal of the Institute of Electronics Engineers of Korea SC
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    • v.41 no.5
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    • pp.57-64
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    • 2004
  • We proposed the eye gaze tracking system under natural head movements, which consists of one narrow-view field CCD camera, two mirrors which of reflective angles are controlled and active infra-red illumination. The mirrors' angles were computed by geometric and linear algebra calculations to put the pupil images on the optical axis of the camera. Our system allowed the subjects head to move 90cm horizontally and 60cm vertically, and the spatial resolutions were about 6$^{\circ}$ and 7$^{\circ}$, respectively. The frame rate for estimating gaze points was 10~15 frames/sec. As gaze mapping function, we used the hierarchical generalized regression neural networks (H-GRNN) based on the two-pass GRNN. The gaze accuracy showed 94% by H-GRNN improved 9% more than 85% of GRNN even though the head or face was a little rotated. Our system does not have a high spatial gaze resolution, but it allows natural head movements, robust and accurate gaze tracking. In addition there is no need to re-calibrate the system when subjects are changed.