• Title/Summary/Keyword: combinatorial object

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A Characterization of Isomorphism Problem of Combinatorial objects and the Historical Note (조합대상의 동형사상 문제의 특성화와 역사적 고찰)

  • Park, Hong-Goo
    • Journal for History of Mathematics
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    • v.19 no.1
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    • pp.33-42
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    • 2006
  • In this paper, we study the theoretical and historical backgrounds with respect to isomorphism problem of combinatorial objects which is one of major problems in the theory of Combinatorics. And also, we introduce a partial result for isomorphism problem of Cayley objects over a finite field.

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Analysis of Variables and Errors of the Combinatorial Problem (순열 조합 문장제의 문제 변인과 오류 분석)

  • Lee, Ji-Hyun;Lee, Jung-Yun;Choi, Young-Gi
    • School Mathematics
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    • v.7 no.2
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    • pp.123-137
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    • 2005
  • Elementary combinatorial problem may be classified into three different combinatorial models(selection, distribution, partition). The main goal of this research is to determine the effect of type of combinatorial operation and implicit combinatorial model on problem difficulty. We also classified errors in the understanding combinatorial problem into error of order, repetition, permutation with repetition, confusing the type of object and cell, partition. The analysis of variance of answers from 339 students showed the influence of the implicit combinatorial model and types of combinatorial operations. As a result of clinical interviews, we particularly noticed that some students were not able to transfer the definition of combinatorial operation when changing the problem to a different combinatorial model. Moreover, we have analysed textbooks, and we have found that the exercises in these textbooks don't have various types of problems. Therefore when organizing the teaching , it is necessary to pose various types of problems and to emphasize the transition of combinatorial problem into the different models.

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COMBINATORIAL AUSLANDER-REITEN QUIVERS AND REDUCED EXPRESSIONS

  • Oh, Se-jin;Suh, Uhi Rinn
    • Journal of the Korean Mathematical Society
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    • v.56 no.2
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    • pp.353-385
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    • 2019
  • In this paper, we introduce the notion of combinatorial Auslander-Reiten (AR) quivers for commutation classes [${\tilde{w}}]$ of w in a finite Weyl group. This combinatorial object is the Hasse diagram of the convex partial order ${\prec}_{[{\tilde{w}}]}$ on the subset ${\Phi}(w)$ of positive roots. By analyzing properties of the combinatorial AR-quivers with labelings and reflection functors, we can apply their properties to the representation theory of KLR algebras and dual PBW-basis associated to any commutation class [${\tilde{w}}_0$] of the longest element $w_0$ of any finite type.

Estimation of Motion Vector for Moving Picture Encoding (동영상 부호화를 위한 움직임 벡터의 추정)

  • 강성관;임춘환;손영수;배상현
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.5 no.7
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    • pp.1340-1345
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    • 2001
  • In this paper, we proposed the method computing the optimal solution of Optical Flow(OF) representing the moving information of moving object and improving the operating speed. In order to do that, we computed the optimal solution of OF using the Combinatorial Hough Transform(CHT) and Voting accumulation and simply searched the moving object compared to conventional method.

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Octree model based fast three-dimensional object recognition (Octree 모델에 근거한 고속 3차원 물체 인식)

  • 이영재;박영태
    • Journal of the Korean Institute of Telematics and Electronics C
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    • v.34C no.9
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    • pp.84-101
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    • 1997
  • Inferring and recognizing 3D objects form a 2D occuluded image has been an important research area of computer vision. The octree model, a hierarchical volume description of 3D objects, may be utilized to generate projected images from arbitrary viewing directions, thereby providing an efficient means of the data base for 3D object recognition. We present a fast algorithm of finding the 4 pairs of feature points to estimate the viewing direction. The method is based on matching the object contour to the reference occuluded shapes of 49 viewing directions. The initially best matched viewing direction is calibrated by searching for the 4 pairs of feature points between the input image and the image projected along the estimated viewing direction. Then the input shape is recognized by matching to the projectd shape. The computational complexity of the proposed method is shown to be O(n$^{2}$) in the worst case, and that of the simple combinatorial method is O(m$^{4}$.n$^{4}$) where m and n denote the number of feature points of the 3D model object and the 2D object respectively.

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Estimation of Distance and Direction for Tracking of the Moving Object

  • Kang, Sung-Kwan;Park, Jong-An
    • 제어로봇시스템학회:학술대회논문집
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    • 2000.10a
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    • pp.557-557
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    • 2000
  • Tracking of the moving object, which is realized by the computer vision, is used for military and industrial fields. It is the application technique with imply complicated processing for understanding the input images. But, in these days, the most moving object tracking algorithms have many difficult problems. A typical problem is the increase of calculation time depending on target number. For this reason, there are many studies to solve real time processing problems and errors for background environmental change. In this paper, we used optical flow which is one of moving object tracking algorithms. It represents vector of the moving object. Optical flow estimation based on the regularization method depends on iteration method but it is very sensitive the noise. We proposed a new method using the Combinatorial Hough Transform (CHT) and Voting Accumulation in order to find optimal constraint lines. Also, we used the logical operation in order to release the operation time. The proposed method can easily and accurately extract the optical flow of moving object area and the moving information. We have simulated the proposed method using the test images. This images are included the noise. Experimental results show that the proposed method get better flow and estimate accurately the moving information.

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A NOTE ON g-SEMISIMPLICITY OF A FINITE-DIMENSIONAL MODULE OVER THE RATIONAL CHEREDNIK ALGEBRA OF TYPE A

  • Gicheol Shin
    • Journal of the Chungcheong Mathematical Society
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    • v.36 no.2
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    • pp.77-86
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    • 2023
  • The purpose of this paper is to show that a certain finite dimensional representation of the rational Cherednik algebra of type A has a basis consisting of simultaneous eigenvectors for the actions of a certain family of commuting elements, which are introduced in the author's previous paper. To this end, we introduce a combinatorial object, which is called a restricted arrangement of colored beads, and consider an action of the affine symmetric group on the set of the arrangements.

Agent-based approach for the construction of a design support system for conceptual chemical process synthesis

  • Han, Chonghun;Stephanopoulos, George
    • 제어로봇시스템학회:학술대회논문집
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    • 1995.10a
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    • pp.328-331
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    • 1995
  • A successful, computer-aided design support system can help a process designer focus on making effective design decisions, not merely tedious routine calculations. Such a system is essential to enhance quality of design in terms of economics, environmental benignity, reliability, robustness, and operability. Such a statement is even more accepted when applied to conceptual design problems, where gross design specifications are given while a combinatorial number of design alternatives exists. This paper presents an agent-based approach as a systematic and efficient way to design a design support system for the synthesis of conceptual chemical processes. An agent-based approach allows us to handle design knowledge as an object and thus greatly improve the modularity and reusability of that knowledge. Such modularity and reusability lead to the increased productivity in the development of a design support system and the increased ease in the relaxation of design decisions and the generation of design alternatives, both of which functions are critically important in dealing with the complexity and uncertainty of conceptual design problems.

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Reconfiguration method for Supervisor Control in Deadlock status Using FSSTP(Forbidden Sequence of State Transition Problem) (순차상태전이금지(FSSTP)를 이용한 교착상태 관리제어를 위한 재구성 방법)

  • Song, Yu-Jin;Lee, Eun-Joo;Lee, Jong-Kun
    • Journal of Institute of Control, Robotics and Systems
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    • v.14 no.3
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    • pp.213-220
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    • 2008
  • The object of this paper is to propose a method to deal with the problem of modeling user specifications in approaches based on supervisory control and Petri nets. However, most of Petri Net approaches are based on forbidden states specifications, and these specifications are suitable the use of tool such as the reachability graph. But these methods were not able to show the user specification easily and these formalisms are generally limited by the combinatorial explosion that occurs when attempting to model complex systems. Herein, we propose a new efficient method using FSSTP (Forbidden Sequences of State-Transitions Problem) and theory of region. Also, to detect and avoid the deadlock problem in control process, we use DAPN method (Deadlock Avoidance Petri nets) for solving this problem in control model.

The Optimal Project Combination for Urban Regeneration New Deal Projects (도시재생 뉴딜사업의 최적 사업지구 선정조합에 관한 연구)

  • Park, Jae Ho;Geem, Zong Woo;Yu, Jung Suk
    • Korea Real Estate Review
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    • v.28 no.1
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    • pp.23-37
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    • 2018
  • The genetic algorithm (GA) and branch and bound (B&B) methods are the useful methods of searching the optimal project combination (combinatorial optimization) to maximize the project effect considering the budget constraint and the balance of regional development with regard to the Urban Regeneration New Deal policy, the core real estate policy of the Moon Jae-in government. The Ministry of Land, Infrastructure, and Transport (MOLIT) will choose 13 central-city-area-type projects, 2 economic-base-type projects, and 10 public-company-proposal-type projects among the numerous projects from 16 local governments while each government can apply only 4 projects, respectively, for the 2017 Urban Regeneration New Deal project. If MOLIT selects only those projects with a project effect maximization purpose, there will be unselected regions, which will harm the balance of regional development. For this reason, an optimization model is proposed herein, and a combinatorial optimization method using the GA and B&B methods should be sought to satisfy the various constraints with the object function. Going forward, it is expected that both these methods will present rational decision-making criteria if the central government allocates a special-purpose-limited budget to many local governments.