• Title/Summary/Keyword: matrix theory

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Simulation of Separating Isoclinics and Isochromatics from Photoelastic Fringes of a Disk using 8-step Phase Shifting Methodology (광탄성 프린지 위상이동법을 적용한 디스크의 등경 및 등색프린지 분리법에 관한 시뮬레이션)

  • Baek, Tae-Hyun;Kim, Myung-Soo;Cho, Sung-Ho
    • Journal of the Korean Society for Nondestructive Testing
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    • v.21 no.2
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    • pp.189-196
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    • 2001
  • Photoelasticity is one of the most widely used methods for whole field stress analysis. In photoelasticity, the difference and the directions of the principal stresses we given isochromatic and isoclinic fringe patterns. Conventionally, principal stress directions are measured manually by relating the polarizer and analyzer of a plane polariscope at the same time. This is known to be the Tardy compensation method. This measurement can be very tedious and time consuming in whole field analysis. It is not possible to separate isoclincs from photoelastic fringes by conventional photoelastic technique. In this study, photoelastic theory is represented by Jones matrices and 4-steps and 8-steps phase shifting methods are described A feasibility study using computer simulation is done to separate isoclincs and isochomatics from photoelastic fringes of a circular disk under diametrical compression. Fringe patterns of the disk are generated using stress optic law. The magnitudes of isoclincs and isochromatics obtained from 8-step phase shifting method are compared with those of theories. From computer simulation, it is verified to separate isoclincs and isochomatics from photoelastic fringes.

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Analysis of Research Trends in SIAM Journal on Applied Mathematics Using Topic Modeling (토픽모델링을 활용한 SIAM Journal on Applied Mathematics의 연구 동향 분석)

  • Kim, Sung-Yeun
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.21 no.7
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    • pp.607-615
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    • 2020
  • The purpose of this study was to analyze the research status and trends related to the industrial mathematics based on text mining techniques with a sample of 4910 papers collected in the SIAM Journal on Applied Mathematics from 1970 to 2019. The R program was used to collect titles, abstracts, and key words from the papers and to analyze topic modeling techniques based on LDA algorithm. As a result of the coherence score on the collected papers, 20 topics were determined optimally using the Gibbs sampling methods. The main results were as follows. First, studies on industrial mathematics were conducted in a variety of mathematics fields, including computational mathematics, geometry, mathematical modeling, topology, discrete mathematics, probability and statistics, with a focus on analysis and algebra. Second, 5 hot topics (mathematical biology, nonlinear partial differential equation, discrete mathematics, statistics, topology) and 1 cold topic (probability theory) were found based on time series regression analysis. Third, among the fields that were not reflected in the 2015 revised mathematics curriculum, numeral system, matrix, vector in space, and complex numbers were extracted as the contents to be covered in the high school mathematical curriculum. Finally, this study suggested strategies to activate industrial mathematics in Korea, described the study limitations, and proposed directions for future research.

Art and Collectivity (미술과 집단성)

  • Kwok, Kian-Chow
    • The Journal of Art Theory & Practice
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    • no.4
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    • pp.181-202
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    • 2006
  • "When it comes to art, nationalism is a goodticket to ride with", says the title of a report in the Indian Express (Mumbai, 29 Oct 2000). The newspaper report goes on to say that since Indian art was kept "ethnic" by colonialism, national liberation meant opening up to the world on India's own terms. Advocacy, at the tail end of the 20th century, would contrast dramatically with the call by Rabindranath Tagore, the founder of the academy at Santiniketan in 1901, to guard against the fetish of nationalism. "The colourless vagueness of cosmopolitanism," Tagore pronounced, "nor thefierce self-idolatry of nation-worship, is the goal of human history" (Nationalism, 1917). This contrast is significant on two counts. First is the positive aspect of "nation" as a frame in art production or circulation, at the current point of globalization when massive expansion of cultural consumers may be realized through prevailing communication networks and technology. The organization of the information market, most vividly demonstrated through the recent FIFA World Cup when one out of every five living human beings on earth watched the finals, is predicated on nations as categories. An extension of the Indian Express argument would be that tagging of artworks along the category of nation would help ensure greatest reception, and would in turn open up the reified category of "art," so as to consider new impetus from aesthetic traditions from all parts of the world many of which hereto fore regarded as "ethnic," so as to liberate art from any hegemony of "international standards." Secondly, the critique of nationalism points to a transnational civic sphere, be it Tagore's notion of people-not-nation, or the much mo re recent "transnational constellation" of Jurgen Habermas (2001), a vision for the European Union w here civil sphere beyond confines of nation opens up new possibilities, and may serve as a model for a liberated sphere on global scale. There are other levels of collectivity which art may address, for instance the Indonesian example of local communities headed by Ketua Rukun Tetangga, the neighbourhood headmen, in which community matters of culture and the arts are organically woven into the communal fabric. Art and collectivity at the national-transnational level yield a contrasting situation of, on the idealized end, the dual inputs of local culture and tradition through "nation" as necessary frame, and the concurrent development of a transnational, culturally and aesthetically vibrant civic sphere that will ensure a cosmopolitanism that is not a "colourless vagueness." In art historical studies, this is seen, for instance, in the recent discussion on "cosmopolitan modernisms." Conversely, we may see a dual tyranny of a nationalism that is a closure (sometimes stated as "ethno-nationalism" which is disputable), and an internationalism that is evolved through restrictive understanding of historical development within privileged expressions. In art historical terms, where there is a lack of investigation into the reality of multiple modernisms, the possibility of a democratic cosmopolitanism in art is severely curtailed. The advocacy of a liberal cosmopolitanism without a democratic foundation returns art to dominance of historical privileged category. A local community with lack of transnational inputs may sometimes place emphasis on neo-traditionalism which is also a double edged sword, as re kindling with traditions is both liberating and restrictive, which in turn interplays with the push and pull of the collective matrix.

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Connection between Fourier of Signal Processing and Shannon of 5G SmartPhone (5G 스마트폰의 샤논과 신호처리의 푸리에의 표본화에서 만남)

  • Kim, Jeong-Su;Lee, Moon-Ho
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.17 no.6
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    • pp.69-78
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    • 2017
  • Shannon of the 5G smartphone and Fourier of the signal processing meet in the sampling theorem (2 times the highest frequency 1). In this paper, the initial Shannon Theorem finds the Shannon capacity at the point-to-point, but the 5G shows on the Relay channel that the technology has evolved into Multi Point MIMO. Fourier transforms are signal processing with fixed parameters. We analyzed the performance by proposing a 2N-1 multivariate Fourier-Jacket transform in the multimedia age. In this study, the authors tackle this signal processing complexity issue by proposing a Jacket-based fast method for reducing the precoding/decoding complexity in terms of time computation. Jacket transforms have shown to find applications in signal processing and coding theory. Jacket transforms are defined to be $n{\times}n$ matrices $A=(a_{jk})$ over a field F with the property $AA^{\dot{+}}=nl_n$, where $A^{\dot{+}}$ is the transpose matrix of the element-wise inverse of A, that is, $A^{\dot{+}}=(a^{-1}_{kj})$, which generalise Hadamard transforms and centre weighted Hadamard transforms. In particular, exploiting the Jacket transform properties, the authors propose a new eigenvalue decomposition (EVD) method with application in precoding and decoding of distributive multi-input multi-output channels in relay-based DF cooperative wireless networks in which the transmission is based on using single-symbol decodable space-time block codes. The authors show that the proposed Jacket-based method of EVD has significant reduction in its computational time as compared to the conventional-based EVD method. Performance in terms of computational time reduction is evaluated quantitatively through mathematical analysis and numerical results.

Comparison between Cournot-Nash and Stackelberg Game in Bi-level Program (Bi-level program에서 Cournot-Nash게임과 Stackelberg게임의 비교연구)

  • Lim, Yong-Taek;Lim, Kang-Won
    • Journal of Korean Society of Transportation
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    • v.22 no.7 s.78
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    • pp.99-106
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    • 2004
  • This paper presents some comparisons between Cournot-Nash and Stackelberg game in bi-level program, composed of both upper level program and lower level one. The upper level can be formulated to optimize a specific objective function, while the lower formulated to express travelers' behavior patterns corresponding to the design parameter of upper level problem. This kind of hi-level program is to determine a design parameter, which leads the road network to an optimal state. Bi-level program includes traffic signal control, traffic information provision, congestion charge and new transportation mode introduction as well as road expansion. From the view point of game theory, many existing algorithms for bi-level program such as IOA (Iterative Optimization Assignment) or IEA (Iterative Estimation Assignment) belong to Cournot-Nash game. But sensitivity-based algorithms belongs to Stackelberg one because they consider the reaction of the lower level program. These two game models would be compared by using an example network and show some results that there is no superiority between the models in deterministic case, but in stochastic case Stackelberg approach is better than that of Cournot-Nash one as we expect.

A Comprehensive Groundwater Modeling using Multicomponent Multiphase Theory: 1. Development of a Multidimensional Finite Element Model (다중 다상이론을 이용한 통합적 지하수 모델링: 1. 다차원 유한요소 모형의 개발)

  • Joon Hyun Kim
    • Journal of Korea Soil Environment Society
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    • v.1 no.1
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    • pp.89-102
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    • 1996
  • An integrated model is presented to describe underground flow and mass transport, using a multicomponent multiphase approach. The comprehensive governing equation is derived considering mass and force balances of chemical species over four phases(water, oil, air, and soil) in a schematic elementary volume. Compact and systemati notations of relevant variables and equations are introduced to facilitate the inclusion of complex migration and transformation processes, and variable spatial dimensions. The resulting nonlinear system is solved by a multidimensional finite element code. The developed code with dynamic array allocation, is sufficiently flexible to work across a wide spectrum of computers, including an IBM ES 9000/900 vector facility, SP2 cluster machine, Unix workstations and PCs, for one-, two and three-dimensional problems. To reduce the computation time and storage requirements, the system equations are decoupled and solved using a banded global matrix solver, with the vector and parallel processing on the IBM 9000. To avoide the numerical oscillations of the nonlinear problems in the case of convective dominant transport, the techniques of upstream weighting, mass lumping, and elementary-wise parameter evaluation are applied. The instability and convergence criteria of the nonlinear problems are studied for the one-dimensional analogue of FEM and FDM. Modeling capacity is presented in the simulation of three dimensional composite multiphase TCE migration. Comprehesive simulation feature of the code is presented in a companion paper of this issue for the specific groundwater or flow and contamination problems.

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A Study on the Biotope Evaluation and Classification of Urban Forests for Landscape Ecological Management (경관생태학적 도시숲 관리를 위한 비오톱 평가지표 및 유형 분류에 관한 연구)

  • Oh, Jeong-Hak;Cho, Jae-Hyung;Cho, Hyun-Je;Choi, Myoung-Sub;Kwon, Jino
    • Journal of the Korean Association of Geographic Information Studies
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    • v.11 no.4
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    • pp.101-111
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    • 2008
  • To provide more natural elements in the harsh urban environment, 'planting trees as urban forests' has been emphasized as having an important role, and trees are expected to be as functional as the trees under more natural conditions in rural areas, and provide people with benefits. To do this, urban forest policies needed a better idea of planting methods and management of trees through the theory of landscape ecology, and also the feedback system according to the evaluation and assessment of urban forests. In this case study, a new principle and assessment indices for the evaluation are applied for the 4 urban forests in two Korean metropolitan cities, Daejeon and Ulsan. The evaluation of Korean urban forest-function as biotope and the assessment for the classification of biotope diversity types are carried out. The AUEM(Adding Up Estimation Matrix) is applied for the analysis of urban forests. Unlikely previous researches on the other Korean metropolitan cities, the size of urban forest has less influence on the vegetation diversity. The most frequent biotope grade is the 3rd grade at Namseon park and Mt. Hamwol, while Mt. Bomun and Mt. Yeompo show the 4th grade. The grades of forest-function as biotope are from 3rd to 5th in which lower than average in forest-function grades. This means that the 4 sites are still not-matured forests and less-functional forests as the urban biotope.

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The Analysis of Forest Successional Trend by Species Replacement Model in the Natural Forest (천연림의 수종 대치 작용 모델에 의한 산림천이 경향 분석)

  • 김지홍
    • Journal of Korea Foresty Energy
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    • v.22 no.3
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    • pp.1-10
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    • 2003
  • The successional status and potential natural vegetation were examined in the natural deciduous forest in Mt. Chombong area. The examination was based on the subsequent process of generation replacement by understory saplings for the dominant canopy trees within 106 20mx20m square sample plots. The transition matrix model, which was modified from mathematical theory of Markov chain, was employed to analyze the successional status of the study forest. The model suggests that study forest is still seral, and it is considered to be more than 500 years away from the steady state or climax in terms of species composition. The simulations predict a remarkable decrease in the proportion of species composition of the present dominant Quercus mongolica and Kalopanax pictus from current 42.6% and 8.1% to less than 13.3% and 0.5%, respectively, at the steady state. On the contrary, the proportions of Abies holophylla, Acer mono, Fraxinus mandshurica, Tilia amurensis, and Acer pseudo-sieboldianum will increase at the steady state. The change of predicted composition ratio was generally coincide with the result of tolerance index to be compared with the study model. The hypothesis and sensitivity of the model were also discussed to evaluate the applicability to the real situation. The overall results indicated that the present dynamics of the forest must reflect the seral state due to previous disturbance mainly by human related interference.

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Topology Design Optimization of Plate Buckling Problems Considering Buckling Performance (좌굴성능을 고려한 평판 좌굴문제의 위상설계최적화)

  • Lee, Seung-Wook;Ahn, Seung-Ho;Cho, Seonho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.28 no.5
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    • pp.441-449
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    • 2015
  • In this paper we perform a linearized buckling analysis using the Kirchhoff plate theory and the von Karman nonlinear strain-displacement relation. Design sensitivity analysis(DSA) expressions for plane elasticity and buckling problems are derived with respect to Young's modulus and thickness. Using the design sensitivity, we can formulate the topology optimization method for minimizing the compliance and maximizing eigenvalues. We develop a topology optimization method applicable to plate buckling problems using the prestress for buckling analysis. Since the prestress is needed to assemble the stress matrix for buckling problem using the von Karman nonlinear strain, we introduced out-of-plane motion. The design variables are parameterized into normalized bulk material densities. The objective functions are the minimum compliance and the maximum eigenvalues and the constraint is the allowable volume. Through several numerical examples, the developed DSA method is verified to yield very accurate sensitivity results compared with the finite difference ones and the topology optimization yields physically meaningful results.

Hierarchical Visualization of the Space of Facial Expressions (얼굴 표정공간의 계층적 가시화)

  • Kim Sung-Ho;Jung Moon-Ryul
    • Journal of KIISE:Computer Systems and Theory
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    • v.31 no.12
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    • pp.726-734
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    • 2004
  • This paper presents a facial animation method that enables the user to select a sequence of facial frames from the facial expression space, whose level of details the user can select hierarchically Our system creates the facial expression space from about 2400 captured facial frames. To represent the state of each expression, we use the distance matrix that represents the distance between pairs of feature points on the face. The shortest trajectories are found by dynamic programming. The space of facial expressions is multidimensional. To navigate this space, we visualize the space of expressions in 2D space by using the multidimensional scaling(MDS). But because there are too many facial expressions to select from, the user faces difficulty in navigating the space. So, we visualize the space hierarchically. To partition the space into a hierarchy of subspaces, we use fuzzy clustering. In the beginning, the system creates about 10 clusters from the space of 2400 facial expressions. Every tine the level increases, the system doubles the number of clusters. The cluster centers are displayed on 2D screen and are used as candidate key frames for key frame animation. The user selects new key frames along the navigation path of the previous level. At the maximum level, the user completes key frame specification. We let animators use the system to create example animations, and evaluate the system based on the results.