• Title/Summary/Keyword: Computer Algebra System

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Formal Semantics of Relational Algebra/Calculus for Spatiotemporal Operator in Spatiotemporal Data Model (시공간 데이터 모델에서 시공간 연산자의 관계 수식적 정형의미)

  • Jo, Yeong-So;Kim, Dong-Ho;Ryu, Geun-Ho
    • The Transactions of the Korea Information Processing Society
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    • v.6 no.1
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    • pp.11-20
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    • 1999
  • Because conventional spatial databases process the spatial information that is valid at current time, it is difficult to manage historical information efficiently which has been changed from the past to current. Recently, there are rapid increasing of interest to solve this problem so that makes databases to support historical information as well as spatial management at the same time. It can be eventually used in a various application areas. The formal semantics in a database is used to represent database structures and operations in order to prove the correctiveness of them in terms or mathematics. It also plays an important role in database to design a database and database management system. So in this paper, we suggest spatiotemporal domain, object, data, and spatiotemporal geometric/topological operations. And we not only formalize relational algebra/calculus using formal semantics for a spatiotemporal data model, but also show the example of real orld with them.

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Calculus of Communicating Systems Domain in PtolemyII (PtolemyII의 CCS 도메인)

  • 황혜정;김윤정;남기혁;김일곤;최진영
    • Journal of KIISE:Computer Systems and Theory
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    • v.31 no.5_6
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    • pp.335-346
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    • 2004
  • PtolemyII is an environment that supports heterogeneous modeling and design of concurrent systems such as embedded system. PtolemyII has several Domains which are physical rules to determine the way of communicating between components. PtolemyII has 11 domains such as PetriNet, Timed Multitasking, SR etc. Components of System can be specified using appropriate domains for their properties. Communicating Sequential Processes(CSP) is implemented as formally designed CSP domain, in PtolemyII. But CCS didn't be implemented as a domain. It is a kind of Process Algebra language which can be used for specifying and verifying concurrent systems formally. Thus, in this paper we implemented CCS domain. And that permitted developers using PtolemyII to use the same modeling pattern used in PtolemyII and to make system specifications in the base of the formal semantics of CCS. This caused the diversity of PtolemyII domains and the power of expression was improved. This paper will explain the structure of CCS domain implemented in PtolemyII and the way of implementing it.

Electromagnetic Behavior of High -$T_c$ Superconductors underthequenchstate -

  • 정동철;최효상;황종선;윤기웅;한병성
    • Progress in Superconductivity
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    • v.3 no.2
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    • pp.183-187
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    • 2002
  • In this paper we analyzed the electromagnetic behavior of high $-T_{c}$ superconductor under the quench state using finite element method. Poisson equation was used in finite element analysis as a governing equation and was solved using algebra equation using Gallerkin method. We first investigate d the electromagnetic behavior of U-type superconductor. Finally we applied our analysis techniques to 5.5 kVA meander-line superconducting fault current limiters (SFCL) which are currently developed by many power-system researcher in the world. Meshes of 14,600 elements were used in analysis of this SFCL. Analysis results show that the distribution of current density was concentrated to inner curvature in meander-line type-superconductors and maximum current density 14.61 $A/\m^2$ and also maximum Joule heat was 6,420 W/㎥. We concluded that this meander line-type SFCL was not pertinet fur uniform electromagnetic field distribution.n.

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Trajectory Controller Design of Mobile Robot based on Back-stepping Procedure (백 스테핑을 이용한 이동 로봇의 경로 제어기의 설계)

  • Lee, Ki-Cheol;Kho, Jae-Won;Park, Min-Yong
    • Proceedings of the KIEE Conference
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    • 2000.07d
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    • pp.2787-2789
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    • 2000
  • In this paper. the constructive modeling procedure of nonholonomic mobile robot system is carried out with the help of controllability Lie algebra used in differential geometry field. and their geometrical properties are also analyzed. And, a new trajectory controller is suggested to guarantee its convergence to reference trajectory. Design procedure of the suggested trajectory controller is back-stepping scheme which was introduced recently in nonlinear control theory. The performance of the proposed trajectory controller is verified via computer simulation. In the simulation the trajectory controller is applied to differentially driven robot system on the assumption that the trajectory planner be given.

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RICH INTERNET MATHEMATICAL SOLUTION SYSTEM

  • Song, Kee-Hong;Song, Tai-Sung
    • The Pure and Applied Mathematics
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    • v.14 no.2 s.36
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    • pp.85-90
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    • 2007
  • Arguably the most important internet technology of today is RIA (rich internet application), whose prime advantage is in improving the user experience on the web. However, the scope and variety of the RIA technology demand an eclectic guideline to build the mathematical services such as mathematical text, graphs, and animations. This paper sorts out and simplifies the complicated roadmap of the RIA technologies by presenting three design patterns for exposing the functionality of the CAS (computer algebra system) with the web browser as the user interface platform.

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A Note on the Relationship between IMTs and the Prototype Design of Computer Applications in the School Mathematics (수학 교수-학습을 위한 컴퓨터 응용 프로그램 모형설계에 따른 대화형 실행매체(IMTs)의 작성에 관한 소고)

  • 허만성;박용범;김부윤
    • Journal of Educational Research in Mathematics
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    • v.9 no.1
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    • pp.321-332
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    • 1999
  • This article made overtures of the relationship between interactive mathematics texts nd the prototype design of computer application with Computer Algebra System Math. Engine, linking together in the school mathematics. School teachers and researchers would try to construct mathematical materials with computers in educating students in the middle and high school grades. As the individual users come to manage hyper-media materials, so they meet with the problem of 'Who does control?'A mass user would be concerned with interactive mathematics materials directly or off-line at realtime and manipulate the process of problem-solving symbolically with MathView/sup 11)/ and ON-Math/sup 12)/. Discussion was made in developing the factor in the domestic situation and reaching out their hands for it. In conclusion, a user may reform the information of math-curriculum limitedly.

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DEGREE OF VERTICES IN VAGUE GRAPHS

  • BORZOOEI, R.A.;RASHMANLOU, HOSSEIN
    • Journal of applied mathematics & informatics
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    • v.33 no.5_6
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    • pp.545-557
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    • 2015
  • A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we define two new operation on vague graphs namely normal product and tensor product and study about the degree of a vertex in vague graphs which are obtained from two given vague graphs G1 and G2 using the operations cartesian product, composition, tensor product and normal product. These operations are highly utilized by computer science, geometry, algebra, number theory and operation research. In addition to the existing operations these properties will also be helpful to study large vague graph as a combination of small, vague graphs and to derive its properties from those of the smaller ones.

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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Modeling and Implementation for Generic Spatio-Temporal Incorporated Information (시간 공간 통합 본원적 데이터 모델링 및 그 구현에 관한 연구)

  • Lee Wookey
    • Journal of Information Technology Applications and Management
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    • v.12 no.1
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    • pp.35-48
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    • 2005
  • An architectural framework is developed for integrating geospatial and temporal data with relational information from which a spatio-temporal data warehouse (STDW) system is built. In order to implement the STDW, a generic conceptual model was designed that accommodated six dimensions: spatial (map object), temporal (time), agent (contractor), management (e.g. planting) and tree species (specific species) that addressed the 'where', 'when', 'who', 'what', 'why' and 'how' (5W1H) of the STDW information, respectively. A formal algebraic notation was developed based on a triplet schema that corresponded with spatial, temporal, and relational data type objects. Spatial object structures and spatial operators (spatial selection, spatial projection, and spatial join) were defined and incorporated along with other database operators having interfaces via the generic model.

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CLASSIFICATION OF BETTI DIAGRAMS OF VARIETIES OF ALMOST MINIMAL DEGREE

  • Lee, Wan-Seok;Park, Eui-Sung
    • Journal of the Korean Mathematical Society
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    • v.48 no.5
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    • pp.1001-1015
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    • 2011
  • In this article we study the problem to determine all occurring Betti diagrams of varieties $X{\subset}\mathbb{P}^r$ of almost minimal degree, i.e. deg(X) = codim(X; $\mathbb{P}^r$)+2. We describe a realistic picture of how many different kind of Betti diagrams exist at all (Theorem 3.1). By means of the computer algebra system "SINGULAR", we obtain a complete list of all occurring Betti diagrams in the cases where codim$(X,\mathbb{P}^r){\leq}8$.