• 제목/요약/키워드: linear algebra

검색결과 283건 처리시간 0.024초

HYERS-ULAM-RASSIAS STABILITY OF ISOMORPHISMS IN C*-ALGEBRAS

  • Park, Choonkil
    • 충청수학회지
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    • 제19권2호
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    • pp.159-175
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    • 2006
  • This paper is a survey on the Hyers-Ulam-Rassias stability of the Jensen functional equation in $C^*$-algebras. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300. Its content is divided into the following sections: 1. Introduction and preliminaries. 2. Approximate isomorphisms in $C^*$-algebras. 3. Approximate isomorphisms in Lie $C^*$-algebras. 4. Approximate isomorphisms in $JC^*$-algebras. 5. Stability of derivations on a $C^*$-algebra. 6. Stability of derivations on a Lie $C^*$-algebra. 7. Stability of derivations on a $JC^*$-algebra.

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Piaget의 개념 발달의 메커니즘과 대수의 역사 (Piaget's Mechanism of the Development of Concepts and the History of Algebra)

  • 민세영
    • 대한수학교육학회지:수학교육학연구
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    • 제8권2호
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    • pp.485-494
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    • 1998
  • This study is on the theory of Piaget's reflective abstraction and the mechanism of the development of knowledge and the history of algebra and its application to understand the difficulties that many students have in learning algebra. Piaget considers the development of knowledge as a linear process. The stages in the construction of different forms of knowledge are sequential and each stage begins with reorganization. The reorganization consists of the projection onto a higher level from the lower level and the reflection which reconstructs and reorganizes within a lager system that is transferred by profection. Piaget shows that the mechanisms mediating transitions from one historical period to the next are analogous to those mediating the transition from one psychogenetic stage to the next and characterizes the mechanism as the intra, inter, trans sequence. The historical development of algebra is characterized by three periods, which are intra inter, transoperational. The analysis of the history of algebra by the mechanism explains why the difficulties that students have in learning algebra occur and shows that the roles of teachers are important to help students to overcome the difficulties.

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자동차 엔진의 운동변위 결정을 위한 선형행렬연산법 (A Method Using Linear Matrix Algebra for Determination of Engine Motion in Automobile)

  • 고병갑;이완익;박경진;하성규
    • 한국자동차공학회논문집
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    • 제2권1호
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    • pp.116-127
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    • 1994
  • A method using the linear matrix algebra is developed in order to determine unknown external forces in linear structural analyses. The method defines a matrix which represents the linearity of the vibrational analysis for a structural system. The unknown external forces are determined by the operations of the matrix. The method is applied to find an engine motion in an automobile system. For a simulation process, an exhaust system is modeled and analyzed by the finite element method. The validity of the simulation is verified by comparing with the experimental results the free vibration. Also, an experiment on the forced vibration is performed to determine the damping ratio of the exhaust sysetm. Estimated model parameters(natural frequency, mode shape) are in accord with the experimental results. Because the method merely repeats the transpose and inverse operations of a matrix, the solution is extremely easy and simple. Moreover, it is more accurate than the existing methods in that there is no artificial assumptions in the calculation processes. Therefore, the method is found to be reliable for the analysis of the exhaust system considering the characteristics of vibrations. Although the suggested method is tested by only the exhaust system here, it can be applied to general structures.

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ON DERIVATIONS IN NONCOMMUTATIVE SEMISIMPLE BANACH ALGEBRAS

  • Jung, Yong-Soo
    • 대한수학회보
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    • 제35권3호
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    • pp.583-590
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    • 1998
  • The purpose of this paper is to prove the following results: Let A be a noncommutative semisimple Banach algebra. (1) Suppose that a linear derivation D : A $\to A$ is such that [D(x),x]x=0 holds for all $x \in A$. Then we have D=0. (2) Suppose that a linear derivation $D:A\to A$ is such that $D(x)x^2 + x^2D(x)=0$ holds for all $x \in A$. Then we have C=0.

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EXTREME SETS OF RANK INEQUALITIES OVER BOOLEAN MATRICES AND THEIR PRESERVERS

  • Song, Seok Zun;Kang, Mun-Hwan;Jun, Young Bae
    • 대한수학회논문집
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    • 제28권1호
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    • pp.1-9
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    • 2013
  • We consider the sets of matrix ordered pairs which satisfy extremal properties with respect to Boolean rank inequalities of matrices over nonbinary Boolean algebra. We characterize linear operators that preserve these sets of matrix ordered pairs as the form of $T(X)=PXP^T$ with some permutation matrix P.

LINEAR JORDAN DERIVATIONS ON NONCOMMUTATIVE BANACH ALGEBRAS

  • Byun, Sang-Hoon
    • 충청수학회지
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    • 제11권1호
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    • pp.115-121
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    • 1998
  • The purpose of this paper is to prove the following result: Let A be a noncom mutative Banach algebra. Suppose that there exist continuous linear Jordan derivations $D:A{\rightarrow}A$, $G:A{\rightarrow}A$ such that [$D^2(x)+G(x)$, $x^n$] lies in the Jacobson radical of A for all $x{\in}A$. Then $D(A){\subset}rad(A)$ and $G(A){\subset}rad(A)$.

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A RESULT OF LINEAR JORDAN DERIVATIONS ON NONCOMMUTATIVE BANACH ALGEBRAS

  • Chang, Ick-Soon
    • 충청수학회지
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    • 제11권1호
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    • pp.123-128
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    • 1998
  • The purpose of this paper is to prove the following result: Let A be a noncom mutative Banach algebra. Suppose that $D:A{\rightarrow}A$ is a continuous linear Jordan derivation such that $D^2(x)D(x)^2{\in}rad(A)$ for all $x{\in}A$. Then D maps A into its radical.

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LINEAR JORDAN DERIVATIONS ON BANACH ALGEBRAS

  • Jung, Yong-Soo
    • Journal of applied mathematics & informatics
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    • 제5권2호
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    • pp.539-546
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    • 1998
  • Let A be a noncommutative Banach algebra. Suppose that a continuos linear Jordan derivation D:A$\longrightarrow$A is such that either $[D^2(\chi),\chi^2]\;or\;(D^2(\chi),\chi]+(D(\chi))^2$ lies in the jacobson radical of A for all $\chi$$\in$A. Then D(A) is contained in the Jacobson radical of A.

ON PERIODIC BOUNDARY VALUE PROBLEMS OF HIGHER ORDER NONLINEAR FUNCTIONAL DIFFERENCE EQUATIONS WITH p-LAPLACIAN

  • Liu, Yuji;Liu, Xingyuan
    • 대한수학회논문집
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    • 제24권1호
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    • pp.29-40
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    • 2009
  • Motivated by [Linear Algebra and its Appl. 420(2007), 218-227] and [Linear Algebra and its Appl. 425(2007), 171-183], we, in this paper, study the solvability of periodic boundary value problems of higher order nonlinear functional difference equations with p-Laplacian. Sufficient conditions for the existence of at least one solution of this problem are established.

바둑판을 이용한 흑백 게임의 최적해를 구하는 선형대수학 알고리즘 (Linear algebra algorithm for the optimal solution in the Blackout game)

  • 이상구;박종빈;양정모;김익표
    • 한국수학교육학회지시리즈A:수학교육
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    • 제43권1호
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    • pp.87-96
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    • 2004
  • For finding the optimal strategy in Blackout game which was introduced in the homepage of popular mono "Beautiful mind", we develope a mathematical proof and an algorithm with a software. We only use the concept of basis and knowledge of basic linear algebra. This process can be extended to the fullsize Go table problem and shows why we have to study mathematics at the college level.

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