• 제목/요약/키워드: discrete mathematics

검색결과 459건 처리시간 0.026초

ASYMPTOTIC EQUIVALENCE OF VOLTERRA DIFFERENCE SYSTEMS

  • Choi, Sung Kyu;Kim, Jin Soon;Koo, Namjip
    • 충청수학회지
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    • 제20권3호
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    • pp.311-320
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    • 2007
  • We obtain a discrete analogue of Nohel's result in [5] about asymptotic equivalence between perturbed Volterra system and unperturbed system.

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TI-92 계산기를 활용한 이산수학의 이해과정 탐구-「행렬과 그래프」단원을 중심으로- (An Inquiry on the Understanding Process of Discrete Mathematics using TI-92 Calculator - Matrix and Graph-)

  • 강윤수;이보라
    • 한국학교수학회논문집
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    • 제7권2호
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    • pp.81-97
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    • 2004
  • 본 논문은 그래픽 계산기를 활용한 이산수학의 ‘행렬과 그래프’개념의 이해과정에 관한 연구이다. 본 연구의 목적을 위해 우리는 TI-92 계산기를 활용하여 ‘행렬과 그래프’ 개념을 학습해 가는 두 명의 중학생을 조사하였다. 이 과정에서 우리는 켐코더나 녹음기를 활용하여 질적자료를 수집하였으며 이 자료들을 테크놀로지에 관한 학생들의 태도, 용어의 의미 이해, 행렬 연산의 이해 과정, 수학적 의사소통 등으로 범주화하였다. 이로부터 우리는 다음과 같은 결론을 얻었다. 첫째, 학생들은 그래픽 계산기를 활용하여 행렬의 의미와 역할을 그들 스스로 탐구하였으며 계산기는 이 과정에서 훌륭한 학습동반자 역할을 수행하였다. 둘째, 탐구과정에서 학생들이 오류를 범했을 때 그래픽 계산기가 에러메시지를 곧바로 출력함으로써 학생들의 자기주도적 학습을 가능하게 하였다. 셋째, 계산기는 교사와 학생들간, 혹은 학생들 사이의 수학적 의사소통을 강화시키는 역할을 하였다.

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DISCRETE SOBOLEV ORTHOGONAL POLYNOMIALS AND SECOND ORDER DIFFERENCE EQUATIONS

  • Jung, H.S.;Kwon, K.H.;Lee, D.W.
    • 대한수학회지
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    • 제36권2호
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    • pp.381-402
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    • 1999
  • Let {Rn($\chi$)}{{{{ { } atop {n=0} }}}} be a discrete Sobolev orthogonal polynomials (DSOPS) relative to a symmetric bilinear form (p,q)={{{{ INT _{ } }}}} pqd$\mu$0 +{{{{ INT _{ } }}}} p qd$\mu$1, where d$\mu$0 and d$\mu$1 are signed Borel measures on . We find necessary and sufficient conditions for {Rn($\chi$)}{{{{ { } atop {n=0} }}}} to satisfy a second order difference equation 2($\chi$) y($\chi$)+ 1($\chi$) y($\chi$)= ny($\chi$) and classify all such {Rn($\chi$)}{{{{ { } atop {n=0} }}}}. Here, and are forward and backward difference operators defined by f($\chi$) = f($\chi$+1) - f($\chi$) and f($\chi$) = f($\chi$) - f($\chi$-1).

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GENERATING SAMPLE PATHS AND THEIR CONVERGENCE OF THE GEOMETRIC FRACTIONAL BROWNIAN MOTION

  • Choe, Hi Jun;Chu, Jeong Ho;Kim, Jongeun
    • 대한수학회보
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    • 제55권4호
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    • pp.1241-1261
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    • 2018
  • We derive discrete time model of the geometric fractional Brownian motion. It provides numerical pricing scheme of financial derivatives when the market is driven by geometric fractional Brownian motion. With the convergence analysis, we guarantee the convergence of Monte Carlo simulations. The strong convergence rate of our scheme has order H which is Hurst parameter. To obtain our model we need to convert Wick product term of stochastic differential equation into Wick free discrete equation through Malliavin calculus but ours does not include Malliavin derivative term. Finally, we include several numerical experiments for the option pricing.

EXISTENCE AND GLOBAL EXPONENTIAL STABILITY OF A PERIODIC SOLUTION TO DISCRETE-TIME COHEN-GROSSBERG BAM NEURAL NETWORKS WITH DELAYS

  • Zhang, Zhengqiu;Wang, Liping
    • 대한수학회지
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    • 제48권4호
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    • pp.727-747
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    • 2011
  • By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the existence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the existence and global exponential stability of periodic solution, the assumptions in existing papers that the value of activation functions at zero is zero are removed.

OPTIMAL L2-ERROR ESTIMATES FOR EXPANDED MIXED FINITE ELEMENT METHODS OF SEMILINEAR SOBOLEV EQUATIONS

  • Ohm, Mi Ray;Lee, Hyun Young;Shin, Jun Yong
    • 대한수학회지
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    • 제51권3호
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    • pp.545-565
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    • 2014
  • In this paper we derive a priori $L^{\infty}(L^2)$ error estimates for expanded mixed finite element formulations of semilinear Sobolev equations. This formulation expands the standard mixed formulation in the sense that three variables, the scalar unknown, the gradient and the flux are explicitly treated. Based on this method we construct finite element semidiscrete approximations and fully discrete approximations of the semilinear Sobolev equations. We prove the existence of semidiscrete approximations of u, $-{\nabla}u$ and $-{\nabla}u-{\nabla}u_t$ and obtain the optimal order error estimates in the $L^{\infty}(L^2)$ norm. And also we construct the fully discrete approximations and analyze the optimal convergence of the approximations in ${\ell}^{\infty}(L^2)$ norm. Finally we also provide the computational results.

ON DISCRETE GROUPS

  • Cho, Young-Hyun;Chung, Jae-Myung
    • 대한수학회논문집
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    • 제9권2호
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    • pp.271-274
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    • 1994
  • The concept of a continuous module is a generalization of that of an injective module, and conditions ($C_1$), (C$_2$) and ($C_3$) are given for this concept in [4]. In this paper, we study modules with properties that are dual to continuity. These will be called discrete and we discuss discrete abelian groups. Throughout R is a ring with identity, M is a module over R, G is an abelian group of finite rank, E is the ring of endomorphisms of G and S is the center of E. Dual to the notion of essential submodules, we define small submodules of a module M over R.(omitted)

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EXPLICIT EXPRESSION OF THE KRAWTCHOUK POLYNOMIAL VIA A DISCRETE GREEN'S FUNCTION

  • Kim, Gil Chun;Lee, Yoonjin
    • 대한수학회지
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    • 제50권3호
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    • pp.509-527
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    • 2013
  • A Krawtchouk polynomial is introduced as the classical Mac-Williams identity, which can be expressed in weight-enumerator-free form of a linear code and its dual code over a Hamming scheme. In this paper we find a new explicit expression for the $p$-number and the $q$-number, which are more generalized notions of the Krawtchouk polynomial in the P-polynomial schemes by using an extended version of a discrete Green's function. As corollaries, we obtain a new expression of the Krawtchouk polynomial over the Hamming scheme and the Eberlein polynomial over the Johnson scheme. Furthermore, we find another version of the MacWilliams identity over a Hamming scheme.

MARKOVIAN EARLY ARRIVAL DISCRETE TIME JACKSON NETWORKS

  • Aboul-Hassan A.;Rabia S.I.
    • Journal of the Korean Statistical Society
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    • 제35권3호
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    • pp.281-303
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    • 2006
  • In an earlier work, we investigated the problem of using linear programming to bound performance measures in a discrete time Jackson network. There it was assumed that the system evolution is controlled by the early arrival scheme. This assumption implies that the system can't be modelled by a Markov chain. This problem was resolved and performance bounds were calculated. In the present work, we use a modification of the early arrival scheme (without corrupting it) in order to make the system evolves as a Markov chain. This modification enables us to obtain explicit expressions for certain moments that could not be calculated explicitly in the pure early arrival scheme setting. Moreover, this feature implies a reduction in the linear program size as well as the computation time. In addition, we obtained tighter bounds than those appeared before due to the new setting.