• Title/Summary/Keyword: difference operator

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Recognition of Car License Plates Using Difference Operator and ART2 Algorithm (차 연산과 ART2 알고리즘을 이용한 차량 번호판 통합 인식)

  • Kim, Kwang-Baek;Kim, Seong-Hoon;Woo, Young-Woon
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.13 no.11
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    • pp.2277-2282
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    • 2009
  • In this paper, we proposed a new recognition method can be used in application systems using morphological features, difference operators and ART2 algorithm. At first, edges are extracted from an acquired car image by a camera using difference operators and the image of extracted edges is binarized by a block binarization method. In order to extract license plate area, noise areas are eliminated by applying morphological features of new and existing types of license plate to the 8-directional edge tracking algorithm in the binarized image. After the extraction of license plate area, mean binarization and mini-max binarization methods are applied to the extracted license plate area in order to eliminated noises by morphological features of individual elements in the license plate area, and then each character is extracted and combined by Labeling algorithm. The extracted and combined characters(letter and number symbols) are recognized after the learning by ART2 algorithm. In order to evaluate the extraction and recognition performances of the proposed method, 200 vehicle license plate images (100 for green type and 100 for white type) are used for experiment, and the experimental results show the proposed method is effective.

OSCILLATIONS FOR EVEN-ORDER NEUTRAL DIFFERENCE EQUATIONS

  • Zhou, Zhan;Yu, Jianshe;Lei, Guanglong
    • Journal of applied mathematics & informatics
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    • v.7 no.3
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    • pp.833-842
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    • 2000
  • Consider the even-order neutral difference equation (*) ${\delta}^m(x_n{-}p_ng(x_{n-k}))-q_nh(x_{n-1})=0$, n=0,1,2,... where $\Delta$ is the forward difference operator, m is even, ${-p_n},{q_n}$ are sequences of nonnegative real numbers, k, l are nonnegative integers, g(x), h(x) ${\in}$ C(R, R) with xg(x) > 0 for $x\;{\neq}\;0$. In this paper, we obtain some linearized oscillation theorems of (*) for $p_n\;{\in}\;(-{\infty},0)$ which are discrete results of the open problem by Gyori and Ladas.

MULTIPLICITY RESULTS FOR A CLASS OF SECOND ORDER SUPERLINEAR DIFFERENCE SYSTEMS

  • Zhang, Guoqing;Liu, Sanyang
    • Bulletin of the Korean Mathematical Society
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    • v.43 no.4
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    • pp.693-701
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    • 2006
  • Using Minimax principle and Linking theorem in critical point theory, we prove the existence of two nontrivial solutions for the following second order superlinear difference systems $$(P)\{{\Delta}^2x(k-1)+g(k,y(k))=0,\;k{\in}[1,\;T],\;{\Delta}^2y(k-1)+f(k,\;x(k)=0,\;k{\in}[1,\;T],\;x(0)=y(0)=0,\;x(T+1)=y(T+1)=0$$ where T is a positive integer, [1, T] is the discrete interval {1, 2,..., T}, ${\Delat}x(k)=x(k+1)-x(k)$ is the forward difference operator and ${\Delta}^2x(k)={\Delta}({\Delta}x(k))$.

A New Approach for the Derivation of a Discrete Approximation Formula on Uniform Grid for Harmonic Functions

  • Kim, Philsu;Choi, Hyun Jung;Ahn, Soyoung
    • Kyungpook Mathematical Journal
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    • v.47 no.4
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    • pp.529-548
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    • 2007
  • The purpose of this article is to find a relation between the finite difference method and the boundary element method, and propose a new approach deriving a discrete approximation formula as like that of the finite difference method for harmonic functions. We develop a discrete approximation formula on a uniform grid based on the boundary integral formulations. We consider three different boundary integral formulations and derive one discrete approximation formula on the uniform grid for the harmonic function. We show that the proposed discrete approximation formula has the same computational molecules with that of the finite difference formula for the Laplace operator ${\nabla}^2$.

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UNIQUENESS RELATED TO HIGHER ORDER DIFFERENCE OPERATORS OF ENTIRE FUNCTIONS

  • Xinmei Liu;Junfan Chen
    • The Pure and Applied Mathematics
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    • v.30 no.1
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    • pp.43-65
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    • 2023
  • In this paper, by using the difference analogue of Nevanlinna's theory, the authors study the shared-value problem concerning two higher order difference operators of a transcendental entire function with finite order. The following conclusion is proved: Let f(z) be a finite order transcendental entire function such that λ(f - a(z)) < ρ(f), where a(z)(∈ S(f)) is an entire function and satisfies ρ(a(z)) < 1, and let 𝜂(∈ ℂ) be a constant such that ∆𝜂n+1 f(z) ≢ 0. If ∆𝜂n+1 f(z) and ∆𝜂n f(z) share ∆𝜂n a(z) CM, where ∆𝜂n a(z) ∈ S ∆𝜂n+1 f(z), then f(z) has a specific expression f(z) = a(z) + BeAz, where A and B are two non-zero constants and a(z) reduces to a constant.

GENERALIZED 𝛼-KÖTHE TOEPLITZ DUALS OF CERTAIN DIFFERENCE SEQUENCE SPACES

  • Sandeep Gupta;Ritu;Manoj Kumar
    • Korean Journal of Mathematics
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    • v.32 no.2
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    • pp.219-228
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    • 2024
  • In this paper, we compute the generalized 𝛼-Köthe Toeplitz duals of the X-valued (Banach space) difference sequence spaces E(X, ∆), E(X, ∆𝜐) and obtain a generalization of the existing results for 𝛼-duals of the classical difference sequence spaces E(∆) and E(∆𝜐) of scalars, E ∈ {ℓ, c, c0}. Apart from this, we compute the generalized 𝛼-Köthe Toeplitz duals for E(X, ∆r) r ≥ 0 integer and observe that the results agree with corresponding results for scalar cases.

RELATIONSHIPS AMONG CHARACTERISTIC FINITE ELEMENT METHODS FOR ADVECTION-DIFFUSION PROBLEMS

  • CHEN, ZHANGXIN
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.6 no.1
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    • pp.1-15
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    • 2002
  • Advection-dominated transport problems possess difficulties in the design of numerical methods for solving them. Because of the hyperbolic nature of advective transport, many characteristic numerical methods have been developed such as the classical characteristic method, the Eulerian-Lagrangian method, the transport diffusion method, the modified method of characteristics, the operator splitting method, the Eulerian-Lagrangian localized adjoint method, the characteristic mixed method, and the Eulerian-Lagrangian mixed discontinuous method. In this paper relationships among these characteristic methods are examined. In particular, we show that these sometimes diverse methods can be given a unified formulation. This paper focuses on characteristic finite element methods. Similar examination can be presented for characteristic finite difference methods.

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On the Properties of OWA Operator Weighting Functions with Constant Value of Orness

  • Ahn, Byeong-Seok
    • Proceedings of the Korean Operations and Management Science Society Conference
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    • 2005.10a
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    • pp.338-341
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    • 2005
  • In this paper, we present analytic forms of the ordered weighted averaging (OWA) operator weighting functions, each of which has properties of rank-based weights and a constant level of orness, irrespective of the number of objectives considered. These analytic forms provide significant advantages for generating OWA weights over previously reported methods. First, OWA weights can be efficiently generated by use of proposed weighting functions without solving a complicated mathematical program. Moreover, convex combinations of these specific OWA operators can be used to generate OWA operators with any predefined values of orness once specific values of orness are α priori stated by decision maker. Those weights have a property of constant level of orness as well. Finally, OWA weights generated at a predefined value of orness make almost no numerical difference with maximum entropy OWA weights in terms of dispersion.

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DERIVATIONS ON CR MANIFOLDS

  • Ryu, Jeong-Seog;Yi, Seung-Hun
    • Communications of the Korean Mathematical Society
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    • v.19 no.1
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    • pp.135-141
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    • 2004
  • We studied the relation between the tangential Cauchy-Riemann operator ${\={\partial}}_b$ CR-manifolds and the derivation $d^{{\pi}^{0,\;1}}$ associated to the natural projection map ${\pi}^{0.1}\;:\;TM\;{\bigotimes}\;{\mathbb{C}}\;=\;T^{1,0}\;{\bigoplus}\;T^{0,\;1}\;{\rightarrow}\;T^{0,\;1}$. We found that these two differential operators agree only on the space of functions ${\Omega}^0(M),\;unless\;T^{1,\;0}$ is involutive as well. We showed that the difference is a derivation, which vanishes on ${\Omega}^0(M)$, and it is induced by the Nijenhuis tensor associated to ${\pi}^{0.1}$.

Eulerian-Lagrangian Modeling of One-Dimensional Dispersion Equation in Nonuniform Flow (부등류조건에서 종확산방정식의 Eulerian-Lagrangian 모형)

  • 김대근;서일원
    • Journal of Environmental Science International
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    • v.11 no.9
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    • pp.907-914
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    • 2002
  • Various Eulerian-Lagrangian models for the one-dimensional longitudinal dispersion equation in nonuniform flow were studied comparatively. In the models studied, the transport equation was decoupled into two component parts by the operator-splitting approach; one part is governing advection and the other is governing dispersion. The advection equation has been solved by using the method of characteristics following fluid particles along the characteristic line and the results were interpolated onto an Eulerian grid on which the dispersion equation was solved by Crank-Nicholson type finite difference method. In the solution of the advection equation, Lagrange fifth, cubic spline, Hermite third and fifth interpolating polynomials were tested by numerical experiment and theoretical error analysis. Among these, Hermite interpolating polynomials are generally superior to Lagrange and cubic spline interpolating polynomials in reducing both dissipation and dispersion errors.