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Explicit expression of the Krawtchouk polynomial via a discrete Green's function
김길천,이윤진 대한수학회 2013 대한수학회지 Vol.50 No.3
A Krawtchouk polynomial is introduced as the classical Mac-Williams identity, which can be expressed in weight-enumerator-free formof a linear code and its dual code over a Hamming scheme. In thispaper we find a new explicit expression for the p-number and the q-number, which are more generalized notions of the Krawtchouk poly-nomial in the P-polynomial schemes by using an extended version of adiscrete Green’s function. As corollaries, we obtain a new expression ofthe Krawtchouk polynomial over the Hamming scheme and the Eber-lein polynomial over the Johnson scheme. Furthermore, we find anotherversion of the MacWilliams identity over a Hamming scheme.
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Cyclic Codes of Even Length over $\mathbb Z_4$
우성식 대한수학회 2007 대한수학회지 Vol.44 No.3
In cite{8}, we showed that any ideal of mathbbZ_4[X]/(X^{2^n}-1) is generated by at most two polynomials of thestandard forms. The purpose of this paper is to find a descriptionof the cyclic codes of even length over mathbb Z_4 namely theideals of mathbb Z_4[X]/(X^l-1), where l is an even integer.
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김회섭,김상동,이용훈 대한수학회 2007 대한수학회지 Vol.44 No.3
We investigate the eigenvalues of the semi-circulantpreconditioned matrix for the finite difference schemecorresponding to the second-order elliptic operatorwith the variable coefficients given byL_v u := -Delta u + a(x,y) u_x + b(x,y) u_y + d(x,y) u,where a and b are continuously differentiable functionsand d is a positive bounded function.The semi-circulant preconditioning operator L_c u is constructedby using the leading term of L_v u plus the constant reaction term suchthat L_c u:= -Delta u + d_c u.Using the field of values arguments,we show that the eigenvalues of the preconditioned matrix areclustered at some number. Some numerical evidences are also provided.
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Asymptotic normality of estimator in non-parametric model under censored samples
Si-Li Niu,Qian-Ru Li 대한수학회 2007 대한수학회지 Vol.44 No.3
Consider the regression modelY_i=g(x_i)+e_i for i=1,2,ldots, n,where: (1) x_i are fixed design points, (2) e_i are independentrandom errors with mean zero, (3) g(cdot) is unknown regressionfunction defined on [0,1]. Under Y_i are censored randomly, wediscuss the asymptotic normality of the weighted kernel estimatorsof g when the censored distribution function is known or unknown.
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Criticality of characteristic vector fields on almost cosymplectic manifolds
박홍경,김태완 대한수학회 2007 대한수학회지 Vol.44 No.3
Main interest of the present paper is to investigate thecriticality of characteristic vector fields on almost cosymplecticmanifolds. Killing critical characteristic vector fields areabsolute minima. This paper contains some examples of non-Killingcritical characteristic vector fields.
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Cycles through a given set of vertices in regular multipartite tournaments
Lutz Volkmann,Stefan Winzen 대한수학회 2007 대한수학회지 Vol.44 No.3
A tournament is an orientation of a complete graph, and in generala multipartite or c-partite tournament is an orientation of acomplete c-partite graph.In a recent article, the authors proved that a regular c-partitetournament with r ge 2 vertices in each partite set contains acycle with exactly r-1 vertices from each partite set, withexception of the case that c = 4 and r = 2. Here we willexamine the existence of cycles with r-2 vertices from eachpartite set in regular multipartite tournaments where the r-2vertices are chosen arbitrarily. Let D be a regular c-partitetournament and let X subseteq V(D) be an arbitrary set withexactly 2 vertices of each partite set. For all c ge 4 wewill determine the minimal value g(c) such that D-X isHamiltonian for every regular multipartite tournament with r geg(c).
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$\Pi$-coherent dimensions and $\Pi$-coherent rings
Lixin Mao 대한수학회 2007 대한수학회지 Vol.44 No.3
R is called a right Pi-coherent ring in case every finitelygenerated torsionless right R-module is finitely presented. Inthis paper, we define a dimension for rings, calledPi-coherent dimension, which measures how far away a ring isfrom being Pi-coherent. This dimension has nice properties whenthe ring in question is coherent. In addition, we study someproperties of Pi-coherent rings in terms of preenvelopes andprecovers.
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Discrete conditions for the holonomy group of a pair of pants
김홍찬 대한수학회 2007 대한수학회지 Vol.44 No.3
A pair of pants Sigma(0,3) is a building block of orientedsurfaces. The purpose of this paper is to determine thediscrete conditions for the holonomy group piof hyperbolic structure of a pair of pants.For this goal, we classify the relationsbetween the locations of principal lines and entries of hyperbolicmatrices in PSL(2,R).In the level of the matrix group SL(2,R), we will showthat the signs of traces of hyperbolic elementsplay a very important role to determinethe discreteness of holonomy group of a pair of pants.
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H\"older convergence of the weak solution to an evolution equation of $p$-Ginzburg-Landau type
Yutian Lei 대한수학회 2007 대한수학회지 Vol.44 No.3
The author studies the local H"older convergence of the solution toan evolution equation of p-Ginzburg-Landau type, to the heat flowof the p-harmonic map, when the parameter tends to zero. Theconvergence is derived by establishing a uniform gradient estimationfor the solution of the regularized equation.
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Persistence of Periodic Trajectories of Planar Systems under two Parametric Perturbations
Zahra Afsharnejad,Omid RabieiMotlagh 대한수학회 2007 대한수학회지 Vol.44 No.3
We consider a two parametric family of the planar systems with theformbegin{eqnarray*}dot{x}&=&P(x,y)+epsilon_1 p_1(x,y)+epsilon_2 p_2(x,y),dot{y}&=&Q(x,y)+epsilon_1 q_1(x,y)+epsilon_2 q_2(x,y),end{eqnarray*}where the unperturbed equation(epsilon_1=epsilon_2=0) is assumed to have at least oneperiodic solution or limit cycle. Our aim here is to study thebehavior of the system under two parametric perturbations; infact, using the Poincare - Andronov technique, we imposeconditions on the system which guarantee persistence of theperiodic trajectories. At the end, we apply the result on the Vander Pol equation ; where, we consider the effect of nonlineardamping on the equation. Also the Hopf bifurcation for the Vander Pol equation will be investigated.
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