- P-ISSN1226-0657
- E-ISSN2287-6081
- KCI
17권 4호
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Abstract
We introduce the concepts of strongly <TEX>$s{\gamma}$</TEX>-closed graph, <TEX>$s{\gamma}$</TEX>-compactness and <TEX>$s{\gamma}-T_2$</TEX> space and study the relationships between such concepts and weakly <TEX>$s{\gamma}$</TEX>-continuous functions.
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A one-holed torus <TEX>${\Sigma}$</TEX>(l, 1) is a building block of oriented surfaces. In this paper we formulate the matrix presentations of the holonomy group of a one-holed torus <TEX>${\Sigma}$</TEX>(1, 1) by the gluing method. And we present an algorithm for deciding the discreteness of the holonomy group of <TEX>${\Sigma}$</TEX>(1, 1).
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In this paper, we propose a second-order prediction/correction (SPC) domain decomposition method for solving one dimensional linear hyperbolic partial differential equation <TEX>$u_{tt}+a(x,t)u_t+b(x,t)u=c(x,t)u_{xx}+{\int}(x,t)$</TEX>. The method can be applied to variable coefficients problems and singular problems. Unconditional stability and error analysis of the method have been carried out. Numerical results support stability and efficiency of the method.
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In this article we consider axes of a complete embedded minimal surface in <TEX>$R^3$</TEX> of finite total curvature, and then prove that there is no planar ends at which the Gauss map have the minimum branching order if the minimal surface has a single axis.
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We provide a new semilocal convergence analysis of the Gauss-Newton method (GNM) for solving nonlinear equation in the Euclidean space. Using our new idea of recurrent functions, and a combination of center-Lipschitz, Lipschitz conditions, we provide under the same or weaker hypotheses than before [7]-[13], a tighter convergence analysis. The results can be extented in case outer or generalized inverses are used. Numerical examples are also provided to show that our results apply, where others fail [7]-[13].
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In this paper, we experiment image warping and morphing. In image warping, we use radial basis functions : Thin Plate Spline, Multi-quadratic and Gaussian. Then we obtain the fact that Thin Plate Spline interpolation of the displacement with reverse mapping is the efficient means of image warping. Reflecting the result of image warping, we generate two examples of image morphing.
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Abstract
We estimate the real rank of a composition series of closed ideals of a <TEX>$C^*$</TEX>-algebra such that its subquotients have continuous trace, which is equivalent to that the <TEX>$C^*$</TEX>-algebra is of type I.
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Abstract
Category <TEX>$E({\Omega},A)$</TEX> forms a topos. We study on some properties of the topos <TEX>$E({\Omega},A)$</TEX>. In particular, we show that <TEX>$E({\Omega},A)$</TEX> is well-pointed.
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Abstract
Exton [Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), 113~119] introduced 20 distinct triple hypergeometric functions whose names are <TEX>$X_i$</TEX> (i = 1, ..., 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions <TEX>$_oF_1$</TEX>, <TEX>$_1F_1$</TEX>, a Humbert function <TEX>${\Psi}_2$</TEX>, a Humbert function <TEX>${\Phi}_2$</TEX>. The object of this paper is to present 16 (presumably new) integral representations of Euler type for the Exton hypergeometric function <TEX>$X_2$</TEX> among his twenty <TEX>$X_i$</TEX> (i = 1, ..., 20), whose kernels include the Exton function <TEX>$X_2$</TEX> itself, the Appell function <TEX>$F_4$</TEX>, and the Lauricella function <TEX>$F_C$</TEX>.
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In this note, we extend the Bresar and Vukman's result [1, Proposition 1.6], which is well-known, to higher left derivations as follows: let R be a ring. (i) Under a certain condition, the existence of a nonzero higher left derivation implies that R is commutative. (ii) if R is semiprime, every higher left derivation on R is a higher derivation which maps R into its center.
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In this paper we obtain the Hyers-Ulam stability of functional equations <TEX>$f(x+y)=f(x)+f(y)+In\;{\alpha}^{2xy-1}$</TEX> and <TEX>$f(x+y)=f(x)+f(y)+In\;{\beta(x,y)^{-1}$</TEX> which is related to the exponential and beta functions.
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We introduce mixed cubic-quartic functional equations. And using the fixed point method, we prove the generalized Hyers-Ulam stability of cubic-quartic functional equations on random normed spaces.
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We investigate the existence of homoclinic orbits of the following systems of <TEX>$Li{\'{e}}nard$</TEX> type: <TEX>$a(x)x^'=h(y)-F(x)$</TEX>, <TEX>$y^'$</TEX>=-a(x)g(x), where <TEX>$h(y)=m{\mid}y{\mid}^{p-2}y$</TEX> with m > 0 and p > 1 and a, F, 9 are continuous functions such that a(x) > 0 for all <TEX>$x{\in}{\mathbb{R}}$</TEX> and F(0)=g(0)=0 and xg(x) > 0 for <TEX>$x{\neq}0$</TEX>. By a series of time and coordinates transformations of the above system, we obtain sufficient conditions for the positive orbits of the above system starting at the points on the curve h(y) = F(x) with x > 0 to approach the origin through only the first quadrant. The method of this paper is new and the results of this paper cover some early results on this topic.
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In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: <TEX>$f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$</TEX> <TEX>${\lambda}$</TEX>: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.