• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.321-338
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• 2008

Let $\bar{M}$ be a smoothly bounded pseudoconvex complex manifold with a family of almost complex structures $\{L^{\tau}\}_{{\tau}{\in}I}$, $0{\in}I$, which extend smoothly up to bM, the boundary of M, and assume that there is ${\lambda}{\in}C^{\infty}$(bM) which is strictly subharmonic with respect to the structure $L^0|_{bM}$ in any direction where the Levi-form vanishes on bM. We obtain explicit estimates for the $\bar{\partial}$-Neumann problem in Sobolev spaces both in space and parameter variables. Also we get a similar result when $\bar{M}$ is strongly pseudoconvex.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.101-108
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• 2008

In this paper we study the existence of global small solutions of the Cauchy problem for the non-isotropically perturbed nonlinear Schr$\"{o}$dinger equation: $iu_t\;+\;{\Delta}u\;+\;{\mid}u{\mid}^{\alpha}u\;+\;a{\Sigma}_i^d\;u_{x_ix_ix_ix_i}$ = 0, where a is real constant, 1 $\leq$ d < n is a integer is a positive constant, and x = $(x_1,x_2,\cdots,x_n)\;\in\;R^n$. For some admissible ${\alpha}$ we show the existence of global(almost global) solutions and we calculate the regularity of those solutions.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.37-50
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• 2022

In this article we define and study the notions of $\mathcal{I}$-convergence and $\mathcal{I}$-Cauchy of triple sequences in the topology induced by random 2-normed spaces and prove some theorems based on them.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.287-291
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• 1997

Assume $H_i : R_+ \times R_+ \to R_+ (i = 1, 2)$ are monotonically increasing (in both variables), homogeneous mapping for which $H_1(tu, tv) = t^p(H_1(u, v) (p > 0)$ and $H_2(u, v)^{t^q} (q \leq 1)$ hold for $t, u, v \geq 0$. Using an idea from the paper of Baker, Lawrence and Zorzitto [2], the superstability problems of the functional inequalities $\Vert f(x+y) - f(x)f(y) \Vert \leq H_i (\Vert x \Vert, \Vert y \Vert)$ shall be investigated.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.1017-1025
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• 2011

In this paper, we survey various notions and results related to statistical convergence of a sequence of fuzzy numbers, in which statistical convergence for fuzzy numbers was first introduced by Nuray and Savas in 1995. We will go over boundedness, convergence of sequences of fuzzy numbers, statistically convergence and statistically Cauchy sequences of fuzzy numbers, statistical limit and cluster point for sequences of fuzzy numbers, statistical mono-tonicity and boundedness of a sequence of fuzzy numbers and finally statistical limit inferior and limit inferior for the statistically bounded sequences of fuzzy numbers.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.731-739
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• 2010

In this paper, we prove stability of the reciprocal difference functional equation $$r\(\frac{{\sum}_{i=1}^{m}x_i}{m}\)-r\(\sum_{i=1}^{m}x_i\)=\frac{(m-1){\prod}_{i=1}^{m}r(x_i)}{{\sum}_{i=1}^{m}{\prod}_{k{\neq}i,1{\leq}k{\leq}m}r(x_k)$$ and the reciprocal adjoint functional equation $$r\(\frac{{\sum}_{i=1}^{m}x_i}{m}\)+r\(\sum_{i=1}^{m}x_i\)=\frac{(m+1){\prod}_{i=1}^{m}r(x_i)}{{\sum}_{i=1}^{m}{\prod}_{k{\neq}i,1{\leq}k{\leq}m}r(x_k)$$ in m-variables. Stability of the reciprocal difference functional equation and the reciprocal adjoint functional equation in two variables were proved by K. Ravi, J. M. Rassias and B. V. Senthil Kumar [13]. We extend their result to m-variables in similar types.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.891-908
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• 1996

Let (X,d) be a metric space and let T be a mapping from X into itself. We say that a metric space (X,d) is T-orbitally complete if every Cauchy sequence of the form ${T^{n_i}x}_{i \in N}$ for $x \in X$ converges to a point in X.

• Journal of Broadcast Engineering
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• v.16 no.6
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• pp.996-1008
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• 2011

This paper proposes a PSNR estimation algorithm of H.264/AVC bitstream for hierarchical B-picture structure. The proposed method consists of a modeling method for DCT coefficients for I-pictures and an error estimation method for blocks encoded by skip mode. The modeling method selects an appropriate model between Laplacian and Cauchy model, and the error of skip mode is estimated from MSE values of reference pictures. Experimental results show that the modeling method predicts more accurate PSNR values than Laplacian and Cauchy model and the error estimation method of skip mode enhances PSNR estimation of hierarchical B-picture structure.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.607-616
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• 1994

I. M. Gelfand and G. E. Shilov [GS] introduced the Gelfand-Shilov spaces of type S, generalized type S and type W of test functions to investigate the uniqueness of the solutions of the Cauchy problems of partial differential equations. Using the heat kernel method Matsuzawa gave structure theorems for distributions, hyperfunctions and generalized functions in the dual space $(S^s_r)'$ of the Gelfand-Shilov space of type S in [M1, M2 and DM], respectively. Also, we gave structure theorems for ultradistributions, Fourier hyperfunctions in [CK, KCK], respectively.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.37-52
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• 2000

This paper is concerned with the impulsive Cauchy problem (equation omitted) where u is a possibly discontinuous vector-valued function and f, $g_{i}$ : $IR^{n}$ -> $IR^{n}$ are suitably smooth functions. We show that the input-output map is Lipschitz continuous and investigate compactness of reachable sets.