Publications (13)14.57 Total impact
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ABSTRACT: In this paper, we show that for a given convolutor Q for tempered Gevrey distribution and positive number M, a Gevrey distribution T whose Fourier transform is supported in the set {ξ∈ℜd :ˆ Q(ξ)≤M} can be characterized by the behaviour of the sequence of the successive convolute powers of Q acting on T. We also deal with the ‘dual’ characterization – a Gevrey distribution T supported in {ξ∈ℜd : ˆ Q(ξ)≥M} can be characterized by the sequence , where T 0=T, and Q* T k+1=T k , k=0, 1, 2, …. As an application, we discuss the problem on sequences characterizing the sine functions and get the most general result of those obtained before. 
Article: Extinction and positivity of the solutions of the heat equations with absorption on networks
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ABSTRACT: In this paper, we propose a discrete version of the following semilinear heat equation with absorption ut=Δu−uq with q>1, which is said to be the ωheat equation with absorption on a network. Using the discrete Laplacian operator Δω on a weighted graph, we define the ωheat equations with absorption on networks and give their physical interpretations. The main concern is to investigate the large time behaviors of nontrivial solutions of the equations whose initial data are nonnegative and the boundary data vanish. It is proved that the asymptotic behaviors of the solutions u(x,t) as t tends to +∞ strongly depend on the sign of q−1.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we propose an algorithm for detecting the combination of monopolar and multipolar point sources for elliptic partial differential equations in the twodimensional domain from their Neumann and Dirichlet boundary data. We prove that the source locations are shown to be the solutions of some characteristic equation related to the inverse of a Hankeltype matrix derived from the boundary data. We then apply this fact to provide a detection algorithm.  [Show abstract] [Hide abstract]
ABSTRACT: ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 200 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.  [Show abstract] [Hide abstract]
ABSTRACT: We characterize Sobolev spaces ℋ s (ℝ n ),s∈ℝ by the initial value of solutions of heat equation with a growth condition. By using an idea in its proof, we also discuss a stability problem for Cauchy functional equation in the Sobolev spaces.  [Show abstract] [Hide abstract]
ABSTRACT: A concise, stereocontrolled synthesis of (+)polyoxamic acid was achieved. Starting from transoxazoline as a chiral building block, the key step involves diastereoselective oxazine formation catalyzed by palladium(0).  [Show abstract] [Hide abstract]
ABSTRACT: A concise, stereocontrolled synthesis of (2S,3R)3hydroxypipecolic acid 1 is described. Key features involve diastereoselective oxazoline formation catalyzed by palladium(0) and intramolecular cyclization by catalytic hydrogenation of an oxazoline.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we discuss discrete versions of the heat equations and the wave equations, which are called the ωdiffusion equations and the ωelastic equations on graphs. After deriving some basic properties, we solve the ωdiffusion equations under (i) the condition that there is no boundary, (ii) the initial condition and (iii) the Dirichlet boundary condition. We also give some additional interesting properties on the ωdiffusion equations, such as the minimum and maximum principles, Huygens property and uniqueness via energy methods. Analogues of the ωelastic equations on graphs are also discussed. © 2007 Research Institute for Mathematical Sciences, Kyoto University. All rights reserved.  [Show abstract] [Hide abstract]
ABSTRACT: Suppose that $P(D)$ is a linear differential operator with complex coefficients and $\{f_k\}_{k \in \mathbb{Z}}$ is a twosided sequence of complexvalued functions on $\mathbb{R}$ such that $f_{k+1} \,{=}\, P(D)f_k$ with the following growth condition: there exist $a\,{\in}\,[0,1)$ and $N\,{\geq}\,0$ such that $f_k(x)\,{\leq}\,M_{k}\exp (Nx^a)$, where the sequence $\{M_k\}_{k=0}^{\infty}$ satisfies that for any $\varepsilon\,{>}\,0$, the sequence $\{{M_k}/{(1+\varepsilon)^{k}}\}_{k=0}^{\infty}$ has a bounded subsequence. Then $f_0$ is an entire function of an exponential growth. This result is a generalization of those of Roe, Burkill and Howard.  [Show abstract] [Hide abstract]
ABSTRACT: We reformulate and solve the stability problem of a Jensen type functional equation in the spaces of some generalized functions such as tempered distributions and Fourier hyperfunctions.  [Show abstract] [Hide abstract]
ABSTRACT: We reformulate a quadratic functional equation of the form f (x + y + z )+ f (xy + z )+ f (x + yz )+ f (�x + y + z )= 4f (x )+ 4f (y )+ 4f (z) and an inequality f (x + y + z )+ f (xy + z )+ f (x + yz )+ f (�x + y + z) � 4f (x) � 4f (y) � 4f (z) ε in the space of distributions. In view of this fact, we use a mollifier and Gauss transform to show that every distributional solution of the inequality is a tempered distribution and finally the stability problem of the equation in the sense of distributions.  [Show abstract] [Hide abstract]
ABSTRACT: Palladium(II)catalyzed carboxylation of chiral olefins 6ad has been examined under various conditions. In the weak basic condition (K2CO3), 7ad were obtained in good yields. Alternatively, in the strong basic condition, pyrrolidinones 8ad were obtained resulting in excellent yields and with high diastereoselectivity.  [Show abstract] [Hide abstract]
ABSTRACT: In this talk, we propose an algorithm for identifying the poles and the residues of meromorphic functions with finite number of poles and zeros on a simply connected bounded domain from their boundary measurements with some stability results. We prove that the pole locations are shown to be the solutions of some characteristic equation related to the inverse of a Hankel matrix derived from the boundary data and apply this fact to provide a detection algorithm.
Publication Stats
67  Citations  
14.57  Total Impact Points  
Top Journals
Institutions

20062014

Sogang University
 Department of Mathematics
Sŏul, Seoul, South Korea


2011

Ewha Womans University
 Institute of Mathematical Sciences
Sŏul, Seoul, South Korea


20052008

Sungkyunkwan University
 School of Pharmacy
Sŏul, Seoul, South Korea
