Publications (13)13.96 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.Integral Transforms and Special Functions 01/2014; 25(2). · 0.73 Impact Factor 
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.Journal of Mathematical Analysis and Applications 08/2011; 380(2):642652. · 1.12 Impact Factor  [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.Inverse Problems 07/2009; 25(8):085006. · 1.80 Impact Factor  ChemInform 08/2008; 39(35).
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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.Communications of the Korean Mathematical Society 07/2008; 23(3):401411.  [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).Organic & Biomolecular Chemistry 05/2008; 6(8):1498501. · 3.49 Impact Factor  [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.Tetrahedron Asymmetry 01/2008; 19(3):318321. · 2.17 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The authors consider the discrete versions of the heat (ωdiffusion) and the wave (ωelastic) equations defined over a weighted graphs. They prove the minimum and maximum principles for the homogeneous ωdiffusion equation. Then they give explicit characterization of the solutions of the inhomogeneous ωdiffusion equation in the following cases (1) problem without boundary conditions, (2) the Cauchy initial condition problem, (3) the Dirichlet boundary condition problem. The representation formulas are obtained by linear algebra arguments applied to the ωLaplace operator. They also prove the Huygens property and uniqueness of the solutions via energy methods. In a similar way the authors prove analogous results for the ωelastic equations on weighted graphs.Publications of the Research Institute for Mathematical Sciences 01/2007; 43(3):699725. · 0.61 Impact Factor  [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.Mathematical Proceedings of the Cambridge Philosophical Society 10/2006; 141(03):509  519. · 0.68 Impact Factor  [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.Journal of Mathematical Analysis and Applications 01/2006; · 1.12 Impact Factor  [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.Mathematical Inequalities and Applications 01/2006; 9(2). · 0.49 Impact Factor  [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.Archives of Pharmacal Research 03/2005; 28(2):1518. · 1.75 Impact Factor  [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
20  Citations  
13.96  Total Impact Points  
Top Journals
Institutions

2006–2009

Sogang University
 Department of Mathematics
Seoul, Seoul, South Korea


2005–2008

Sungkyunkwan University
 School of Pharmacy
Seoul, Seoul, South Korea
