• Journal of applied mathematics & informatics
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• v.6 no.2
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• pp.329-368
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• 1999

This paper surveys recent remarkable progress in the study of potential theory for symmetric stable processes. It also contains new results on the two-sided estimates for Green functions Poisson kernels and Martin kernels of discontinuous symmetric $alpha$ -stable process in bounded $C^{1,1}$ open sets. The new results give ex-plicit information on how the comparing constants depend on pa-rametrer $alpha$ and consequently recover the green function and Poisson kernel estimates for Brownian motion by passing $alpha{\uparrow}2$. In addition to these new estimates this paper surveys recent progress in the study of notions of harmonicity integral representation of harmonic func-tions boundary harnack inequality conditional gauge and intrinsic ultracontractivity for symmetric stable processes. Here is a table of contents.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.825-855
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• 2019

We establish the existence of $C^1$ stable invariant manifolds for differential equations $u^{\prime}=A(t)u+f(t,u,{\lambda})$ obtained from sufficiently small $C^1$ perturbations of a nonuniform exponential dichotomy. Since any linear equation with nonzero Lyapunov exponents has a nonuniform exponential dichotomy, this is a very general assumption. We also establish the $C^1$ dependence of the stable manifolds on the parameter ${\lambda}$. We emphasize that our results are optimal, in the sense that the invariant manifolds are as regular as the vector field. We use the fiber contraction principle to establish the smoothness of the invariant manifolds. In addition, we can also consider linear perturbations, and thus our results can be readily applied to the robustness problem of nonuniform exponential dichotomies.

• Communications of the Korean Mathematical Society
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• v.10 no.1
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• pp.163-173
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• 1995

Inspired in [2,9,10,17], pp. E. Ehrlich and S. B. Kim in [4] cultivated the Riccati equation related to the Raychaudhuri equation of General Relativity for the stable Jacobi tensor along the geodesics to extend the Hawking-Penrose conjugacy theorem to $$ f(t) = Ric(c(t)',c'(t)) + tr(\sigma(A)^2) $$ where $\sigma(A)$ is the shear tensor of A for the stable Jacobi tensor A with $A(t_0) = Id$ along the complete Riemannian or complete nonspacelike geodesics c.

• 한국정보디스플레이학회:학술대회논문집
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• 2007.08b
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• pp.1199-1202
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• 2007

The improvement of the electron injection is of critical importance for obtaining efficient and stable organic light-emitting diodes(OLEDs). Here, we report some of our recent results on the development of new cathode interlayer materials for OLEDs. Some of our new materials show performance superior to that of LiF.

• 한국정보디스플레이학회:학술대회논문집
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• 2007.08b
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• pp.1757-1760
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• 2007

Moving a droplet by electrowetting is the basis of our novel displays. This enables mechanical bistable and high reflective monochrome as well as color systems. Since no high temperature process is required, plastic substrates can be used. Our prototypes show promising performance in terms of a wide temperature range, contrast ratio and color.

• Proceedings of the Polymer Society of Korea Conference
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• 2006.10a
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• pp.321-321
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• 2006

Aromatic diacetylenes form stable oligomeric diradicals when irradiated with UV light or heated at temperatures above their melting points. In this paper, the formation of stable diradicals is discussed, and the mechanism of polymerization in the presence of peroxide in solution, is discussed. The diphenyldiacetylene undergoes polymerization through coupling of diradicals, and not by the successive addition of radical species.

• Kyungpook Mathematical Journal
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• v.47 no.1
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• pp.31-56
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• 2007

In this paper, we consider a delay differential equation model of two competing species with harvesting of the mature and immature members of each species. The time delay in the model represents the time from birth to maturity of that species, which appears in the adults recruitment terms. We study the dynamics of our model analytically and we present results on positivity and boundedness of the solution, conditions for the existence and globally asymptotically stable of equilibria, a threshold of harvesting, and the optimal harvesting of the mature populations of each species.

• IEIE Transactions on Smart Processing and Computing
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• v.6 no.3
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• pp.175-182
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• 2017

In this paper, we present a multi-depth generation method using a time-of-flight (ToF) fusion camera system. Multi-view color cameras in the parallel type and ToF depth sensors are used for 3D scene capturing. Although each ToF depth sensor can measure the depth information of the scene in real-time, it has several problems to overcome. Therefore, after we capture low-resolution depth images by ToF depth sensors, we perform a post-processing to solve the problems. Then, the depth information of the depth sensor is warped to color image positions and used as initial disparity values. In addition, the warped depth data is used to generate a depth-discontinuity map for efficient stereo matching. By applying the stereo matching using belief propagation with the depth-discontinuity map and the initial disparity information, we have obtained more accurate and stable multi-view disparity maps in reduced time.

• Korean Journal of Microbiology
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• v.26 no.2
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• pp.82-87
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• 1988

The genetic analysis and characterization of protoplast fusion hybrids between complementary auxotrophic mutants of Candida pseudotropicalis were carried out. Nuclear fusion appeared to occur in fusion hybrids (e.g., F15 and F33), as strongly suggested by isolation of recombinants after mitotic segregation of parental genetic markers. This was confirmed by KNA content, nuclear staining and comparison of survival rate to UV light. After keeping fusion hybrids for approximately one year, the frequency of spontaneous mitotic segregation was $3.0\times 10^{-4}$ - $8.1\times 10^{-4}$ while that of induced mitotic segregation was $1.4\times 10^{-3}$- $1.7\times 10^{-3}$. These results suggested that they maintained stable karyogamy state. It was also found that the production of $\beta$-D-galactosidase from F15, F33 and F158 was somewhat increased when compared with that from either auxotrophic parents or wild type.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.167-176
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• 2010

Let (B, $\check{g}$) and (N, $\hat{g}$) be Einstein manifolds. Then, we get a complete (necessary and sufficient) condition for the warped product manifold $B\;{\times}_f\;N\;:=\;(B\;{\times}\;N,\;\check{g}\;+\;f{\hat{g}}$) to be Einstein, and obtain a complete condition for the Einstein warped product manifold $B\;{\times}_f\;N$ to be weakly stable. Moreover, we get a complete condition for the map i : ($B,\;\check{g})\;{\times}\;(N,\;\hat{g})\;{\rightarrow}\;B\;{\times}_f\;N$, which is the identity map as a map, to be harmonic. Under the assumption that i is harmonic, we obtain a complete condition for $B\;{\times}_f\;N$ to be Einstein.