• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.79-90
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• 2005

In this paper we study the numerical solutions of the stochastic differential equations of the form $$du(x,\;t)=f(x,\;t,\;u)dt\;+\;g(x,\;t,\;u)dW(t)\;+\;\sum\limits_{|q|\leq2m}\;A_q(x,\;t)D^qu(x,\;t)dt$$ where $0\;{\leq}\;t\;{\leq}\;T,\;x\;{\in}\;R^{\nu}$, ($R^{nu}$ is the $\nu$-dimensional Euclidean space). Here $u\;{\in}\;R^n$, W(t) is an n-dimensional Brownian motion, $$f\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^n,\;g\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^{n{\times}n},$$, and $$A_q\;:\;R^{\nu}\;{\times}\;[0,\;T]\;{\rightarrow}\;R^{n{\times}n}$$ where ($A_q,\;|\;q\;|{\leq}\;2m$) is a family of square matrices whose elements are sufficiently smooth functions on $R^{\nu}\;{\times}\;[0,\;T]\;and\;D^q\;=\;D^{q_1}_1_{\ldots}_{\ldots}D^{q_{\nu}}_{\nu},\;D_i\;=\;{\frac{\partial}{\partial_{x_i}}}$.

• Journal of the Korean Mathematical Society
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• v.38 no.2
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• pp.469-483
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• 2001

The configuration space and phase space oscillatory path integrals are computed in the case of the stochastic Schrodinger equation for the harmonic oscillator with a stochastic term of the form (K$\psi$(sub)t)(x) o dW(sub)t, where K is either the position operator or the momentum operator, and W(sub)t is the Wiener process. In this way formulae are derived for the stochastic analogues of the Mehler kernel.

• East Asian mathematical journal
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• v.6 no.1
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• pp.111-121
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• 1990

Let E be a locally convex Hausdorff space and let $\Gamma$ be a calibration for E. In this note we proved that if E is sequentially complete and a multi-vaiued operaturA in E is $\Gamma$-accretive such that $D(A){\subset}Re$ (I+$\lambda$A) for all sufficiently small positive $\lambda$, then A generates a nonlinear $\Gamma$-contraction semiproup {T(t) ; t>0}. We also proved that if E is complete, $Gamma$ is a dually uniformly convex calibration, and an operator A is m-$\Gamma$-accretive, then the initial value problem $$\{{\frac{d}{dt}u(t)+Au(t)\;\ni\;0,\;t >0,\atop u(0)=x}\.$$ has a solution $u:[0,\infty){\rightarrow}E$ given by $u(t)=T(t)x={lim}\limit_{n\rightarrow\infty}(I+\frac{t}{n}A)^{-n}x$ each $x{\varepsilon}D(A)$.

• The Pure and Applied Mathematics
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• v.5 no.1
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• pp.17-21
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• 1998

In [5], Zhu introduces a bounded operator T from $L^{\infty}$(D) into Bloch space B. In this paper, we will consider the generalized Bloch spaces $B_{q}$ and find bounded operator from $L^{\infty}$(D) into $B_{q}$.

• Bulletin of the Korean Space Science Society
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• 2009.10a
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• pp.26.2-26.2
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• 2009

The Solar and Space Weather Research Group (SOS) in Korea Astronomy and Space Science Institute (KASI) is constructing the Space Weather Prediction Center since 2007. As a part of the project, we are developing automatic real-time system of the global 3-D magnetohydrodynamics (MHD) simulation. The MHD simulation model of earth's magnetosphere is designed as modified leap-frog scheme by T. Ogino, and it was parallelized by using message passing interface (MPI). Our work focuses on the automatic processing about simulation of 3-D MHD model and visualization of the simulation results. We used PC cluster to compute, and virtual reality modeling language (VRML) file format to visualize the MHD simulation. The system can show the variation of earth's magnetosphere by the solar wind in quasi real time. For data assimilation we used four parameters from ACE data; density, pressure, velocity of solar wind, and z component of interplanetary magnetic field (IMF). In this paper, we performed some initial tests and made a animation. The automatic real-time system will be valuable tool to understand the configuration of the solar-terrestrial environment for space weather research.

• Journal of Korea Multimedia Society
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• v.3 no.4
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• pp.339-346
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• 2000

Medical image is analyzed to get an anatomical information for diagnostics. Segmentation must be preceded to recognize and determine the lesion more accurately. In this paper, we propose automatic segmentation algorithm for MR brain images using T1-weighted, T2-weighted and PD images complementarily. The proposed segmentation algorithm is first, extracts cerebrum images from 3 input images using cerebrum mask which is made from PD image. And next, find 3D clusters corresponded to cerebrum tissues using scale filtering and 3D clustering in 3D space which is consisted of T1, T2, and PD axis. Cerebrum images are segmented using FCM algorithm with its initial centroid as the 3D cluster's centroid. The proposed algorithm improved segmentation results using accurate cluster centroid as initial value of FCM algorithm and also can get better segmentation results using multi spectral analysis than single spectral analysis.

• The Bulletin of The Korean Astronomical Society
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• v.35 no.1
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• pp.69.1-69.1
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• 2010

IC 443 is famous for its interaction with nearby molecular clouds and intense H2 emission lines in infrared. Therefore, it has been studied extensively for the understanding of molecular shocks. We observed H2 mission lines toward the shock-cloud interaction regions of IC 443, known as clumps B, C, and G. The observations were performed with the InfraRed Camera (IRC) onboard a satellite AKARI over 2.5-5.0 um, where previous space observations, e.g. Infrared Space Observatory (ISO) and Spitzer, do not cover. Our AKARI observations provide spectra of sequential pure-rotational and ro-vibrational H2 emission lines. For the clumps C and G, combining with previous mid-infrared observational results, we found that the H2 level populations show a significant separation between v=0 and v=1 levels; v=1 levels are under-populated than v=0 levels, therefore, the population cannot be described by two temperature LTE model, as many people have analyzed for the shocked H2 gas. We also applied the thermal admixture model, dN(H2; T)~T^(-b) dT, with varying ortho-to-para ratios according to the temperature, to describe the level population, and obtained plausible ranges of the H2 gas density and power-law index b.

• Progress in Superconductivity and Cryogenics
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• v.24 no.3
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• pp.41-46
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• 2022

The superconducting properties of high temperature superconducting (HTS) GdBCO coated conductor (CC) tape (Ag/GdBCO/Buffer-layers/Stainless Steel) were investigated, specifically a series of samples prepared by vacuum heat treatment (200℃ to 600℃), using a Quantum Design PPMS-14. The critical current density J_c value was obtained by applying the modified Bean model to the irreversible magnetization ∆M_irr(H) data which was estimated from the magnetization M(H) loop. The reduction rates of lnJ_c and T_c values according to the increase of the vacuum annealing temperature T_an were d(lnJ_c)/dT_an = - 0.016 A/(cm²∙℃) and dT_c/dT_an = - 0.24, respectively. We examined the effect of recovery temperature T_re (475℃ to 700℃) and recovery duration time t (0.5 h to 24 h) on the restoration of previously completely lost superconductivity in samples that subsequently received heat treatment in an O₂ gas flow space. All samples were fully restored to superconductivity by heat treatment in an O₂ gas flow space. The recovery temperatures T_re (475℃ to 700℃) and recovery duration times t (0.5 h to 24 h) were both independent of the superconductivity recovery characteristics.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.1-7
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• 2002

For A bounded subset G of a metric Space (X,d) and $\chi \in X$, let $f_{G}$ be the real-valued function on X defined by $f_{G}$($\chi$)=sup{$d (\chi, g)\in:G$}, and $F(G,\chi)$={$z \in X:sup_{g \in G}d(g,z)=sup_{g \in G}d(g,\chi)+d(\chi,z)$}. In this paper we discuss some properties of the map $f_G$ and of the set $ F(G, \chi)$ in convex metric spaces. A sufficient condition for an element of a convex metric space X to lie in $ F(G, \chi)$ is also given in this pope.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.777-791
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• 1996

Let $S(R^d)$ be the Schwartz space of infinitely differentiable functions on $R^d$ which vanish at $\infty$ and $S'(R^d)$ be its dual space. The theory of stochastic differential equations(SDEs) governing processes that takes values in the dual of countably Hilbertian nuclear space such as $S'(R^d)$ studied by many authors(e.g [M],[KM]). Let M be a martingale measure defined by Walsh[W], then M can be considered as a $S'(R^d)$-valued process in a certain condition i.e. M has a version of $S'(R^d)$-valued martingale process. (See [W] for detailed discussion)