• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.269-273
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• 2010

We introduce the concepts of strongly $s{\gamma}$-closed graph, $s{\gamma}$-compactness and $s{\gamma}-T_2$ space and study the relationships between such concepts and weakly $s{\gamma}$-continuous functions.

• Korean Journal of Mathematics
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• v.8 no.2
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• pp.163-172
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• 2000

Let $\mathcal{S}^{\prime}(\mathbb{R})$ be the dual of the Schwartz spaces $\mathcal{S}(\mathbb{R})$), A be a self-adjoint operator in $L^2(\mathbb{R})$ and ${\Gamma}(A)^*$ be the adjoint operator of ${\Gamma}(A)$ which is the second quantization operator of A. It is proven that under a suitable condition on A there exists a nuclear subspace $\mathcal{S}$ of a fundamental space $\mathcal{S}_A$ of Hida's type on $\mathcal{S}^{\prime}(\mathbb{R})$) such that ${\Gamma}(A)\mathcal{S}{\subset}\mathcal{S}$ and $e^{-t{\Gamma}(A)}\mathcal{S}{\subset}\mathcal{S}$, which enables us to show that a stochastic differential equation: $$dX(t)=dW(t)-{\Gamma}(A)^*X(t)dt$$, arising from the central limit theorem for spatially extended neurons has an unique solution on the dual space $\mathcal{S}^{\prime}$ of $\mathcal{S}$.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.1025-1050
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• 2007

Let $X_k(x)=({\int}^T_o{\alpha}_1(s)dx(s),...,{\int}^T_o{\alpha}_k(s)dx(s))\;and\;X_{\tau}(x)=(x(t_1),...,x(t_k))$ on the classical Wiener space, where ${{\alpha}_1,...,{\alpha}_k}$ is an orthonormal subset of $L_2$ [0, T] and ${\tau}:0 is a partition of [0, T]. In this paper, we establish a change of scale formula for conditional Wiener integrals $E[G_{\gamma}|X_k]$ of functions on classical Wiener space having the form $$G_{\gamma}(x)=F(x){\Psi}({\int}^T_ov_1(s)dx(s),...,{\int}^T_o\;v_{\gamma}(s)dx(s))$$, for $F{\in}S\;and\;{\Psi}={\psi}+{\phi}({\psi}{\in}L_p(\mathbb{R}^{\gamma}),\;{\phi}{\in}\hat{M}(\mathbb{R}^{\gamma}))$, which need not be bounded or continuous. Here S is a Banach algebra on classical Wiener space and $\hat{M}(\mathbb{R}^{\gamma})$ is the space of Fourier transforms of measures of bounded variation over $\mathbb{R}^{\gamma}$. As results of the formula, we derive a change of scale formula for the conditional Wiener integrals $E[G_{\gamma}|X_{\tau}]\;and\;E[F|X_{\tau}]$. Finally, we show that the analytic Feynman integral of F can be expressed as a limit of a change of scale transformation of the conditional Wiener integral of F using an inversion formula which changes the conditional Wiener integral of F to an ordinary Wiener integral of F, and then we obtain another type of change of scale formula for Wiener integrals of F.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.13-30
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• 2010

Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by $x_0\;{\in}\;C$ arbitrarily chosen, $x_{n+1}\;=\;{\alpha}_n{\gamma}f(W_nx_n)+{\beta}_nx_n+((1-{\beta}_n)I-{\alpha}_nA)W_nP_C(I-s_nB)x_n$, ${\forall}_n\;{\geq}\;0$, where $\gamma$ > 0, B : C $\rightarrow$ H is a $\beta$-inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient $\alpha$ (0 < $\alpha$ < 1), $P_C$ is a projection of H onto C, A is a strongly positive linear bounded operator on H and $W_n$ is the W-mapping generated by a finite family of nonexpansive mappings $T_1$, $T_2$, ${\ldots}$, $T_N$ and {$\lambda_{n,1}$}, {$\lambda_{n,2}$}, ${\ldots}$, {$\lambda_{n,N}$}. Nonexpansivity of each $T_i$ ensures the nonexpansivity of $W_n$. We prove that the sequence {$x_n$} generated by the above iterative algorithm converges strongly to a common fixed point $q\;{\in}\;F$ := $\bigcap^N_{i=1}F(T_i)\;\bigcap\;VI(C,\;B)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)q,\;p\;-\;q{\rangle}\;{\leq}\;0$ for all $p\;{\in}\;F$. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.

• Journal of Astronomy and Space Sciences
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• v.16 no.1
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• pp.31-40
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• 1999

With a total 761 contact binary systems in Svechnikov & Kuznetsova(1990)'s catalogue, their physical properties by the mass ratio are investigated - for the early CE type with a common radiative envelope and the late CW type with a common convective envelope. It is found that the early CE type shows a higher temperature difference($\mid$$DeltaT$$\mid$) between the primary and secondary components, and also longer period, than the late CW type. The mass ratio of the CW type are distributed in period, than the late CW type. The mass ratio of the CW type are distributed in smaller ranges, from 0.3 to 0.7, than the CE type. Further, the relation between mass ratio and luminosity for the CW type shows a well-defined linear relation, such as ratio and luminosity for the CW type shows a well-defined linear relation, such as $L_2/L_1$ = 0.01 = 0.89q. In the mass ratio-radii relation, it is confirmed that the physical difference of the CE and CW types is a result of the secondary radius. A new mass ratio-radii relation for the CW type is suggested for both the total radius $({gamma}_1/{gamma}_2$ and the radius ratio $({gamma}_2/{gamma}_1$, respectively.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.389-399
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• 1995

We consider the reaction-diffusion system of two-component model in one-dimensional space described by $$ (1) u_s = d_1 u_{xx} + f(u, \upsilon) \upsilon_t = d_2\upsilon_{xx} + \gammag(u, \upsilon) $$ where $d_1$ and $d_2$ are the diffusion rates of u and $\upsilon$, and $\gamma$ is the ration of reaction rates. It is interesting the case of that there are differences in the diffusion and reaction rates of u and $\upsilon$.

• Korean Journal of Plant Resources
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• v.27 no.5
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• pp.429-438
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• 2014

This study was designed to investigate the effects on anti-oxidative activities and increasing extraction yield of Aralia elata Cortex by gamma irradiation. Electron spin resonance (ESR) analysis as physical techniques for irradiation identification of Aralia elata showed that a pair of peak appeared on a space of 6.0 mT at the left and right of symmetric unspecific central ESR spectrums, confirming that the plant was gamma-irradiated. The optimum extracting conditions for preparing gamma irradiated samples from Aralia elata Cortex were to extract with 50% ethanol for 15 hrs after 10 kGy irradiation. DPPH scavenging activity and ABTS radical cation inhibitory activity of the water and 50% ethanol extracts from non irradiated and irradiated Aralia elata Cortex was very high as over 80% and 98%, respectively, at tested low concentration of $50{\mu}g/mL$. Antioxidant protection factor (PF) as anti-oxidation indicator of lipophilic compounds showed a very high level of activity as 2.18~2.78 PF. As for TBARs, water and ethanol extracts showed high level. Increase of TBARs inhibitory activity of water extracts was not shown by gamma-ray irradiation but ethanol extracts showed slight increasement of TBARs inhibitory activity with 10 kGy gamma-ray irradiation. These results shown confirmed increasement of extraction yield for phenolic compounds and anti-oxidative activity from Aralia elata. Thus, the treatment of gamma-irradiation can be used a way to amplify a solubility for biological active compounds and anti-oxidative activity in plants.

• The Bulletin of The Korean Astronomical Society
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• v.42 no.2
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• pp.43.3-43.3
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• 2017

NGC 6822 is a dwarf irregular galaxy in the Local Group and it is located in 500 kpc, further than the Large Magellanic Cloud and the Small Magellanic Cloud. Therefore, we can study star-forming processes by local condition in NGC 6822 instead of tidal force of the Galactic gravitational field. Hubble V is the brightest of several H II complexes in this galaxy. We observed Hubble V by using IGRINS attached on the 2.7 m telescope at the McDonald Observatory in Texas, US in May 2016. We performed a spectral mapping of $15^{{\prime}{\prime}}{\times} 7^{{\prime}{\prime}}$area on H and K bands, and detected emission lines of bright $Br{\gamma}\;{\lambda}2.1661{\mu}m$ and weak He I ${\lambda}2.0587{\mu}m$. Molecular hydrogen lines of 1-0S(1) ${\lambda}2.1218{\mu}m$, 2-1 S(1) ${\lambda}2.2477{\mu}m$, and 1-0 S(0) ${\lambda}2.2227{\mu}m$ was also detected. These emission lines show the structure of an ionized core and excited surface of clouds by far-ultraviolet photons, photodissociation region (PDR). We present three-dimensional maps of emission line distributions through multi slit scanning data and compare these results with the previous study. This presentation shows the physical structure of the star-forming regions and we discuss a PDR model and an evolution of Hubble V complex.

• Journal of the Korean Chemical Society
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• v.35 no.6
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• pp.603-606
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• 1991

The crystal structure of Probenecid has been determined from 2574 independent reflections collected on an automatic ENRAF-NONIUS CAD-4 diffractometer using graphite-monochromated $Mo-K{\alpa}$ radiation. The crystal is triclinic, space group P$\bar{1}$ with unit cell dimensions a = 7.535(2)${\AA}$, b = 18.473 (5)${\AA}$, c = 5.317(9)${\AA}$, ${\alpha} = 92.00(5)^{\circ}$, ${\beta} = 99.02(5)^{\circ}$, ${\gamma} = 94.89(2)^{\circ}$, V = 727.4(2)${\AA}^3$, Z = 2, $D_m$ = 1.310, $D_x$ = $1.302 gcm^{-3}$, ${\mu}$ = $1.88 cm^{-1}$, F(000) = 304, and T = 298 K. Final R = 0.0676 and $R_w$ = O.0630 for 1209 reflections > 5${\sigma}(F_o)$. In the spacial arrangement about N(13), the sum of bond angles about nitrogen is 350.9° and the nitrogen lies only 0.268(6)${\AA}$ out of S(1)-C(14)-C(17) plane. The S(1)-C(4) distance is 1.792(6)${\AA}$ and the C(4)-S(1)-N(13) angle is $106.5(3)^{\circ}$. The overall conformation of the molecule is folded with respect to sulfur.

• Publications of The Korean Astronomical Society
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• v.30 no.2
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• pp.679-682
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• 2015

The Hiroshima Astrophysical Science Center (HASC) was founded in 2004 at Hiroshima University, Japan. The main mission of this institute is the observational study of various transient objects including gamma-ray bursts, supernovae, novae, cataclysmic variables, and active galactic nuclei by means of multi-wavelength observations. HASC consists of three divisions; the optical-infrared astronomy division, high-energy astronomy division, and theoretical astronomy division. HASC is operating the 1.5m optical-infrared telescope Kanata, which is dedicated to follow-up and monitoring observations of transient objects. The high-energy division is the key operation center for the Fermi gamma-ray space telescope. HASC and the high-energy astronomy group in the department of physical science at Hiroshima University are closely collaborating with each other to promote multi-wavelength time-domain astronomy. We report the recent activities of HASC and some science topics pursued by this multi-wavelength collaboration.