• 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 The Korean Astronomical Society
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• v.50 no.6
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• pp.167-178
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• 2017

We present a study of the inexplicit connection between radio jet activity and ${\gamma}$-ray emission of BL Lacertae (BL Lac; 2200+420). We analyze the long-term millimeter activity of BL Lac via interferometric observations with the Korean VLBI Network (KVN) obtained at 22, 43, 86, and 129 GHz simultaneously over three years (from January 2013 to March 2016); during this time, two ${\gamma}$-ray outbursts (in November 2013 and March 2015) can be seen in ${\gamma}$-ray light curves obtained from Fermi observations. The KVN radio core is optically thick at least up to 86 GHz; there is indication that it might be optically thin at higher frequencies. To first order, the radio light curves decay exponentially over the time span covered by our observations, with decay timescales of $411{\pm}85$ days, $352{\pm}79$ days, $310{\pm}57$ days, and $283{\pm}55$ days at 22, 43, 86, and 129 GHz, respectively. Assuming synchrotron cooling, a cooling time of around one year is consistent with magnetic field strengths $B{\sim}2{\mu}T$ and electron Lorentz factors ${\gamma}$ ~ 10 000. Taking into account that our formal measurement errors include intrinsic variability and thus over-estimate the statistical uncertainties, we find that the decay timescale ${\tau}$ scales with frequency ${\nu}$ like ${\tau}{\propto}{\nu}^{-0.2}$. This relation is much shallower than the one expected from opacity effects (core shift), but in agreement with the (sub-)mm radio core being a standing recollimation shock. We do not find convincing radio flux counterparts to the ${\gamma}$-ray outbursts. The spectral evolution is consistent with the 'generalized shock model' of Valtaoja et al. (1992). A temporary increase in the core opacity and the emergence of a knot around the time of the second ${\gamma}$-ray event indicate that this ${\gamma}$-ray outburst might be an 'orphan' flare powered by the 'ring of fire' mechanism.

• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.385-397
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• 2003

In this paper, we introduce and study a system of nonlinear implicit variational inclusions (SNIVI) in real Banach spaces: determine elements $x^{*},\;y^{*},\;z^{*}\;\in\;E$ such that ${\theta}\;{\in}\;{\alpha}T(y^{*})\;+\;g(x^{*})\;-\;g(y^{*})\;+\;A(g(x^{*}))\;\;\;for\;{\alpha}\;>\;0,\;{\theta}\;{\in}\;{\beta}T(z^{*})\;+\;g(y^{*})\;-\;g(z^{*})\;+\;A(g(y^{*}))\;\;\;for\;{\beta}\;>\;0,\;{\theta}\;{\in}\;{\gamma}T(x^{*})\;+\;g(z^{*})\;-\;g(x^{*})\;+\;A(g(z^{*}))\;\;\;for\;{\gamma}\;>\;0,$ where T, g : $E\;{\rightarrow}\;E,\;{\theta}$ is zero element in Banach space E, and A : $E\;{\rightarrow}\;{2^E}$ be m-accretive mapping. By using resolvent operator technique for n-secretive mapping in real Banach spaces, we construct some new iterative algorithms for solving this system of nonlinear implicit variational inclusions. The convergence of iterative algorithms be proved in q-uniformly smooth Banach spaces and in real Banach spaces, respectively.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.221-227
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• 2016

This paper will discuss the huge change of b - separated, b - connectedness, b - disconnectedness and their applications when the definition of b - separated and b - connectedness are small changed.

• 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.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.1
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• pp.95.2-95.2
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• 2012

We have compared the geoeffective parameters of halo coronal mass ejections (CMEs) to predict geomagnetic storms. For this we consider 50 front-side full halo CMEs whose asymmetric cone model parameters and earthward direction parameter were available. For each CME we use its projected velocity (Vp), radial velocity (Vr), angle between cone axis and sky plane (${\gamma}$) from the cone model, earthward direction parameter (D), source longitude (L), and magnetic field orientation (M) of the CME source region. We make a simple and multiple linear regression analysis to find out the relationship between CME parameters and Dst index. Major results are as follows. (1) $Vr{\times}{\gamma}$ has a higher correlation coefficient (cc = 0.70) with the Dst index than the others. When we make a multiple regression of Dst and two parameters ($Vr{\times}{\gamma}$, D), the correlation coefficient increases from 0.70 to 0.77. (2) Correlation coefficients between Dst index and $Vr{\times}{\gamma}$ have different values depending on M and L. (3) Super geomagnetic storms (Dst ${\leq}$ -200 nT) only appear in the western and southward events. Our results demonstrate that not only the cone model parameters together with the earthward direction parameter improve the relationship between CME parameters and Dst index but also the source longitude and its magnetic field orientation play a significant role in predicting geomagnetic storms.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.6-6
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• 2003

In this work we consider the mathematical formulation and numerical resolution of the linear feedback control problem for Boussinesq equations. The controlled Boussinesq equations is given by $$\frac{{\partial}u}{{\partial}t}-{\nu}{\Delta}u+(u{\cdot}{\nabla}u+{\nabla}p={\beta}{\theta}g+f+F\;\;in\;(0,\;T){\times}\;{\Omega}$$, $${\nabla}{\cdot}u=0\;\;in\;(0,\;T){\times}{\Omega}$$, $$u|_{{\partial}{\Omega}=0,\;u(0,x)=\;u_0(x)$$ $$\frac{{\partial}{\theta}}{{\partial}t}-k{\Delta}{\theta}+(u{\cdot}){\theta}={\tau}+T,\;\;in(0,\;T){\times}{\Omega}$$ $${\theta}|_{{\partial}{\Omega}=0,\;\;{\theta}(0,X)={\theta}_0(X)$$, where $\Omega$ is a bounded open set in $R^{n}$, n=2 or 3 with a $C^{\infty}$ boundary ${\partial}{\Omega}$. The control is achieved by means of a linear feedback law relating the body forces to the velocity and temperature field, i.e., $$f=-{\gamma}_1(u-U),\;\;{\tau}=-{\gamma}_2({\theta}-{\Theta}}$$ where (U,$\Theta$) are target velocity and temperature. We show that the unsteady solutions to Boussinesq equations are stabilizable by internal controllers with exponential decaying property. In order to compute (approximations to) solution, semi discrete-in-time and full space-time discrete approximations are also studied. We prove that the difference between the solution of the discrete problem and the target solution decay to zero exponentially for sufficiently small time step.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1051-1060
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• 2009

In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact $T_1$-subspace. We also study the zero-divisor graph $\Gamma_I$(R) with respect to the completely semiprime ideal I of N. We show that ${\Gamma}_{\mathbb{P}}$ (R), where $\mathbb{P}$ is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph ${\Gamma}_{\mathbb{P}}$ (R).

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.625-639
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• 1996

A convex $RP^n$-structure on a smooth anifold M is a representation of M as a quotient of a convex domain $\Omega \subset RP^n$ by a discrete group $\Gamma$ of collineations of $RP^n$ acting properly on $\Omega$. When M is a closed surface of genus g > 1, then the equivalence classes of such structures form a moduli space $B(M)$ homeomorphic to an open cell of dimension 16(g-1) (Goldman [2]). This cell contains the Teichmuller space $T(M)$ of M and it is of interest to know what of the rich geometric structure extends to $B(M)$. In [3], a symplectic structure on $B(M)$ is defined, which extends the symplectic structure on $T(M)$ defined by the Weil-Petersson Kahler form.

• 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 $\upsilon$.