• Kyungpook Mathematical Journal
• /
• v.54 no.2
• /
• pp.173-188
• /
• 2014

In this paper, a new class of open sets, namely ${\gamma}^*$-pre-open sets was introduced and its basic properties were studied. Moreover a new type of topology ${\tau}_{{\gamma}p^*}$ was generated using ${\gamma}^*$-pre-open sets and characterized the resultant topological space (X, ${\tau}_{{\gamma}p^*}$) as ${\gamma}^*$-pre-$T_{\frac{1}{2}}$ space.

• Communications of the Korean Mathematical Society
• /
• v.26 no.2
• /
• pp.291-296
• /
• 2011

Cs$\'{a}$sz$\'{a}$r [3] introduced the notions of ${\gamma}$-compact and ${\gamma}$-operation on a topological space. In this paper, we introduce the notions of almost ${\Gamma}$-compact, (${\gamma},{\tau}$)-continuous function and (${\gamma},{\tau}$)-open function defined by ${\gamma}$-operation on a topological space and investigate some properties for such notions.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2001.05a
• /
• pp.34-37
• /
• 2001

Park et al. [Proc. KFIS Fall Conf. 10(2) (2000), 59-62] defined fuzzy ${\gamma}$-open sets by using an operation ${\gamma}$ on a fts (X, $\tau$) and investigated the related fuzzy topological properties of the associated fuzzy topology $\tau$/seb ${\gamma}$/ and $\tau$. As generalizations of the notion of fuzzy ${\gamma}$-closed sets, we define gf. ${\gamma}$-closed sets and g*f. ${\gamma}$-closed sets and study basic properties of these sets relative to union and intersection. Also, we introduce and study two classes of ftss called fuzzy ${\gamma}$-T* and fuzzy ${\gamma}$-T$_{1}$2/ spaces by using the notions of gf. ${\gamma}$-closed and g*f. ${\gamma}$-closed sets.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2000.11a
• /
• pp.59-62
• /
• 2000

In this paper we introduce the notion of fuzzy ${\gamma}$-open sets by using an operation ${\gamma}$ on fuzzy topological space (X, $\tau$) and investigate the related fuzzy topological properties of the associated fuzzy topology $\tau$$\_$${\gamma}$/ and $\tau$. And ${\gamma}$-T$\_$i/(i=0,1,2) separation axioms are defined in fuzzy topological spaces and the validity of some results analogous to those in fuzzy T$\_$i/ spaces due to Ganguly and Saha [2] are examined.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
• /
• 2003.09a
• /
• pp.9-9
• /
• 2003

Let $\Omega$ be a bounded, open, and polygonal domain in $R^2$ with re-entrant corners. We consider the following Partial Differential Equations: $$(I-\nabla\nabla\cdot+\nabla^{\bot}\nabla\times)u\;=\;f\;in\;\Omega$$, $$n\cdotu\;0\;0\;on\;{\Gamma}_{N}$$, $${\nabla}{\times}u\;=\;0\;on\;{\Gamma}_{N}$$, $$\tau{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$, $$\nabla{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$ where the symbol $\nabla\cdot$ and $\nabla$ stand for the divergence and gradient operators, respectively; $f{\in}L^2(\Omega)^2$ is a given vector function, $\partial\Omega=\Gamma_{D}\cup\Gamma_{N}$ is the partition of the boundary of $\Omega$; nis the outward unit vector normal to the boundary and $\tau$represents the unit vector tangent to the boundary oriented counterclockwise. For simplicity, assume that both $\Gamma_{D}$ and $\Gamma_{N}$ are nonempty. Denote the curl operator in $R^2$ by $$\nabla\times\;=\;(-{\partial}_2,{\partial}_1$$ and its formal adjoint by $${\nabla}^{\bot}\;=\;({-{\partial}_1}^{{\partial}_2}$$ Consider a weak formulation(WF): Find $u\;\in\;V$ such that $$a(u,v):=(u,v)+(\nabla{\cdot}u,\nabla{\cdot}v)+(\nabla{\times}u,\nabla{\times}V)=(f,v),\;A\;v{\in}V$$. (2) We assume there is only one singular corner. There are many methods to deal with the domain singularities. We introduce them shortly and we suggest a new Finite Element Methods by using Singular representation for the solution.

• Journal of The Korean Astronomical Society
• /
• v.43 no.5
• /
• pp.141-152
• /
• 2010

UBV I CCD photometry is obtained for the open clusters NGC 4609 and Hogg 15 in Crux. For NGC 4609, CCD data are presented for the first time. From new photometry we derive the reddening, distance modulus and age of each cluster - NGC 4609 : E(B-V ) = $0.37{\pm}0.03$, $V_0-M_V=10.60{\pm}0.08$, log $\tau$= 7.7 $\pm$ 0.1; Hogg 15 : E(B - V ) = 1.13 $\pm$ 0.11, $V_0-M_V$ = 12.50 $\pm$ 0.15, log $\tau$ $\lesssim$ 6.6. The young age of Hogg 15 strongly implies that WR 47 is a member of the cluster. We also determine the mass function of these clusters and obtain a slope $\Gamma$ = -1.2 ($\pm$0.3) for NGC 4609 which is normal and a somewhat shallow slope (${\Gamma}=-0.95{\pm}0.5$) for Hogg 15.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
• /
• 2003.09a
• /
• pp.6-6
• /
• 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
• /
• v.55 no.2
• /
• pp.405-413
• /
• 2018

In this work, we use the Faber polynomial expansions to find upper bounds for the coefficients of analytic bi-univalent functions in subclass $\Sigma({\tau},{\gamma},{\varphi})$ which is defined by subordination conditions in the open unit disk ${\mathbb{U}}$. In certain cases, our estimates improve some of those existing coefficient bounds.

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.30 no.2
• /
• pp.91-97
• /
• 2002

Dynamic extinction of solid propellants subjected to rapid pressure drop was studied with the aid of energy equation of condensed phase and flame model in gas phase. It is found that the total residence time($\tau_\gamma$) which measures the residing time of fuel in the reaction zone may play a crucial role in determining the dynamic response of the combustuion to extinction. Residence time was modeled by various combinations of diffusion and chemocal kinetic time scale. Effect of pressure history coupled with chamber volume on the extinction response was also performed and was found that dynamic extinction is more susceptible in a confined chamber than in open geometry. And, dynamic extinction was revealed to be affected profoundly by diffysion time scale rather than chemical kinetic time scale.