• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.1
• /
• pp.65-70
• /
• 2007

We study the existence of nontrivial solutions of the Gradient type Dirichlet boundary value problem for elliptic systems of the form $-{\Delta}U(x)={\nabla}F(x,U(x)),x{\in}{\Omega}$, where ${\Omega}{\subset}R^N(N{\geq}1)$ is a bounded regular domain and U = (u, v) : ${\Omega}{\rightarrow}R^2$. To study the system we use the liking theorem on product space.

• Journal of the Chungcheong Mathematical Society
• /
• v.25 no.3
• /
• pp.401-413
• /
• 2012

In the present paper we construct and introduce a new topology from an old one which are independent each of the other. The members of this topology are called ${\omega}_{\delta}$-open sets. We investigate some basic properties and their relationships with some other types of sets. Furthermore, a new characterization of regular and semi-regular spaces are obtained. Also, we introduce and study some new types of continuity, and we obtain decompositions of some types of continuity.

• Journal of the Korean Mathematical Society
• /
• v.34 no.4
• /
• pp.871-894
• /
• 1997

For a lifted nontrivial additive character $\lambda'$ and a multiplicative character $\chi$ of the finite field with $q^2$ elements, the 'Gauss' sums $\Sigma\lambda'$(tr $\omega$) over $\omega$ $\in$ SU(2n + 1, $q^2$) and $\Sigma\chi$(det $\omega$)$\lambda'$(tr $\omega$) over $\omega$ $\in$ U(2n + 1, $q^2$) are considered. We show that the first sum is a polynomial in q with coefficients involving certain new exponential sums and that the second one is a polynomial in q with coefficients involving powers of the usual twisted Kloosterman sums and the average (over all multiplicative characters of order dividing q-1) of the usual Gauss sums. As a consequence we can determine certain 'generalized Kloosterman sum over nonsingular Hermitian matrices' which were previously determined by J. H. Hodges only in the case that one of the two arguments is zero.

• Journal of applied mathematics & informatics
• /
• v.31 no.5_6
• /
• pp.677-693
• /
• 2013

We construct exponentially fitted interpolation formulas using the values of the ${\omega}$-dependent function $f$ as well as its derivatives up to the $n$th order at a finite number of nodes on a closed interval ${\Omega}$. The function $f$ is of the form, $$f(x)=f_1(x)cos({\omega}x)+f_2(x)sin({\omega}x),x{\in}{\Omega}$$, where $f_1$ and $f_2$ are smooth enough to be approximated by polynomials on ${\Omega}$. Some properties of the formulas are newly found. The properties are numerically investigated and reexamined by producing some figures.

• Korean Journal of Mathematics
• /
• v.17 no.4
• /
• pp.473-480
• /
• 2009

We prove the existence and multiplicity of nontrivial solutions for a fourth order problem ${\Delta}^2u+c{\Delta}u={\alpha}u-{\beta}(u+1)^-$ in ${\Omega}$, ${\Delta}u=0$ and $u=0$ on ${\partial}{\Omega}$, where ${\lambda}_1{\leq}c{\leq}{\lambda}_2$ (where $({\lambda}_i)_{i{\geq}1}$ is the sequence of the eigenvalues of $-{\Delta}$ in$H_0^1({\Omega})$) and ${\Omega}$ is a bounded open set in $R^N$ with smooth boundary ${\partial}{\Omega}$. The results are proved by applying minimax arguments and linking theory.

• Journal of the Korean Mathematical Society
• /
• v.48 no.2
• /
• pp.341-365
• /
• 2011

In this paper, we establish general stratawise higher jet evaluation transversality of J-holomorphic curves for a generic choice of almost complex structures J (tame to a given symplectic manifold (M, $\omega$)). Using this transversality result, we prove that there exists a subset $\cal{J}^{ram}_{\omega}\;{\subset}\;\cal{J}_{\omega}$ of second category such that for every $J\;{\in}\;\cal{J}^{ram}_{\omega}$, the dimension of the moduli space of (somewhere injective) J-holomorphic curves with a given ramication prole goes down by 2n or 2(n - 1) depending on whether the ramication degree goes up by one or a new ramication point is created. We also derive that for each $J\;{\in}\;\cal{J}^{ram}_{\omega}$ there are only a finite number of ramication profiles of J-holomorphic curves in a given homology class $\beta\;{\in}\;H_2$(M; $\mathbb{Z}$) and provide an explicit upper bound on the number of ramication proles in terms of $c_1(\beta)$ and the genus g of the domain surface.

• Communications of the Korean Mathematical Society
• /
• v.11 no.2
• /
• pp.503-514
• /
• 1996

We consider non-constant coefficient elliptic equations of the type -div(a \bigtriangledown u) = f$, and employ the P-version of the finite element method as a numerical method for the approximate solutions. To compute the integrals in the variational form of the discrete problem we need the numerical quadrature rule scheme. In practice the integrations are seldom computed exactly. In this paper, we give an $L_2(\Omega)$-error estimate of $\Vert u = \tilde{u}_p \Vert_{0,omega}$ in comparison with $\Vert u = \tilde{u}_p \Vert_{1,omega}$, under numerical quadrature rules which are used for calculating the integrations in each of the stiffness matrix and the load vector.

• Communications of the Korean Mathematical Society
• /
• v.21 no.1
• /
• pp.65-74
• /
• 2006

In this paper, we will define the Bergman projection type operator Pr and find conditions on which the operator Pr is bound-ed on $L^p$(B, dv). By using the properties of the Bergman projection type operator Pr, we will show that if $f{\in}L_a^p$(B, dv), then $(1-{\parallel}{\omega}{\parallel}^2){\nabla}f(\omega){\cdot}z{\in}L^p(B,dv)$. We will also show that if $(1-{\parallel}{\omega}{\parallel}^2)\; \frac{{\nabla}f(\omega){\cdot}z}{},\;{\in}L^p{B,\;dv),\;then\;f{\in}L_a^p(B,\;dv)$.

• Bulletin of the Korean Mathematical Society
• /
• v.49 no.5
• /
• pp.1067-1079
• /
• 2012

Let M be a right R-module, (S, ${\leq}$) a strictly totally ordered monoid which is also artinian and ${\omega}:S{\rightarrow}Aut(R)$ a monoid homomorphism, and let $[M^{S,{\leq}}]_{[[R^{S,{\leq}},{\omega}]]$ denote the generalized inverse polynomial module over the skew generalized power series ring [[$R^{S,{\leq}},{\omega}$]]. In this paper, we prove that $[M^{S,{\leq}}]_{[[R^{S,{\leq}},{\omega}]]$ has the same uniform dimension as its coefficient module $M_R$, and that if, in addition, R is a right perfect ring and S is a chain monoid, then $[M^{S,{\leq}}]_{[[R^{S,{\leq}},{\omega}]]$ has the same couniform dimension as its coefficient module $M_R$.

• Journal of Electrical Engineering and Technology
• /
• v.8 no.3
• /
• pp.610-612
• /
• 2013

A novel balanced distributed amplifier (DA) was proposed using novel impedance transforming MEMS baluns. The impedance transforming MEMS balun is matched to $50{\Omega}$ at one input port and $25{\Omega}$ at two output ports. It is based on the electric field mode-change method, thus it is strongly independent of frequency and very compact. The novel balanced DA consists of two $25{\Omega}$-matched DAs and these are combined by $50{\Omega}$-to-$25{\Omega}$ baluns. Theoretically, it has two times wider bandwidth and power capability than the conventional DA. So as to verify the proposed concept, we designed and fabricated a conventional DA and the proposed one using 0.15-${\mu}m$ GaAs pHEMT technology.