• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.17-31
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• 1995

A Lorentzian para-Sasakian manifold M$(\varphi, \zeta, \eta, g)$ (abr. LPS-manifold) has been defined and studied in [9] and [10]. On the other hand, para-Sasakian (abr. PS)-manifolds are special semi-cosympletic manifolds (in the sense of [2]), that is, they are endowed with an almost cosympletic 2-form $\Omega$ such that $d^{2\eta}\Omega = \psi(d^\omega$ denotes the cohomological operator [6]), where the 3-form $\psi$ is the associated Lefebvre form of $\Omega$ ([8]). If $\eta$ is exact, $\psi$ is a $d^{2\eta}$-exact form, the manifold M is called an exact Ps-manifold. Clearly, any LPS-manifold is endowed with a semi-cosymplectic structure (abr. SC-structure).

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.409-421
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• 2014

This paper deals with the superlinear elliptic problem without Ambrosetti and Rabinowitz type growth condition of the form: $$\{-div\((1+\frac{|{\nabla}u|^{p(x)}}{\sqrt{1+|{\nabla}u|^{2p(x)}}}})|{\nabla}u|^{p(x)-2}{\nabla}u\)={\lambda}f(x,u)\;a.e.\;in\;{\Omega}\\u=0,\;on\;{\partial}{\Omega}$$ where ${\Omega}{\subset}R^N$ is a bounded domain with smooth boundary ${\partial}{\Omega}$, ${\lambda}$ > 0 is a parameter. The purpose of this paper is to obtain the existence results of nontrivial solutions for every parameter ${\lambda}$. Firstly, by using the mountain pass theorem a nontrivial solution is constructed for almost every parameter ${\lambda}$ > 0. Then we consider the continuation of the solutions. Our results are a generalization of that of Manuela Rodrigues.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.303-308
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• 1995

We consider a torus T, that is, a compact surface with genus 1 and $\Omega = D^2 \times S^1$ topologically with $\partial\Omega = T$, where $D^2$ is the open unit disk and $S^1$ is the unit circle. Let $\omega = (x,y)$ denote the generic point on T. For a smooth immersion $u : T \to R^3$, we define the Dirichlet functional by $$ E(u) = \frac{2}{1} \int_{T} $\mid$\nabla u$\mid$^2 d\omega $$ and the volume functional by $$ V(u) = \frac{3}{1} \int_{T} u \cdot u_x \Lambda u_y d\omege $$.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.25-31
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• 1999

Let $\nu$ be a positive Borel measure on a space of homogeneous type (X, d, $\mu$), satisfying the doubling property. A condition on a weight $\omega$ for whixh a maximal operator $M\nu f$(x) defined by M$mu$f(x)=supr>0{{{{ { 1} over {ν(B(x,r)) } INT _{ B(x,r)} │f(y)│d mu (y)}}}}, is of weak type (p,p) with respect to (ν, $omega$), is that there exists a constant C such that C $omega$(y) for a.e. y$\in$B(x, r) if p=1, and {{{{( { 1} over { upsilon (B(x,r) } INT _{ B(x,r)}omega(y) ^ (-1/p-1) d mu (y))^(p-1)}}}} C, if 1$infty$.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.83-91
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• 2003

We prove a unique continuation theorem for $C^{\infty}$ functions in pseudoconvex domains in ${\mathbb{C}}^{n}$. More specifically, we show that if ${\Omega}$ is a pseudoconvex domain in ${\mathbb{C}}^n$, if f is in $C^{\infty}({\Omega})$ such that for all multi-indexes ${\alpha},{\beta}$ with ${\mid}{\beta}{\mid}{\geq}1$ and for any positive integer k, there exists a positive constant $C_{{\alpha},{\beta},{\kappa}}$ such that $$|{\frac{{\partial}^{{\mid}{\alpha}{\mid}+{\mid}{\beta}{\mid}}f}{{\partial}z^{\alpha}{\partial}{\bar{z}}^{\beta}}{\mid}{\leq}C_{{\alpha},{\beta},{\kappa}}{\mid}f{\mid}^{\kapp}}\;in\;{\Omega}$$, and if there exists $z_0{\in}{\Omega}$ such that f vanishes to infinite order at $z_0$, then f is identically zero. We also have a sharp result for the case of strongly pseudoconvex domains.

• East Asian mathematical journal
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• v.14 no.1
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• pp.63-76
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• 1998

we consider the hp-version to solve non-constant coefficients elliptic equations $-div(a{\nabla}u)=f$ with Dirichlet boundary conditions on a bounded polygonal domain $\Omega$ in $R^2$. In [6], M. Suri obtained an optimal error-estimate for the hp-version: ${\parallel}u-u^h_p{\parallel}_{1,\Omega}{\leq}Cp^{(\sigma-1)}h^{min(p,\sigma-1)}{\parallel}u{\parallel}_{\sigma,\Omega}$. This optimal result follows under the assumption that all integrations are performed exactly. In practice, the integrals are seldom computed exactly. The numerical quadrature rule scheme is needed to compute the integrals in the variational formulation of the discrete problem. In this paper we consider a family $G_p=\{I_m\}$ of numerical quadrature rules satisfying certain properties, which can be used for calculating the integrals. Under the numerical quadrature rules we will give the variational form of our non-constant coefficients elliptic problem and derive an error estimate of ${\parallel}u-\tilde{u}^h_p{\parallel}_{1,\Omega}$.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.591-599
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• 2009

For given ${\alpha},{\omega}\;{\in}\;{\mathbb{R}}$ and ${\beta}$ > 1, let $T_{{\beta},{\alpha},{\omega}}$ be the skew-product transformation on the torus, [0, 1) ${\times}$ [0, 1) defined by (x, y) ${\longmapsto}\;({\beta}x,y+{\alpha}x+{\omega})$ (mod 1). In this paper, we give a criterion of ergodicity and weakly mixing for the transformation $T_{{\beta},{\alpha},{\omega}}$ when the natural extension of the given ${\beta}$-transformation can be viewed as a generalized baker's transformation, i.e., they flatten and stretch and then cut and stack a two-dimensional domain. This is a generalization of theorems in [10].

• Korean Journal of Poultry Science
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• v.30 no.4
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• pp.289-299
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• 2003

Effects of various combinations of corn oil (CO) and perilla oil (PO) as respective dietary sources of ${\omega}$-6 and ${\omega}$-3 polyunsaturated fatty acids on fatty acid profiles of immune organs were studied in young chicks. Seventy-five 1-day-old male (ISA Brown) chicks were assigned to five treatments with three replications. Semi-purified-type diets containing glucose and soybean meal as major ingredients were added with 8% CO, 6% CO+2% PO, 4% CO+4% PO, 2% CO+6% PO and 8% PO and fed for 7 weeks. There were no significant differences in body weight gain, feed intake and relative weights of liver and immune organs (g/100g weight) among dietary groups. Dietary fatty acid patterns were generally reflected in the fatty acid compositions of all immune organs such as spleen, thymus and bursa of Fabricius. The levels of a-linolenic acid(LNA), eicosapentaenoic acid (EPA) and docosahexaenoic acid in various immune organs increased with increasing levels of perilla oil in the diets, whilet the levels of linoleic acid (LA) and arachidonic acid (AA) decreased. Thymus appeared to have capacity to retain remarkably higher (P<0.05) levels of LA and LNA up to 37 and 22%, respectively, compared to the other organs. Thymic tissue contained ${\omega}$-3 fatty acid and ${\omega}$-6 fatty acid 10~36 times and 3~5 times higher than the other organs, respectively. Spleen tissue was specifically higher (P<0.05) in the levels of AA and EPA and the ratios of AA/LA and EPA/LNA, compared to the other organs, suggesting that the tissue might have high desaturase activity to convert LA or LNA to AA or EPA, respectively. BSA antibody production tended to increase by 18 ~ 32% with higher levels of perilla oil in diet, although the increase was not statistically significant. In conclusion, fatty acid compositions of immune organs very depending on the lipid composition of the diets and each organ appears to respond differently for its fatty acid profile to dietary lipids. Considering AA and EPA are precursors of many important eicosanoids, further studies are required to clarify the responses of the immune organs to the dietary fatty acids.

• Journal of the Korean Society of Food Culture
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• v.15 no.3
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• pp.163-174
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• 2000

This research was designed to develop a computer program and evaluate the nutritional balances especially the balance of fatty acids, amino acids and antioxidant vitamins for convenience foods. The Korean convenience food, Kimbab purchased from markets was evaluated by using the self-developed computer program. Contents of calories, protein and calcium were lower$(1/3^{\circ}{\neq}1/2)$ than the recommended levels of Korean adult woman, and the carbohydrate/ protein/ fat(CPF) energy ratio was 70: 13: 17. The mean P/ M/ S ratio was 2.2/ 1.4/ 1 and that of ${\omega}6/\;{\omega}3$ fatty acids was 17.9/ 1, which was higher than the desirable ratio of $4{\sim}8/\;1$. Average essential amino acid balance of market-Kimbab samples was within the desirable range even though the absolute amount of protein was lower than the recommended level. Contents of antioxidant vitamins (A, C &E) were lower than recommended levels. Two kinds of nutritionally adjusted Kimbab menu were established by self-developed computer program. Some of major changes was adding food ingredients such as tuna fish and perilla leaf cooked with sesame oil and soybean oil to increase ${\omega}3$ series fatty acids. Some fruits and milk were also added to the menu. The adjusted CPF ratios was 63: 15: 22 and the new values for P/ M/ S and ${\omega}6/\;{\omega}3$ fatty acids ratios were 1.0/ 1.2/ 1/0 and 6.1/ 1 respectively. In sensory evaluation of two kinds of adjusted Kimbab, the taste and overall estimation scores were higher than unadjusted Kimbab. The computer program developed in this study might be used as a tool for the evaluation of nutritional balance of other convenience foods and menu planning.

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