• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.381-386
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• 1996

We consider the behavior of positive radial solutions (or, briefly, pp.r.s.) of the equation $$ (1.1) ^\Delta u + \lambda f(u) = 0 in\Omega, _u = 0 on \partial\Omega, $$ where $\Omega = {x \in R^n$\mid$A < $\mid$x$\mid$ < B}$ is an annulus in $R^n, n \geq 2, \lambda > 0 and f \geq 0$ is superlinear in u and satisfies f(0) = 0.

• Journal of the Korean Mathematical Society
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• v.32 no.2
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• pp.329-339
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• 1995

Let us consider the Neumann problem for a quasilinear equation $$ (I_\varepsilon) {\varepsilon^m div($\mid$\nabla_u$\mid$^{m-2}\nabla_u) - u$\mid$u$\mid$^{m-2} + f(u) = 0 in \Omega {\frac{\partial\nu}{\partial u} = 0 on \partial\Omega. $$ where $1 < m < N, N \geq 2, \varepsilon > 0, \Omega$ is a smooth bounded domain in $R^n$ and $\nu$ is the unit outer normal vector to $\partial\Omega$.

• Journal of Physiology & Pathology in Korean Medicine
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• v.25 no.1
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• pp.29-36
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• 2011

Nardostachyts chinensis (N. chinensis) belonging to the family Valerianaceae has been used to elicit stomachic and sedative effects. The MAPKs are serine/threonine kinases involved in the regulation of various cellular responses, such as cell proliferation, differentiation and apoptosis. The PKC also plays a key role in regulating the response of hematopoietic cells to both physiological and pathological inducers of proliferation and differentiation. This study investigated the signaling pathways on the U937 cell differentiation induced by N. chinensis. N. chinensis induced the differentiation of U937 cells, as shown by increased of differentiation surface antigen CD11b. Activation of ERK increased time-dependently in differentiation of U937 cells induced by N. chinensis, but activations of JNK and p38 were unaffected. Inhibitor of ERK (PD98059) significantly reduced CD11b expression induced by N. chinensis in U937 cells. In addition, N. chinensis increased protein level of PKC ${\beta}$I and PKC ${\beta}$II isoforms, but the protein level of PKC ${\alpha}$ and PKC ${\gamma}$was constant. PKC inhibitors (GF 109203X and H-7) inhibited U937 cell differentiation and the ERK activation induced by N. chinensis. These results indicated that PKC and ERK may be involved in U937 cell differentiation induced by N. chinensis.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.223-230
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• 2001

In this parper, we considered the uniqueness of positive time-solution to equation ${\Box}_g$u(t,$\chi$) - $c_n$u(t,$\chi$) + $c_n$u(t,$\chi$)$^[\frac{n+3}{n-3}]$ = 0, where $c_n$ = $\frac{n-1}{4n}$ and ${\Box}_g$ is the d'Alembertian for a Lorentzian warped manifold M = {a,$\infty$] $\times_f$ N.

• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.275-282
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• 2004

Let {$a_{ni},\;u_n\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be an arry of constants. Let {X_{ni},\;u_n\;{\leq}\;i\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be {$a_{ni}$}-uniformly integrable random variables. Weak laws for the weighted sums ${{\Sigma}_{i=u_n}}^{{\upsilon}_n}\;a_{ni}X_{ni}$ are obtained.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.10 no.11
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• pp.3296-3301
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• 2009

The results of PCPT(Pezocone Penetration Test) are widely used for the estimation of the undrained shear strength, for which the empirical cone factors($N_{kt}$, $N_{ke}$, $N_{{\Delta}u}$) need to be obtained at each site. In this study, the cone factors were estimated, for the soils at Bookmyun area in Changwon city, using the undrained shear strengths from the unconfined and UU triaxial compression tests. The parametric studies with plastic index and pore water pressure ratio were performed as well. $N_{kt}$, $N_{ke}$ and $N_{{\Delta}u}$ were estimated in the ranges of 8~40, 7~37, and 1~26 respectively. It was observed that there is a relationship between the cone factors, specially $N_{{\Delta}u}$, and the pore pressure ratio.

• East Asian mathematical journal
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• v.34 no.5
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• pp.703-713
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• 2018

Let $N{\geq}3$, $2^*=2N/(N-2)$ and $p{\in}(2,2^*)$. Our purpose in this paper is to consider multiple existence of solutions of problem $$-{\Delta}u-{\frac{\mu}{{\mid}x{\mid}^2}}+{\alpha}u={\mid}u{\mid}^{p-2}u+{\lambda}f\;u{\in}H^1({\mathbb{R}}^n)$$, where a, ${\lambda}$ > 0, ${\mu}{\in}(0,(N-2)^2/4)f{\in}H^{-1}({\mathbb{R}}^N)$, $f{\geq}0$ and $f{\neq}0$.

• Proceedings of the Korean Society of Crop Science Conference
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• 2000.04a
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• pp.72-73
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• 2000

• 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.

• Asian-Australasian Journal of Animal Sciences
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• v.10 no.4
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• pp.364-370
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• 1997

Four local cattle were ($145{\pm}9.7kg$) used in a $4{\times}4$ Latin square design to study the effect of different levels of rumen degradable protein (RDP) in straw based ration on purine derivatives excretion and microbial N supply in cattle. The four rations were formulated at the same amount of energy but varying RDP approximately 50 (U0), 75 (U1), 100 (U2) and 150 (U3) percent levels of RDP requirement for maintenance. They were fed ranged from 101 to 304 g RDP/d. Apparent digestibility of all nutrients increased significantly (p < 0.01) in cattle fed ration U2 than other rations. Rumen $NH_3-N$ concentration increased from 43 to 130 mg/l in response of RDP intake. Purine derivatives excretion increased significantly (p < 0.01) with incremental level of 203 g RDP/d (U2) intake and positively correlated (r=0.69, p < 0.01, n=16) with amount of RDP intake. The rates of rumen microbial N supply were 16.8, 27.2, 39.1 and 32.9 g/d for rations U0, U1, U2 and U3 respectively. Efficiency of microbial N supply (EMNS) per kg of DOMR were 19.0, 25.3, 33.0, and 28.6 g and per MJ of ME. Intake were 0.62, 1.00, 1.44 and 1.21 g for U0, U1, U2 and U3 respectively and highest results were obtained in cattle fed U2 ration. Results of this study suggest that PD excretion and EMNS were increased as incremental level of RDP intake (U2) in local cattle.