• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1561-1576
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• 2008

In this paper we shall prove some weighted norm inequalities of the form $${\int}_{R^n}\;|Tf(x)|^pu(x)dx\;{\leq}\;C_p\;{\int}_{R^n}\;|f(x)|^pNu(x)dx$$ for certain rough singular integral T and maximal singular integral $T^*$. Here u is a nonnegative measurable function on $R^n$ and N denotes some maximal operator. As a consequence, some vector valued inequalities for both T and $T^*$ are obtained. We shall also get a boundedness result of T on the Triebel-Lizorkin spaces.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1299-1324
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• 2014

We prove the existence of uniform attractors $\mathcal{A}_{\varepsilon}$ in the space $H^1(\mathbb{R}^N){\cap}L^p(\mathbb{R}^N)$ for the following non-autonomous nonclassical diffusion equations on $\mathbb{R}^N$, $$u_t-{\varepsilon}{\Delta}u_t-{\Delta}u+f(x,u)+{\lambda}u=g(x,t),\;{\varepsilon}{\in}(0,1]$$. The upper semicontinuity of the uniform attractors $\{\mathcal{A}_{\varepsilon}\}_{{\varepsilon}{\in}[0,1]}$ at ${\varepsilon}=0$ is also studied.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.85-92
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• 2021

In present paper, inspired by the recently paper [1], we give the mixed pressure-velocity regular criteria in view of Lorentz spaces for weak solutions to 3D micropolar equations in a half space. Precisely, if (0.1) ${\frac{P}{(e^{-{\mid}x{\mid}^2}+{\mid}u{\mid})^{\theta}}{\in}L^p(0,T;L^{q,{\infty}}({\mathbb{R}}^3_+))$, p, q < ∞, and (0.2) ${\frac{2}{p}}+{\frac{3}{q}}=2-{\theta}$, 0 ≤ θ ≤ 1, then (u, w) is regular on (0, T].

• Kyungpook Mathematical Journal
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• v.16 no.2
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• pp.177-182
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• 1976

• Kyungpook Mathematical Journal
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• v.46 no.2
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• pp.219-229
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• 2006

Using the integral average method, we establish some oscillation criteria for the nonlinear differential equation with damped term $$a(t)|{x}^{\prime}(t)|^{\sigma-1}{x}^{\prime}(t)^{\prime}+p(t)|{x}^{\prime}(t)|^{\sigma-1}{x}^{\prime}(t)+q(t)f(x(t))=0,\;{\sigma}>1$$, where the functions $a,\;p$ and $q$ are real-valued continuous functions defined on $[t_o,{\infty})$ with $a(t)>0,\;f(x){\in}C^1(\mathbb{R})$ and $\frac{f^{\prime}(u)}{|f^{({\sigma}-1)/{\sigma}}(u)|}{\geq}k>0$ for $u{\neq}0$.

• The Korean Journal of Nuclear Medicine
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• v.19 no.1
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• pp.103-111
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• 1985

Recently changes in thyroid physiology during acute and chronic medical illness were demonstrated. The serum $fT_3,\;rT_3,\;T_4,\;T_3,\;fT_4$, and TSH concentration were measured by radioimmunoassay method in 49 patients with critical illness and 10 normal subjects to assess the change of thyroid function in critical illness. The results were as follows; 1) The mean serum $fT_3$ concentration was $6.68{\pm}1.05pmol/ml$ in normal subjects while in patients with critical illness the serum $fT_3$ concentration was significantly lowered to $1.55{\pm}1.15pmol/ml$(p<0.001). 2) The mean serum $rT_3$ concentration was $0.22{\pm}0.44ng/ml$ in normal subjects and $0.42{\pm}0.37ng/ml$ in patient with critical illness. There was increment in critically ill patients as compared to normal subjects but no statistically significant difference(p>0.05). 3) The mean serum $T_3$ concentration was $1.24{\pm}0.25ng/ml$ in normal subjects and $0.56{\pm}0.56ng/ml$ in patients with criticial illness and there was significant difference in each other(p<0.005). 4) The mean serum $T_4,\;fT_4$, and TSH concentrations were $7.80{\pm}1.02{\mu}g/dl,\;1.26{\pm}0.39ng/dl,\;1.87{\pm}0.45{\mu}U/ml$ in normal subjects respectively and $6.02{\pm}3.06{\mu}g/dl,\;1.46{\pm}0.80ng/dl,\;1.74{\pm}0.79{\mu}U/ml$ in patients with critical illness and there was no significant difference between critically ill patients and normal subjects. 5) The ratio of mean serum concentration of $fT_3$ and $rT_3(fT_3/rT_3)$, $30.42{\pm}5.58$ in normal subjects was significantly higher(p<0.005) than the coresponding patients with critical illness. 6) The mean serum $fT_3$ concentration in expired cases(n=12) during admission was significant difference between expired and survived cases(p<0.005). The mean serum $rT_3$ centration was $0.67{\pm}0.58ng/ml$ in expired cases and $0.34{\pm}0.22ng/ml$ in survived cases with significant difference(p<0.005). Half of the cases who showed less than $3{\mu}g/dl$ of serum $T_4$ level were expired.

• Kyungpook Mathematical Journal
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• v.47 no.3
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• pp.425-438
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• 2007

In this paper, we establish some new oscillation criteria for a second-order delay dynamic equation $$u^{{\Delta}{\Delta}}(t)+p(t)u(\tau(t))=0$$ on a time scale $\mathbb{T}$. The results can be applied on differential equations when $\mathbb{T}=\mathbb{R}$, delay difference equations when $\mathbb{T}=\mathbb{N}$ and for delay $q$-difference equations when $\mathbb{T}=q^{\mathbb{N}}$ for q > 1.

• Korean Journal of Microbiology
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• v.31 no.1
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• pp.44-47
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• 1993

A replication initiation gene was identified and its nucleotide sequence has been determined from a 3.8 kb, chloramphenicol acethyltransferase conferring R-plasmid pSBK203 of Staphylococcus aures. Location of the replication related region of pSBK 203 was determined by interuption with pUC 119 at XBaI and MspI sites which resulted in inactivation of replication in Bacilius subtilis. Base sequence of this region revealed on open reading frame of 942 base pairs, which encoded a 314 amino acid protein. Base sequence homology with other rep of pT181 family plasmids such as pT181, pC221, pC223, pS194, pU112, and pCW7 was ranged from 78% to 97% and the predicted amino acid sequence homology was from 72% to 95%.

• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.55-66
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• 2014

In this paper, the authors establish the conditions for the extinction of solutions, in finite time, of the fast diffusive p-Laplace equation $u_t=div({\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)+a{\int}_{\Omega}u^q(y,t)dy$, 1 < p < 2, in a bounded domain ${\Omega}{\subset}R^N$ with $N{\geq}1$. More precisely, it is shown that if q > p-1, any solution vanishes in finite time when the initial datum or the coefficient a or the Lebesgue measure of the domain is small, and if 0 < q < p-1, there exists a solution which is positive in ${\Omega}$ for all t > 0. For the critical case q = p-1, whether the solutions vanish in finite time or not depends crucially on the value of $a{\mu}$, where ${\mu}{\int}_{\Omega}{\phi}^{p-1}(x)dx$ and ${\phi}$ is the unique positive solution of the elliptic problem -div(${\mid}{\nabla}{\phi}{\mid}^{p-2}{\nabla}{\phi}$) = 1, $x{\in}{\Omega}$; ${\phi}(x)$=0, $x{\in}{\partial}{\Omega}$. This is a main difference between equations with local and nonlocal sources.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.65-72
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• 2012

Let T > 0 be given. Let $(C[0,T],m_{\varphi})$ be the analogue of Wiener measure space, associated with the Borel proba-bility measure ${\varphi}$ on ${\mathbb{R}}$, let $(L_{2}[0,T],\tilde{\omega})$ be the centered Gaussian measure space with the correlation operator $(-\frac{d^{2}}{dx^{2}})^{-1}$ and ${\el}_2,\;\tilde{m}$ be the abstract Wiener measure space. Let U be the space of all sequence $<c_{n}>$ in ${\el}_{2}$ such that the limit $lim_{{m}{\rightarrow}\infty}\;\frac{1}{m+1}\;\sum{^{m}}{_{n=0}}\;\sum_{k=0}^{n}\;c_{k}\;cos\;\frac{k{\pi}t}{T}$ converges uniformly on [0,T] and give a set function m such that for any Borel subset G of $\el_2$, $m(\mathcal{U}\cap\;P_{0}^{-1}\;o\;P_{0}(G))\;=\tilde{m}(P_{0}^{-1}\;o\;P_{0}(G))$. The goal of this note is to study the relationship among the measures $m_{\varphi},\;\tilde{\omega},\;\tilde{m}$ and $m$.