• Communications of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.1141-1158
• /
• 2018

Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

• Journal of the Korean Mathematical Society
• /
• v.42 no.3
• /
• pp.405-434
• /
• 2005

We establish appropriate $L^p$ estimates for a class of maximal operators $S_{\Omega}^{(\gamma)}$ on the product space $R^n\;\times\;R^m\;when\;\Omega$ lacks regularity and $1\;\le\;\gamma\;\le\;2.\;Also,\;when\;\gamma\;=\;2$, we prove the $L^p\;(2\;{\le}\;P\;<\;\infty)\;boundedness\;of\;S_{\Omega}^{(\gamma)}\;whenever\;\Omega$ is a function in a certain block space $B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ (for some q > 1). Moreover, we show that the condition $\Omega\;{\in}\;B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ is nearly optimal in the sense that the operator $S_{\Omega}^{(2)}$ may fail to be bounded on $L^2$ if the condition $\Omega\;{\in}\;B_q^{(0,0)}(S^{n-1}\;\times\;S^{m-1})$ is replaced by the weaker conditions $\Omega\;{\in}\;B_q^{(0,\varepsilon)}(S^{n-1}\;\times\;S^{m-1})\;for\;any\;-1\;<\;\varepsilon\;<\;0.$

• Journal of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.331-340
• /
• 1998

We define the spherical non-commutative torus $L_{\omega}$/ as the crossed product obtained by an iteration of l crossed products by actions of, the first action on C( $S^{2n＋l}$). Assume the fibres are isomorphic to the tensor product of a completely irrational non-commutative torus $A_{p}$ with a matrix algebra $M_{m}$ ( ) (m > 1). We prove that $L_{\omega}$/ $M_{p}$ (C) is not isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{mp}$ (C), and that the tensor product of $L_{\omega}$/ with a UHF-algebra $M_{p{\infty}}$ of type $p^{\infty}$ is isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{m}$ (C) $M_{p{\infty}}$ if and only if the set of prime factors of m is a subset of the set of prime factors of p. Furthermore, it is shown that the tensor product of $L_{\omega}$/, with the C＊-algebra K(H) of compact operators on a separable Hilbert space H is not isomorphic to C(Prim( $L_{\omega}$/)) $A_{p}$ $M_{m}$ (C) K(H) if Prim( $L_{\omega}$/) is homeomorphic to $L^{k}$ (n)$\times$ $T^{l'}$ for k and l' non-negative integers (k > 1), where $L^{k}$ (n) is the lens space.$T^{l'}$ for k and l' non-negative integers (k > 1), where $L^{k}$ (n) is the lens space.e.

• Korean Journal of Environment and Ecology
• /
• v.30 no.3
• /
• pp.415-422
• /
• 2016

This study measured the vitality of Pinus densiflora and Ginko biloba and analyzed the differences of vitality levels among trees based on artificial management. Research has shown that the mean value of cambial electrical resistance (CER) on Pinus densiflora was $14.9K{\Omega}$(between $8.5{\sim}37.5K{\Omega}$), and for Ginko biloba it was $13.5K{\Omega}$ (between 6.4 and $40.5K{\Omega}$). For the purpose of artificial management, over 50% of trees were covered up with soil and about 40% of trees were not protected by fence to enable growth spaces. It was seen that the CER of trees covered up with soil was significantly higher than that of trees which were not covered up with soil. These results indicate that it is necessary to remove the soil covering for effective management of monumental trees.

• Pediatric Gastroenterology, Hepatology & Nutrition
• /
• v.17 no.2
• /
• pp.121-124
• /
• 2014

Omega (${\omega}$)-3 polyunsaturated fatty acids appear to be effective in preventing and treating parenteral nutrition-associated liver disease, and several mechanisms were proposed for this observation. An 8-week-old male infant with cholestasis and acholic stool was diagnosed non-syndromic intrahepatic interlobular bile duct paucity by open-wedge liver biopsy. Initially he was treated with usual supportive medical therapy, including ursodeoxycholic acid. However, the clinical status and laboratory tests did not improve. Omega (${\omega}$)-3 polyunsaturated fatty acids (initially intravenous administration and oral administration later), were started and his liver function, including aminotransferase level and bilirubin levels normalized, and the ivory stool color turned green. We report the possible effectiveness of ${\omega}$-3 polyunsaturated fatty acids as a potent choleretic agent for non-syndromic intrahepatic interlobular bile duct paucity, a very rare structural pediatric hepatic disease.

• The Pure and Applied Mathematics
• /
• v.17 no.4
• /
• pp.341-346
• /
• 2010

Category $E({\Omega},A)$ forms a topos. We study on some properties of the topos $E({\Omega},A)$. In particular, we show that $E({\Omega},A)$ is well-pointed.

• Communications of the Korean Mathematical Society
• /
• v.26 no.1
• /
• pp.135-149
• /
• 2011

Using (r, s)-preopen sets [14] and pre-${\omega}_t$-closures [6], a new kind of covering property $P^t_{({\omega}_r,s)}$-closedness is introduced in a bitopological space and several characterizations via filter bases, nets and grills [30] along with various properties of such concept are investigated. Two new types of cluster sets, namely pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets and (r, s)t-${\theta}_f$-precluster sets of functions and multifunctions between two bitopological spaces are introduced. Several properties of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets are investigated and using the degeneracy of such cluster sets, some new characterizations of some separation axioms in topological spaces or in bitopological spaces are obtained. A sufficient condition for $P^t_{({\omega}_r,s)}$-closedness has also been established in terms of pre-(${\omega}_r$, s)t-${\theta}_f$-cluster sets.

• Journal of the Korean Mathematical Society
• /
• v.55 no.1
• /
• pp.17-28
• /
• 2018

In this paper, we enlarge the ball of convergence of a uniparametric family of secant-like methods for solving non-differentiable operators equations in Banach spaces via using ${\omega}$-condition and centered-like ${\omega}$-condition meantime as well as some fine techniques such as the affine invariant form. Numerical examples are also provided.

• Structural Engineering and Mechanics
• /
• v.13 no.6
• /
• pp.671-694
• /
• 2002

This paper presents theoretical investigation on the cross correlation between torsional vibration ($u_{\theta}$) and translation vibration ($u_x$) of asymmetrical structure under white noise excitation. The formula reveals that the cross correlation coefficient (${\rho}$) is a function of uncoupled frequency ratio (${\Omega}={\omega}_{\theta}/{\omega}_x$), eccentricity, and damping ratio (${\xi}$). Simulations involving acceleration records from fifteen different earthquakes show correlation coefficients results similar to the theoretical correlation coefficients. The uncoupled frequency ratio is the dominating parameter to ${\rho}$; generally, ${\rho}$ is positive for ${\omega}_{\theta}/{\omega}_x$ > 1.0, negative for ${\omega}_{\theta}/{\omega}_x$ < 1.0, and close to zero for ${\omega}_{\theta}/{\omega}_x$ = 1.0. When the eccentricity or damping ratio increases, ${\rho}$ increases moderately for small ${\Omega}$ (< 1.0) only. The relation among $u_x$, $u_{\theta}$ and corner displacement are best presented by ${\rho}$; a simple way to hand-calculate the theoretical dynamic corner displacements from $u_x$, $u_{\theta}$ and ${\rho}$ is proposed as an alternative to dynamic analysis.

• Journal of the Korean Applied Science and Technology
• /
• v.2 no.1
• /
• pp.33-36
• /
• 1985

The fatty acid composition of Phospholipids from human mature milk, modified milk formula and market milk were analyzed by gas-liquid chromatography. The levels of 8:0, 10:0, 19:0, 20:0 and 22:0 were significantly higher in modified milk formula than in human milk. The levels of 14:0 and 16:0 were significantly lower in modified milk formula than in human milk. Modified milk formula had a higher $18:2{\omega}6$ content than human milk (17.9 versus 7.9%). The metabolites of the ${\omega}$9-, ${\omega}$6-$ and ${\omega}$3-series showed lower levels in modified milk formula than in human milk. The fatty acid composition of phospholipids from modified milk formula was similar to that of market milk.