• Honam Mathematical Journal
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• v.30 no.3
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• pp.567-579
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• 2008

We obtain generalized super stability of Cauchy's gamma-beta functional equation B(x, y) f(x + y) = f(x)f(y), where B(x, y) is the beta function and also generalize the stability in the sense of R. Ger of this equation in the following setting: ${\mid}{\frac{B(x,y)f(x+y)}{f(x)f(y)}}-1{\mid}$ < H(x,y), where H(x,y) is a homogeneous function of dgree p(0 ${\leq}$ p < 1).

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.75-85
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• 2018

In this paper, we study nonconstant warping functions on an Einstein warped product manifold $M=B{\times}_{f^2}F$ with a warped product metric $g=g_B+f(t)^2g_F$. And we consider a 2-dimensional base manifold B with a metric $g_B=dt^2+(f^{\prime}(t))^2du^2$. As a result, we prove the following: if M is an Einstein warped product manifold with a 2-dimensional base, then there exist generally nonconstant warping functions f(t).

• Biomedical Science Letters
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• v.10 no.2
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• pp.153-161
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• 2004

Antibiotic resistance is often associated with the production of inner membrane proteins (for example, AcrAB/TolC efflux pump) that are capable to extrude antibiotics, detergents, dyes and organic solvents. In order to evaluate the unknown MarB function of Escherichia coli, especially focused on the function of OmpF porin, several mutants were construted by T4GT7 transduction. MarA plays a major roles in mar (multiple antibiotic resistance) phenotype with AcrAB/TolC efflux pump in E. coli K-12. Futhermore, MarA decreases OmpF porin expression via micF antisense RNA. Expression of acrAB is increased in strains containing mutation in marR, and in those carrying multicopy plasmid expressing marA. MarB protein of E. coli K-12 showed its activity at OmpF porin & TolC protein as target molecule. Some paper reported MarB positively regulates OmpF function. MarA shows mar phenotype, and MarB along with MarA show decreased MIC through OmpF function. By this experiment, MarB could decrease MIC through the OmpF porin & TolC protein as target.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.5
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• pp.251-257
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• 2018

We will be establish the new k stores of identical product firm $F_B$ to gain competitive advantage over rival firm $F_A$ that has already monopolize a market with k stores. In this situation, how we can decide the location of k stores? For this problem, Serra and Revelle proposes k-Median and MAXCAP integer programming using LP+BB to decide the k stores of firm $F_B$. Then they exchange the k stores to another location that cover more customers. This paper suggests non-neighborhood search method that finds the ${\upsilon}{\not\in}N_G(u)$nodes for u of firm $F_A$ without most outer loop nodes using just MS-Excel. As a result of experiment, the proposed algorithm can be get the optimal solution easier and faster than integer programming.

• Polymer(Korea)
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• v.31 no.6
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• pp.497-504
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• 2007

We have prepared the dinuclear half-sandwich CGC(constrained geometry catalyst) with polymethylene bridge $[Zr(({\eta}^5\;:\;{\eta}^1-C_9H_5SiMe_2NCMe_3)Me_2)_2\;[(CH_2)_n]$ [n=6(4), 9(5), 12(6)] by treating 2 equivalents of MeLi with the corresponding dichlorides compounds. To study the catalytic behavior of the dinuclear catalysts we conducted copolymerization of ethylene and 1-hexene in the presence of three kinds of boron cocatalysts, $Ph_3C^+[B(C_6F_5)_4]^-\;(B_1),\;B(C_6F_5)_3\;(B_3)$, and $Ph_3C^+[(C_6F_5)_3B-C_6F_4-B(C_6F_5)_3]^{2-}\;(B_2)$. It turned out that all active species formed by the combination of three dinuclear CGCs with three cocatalyst were very efficient catalysts for the polymerization of olefins. The activities increase as the bridge length of the dinuclear CGCs increases. At the same time the dinuclear cocatalyst exhibited the lowest activity among three cocatalysts. The prime observation is that the dinuclear cocatalyst gave rise to the formation of the copolymers with the least branches on the polyethylene backbone.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.497-504
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• 2011

In 1973, B. Y. Chen and K. Yano introduced the special conformally flat space for the generalization of a subprojective space. The typical example is a canal hypersurface of a Euclidean space. In this paper, we study the conditions for the base space B to be special conformally flat in the conharmonically flat warped product space $B^n{\times}_fR^1$. Moreover, we study the special conformally flat warped product space $B^n{\times}_fF^p$ and characterize the geometric structure of $B^n{\times}_fF^p$.

• Korean Journal of Food Science and Technology
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• v.16 no.2
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• pp.235-241
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• 1984

Two fractions of pectinesterase from Chinese cabbage were isolated by ammonium sulfate fractionation, ion exchange chromatography on DEAE-cellulose and Sephadex G-150 gel filtration. The fraction F-A and F-B were purified approximately 340- and 10-fold. The similar salt effects and pH optima (pH 7.5-8.0) were obtained for the two pectinesterase fractions. The maximum activity of both two. fractions were obtained at 20-50mM of divalent rations and at 250mM of monovalent rations. The apparent Michaelis constant of the F-A was 0.01% for citrus pectin. The temperature optima for F-A and F-B were $48^{\circ}$ and $55^{\circ}C$, respectively and both fractions were stable in the region of pH 5.0-8.0 at room temperature. The thermal inactivation of the two fractions followed the first order reaction kinetics. From D and Z-values obtained the thermal resistance of the two fractions were characterized.

• Kyungpook Mathematical Journal
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• v.13 no.2
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• pp.235-240
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• 1973

A k-dimensional vector bundle is a bundle ${\xi}=(E,P,B,F^k)$ with fibre $F^k$ satisfying the local triviality, where F is the field of real numbers R or complex numbers C ([1], [2] and [3]). Let $Vect_k(X)$ be the set consisting of all isomorphism classes of k-dimensional vector bundles over the topological space X. Then $Vect_F(X)=\{Vect_k(X)\}_{k=0,1,{\cdots}}$ is a semigroup with Whitney sum (${\S}1$). For a pair (X, A) of topological spaces, a difference isomorphism over (X, A) is a vector bundle morphism ([2], [3]) ${\alpha}:{\xi}_0{\rightarrow}{\xi}_1$ such that the restriction ${\alpha}:{\xi}_0{\mid}A{\longrightarrow}{\xi}_1{\mid}A$ is an isomorphism. Let $S_k(X,A)$ be the set of all difference isomorphism classes over (X, A) of k-dimensional vector bundles over X with fibre $F^k$. Then $S_F(X,A)=\{S_k(X,A)\}_{k=0,1,{\cdots}}$, is a semigroup with Whitney Sum (${\S}2$). In this paper, we shall prove a relation between $Vect_F(X)$ and $S_F(X,A)$ under some conditions (Theorem 2, which is the main theorem of this paper). We shall use the following theorem in the paper. THEOREM 1. Let ${\xi}=(E,P,B)$ be a locally trivial bundle with fibre F, where (B, A) is a relative CW-complex. Then all cross sections S of ${\xi}{\mid}A$ prolong to a cross section $S^*$ of ${\xi}$ under either of the following hypothesis: (H1) The space F is (m-1)-connected for each $m{\leq}dim$ B. (H2) There is a relative CW-complex (Y, X) such that $B=Y{\times}I$ and $A=(X{\times}I)$ ${\cap}(Y{\times}O)$, where I=[0, 1]. (For proof see p.21 [2]).

• East Asian mathematical journal
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• v.17 no.2
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• pp.233-237
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• 2001

The authors aim at presenting summation formulas of Appell's function $F_1$: $$F_1(a;b,b';1+a+b-b'+i;1,-1)\;(i=0,\;{\pm}1,\;{\pm}2,\;{\pm}3,\;{\pm}4,\;{\pm}5)$$, which, for i=0, yields a known result due to Srivastava.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.167-176
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• 2010

Let (B, $\check{g}$) and (N, $\hat{g}$) be Einstein manifolds. Then, we get a complete (necessary and sufficient) condition for the warped product manifold $B\;{\times}_f\;N\;:=\;(B\;{\times}\;N,\;\check{g}\;+\;f{\hat{g}}$) to be Einstein, and obtain a complete condition for the Einstein warped product manifold $B\;{\times}_f\;N$ to be weakly stable. Moreover, we get a complete condition for the map i : ($B,\;\check{g})\;{\times}\;(N,\;\hat{g})\;{\rightarrow}\;B\;{\times}_f\;N$, which is the identity map as a map, to be harmonic. Under the assumption that i is harmonic, we obtain a complete condition for $B\;{\times}_f\;N$ to be Einstein.