• Communications of the Korean Mathematical Society
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• v.22 no.1
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• pp.65-74
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• 2007

Suppose that $\mu$ is a finite positive Borel measure on bounded symmetric domain $\Omega{\subset}\mathbb{C}^n\;and\;\nu$ is the Euclidean volume measure such that $\nu(\Omega)=1$. Suppose 1 < p < $\infty$ and r > 0. In this paper, we will show that the norms $sup\{\int_\Omega{\mid}k_z(w)\mid^2d\mu(w)\;:\;z\in\Omega\}$, $sup\{\int_\Omega{\mid}h(w)\mid^pd\mu(w)/\int_\Omega{\mid}h(w)^pd\nu(w)\;:\;h{\in}L_a^p(\Omega,d\nu),\;h\neq0\}$ and $$sup\{\frac{\mu(E(z,r))}{\nu(E(z,r))}\;:\;z\in\Omega\}$$ are are all equivalent. We will also show that the inclusion mapping $ip\;:\;L_a^p(\Omega,d\nu){\rightarrow}L^p(\Omega,d\mu)$ is compact if and only if lim $w\rightarrow\partial\Omega\frac{\mu(E(w,r))}{\nu(E(w,r))}=0$.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.211-214
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• 1995

Let M and N be compact Riemannian manifolds and $f : M \to N$ be a smooth map. Following J. Eells, f is exponentially harmonic if it represents a critical point of the exponential energy integral $$ E(f) = \int_{M} exp(\left\$\mid$ df \right\$\mid$^2) dM $$ where $(\left\ df $\mid$\right\$\mid$^2$ is the energy density defined as $\sum_{i=1}^{m} \left\$\mid$ df(e_i) \right\$\mid$^2$, m = dimM, for orthonormal frame $e_i$ of M. The Euler- Lagrange equation of the exponential energy functional E can be written $$ exp(\left\$\mid$ df \right\$\mid$^2)(\tau(f) + df(\nabla\left\$\mid$ df \right\$\mid$^2)) = 0 $$ where $\tau(f)$ is the tension field along f. Hence, if the energy density is constant, every harmonic map is exponentially harmonic and vice versa.

• BMB Reports
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• v.50 no.4
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• pp.186-193
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• 2017

In mammals, cap-dependent translation of mRNAs is initiated by two distinct mechanisms: cap-binding complex (CBC; a heterodimer of CBP80 and 20)-dependent translation (CT) and eIF4E-dependent translation (ET). Both translation initiation mechanisms share common features in driving cap- dependent translation; nevertheless, they can be distinguished from each other based on their molecular features and biological roles. CT is largely associated with mRNA surveillance such as nonsense-mediated mRNA decay (NMD), whereas ET is predominantly involved in the bulk of protein synthesis. However, several recent studies have demonstrated that CT and ET have similar roles in protein synthesis and mRNA surveillance. In a subset of mRNAs, CT preferentially drives the cap-dependent translation, as ET does, and ET is responsible for mRNA surveillance, as CT does. In this review, we summarize and compare the molecular features of CT and ET with a focus on the emerging roles of CT in translation.

• BMB Reports
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• v.50 no.4
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• pp.194-200
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• 2017

Eukaryotic gene expression is precisely regulated at all points between transcription and translation. In this review, we focus on translational control mediated by the 3'-untranslated regions (UTRs) of mRNAs. mRNA 3'-UTRs contain cis-acting elements that function in the regulation of protein translation or mRNA decay. Each RNA binding protein that binds to these cis-acting elements regulates mRNA translation via various mechanisms targeting the mRNA cap structure, the eukaryotic initiation factor 4E (eIF4E)-eIF4G complex, ribosomes, and the poly (A) tail. We also discuss translation-mediated regulation of mRNA fate.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.3
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• pp.555-564
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• 1994

This study has been made to investigate the stress distribution around defects and inclusions that behave as stress concentrators. The stress distribution and interation effects around defects and inclusions was analyzed using Finite Element Method. The results are as follows;(1) Maximum stress point in case of $E_I/E_M>1$($E_I$:elasticity modulus forthe inclusion, $E_M$/:elasticity modulus for the base material)is the vertical point with respect to force direction and in case of $E_I/E_M<1$ it is the parallel point along the hole edge. (2) Interaction effects of ${\sigma}_y$ for the inclusion side is larger than the defect side when the interval between inclusion and defect is near. (3) stress interation effects is large if the difference of ${\sigma}_y$ is small and it is small if the difference of ${\sigma}_y$ is large for the case that the interval between inclusion and defect whose size and property are different is near.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1157-1163
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• 2009

Let G be a graph with vertex set V(G) and let f be a nonnegative integer-valued function defined on V(G). A spanning subgraph F of G is called a fractional f-factor if $d^h_G$(x)=f(x) for all x $\in$ for all x $\in$ V (G), where $d^h_G$ (x) = ${\Sigma}_{e{\in}E_x}$ h(e) is the fractional degree of x $\in$ V(F) with $E_x$ = {e : e = xy $\in$ E|G|}. In this paper it is proved that if ${\delta}(G){\geq}{\frac{b^2(k-1)}{a}},\;n>\frac{(a+b)(k(a+b)-2)}{a}$ and $|N_G(x_1){\cup}N_G(x_2){\cup}{\cdots}{\cup}N_G(x_k)|{\geq}\frac{bn}{a+b}$ for any independent subset ${x_1,x_2,...,x_k}$ of V(G), then G has a fractional f-factor. Where k $\geq$ 2 be a positive integer not larger than the independence number of G, a and b are integers such that 1 $\leq$ a $\leq$ f(x) $\leq$ b for every x $\in$ V(G). Furthermore, we show that the result is best possible in some sense.

• THE INTERNATIONAL COMMERCE & LAW REVIEW
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• v.20
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• pp.387-421
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• 2003

On the above, a comparison between preliminary draft conventions and comments by the Int'l Chamber of Commerce, contents of preliminary draft convention, problems and alternative are discussed. The conclusions are as follows thereof : The laws of MLEC and MLES made preparation for electronic era of CISG. But electronic circumstances are more changed than the time of regulation of them. Therefore the business world needs a stand-alone convention dealing broadly with the issues of contract formation in electronic commerce. At last, preliminary draft convention delivered a second round. But the base of the instrument was also MLEC and MLES. The revised preliminary draft convention is much amended beyond preliminary draft convention. At its forty-one sessions, the working group reviewed articles 1-11 of the revised preliminary draft convention presented by the secretariat. The remainder was pending until the time of its forty-two sessions. Therefore, on the base of deliberations and decisions of that sessions and them of thirty-six sessions of UNCITRAL, which will be held on comming november, the draft convention which will be prepared by the secretariate, be re-revised preliminary draft convention. According to review of working group on them, preliminary draft convention will officially be draft convention or revise by secretariate. Under these situations, my points of view on draft convention are as follows : As though e-UCP is used carring out side by side with UCP, after e-CISG making in order to adjust CISG to "on" transaction, it is very easy and prompt for business worked to use CISG with e-CISG. This will facilitate ratification of the CISG. For this case, I already presented contents of e-CISG. It is very important for the preliminary draft convention to deal specially with issues related to electronic contracting or to electronic transaction, because according to which way, its contents and scope of application will be different. But the revised draft convention is regretably compromising both them. Consequently, its contents are very confusing and we could not expect its success. If e-CISG will regulate, it is desirable that, if possible, working group has to make the general rule, and the making of useful, practical, affordable rule for electronic commerce, for example Uniform Customs and Practices for Electronic Commerce(e-UEC) in order to solve the specific practical problems, if any, which business currently faces regarding electronic contracting, has to entrust ICC. If working group want to make e-CISG, it is important not to hesitate and take a significant amount of time.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.209-215
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• 2000

Let X be a locally convex space. A series of clearcut characterizations for the boundedness of vector measure $\mu{\;}:{\;}\sum\rightarrow{\;}X$ is obtained, e.g., ${\mu}$ is bounded if and only if ${\mu}(A_j){\;}\rightarrow{\;}0$ weakly for every disjoint $\{A_j\}{\;}\subseteq{\;}\sum$ and if and only if $\{\frac{1}{j^j}{\mu}(A_j)\}^{\infty}_{j=1}$ is bounded for every disjoint $\{A_j\}{\;}\subseteq{\;}\sum$.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.677-685
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• 2023

For n ≥ 2 and a real Banach space E, 𝓛(ⁿE : E) denotes the space of all continuous n-linear mappings from E to itself. Let Π (E) = {[x^*, (x₁, . . . , x_n)] : x^*(x_j) = ||x^*|| = ||x_j|| = 1 for j = 1, . . . , n }. An element [x^*, (x₁, . . . , x_n)] ∈ Π(E) is called a numerical radius point of T ∈ 𝓛(ⁿE : E) if |x^*(T(x₁, . . . , x_n))| = v(T), where the numerical radius v(T) = sup_{[y^*,y1,...,yn]∈Π(E)}|y^*(T(y₁, . . . , y_n))|. For T ∈ 𝓛(ⁿE : E), we define Nradius(T) = {[x^*, (x₁, . . . , x_n)] ∈ Π(E) : [x^*, (x₁, . . . , x_n)] is a numerical radius point of T}. T is called a numerical radius peak n-linear mapping if there is a unique [x^*, (x₁, . . . , x_n)] ∈ Π(E) such that Nradius(T) = {±[x^*, (x₁, . . . , x_n)]}. In this paper we present explicit formulae for the numerical radius of T for every T ∈ 𝓛(ⁿE : E) for E = c₀ or l_∞. Using these formulae we show that there are no numerical radius peak mappings of 𝓛(ⁿc₀ : c₀).

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.167-169
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• 2005

Here we introduce and study vector bundles, E, on a smooth projective curve X having many "spread" sections and for which $E^{*}\;{\otimes}{\omega}X$ has many "spread" sections. We show that no such bundle exists on X if the gonality of X is too low.