• Journal of the Chungcheong Mathematical Society
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• v.4 no.1
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• pp.11-38
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• 1991

Let $E_n$ be the real ordered space of all $n{\times}n$ Hermitian Matrices and let T be a positive linear operator from $E_2$ to $E_3$. We prove in this paper that T is extreme if and only if T is unitarily equivalent to a map of the form $S_z$ for some $z{\in}C^2$ where $S_z$ is defined by $S_z(xx^*)=ww^*$, $w_i=x_iz_i$ for i = 1, 2 and $w_3=0$.

• 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.

• Communications of the Korean Mathematical Society
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• v.27 no.4
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• pp.689-699
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• 2012

(S, *) is a semigroup S equipped with a unary operation "*". This work is devoted to a class of unary semigroups, namely E-$inversive$ *-$semigroups$. A unary semigroup (S, *) is called an E-inversive *-semigroup if the following identities hold: $$x^*xx^*=x^*$$, $$(x^*)^*=xx^*x$$, $$(xy)^*=y^*x^*$$. In this paper, E-inversive *-semigroups are characterized by several methods. Furthermore, congruences on these semigroups are also studied.

• BMB Reports
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• v.44 no.3
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• pp.147-157
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• 2011

The meiotic process from the primordial stage to zygote in female germ cells is mainly adjusted by post-transcriptional regulation of pre-existing maternal mRNA and post-translational modification of proteins. Several key proteins such as the cell cycle regulator, Cdk1/cyclin B, are post-translationally modified for precise control of meiotic progression. The second messenger (cAMP), kinases (PKA, Akt, MAPK, Aurora A, CaMK II, etc), phosphatases (Cdc25, Cdc14), and other proteins (G-protein coupled receptor, phosphodiesterase) are directly or indirectly involved in this process. Many proteins, such as CPEB, maskin, eIF4E, eIF4G, 4E-BP, and 4E-T, post-transcriptionally regulate mRNA via binding to the cap structure at the 5' end of mRNA or its 3' untranslated region (UTR) to generate a closed-loop structure. The 3' UTR of the transcript is also implicated in post-transcriptional regulation through an association with proteins such as CPEB, CPSF, GLD-2, PARN, and Dazl to modulate poly(A) tail length. RNA interfering is a new regulatory mechanism of the amount of mRNA in the mouse oocyte. This review summarizes information about post-transcriptional and post-translational regulation during mouse oocyte meiotic maturation.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1101-1113
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• 2014

We give analogous criterion to admit a real parabolic connection on real parabolic bundles over a real curve. As an application of this criterion, if real curve has a real point, then we proved that a real vector bundle E of rank r and degree d with gcd(r, d) = 1 is real indecomposable if and only if it admits a real logarithmic connection singular exactly over one point with residue given as multiplication by $-\frac{d}{r}$. We also give an equivalent condition for real indecomposable vector bundle in the case when real curve has no real points.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.441-446
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• 2014

In this paper the following is proved: Let $\mathcal{L}$ be a subspace lattice on a Hilbert space $\mathcal{H}$ and X and Y be operators acting on $\mathcal{H}$. Then there exists a compact operator A in $Alg\mathcal{L}$ such that AX = Y if and only if ${\sup}\{\frac{{\parallel}E^{\perp}Yf{\parallel}}{{\parallel}E^{\perp}Xf{\parallel}}\;:\;f{\in}\mathcal{H},\;E{\in}\mathcal{L}\}$ = K < ${\infty}$ and Y is compact. Moreover, if the necessary condition holds, then we may choose an operator A such that AX = Y and ${\parallel}A{\parallel}=K$.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.747-759
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• 2018

A graph G = (V (G), E(G) of order n = |V (G)| and size m = |E(G)| is said to be odd harmonious if there exists an injection $f:V(G){\rightarrow}\{0,\;1,\;2,\;{\ldots},\;2m-1\}$ such that the induced function $f^*:E(G){\rightarrow}\{1,\;3,\;5,\;{\ldots},\;2m-1\}$ defined by $f^*(uv)=f(u)+f(v)$ is bijection. While a bipartite graph G with partite sets A and B is said to be bigraceful if there exist a pair of injective functions $f_A:A{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ and $f_B:B{\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ such that the induced labeling on the edges $f_{E(G)}:E(G){\rightarrow}\{0,\;1,\;{\ldots},\;m-1\}$ defined by $f_{E(G)}(uv)=f_A(u)-f_B(v)$ (with respect to the ordered partition (A, B)), is also injective. In this paper we prove that odd harmonious graphs and bigraceful graphs are equivalent. We also prove that the number of distinct odd harmonious labeled graphs on m edges is m! and the number of distinct strongly odd harmonious labeled graphs on m edges is [m/2]![m/2]!. We prove that the Cartesian product of strongly odd harmonious trees is strongly odd harmonious. We find some new disconnected odd harmonious graphs.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.885-892
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• 2015

In this paper, we mainly obtain the following assertions: (1) If T is a quasi-*-n-paranormal operator, then T is finite and simply polaroid. (2) If T or $T^*$ is a quasi-*-n-paranormal operator, then Weyl's theorem holds for f(T), where f is an analytic function on ${\sigma}(T)$ and is not constant on each connected component of the open set U containing ${\sigma}(T)$. (3) If E is the Riesz idempotent for a nonzero isolated point ${\lambda}$ of the spectrum of a quasi-*-n-paranormal operator, then E is self-adjoint and $EH=N(T-{\lambda})=N(T-{\lambda})^*$.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.881-889
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• 1994

Let ($X, \Beta, \mu$) be a measure space with the $\sigma$-algebra $\Beta$ and the probability measure $\mu$. Throughouth this article set equalities and inclusions are understood as being so modulo measure zero sets. A transformation T defined on a probability space X is said to be measure preserving if $\mu(T^{-1}E) = \mu(E)$ for $E \in B$. It is said to be ergodic if $\mu(E) = 0$ or i whenever $T^{-1}E = E$ for $E \in B$. Consider the sequence ${x, Tx, T^2x,...}$ for $x \in X$. One may ask the following questions: What is the relative frequency of the points $T^nx$ which visit the set E\ulcorner Birkhoff Ergodic Theorem states that for an ergodic transformation T the time average $lim_{n \to \infty}(1/N)\sum^{N-1}_{n=0}{f(T^nx)}$ equals for almost every x the space average $(1/\mu(X)) \int_X f(x)d\mu(x)$. In the special case when f is the characteristic function $\chi E$ of a set E and T is ergodic we have the following formula for the frequency of visits of T-iterates to E : $$ lim_{N \to \infty} \frac{$\mid${n : T^n x \in E, 0 \leq n $\mid$}{N} = \mu(E) $$ for almost all $x \in X$ where $$\mid$\cdot$\mid$$ denotes cardinality of a set. For the details, see [8], [10].

• Journal of Satellite, Information and Communications
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• v.4 no.1
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• pp.36-44
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• 2009

The key technologies of GNSS receiver for GNSS sensor station are under development as a part of a GNSS ground station in ETRI. This paper presents the GNSS receiver implementation and signal processing result which is implemented based on FPGA to process the Galileo E1 and E5 signal. To verify the working and performance for GNSS receiver which is implemented based on FPGA, live signal received from GIOVE-B which is second test satellite is used. We gather GIOVE-B signal by using prototyping antenna and RF/IF units including IF-component. To verify Galileo E1 and E5 signal processing function from GIOVE-B, FPGA based signal processing module is implemented as a prototyping hardware board.