• 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 $EH=N(T-{\lambda})=N(T-{\lambda})^*$.

• Bulletin of the Korean Mathematical Society
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• v.25 no.2
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• pp.203-209
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• 1988

In this paper, we define a g-regular semigroup which is a generalization of a regular semigroup. And we want to find some properties of g-regular semigroup. G-regular semigroups contains the variety of all regular semigroup and the variety of all periodic semigroup. If a is an element of a semigroup S, the smallest left ideal containing a is Sa.cup.{a}, which we may conveniently write as $S^{I}$a, and which we shall call the principal left ideal generated by a. An equivalence relation l on S is then defined by the rule alb if and only if a and b generate the same principal left ideal, i.e. if and only if $S^{I}$a= $S^{I}$b. Similarly, we can define the relation R. The equivalence relation D is R.L and the principal two sided ideal generated by an element a of S is $S^{1}$a $S^{1}$. We write aqb if $S^{1}$a $S^{1}$= $S^{1}$b $S^{1}$, i.e. if there exist x,y,u,v in $S^{1}$ for which xay=b, ubv=a. It is immediate that D.contnd.q. A semigroup S is called periodic if all its elements are of finite order. A finite semigroup is necessarily periodic semigroup. It is well known that in a periodic semigroup, D=q. An element a of a semigroup S is called regular if there exists x in S such that axa=a. The semigroup S is called regular if all its elements are regular. The following is the property of D-classes of regular semigroup.group.

• Honam Mathematical Journal
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• v.34 no.1
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• pp.93-101
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• 2012

Let $E_A^B$ denote the elliptic curve $E_A^B:y^2=x^3+Ax+B$. In this paper, we calculate the number of points on elliptic curves $E_A^0:y^2=x^3+Ax$ over $\mathbb{F}_p$ mod 24. For example, if $p{\equiv}1$ (mod 24) is a prime, $3t^2{\equiv}1$ (mod p) and A(-1 + 2t) is a quartic residue modulo p, then the number of points in $E_A^0:y^2=x^3+Ax$ is congruent to 0 modulo 24.

• Journal of Microbiology and Biotechnology
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• v.11 no.6
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• pp.986-993
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• 2001

Translation Initiation in prokaryotes involves the formation of a 30 S preinitiation complex, in which translation initiation factors play a role in the stimulation of fMet-tRNA (fMet) binding. However, the specific function and precise mechanism of initiation factor IF1 are still unclear. One a functionally active factor with a high purity. In the present study a large quantity of active IF was rapidly purified, obtained by the overexpression of the infA gene, and then used for a functional study. The induction of infA did not appreciably affect the growth rate of the protease-deficient strain E. coli AR68 harboring the IF1 overproducing plasmid. The level of IF1 obtained was approximately $1-2\%$ of the total cell protein, which enabled the yield of highly purified IF1 (>$98\%$ pure) to be increased to 0.15 mg of IF1/g of cells. The IF1 was isolated within one day by the centrifugatioin of the ribosomal washed fraction, by ammonium sulfate fractionation, chromatography on batch of phosphocellulose, and FPLC Mono S. The overexpressed IF1 was found to be comparable to the factor isolated from normal cells, as determined by migration in NEPHGE/SDS 2-D gels. For binding of fMet-tRNA(fMet) to the 30 S ribosomal subunitis, relatively high levels of binding were obtained when IF2 was present. The addition of IF1 up to 110 pmol proportionally stimulated the binding to a variable extent. This IF1-dependent stimulation of the 30 S preinitiation complex formation demonstrated that IF1 would appear to be exclusively essential for promoting the initiation phase of protein synthesis.

• 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).

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.5
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• pp.1259-1268
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• 1995

The stress distribution around micro holes and the behavior of stress interaction between micro holes are considerd in the study. Several conclusions are extracted as follows : (1) The stress interaction varies with the distance e between micro holes. When the two micro holes are spaced in such a manner that theri two closest points are separated by a distance of micro hole radius (e=1), stress distribution is affected by a opposite micro hole in all the closest region. In addition, if two closest points are seperated by twice the distance of a micro hole radius (e=2), stress distribution is affected by a opposite micro hole in the region of -0.8.leq.x/r.leq.0.8 and the interaction effect can be neglected for e=4. (2)If the depth becomes larger than the radius, or the radius varies, the shape and magnitude of stress distribution around micro holes varies. (3) Hoop stress around a micro hole for the two dimensional configuration is larger than that of the three dimensional micro hole located on the surface of material for .theta. < 60.deg., but it is reversed for .theta > 60.deg.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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• pp.25-37
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• 2019

Let G be a bipartite graph with (X, Y ) as its bipartition. Let B be a complete bipartite graph with a bipartition ($V_1$, $V_2$) such that $X{\subseteq}V_1$ and $Y{\subseteq}V_2$. A bi-packing of G in B is an injection ${\sigma}:V(G){\rightarrow}V(B)$ such that ${\sigma}(X){\subseteq}V_1$, ${\sigma}(Y){\subseteq}V_2$ and $E(G){\cap}E({\sigma}(G))={\emptyset}$. In this paper, we show that if G is a bipartite graph of order n with girth at least 12, then there is a complete bipartite graph B of order n + 1 such that there is a bi-packing of G in B. We conjecture that the same conclusion holds if the girth of G is at least 8.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.435-440
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• 2006

Let G be a simple graph with vertex set V(G) and edge set E(G). A subset S of E(G) is called an edge cover of G if the subgraph induced by S is a spanning subgraph of G. The maximum number of edge covers which form a partition of E(G) is called edge covering chromatic number of G, denoted by X'c(G). It is known that for any graph G with minimum degree ${\delta},\;{\delta}-1{\le}X'c(G){\le}{\delta}$. If $X'c(G) ={\delta}$, then G is called a graph of CI class, otherwise G is called a graph of CII class. It is easy to prove that the problem of deciding whether a given graph is of CI class or CII class is NP-complete. In this paper, we consider the classification of nearly bipartite graph and give some sufficient conditions for a nearly bipartite graph to be of CI class.

• Journal of applied mathematics & informatics
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• v.33 no.1_2
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• pp.229-234
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• 2015

In the setting of semidefinite linear complementarity problems on $S^n$, we focus on the Stein Transformation $S_A(X):=X-AXA^T$ for $A{\in}R^{n{\times}n}$ that is positive semidefinite preserving (i.e., $S_A(S^n_+){\subseteq}S^n_+$) and show that such transformation is strictly monotone if and only if it is nondegenerate. We also show that a positive semidefinite preserving $S_A$ has the Ultra-GUS property if and only if $1{\not\in}{\sigma}(A){\sigma}(A)$.

• Journal of The Korean Astronomical Society
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• v.45 no.5
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• pp.127-138
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• 2012

We explore how wave-particle interactions affect diffusive shock acceleration (DSA) at astrophysical shocks by performing time-dependent kinetic simulations, in which phenomenological models for magnetic field amplification (MFA), Alfv$\acute{e}$nic drift, thermal leakage injection, Bohm-like diffusion, and a free escape boundary are implemented. If the injection fraction of cosmic-ray (CR) particles is ${\xi}$ > $2{\times}10^{-4}$, for the shock parameters relevant for young supernova remnants, DSA is efficient enough to develop a significant shock precursor due to CR feedback, and magnetic field can be amplified up to a factor of 20 via CR streaming instability in the upstream region. If scattering centers drift with Alfv$\acute{e}$n speed in the amplified magnetic field, the CR energy spectrum can be steepened significantly and the acceleration efficiency is reduced. Nonlinear DSA with self-consistent MFA and Alfv$\acute{e}$nic drift predicts that the postshock CR pressure saturates roughly at ~10 % of the shock ram pressure for strong shocks with a sonic Mach number ranging $20{\leq}M_s{\leq}100$. Since the amplified magnetic field follows the flow modification in the precursor, the low energy end of the particle spectrum is softened much more than the high energy end. As a result, the concave curvature in the energy spectra does not disappear entirely even with the help of Alfv$\acute{e}$nic drift. For shocks with a moderate Alfv$\acute{e}$n Mach number ($M_A$ < 10), the accelerated CR spectrum can become as steep as $E^{-2.1}$ - $E^{-2.3}$, which is more consistent with the observed CR spectrum and gamma-ray photon spectrum of several young supernova remnants.