• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.343-348
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• 1995

Let X and Y be two normed spaces and D a nonempty convex subset of X. Let $T : X \ to L(X,Y)$ be a mapping, where L(X,Y) is the space of all continuous linear mappings from X into Y. And let $C : D \to 2^Y$ be a set-valued map such that for each $x \in D$, C(x) is a convex cone in Y such that Int $C(x) \neq 0 and C(x) \neq Y$, where Int denotes the interior.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.331-342
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• 2017

Let R be a commutative ring with nonzero identity and G be a nontrivial finite group. Also, let Z(R) be the set of zero-divisors of R and, for $a{\in}Z(R)$, let $ann(a)=\{r{\in}R{\mid}ra=0\}$. The annihilator graph of the group ring RG is defined as the graph AG(RG), whose vertex set consists of the set of nonzero zero-divisors, and two distinct vertices x and y are adjacent if and only if $ann(xy){\neq}ann(x){\cup}ann(y)$. In this paper, we study the annihilator graph associated to a group ring RG.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.909-912
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• 2010

In this note we present a short proof of the following result by Zhou, Liu and Xu. Let G be a graph of order n, and let a and b be two integers with 1 $\leq$ a < b and b $\geq$ 3, and let g and f be two integer-valued functions defined on V(G) such that a $\leq$ g(x) < f(x) $\leq$ b for each $x\;{\in}\;V(G)$ and f(V(G)) - V(G) even. If $n\;{\geq}\;\frac{(a+b-1)^2+1}{a}$ and $\delta(G)\;{\geq}\;\frac{(b-1)n}{a+b-1}$,then G has a connected (g, f)-factor.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.91-103
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• 2013

Let (D,B) be an admissible pair. Then recall that $B\;{\times}^L_HD^{{\rightarrow}{\pi}_D}_{{\leftarrow}i_D}\;D$ are bialgebra maps satisfying ${\pi}_D{\circ}i_D=I$. We have solved a converse in case D is a Hopf algebra. Let D be a Hopf algebra with antipode $S_D$ and be a left H-comodule algebra and a left H-module coalgebra over a field $k$. Let A be a bialgebra over $k$. Suppose $A^{{\rightarrow}{\pi}}_{{\leftarrow}i}D$ are bialgebra maps satisfying ${\pi}{\circ}i=I_D$. Set ${\Pi}=I_D*(i{\circ}s_D{\circ}{\pi}),B=\Pi(A)$ and $j:B{\rightarrow}A$ be the inclusion. Suppose that ${\Pi}$ is an algebra map. We show that (D,B) is an admissible pair and $B^{\leftarrow{\Pi}}_{\rightarrow{j}}A^{\rightarrow{\pi}}_{\leftarrow{i}}D$ is an admissible mapping system and that the generalized biproduct bialgebra $B{\times}^L_HD$ is isomorphic to A as bialgebras.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.941-947
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• 2007

Let M be a complete Riemannian manifold and let N be a Riemannian manifold of nonpositive scalar curvature. Let ${\mu}0$ be the least eigenvalue of the Laplacian acting on $L^2-functions$ on M. We show that if $Ric^M{\ge}-{\mu}0$ at all $x{\in}M$ and either $Ric^M>-{\mu}0$ at some point x0 or Vol(M) is infinite, then every harmonic morphism ${\phi}:M{\to}N$ of finite energy is constant.

• Bulletin of the Korean Mathematical Society
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• v.42 no.1
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• pp.157-164
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• 2005

Let $RRat_k$ ($CP^n$) denote the space of basepoint-preserving conjugation-equivariant holomorphic maps of degree k from $S^2$ to $CP^n$. A map f ; $S^2 {\to}CP^n$ is said to be full if its image does not lie in any proper projective subspace of $CP^n$. Let $RF_k(CP^n)$ denote the subspace of $RRat_k(CP^n)$ consisting offull maps. In this paper we determine $H{\ast}(RF_k(CP^2); Z/p)$ for all primes p.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1805-1827
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• 2014

Let $\mathcal{K}^{\prime}_M$ be the generalized tempered distributions of $e^{M(t)}$-growth, where the function M(t) grows faster than any linear functions as ${\mid}t{\mid}{\rightarrow}{\infty}$, and let $K^{\prime}_M$ be the Fourier transform spaces of $\mathcal{K}^{\prime}_M$. We obtain the relationship between certain classes of analytic functions in tubes, $\mathcal{K}^{\prime}_M$ and $K^{\prime}_M$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.949-955
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• 2014

Let ${\Phi}_n(x)={\sum}^{{\phi}(n)}_{k=0}a(n,k)x^k$ denote the n-th cyclotomic polynomial. In this note, let p < q < r be odd primes, where $q{\not{\equiv}}1$ (mod p) and $r{\equiv}-2$ (mod pq), we construct an explicit k such that a(pqr, k) = -2.

• Kyungpook Mathematical Journal
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• v.63 no.2
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• pp.235-250
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• 2023

Let 1 ≤ p, q < ∞ be fixed, and let R = [r_jk] be an infinite scalar matrix such that 1 ≤ r_jk < ∞ and sup_j,k r_jk < ∞. Let 𝓑(𝑙_p, 𝑙_q) be the set of all bounded linear operator from 𝑙_p into 𝑙_q. For a fixed Banach algebra 𝐁 with identity, we define a new vector space S^R_p,q(𝐁) of infinite matrices over 𝐁 and a paranorm G on S^R_p,q(𝐁) as follows: let $$S^R_{p,q}({\mathbf{B}})=\{A:A^{[R]}{\in}{\mathcal{B}}(l_p,l_q)\}$$ and $G(A)={\parallel}A^{[R]}{\parallel}^{\frac{1}{M}}_{p,q}$, where $A^{[R]}=[{\parallel}a_{jk}{\parallel}^{r_{jk}}]$ and M = max{1, sup_j,k r_jk}. The existance of S^R_p,q(𝐁) equipped with the paranorm G(·) including its completeness are studied. We also provide characterizations of β -dual of the paranormed space.

• Journal of the Chungcheong Mathematical Society
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• v.8 no.1
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• pp.173-181
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• 1995

Let H and G be finite dimensional semisimple Hopf algebras and let A and B be left H and G-module algebras respectively. We use smash product algebras to show that 1) if A is right Artinian then $A^H$ is right Artinian, 2) $Soc\;V_A{\subset}Soc\;V_{A^H}$ and rad $V_A{\supset}\;radV_{A^H}$, 3) $K\;dim\;_BV_A=K\;dim\;_{B^G}V_{A^H}$.