• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.11-27
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• 2010

Let $\Omega$ be a domain with smooth boundary in ${\mathbb{C}}^{n+1}$ and let $p{\in}{\partial}{\Omega}$. Suppose that $\Omega$ is Kobayashi hyperbolic and p is of Catlin multi-type ${\tau}=({\tau}_0,{\ldots},{\tau}_n)$. In this paper, we show that $\Omega$ admits a $C^{k}$ contraction at p with $k{\geq}\mid{\tau}\mid+1$ if and only if $\Omega$ is biholomorphically equivalent to a domain defined by a weighted homogeneous polynomial.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.331-351
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• 2007

Let k be an imaginary quadratic field, h the complex upper half plane, and let $\tau{\in}h{\cap}k$, $q=e^{{\pi}i\tau}$. We find a lot of algebraic properties derived from theta functions, and by using this we explore some new algebraic numbers from Rogers-Ramanujan continued fractions.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.423-433
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• 2004

In this paper we obtained the following: Let H. be a Hilbert space and (equation omitted) be a subspace lattice on H. Let X and Y be operators acting on H. If the range of X is dense in H, then the following are equivalent: (1) there exists an operator A in Alg(equation omitted) such that AX = Y, (2) sup (equation omitted) Moreover, if condition (2) holds, we may choose the operator A such that ∥A∥ = K.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.61-74
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• 2006

Let G be a simple graph and let G denote its complement. We say that $\bar{G}$ is integral if its spectrum consists of integral values. In this work we establish a characterization of integral graphs which belong to the class $\bar{{\alpha}K_{a,a}\cup{\beta}K_{b,b}}$, where mG denotes the m-fold union of the graph G.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.257-267
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• 2016

We find examples of Ideals in a tridiagonal algebra ALGL_∞ and study some properties of Ideals in ALGL_∞. We prove the following theorems: Let k and j be fixed natural numbers. Let A be a subalgebra of ALGL_∞ and let A_2,{k} ⊂ A ⊂ {T ∈ ALGL_∞ | T_(2k-1,2k) = 0}. Then A is an ideal of ALGL_∞ if and only if A = A_2,{k} where A_2,{k} = {T ∈ ALGL_∞ | T_(2k-1,2k) = 0, T_(2k-1,2k-1) = T_(2k,2k) = 0}. Let B be a subalgebra of ALGL_∞ such that B_2,{j} ⊂ B ⊂ {T ∈ ALGL_∞ | T_(2j+1,2j) = 0}. Then B is an ideal of ALGL_∞ if and only if B = B_2,{j}, where B_2,{j} = {T ∈ ALGL_∞ | T_(2j+1,2j) = 0, T_(2j,2j) = T_(2j+1,2j+1) = 0}.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.623-631
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• 2001

Let $\kappa$ be a real abelian field of conductor f and $\kappa$(sub)$\infty$ = ∪(sub)n$\geq$0$\kappa$(sub)n be its Z(sub)p-extension for an odd prime p such that płf$\phi$(f). he aim of this paper is ot compute the cohomology groups of circular units. For m>n$\geq$0, let G(sub)m,n be the Galois group Gal($\kappa$(sub)m/$\kappa$(sub)n) and C(sub)m be the group of circular units of $\kappa$(sub)m. Let l be the number of prime ideals of $\kappa$ above p. Then, for mm>n$\geq$0, we have (1) C(sub)m(sup)G(sub)m,n = C(sub)n, (2) H(sup)i(G(sub)m,n, C(sub)m) = (Z/p(sup)m-n Z)(sup)l-1 if i is even, (3) H(sup)i(G(sub)m,n, C(sub)m) = (Z/P(sup)m-n Z)(sup l) if i is odd (※Equations, See Full-text).

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.29-36
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• 2004

Given vectors x and ｙ in a Hilbert space, an interpolating operator is a bounded operator T such that Tx=y. In this paper the following is proved: Let $\cal{L}$ be a subspace lattice on a Hilbert space $\cal{H}$. Let x and ｙ be vectors in $\cal{H}$ and let $P_x$, be the projection onto sp(x). If $P_xE=EP_x$ for each $ E \in \cal{L}$ then the following are equivalent. (1) There exists an operator A in Alg(equation omitted) such that Ax=y, Af = 0 for all f in ($sp(x)^\perp$) and $A=-A^\ast$. (2) (equation omitted)

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.4.1-4
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• 2003

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX= Y. An interpolating operator for n-operators satisfies the equation AXi= Yi, for i = 1,2,...,n, In this article, we showed the following : Let H be a Hilbert space and let L be a subspace lattice on H. Let X and Y be operators acting on H. Assume that rangeX is dense in H. Then the following statements are equivalent : (1) There exists an operator A in AlgL such that AX = Y, A$\^$*/=A and every E in L reduces A. (2) sup｛(equation omitted) : n $\in$ N f$\sub$I/ $\in$ H and E$\sub$I/ $\in$ L｝<$\infty$ and = for all E in L and all f, g in H.

• Bulletin of the Korean Mathematical Society
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• v.43 no.2
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• pp.309-318
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• 2006

Let X and Y be real Banach spaces and ${\varepsilon}\;>\;0$, p > 1. Let f : $X\;{\to}\;Y$ be a bijective mapping with f(0) = 0 satisfying $$|\;{\parallel}f(x)-f(y){\parallel}-{\parallel}{x}-y{\parallel}\;|\;{\leq}{\varepsilon}{\parallel}{x}-y{\parallel}^p$$ for all $x\;{\in}\;X$ and, let $f^{-1}\;:\;Y\;{\to}\;X$ be uniformly continuous. Then there exist a constant ${\delta}\;>\;0$ and N(${\varepsilon},p$) such that lim N(${\varepsilon},p$)=0 and a unique surjective isometry I : X ${\to}$ Y satisfying ${\parallel}f(x)-I(x){\parallel}{\leq}N({\varepsilon,p}){\parallel}x{\parallel}^p$ for all $x\;{\in}\;X\;with\;{\parallel}x{\parallel}{\leq}{\delta}$.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1015-1025
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• 2012

Let $[n]=\{1,2,{\cdots},n\}$, and let $PO_n$ be the partial order-preserving transformation semigroup on [n]. Let $$CPO_n=\{{\alpha}{\in}PO_n:({\forall}x,y{\in}dom{\alpha}),\;|x{\alpha}-y{\alpha}|{\leq}|x-y|\}$$ Then $CPO_n$ is a subsemigroup of $PO_n$. In this paper, we characterize Green's relations and the regularity of elements for $CPO_n$.