• 대한수학회지
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• 제47권2호
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• pp.235-246
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• 2010

A Banach space operator A $\in$ B(X) is polaroid if the isolated points of the spectrum of A are poles of the resolvent of A; A is hereditarily polaroid, A $\in$ ($\mathcal{H}\mathcal{P}$), if every part of A is polaroid. Let $X^n\;=\;\oplus^n_{t=i}X_i$, where $X_i$ are Banach spaces, and let A denote the class of upper triangular operators A = $(A_{ij})_{1{\leq}i,j{\leq}n$, $A_{ij}\;{\in}\;B(X_j,X_i)$ and $A_{ij}$ = 0 for i > j. We prove that operators A $\in$ A such that $A_{ii}$ for all $1{\leq}i{\leq}n$, and $A^*$ have the single-valued extension property have spectral properties remarkably close to those of Jordan operators of order n and n-normal operators. Operators A $\in$ A such that $A_{ii}$ $\in$ ($\mathcal{H}\mathcal{P}$) for all $1{\leq}i{\leq}n$ are polaroid and have SVEP; hence they satisfy Weyl's theorem. Furthermore, A+R satisfies Browder's theorem for all upper triangular operators R, such that $\oplus^n_{i=1}R_{ii}$ is a Riesz operator, which commutes with A.

• Journal of applied mathematics & informatics
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• 제29권3_4호
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• pp.981-986
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• 2011

Given vectors x and y in a Hilbert space $\cal{H}$, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equations $Tx_i=y_i$, for i = 1, 2, ${\cdots}$, n. 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$\cal{L}$ such that Ax = y, Af = 0 for all f in $sp(x)^{\perp}$ and $A=A^*$. (2) sup $sup\;\{\frac{{\parallel}E^{\perp}y{\parallel}}{{\parallel}E^{\perp}x{\parallel}}\;:\;E\;{\in}\;{\cal{L}}\}$ < ${\infty}$, $y\;{\in}\;sp(x)$ and < x, y >=< y, x >.

• 대한수학회지
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• 제58권6호
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• pp.1347-1365
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• 2021

For µ = (µ₁, …, µ_t) (µ_j > 0), ξ = (z₁, …, z_t, w) ∈ ℂ^n₁ × … × ℂ^n_t × ℂ^m, define $${\Omega}({\mu},t)=\{{\xi}{\in}\mathbb{B}_{n_1}{\times}{\cdots}{\times}\mathbb{B}_{n_t}{\times}\mathbb{C}^m:{\parallel}w{\parallel}^2 where $\mathbb{B}_{n_j}$ is the unit ball in ℂ^n_j (1 ≤ j ≤ t), C(χ, µ) is a constant only depending on χ = (n₁, …, n_t) and µ = (µ₁, …, µ_t), which is a special type of generalized Cartan-Hartogs domain. We will give some sufficient and necessary conditions for the boundedness of some type of operators on L^p(Ω(µ, t), ω) (the weighted L^p space of Ω(µ, t) with weight ω, 1 < p < ∞). This result generalizes the works from certain classes of generalized complex ellipsoids to the generalized Cartan-Hartogs domain Ω(µ, t).

• 대한수학회지
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• 제38권6호
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• pp.1191-1204
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• 2001

The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration $\int_{a}^{x}(t/x)^{\mu}f(t)dt/t$ and the modified differentiation ${\delta}+{\mu}({\delta}=xD,D=d/dx)$ with real $\mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{\infty})$ such that for c${\in}R=(-{\infty}{\infty})$, in particular in the space $L^{p}(0,{\infty})\;(1{\le}{\le}{\infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $\delta$ derivatives up to order n-1 on [a, b] and ${\delta}^{n-1}[x^{\mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.

• 대한수학회지
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• 제40권6호
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• pp.933-942
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• 2003

It is shown that if a paranormal contraction T has no nontrivial invariant subspace, then it is a proper contraction. Moreover, the nonnegative operator Q = T/sup 2*/T/sup 2/ - 2T/sup */T ＋ I also is a proper contraction. If a quasihyponormal contraction has no nontrivial invariant subspace then, in addition, its defect operator D is a proper contraction and its itself-commutator is a trace-class strict contraction. Furthermore, if one of Q or D is compact, then so is the other, and Q and D are strict ontraction.

• 대한수학회지
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• 제56권2호
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• pp.507-521
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• 2019

For any $m{\times}n$ nonbinary Boolean matrix A, its spanning column rank is the minimum number of the columns of A that spans its column space. We have a characterization of spanning column rank-1 nonbinary Boolean matrices. We investigate the linear operators that preserve the spanning column ranks of matrices over the nonbinary Boolean algebra. That is, for a linear operator T on $m{\times}n$ nonbinary Boolean matrices, it preserves all spanning column ranks if and only if there exist an invertible nonbinary Boolean matrix P of order m and a permutation matrix Q of order n such that T(A) = PAQ for all $m{\times}n$ nonbinary Boolean matrix A. We also obtain other characterizations of the (spanning) column rank preserver.

• 수산해양기술연구
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• 제32권3호
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• pp.235-240
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• 1996

Forecasts of monthly landings of walleye pollock, Theragra chalcogramma, in Korea were carried out by the seasonal Autoregressive Integrated Moving Average(ARlMA) model. The Box - Cox transformation on the walleye pollock catch data handles nonstationary variance. The equation of Box - Cox transformation was Y'=($Y^0.31$_ 1)/0.31. The model identification was determined by minimum AIC(Akaike Information Criteria). And the seasonal ARlMA model is presented (1- O.583B)(1- $B^1$)(l- $B^12$)$Z_t$ =(l- O.912B)(1- O.732$B^12$)et where: $Z_t$=value at month t ; $B^p$ is a backward shift operator, that is, $B^p$$Z_t$=$Z_t$-P; and et= error term at month t, which is to forecast 24 months ahead the walleye pollock landings in Korea. Monthly forecasts of the walleye pollock landings for 1993~ 1994, which were compared with the actual landings, had an absolute percentage error(APE) range of 20.2-226.1 %. Thtal observed annual landings in 1993 and 1994 were 16, 61OM/T and 1O, 748M/T respectively, while the model predicted 10, 7 48M/T and 8, 203M/T(APE 37.0% and 23.7%, respectively).

• 한국IT서비스학회지
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• 제14권1호
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• pp.69-83
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• 2015

The e-commerce market has been more diversified via B2B or P2P, and the size of this market has gradually been expanded as well. A noteworthy phenomenon is the P2P market, which has shown a rapid, approximately 200-fold or more increase in size since 2005. Specifically, the online secondhand-goods market that makes transaction easier and more convenient has attained a fast growth as well, but either sellers or buyers of secondhand goods are properly protected due to a lack of legal regulations on secondhand-goods transaction. The purpose of this study was to examine problems with online secondhand-goods transaction and to suggest some reform measures. There is something wrong with the legal status of brokers for secondhand-goods sales. According to the current law, individual brokers are neither mail-order sellers nor mail-order brokers. So they don't have lots of liabilities, and it means that the burden of risk is all imposed on buyers. Therefore it's suggested that individual brokers should be defined as 'involved operator of electronic commerce' so that proper liability might be imposed on them.

• 대한수학회논문집
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• 제31권3호
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• pp.549-565
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• 2016

A Hilbert space operator $T{\in}{\mathfrak{B}}(\mathfrak{H})$ is said to be n-*-paranormal, $T{\in}C(n)$ for short, if ${\parallel}T^*x{\parallel}^n{\leq}{\parallel}T^nx{\parallel}\;{\parallel}x{\parallel}^{n-1}$ for all $x{\in}{\mathfrak{H}}$. We proved some properties of class C(n) and we proved an asymmetric Putnam-Fuglede theorem for n-*-paranormal. Also, we study some invariants of Weyl type theorems. Moreover, we will prove that a class n-* paranormal operator is finite and it remains invariant under compact perturbation and some orthogonality results will be given.

• 대한수학회논문집
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• 제9권2호
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• pp.423-438
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• 1994

We employ the Galerkin method to solve the nonlinear Urysohn integral equation (1.1) x(t) = f(t) ＋ $∫_{D}$ k(t, s, x(s))ds (t $\in$ D), where D is a bounded domain in $R^{d}$ , the function f and k are known and x is the solution to be determined. We assume that D has a locally Lipschitz boundary ([1, p. 67]). We can rewrite (1.1) in operator notation as x = f ＋ Kx. We consider (1.1) as an operator equation on $L_{\infty$}$(D) and assume that K is defined on the closure $\Omega$ of a bounded open set $\Omega$ ⊂ $L_{\infty}$(D). Throughout our analysis we put the following assumptions on (1.1).(omitted)(1.1).(omitted)