• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.889-895
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• 1995

Let $H$ be a separable, infinite dimensional, complex Hilbert space and let $L(H)$ denote the algebra of all bounded linear operators on $H$.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.893-912
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• 2005

We discuss a certain geometric property $X_{{\theta},{\gamma}}$ of dual algebras generated by a polynomially bounded operator and property ($\mathbb{A}_{N_0,N_0}$; these are central to the study of $N_{0}\timesN_{0}$-systems of simultaneous equations of weak$^{*}$-continuous linear functionals on a dual algebra. In particular, we prove that if T $\in$ $\mathbb{A}$$^{M}$ satisfies a certain sequential property, then T $\in$ $\mathbb{A}^{M}_{N_0}(H) if and only if the algebra $A_{T}$ has property $X_{0, 1/M}$, which is an improvement of Li-Pearcy theorem in [8].

• Journal of Korean Institute of Industrial Engineers
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• v.15 no.2
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• pp.11-22
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• 1989

The problem of scheduling n-jobs on m-uniform parallel machines is considered, in which each job has a release time, a deadline, and a processing requirement. The job processing requirements are allocated to the machines so that the maximum of the load differences between time periods is minimized. Based on Federgruen's maximum flow network model to find a feasible schedule, a polynomially bounded algorithm is developed. An example to show the effectiveness of our algorithm is presented.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.183-201
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• 1999

Let M be an 0-minimal structure on the standard structure :=( , +, ,<) of the field of real numbers. We study Cr -G manifolds (0$\leq$r$\leq$w) which are generalizations of Nash manifolds and Nash G manifolds. We prove that if M is polynomially bounded, then every Cr -G (0$\leq$r<$\infty$) manifold is Cr -G imbeddable into some n, and that if M is exponential and G is a compact affine Cw -G group, then each compact $C\infty$ -G imbeddable into some representation of G.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.537-557
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• 2021

In this paper, we investigate the curvature behavior of complete noncompact gradient expanding Ricci solitons with nonnegative Ricci curvature. For such a soliton in dimension four, it is shown that the Riemann curvature tensor and its covariant derivatives are bounded. Moreover, the Ricci curvature is controlled by the scalar curvature. In higher dimensions, we prove that the Riemann curvature tensor grows at most polynomially in the distance function.

• Honam Mathematical Journal
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• v.26 no.3
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• pp.299-308
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• 2004

Let $\{{\beta}(n)\}^{\infty}_{n=0}$ be a sequence of positive numbers such that ${\beta}(0)=1$. We consider the space $H^2({\beta})$ of all power series $f(z)=^{Po}_{n=0}{\hat{f}}(n)z^n$ such that $^{Po}_{n=0}{\mid}{\hat{f}}(n){\mid}^2{\beta}(n)^2<{\infty}$. We link the ideas of subspaces of $H^2({\beta})$ and zero sets. We give some sufficient conditions for a vector in $H^2({\beta})$ to be cyclic for the multiplication operator $M_z$. Also we characterize the commutant of some multiplication operators acting on $H^2({\beta})$.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.617-627
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• 2004

Let (equation omitted) denote the class of bounded linear Hilbert space operators with the property that $\midA^2\mid\geq\midA\mid^2$. In this paper we show that (equation omitted)-operators are finitely ascensive and that, for non-zero operators A and B, A (equation omitted) B is in (equation omitted) if and only if A and B are in (equation omitted). Also, it is shown that if A is an operator such that p(A) is in (equation omitted) for a non-trivial polynomial p, then Weyl's theorem holds for f(A), where f is a function analytic on an open neighborhood of the spectrum of A.

• Journal of the Korean Operations Research and Management Science Society
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• v.6 no.1
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• pp.65-70
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• 1981

L.G. Khachiyan's algorithm for solving a system of strict (or open) linear inequalities with integral coefficients is described. This algorithm is based on the construction of a sequence of ellipsoids in R$^n$ of decreasing n-dimensional volume and contain-ing feasible region. The running time of the algorithm is polynomial in the number of bits of computer core memory required to store the coefficients. It can be applied to solve linear programming problems in polynomially bounded time by the duality theorem of the linear programming problem. But it is difficult to use in solving practical problems. Because it requires the computation of a square roots, besides other arithmatic operations, it is impossible to do these computations exactly with absolute precision.

• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.275-283
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• 2015

Let T be a bounded linear operator on a complex Hilbert space H. For a positive integer k, an operator T is said to be a k-quasi-2-isometric operator if T^∗k(T^∗2T² − 2T^∗T + I)T^k = 0, which is a generalization of 2-isometric operator. In this paper, we consider basic structural properties of k-quasi-2-isometric operators. Moreover, we give some examples of k-quasi-2-isometric operators. Finally, we prove that generalized Weyl’s theorem holds for polynomially k-quasi-2-isometric operators.

• Journal of Korean Institute of Industrial Engineers
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• v.24 no.4
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• pp.571-578
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• 1998

In this paper, we deal with a node weighted Steiner Ring Problem (SRP) arising from the deployment of Synchronous Optical Networks (SONET), a standard of transmission using optical fiber technology. The problem is to find a minimum weight cycle (ring) covering a subset of nodes in the network considering node and link weights. We have developed two mathematical models, one of which is stronger than the other in terms of LP bounds, whereas the number of constraints of the weaker one is polynomially bounded. In order to solve the problem optimally, we have developed some preprocessing rules and valid inequalities. We have also prescribed an effective heuristic procedure for providing tight upper bounds. Computational results show that the stronger model is better in terms of computation time, and valid inequalities and preprocessing rules are effective for solving the problem optimally.