• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.4
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• pp.47-54
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• 2007

In [6] some computation of spectral measures induced by normal operators $T^{*n}T^n$ was introduced. In this note we improve some computations by using spectral measures, which are related t o extremal vectors. Also, we discuss the extremal value properties and apply our spectral measure equations to moment sequences which are induced by weighted shifts.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.489-494
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• 2018

The first purpose of this note is to generalize two nice theorems of H. J. Kim concerning hyperinvariant subspaces for certain classes of operators on Hilbert space, proved by him by using the technique of "extremal vectors". Our generalization (Theorem 1.2) is obtained as a consequence of a new theorem of the present authors, and doesn't utilize the technique of extremal vectors. The second purpose is to use this theorem to obtain the existence of hyperinvariant subspaces for a class of $2{\times}2$ operator matrices (Theorem 3.2).

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.239-252
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• 2002

A sort sequence $S_n$ is sequence of all unordered pairs of indices in $I_n$={1,2,…n}. With a sort sequence $S_n$ = ($s_1,S_2,...,S_{\frac{n}{2}}$),one can associate a predictive sorting algorithm A($S_n$). An execution of the a1gorithm performs pairwise comparisons of elements in the input set X in the order defined by the sort sequence $S_n$ except that the comparisons whose outcomes can be inferred from the results of the preceding comparisons are not performed. A sort sequence is said to be extremal if it maximizes a given objective function. First we consider the extremal sort sequences with respect to the objective function $\omega$($S_n$) - the expected number of tractive predictions in $S_n$. We study $\omega$-extremal sort sequences in terms of their prediction vectors. Then we consider the objective function $\Omega$($S_n$) - the minimum number of active predictions in $S_n$ over all input orderings.

• Honam Mathematical Journal
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• v.30 no.4
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• pp.659-670
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• 2008

We denote by $\mathcal{Q}$(A) the set of all real matrices with the same sign pattern as a real matrix A. A matrix A is an SN-matrix provided there exists a set S of sign pattern such that the set of sign patterns of vectors in the -space of $\tilde{A}$ is S, for each ${\tilde{A}}{\in}\mathcal{Q}(A)$. Some properties of SN-matrices arc investigated.