• 대한수학회논문집
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• 제37권2호
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• pp.409-414
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• 2022

Let A ∈ B(X) be a spectral operator on a non-archimedean Banach space over an algebraically closed field. In this note, we give a necessary and sufficient condition on the resolvent of A so that the discrete semigroup consisting of powers of A is uniformly-bounded.

• 대한수학회논문집
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• 제37권1호
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• pp.91-103
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• 2022

In this paper, we introduce Toeplitz operators and Hankel operators with complex Borel measures on the closed unit disk. When a positive measure 𝜇 on (-1, 1) is a Carleson measure, it is known that the corresponding Hankel matrix is bounded and vice versa. We show that for a positive measure 𝜇 on 𝔻, 𝜇 is a Carleson measure if and only if the Toeplitz operator with symbol 𝜇 is a densely defined bounded linear operator. We also study Hankel operators of Hilbert-Schmidt class.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1525-1532
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• 2011

The $m{\times}n$ Boolean matrix A is said to be of Boolean rank r if there exist $m{\times}r$ Boolean matrix B and $r{\times}n$ Boolean matrix C such that A = BC and r is the smallest positive integer that such a factorization exists. We consider the the sets of matrix ordered pairs which satisfy extremal properties with respect to Boolean rank inequalities of matrices over nonbinary Boolean algebra. We characterize linear operators that preserve these sets of matrix ordered pairs as the form of $T(X)=PXP^T$ with some permutation matrix P.

• 대한수학회보
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• 제52권2호
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• pp.593-601
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• 2015

Let $f{\in}C^r$ ([-1,1]), $r{\geq}0$ and let $L^*$ be a linear left fractional differential operator such that $L^*$ $(f){\geq}0$ throughout [0, 1]. We can find a sequence of polynomials $Q_n$ of degree ${\leq}n$ such that $L^*$ $(Q_n){\geq}0$ over [0, 1], furthermore f is approximated left fractionally and simulta-neously by $Q_n$ on [-1, 1]. The degree of these restricted approximations is given via inequalities using a higher order modulus of smoothness for $f^{(r)}$.

• 대한수학회보
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• 제55권3호
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• pp.819-835
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• 2018

Let $f=h+{\bar{g}}$ be a normalized harmonic mapping in the unit disk $\mathbb{D}$. In this paper, we obtain the sharp radius of univalence, fully starlikeness and fully convexity of the harmonic linear differential operators $D^{\epsilon}{_f}=zf_z-{\epsilon}{\bar{z}}f_{\bar{z}}({\mid}{\epsilon}{\mid}=1)$ and $F_{\lambda}(z)=(1-{\lambda)f+{\lambda}D^{\epsilon}{_f}(0{\leq}{\lambda}{\leq}1)$ when the coefficients of h and g satisfy harmonic Bieberbach coefficients conjecture conditions. Similar problems are also solved when the coefficients of h and g satisfy the corresponding necessary conditions of the harmonic convex function $f=h+{\bar{g}}$. All results are sharp. Some of the results are motivated by the work of Kalaj et al. [8].

• Journal of applied mathematics & informatics
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• 제36권3_4호
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• pp.237-244
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• 2018

Let ${\mathcal{H}}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let L be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in ${\mathcal{L}}$. Let p and q be natural numbers (p < q). Let ${\mathcal{A}}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $T_{(p,q)}=0$ for all T in ${\mathcal{A}}$. If ${\mathcal{A}}$ is a Lie ideal, then $T_{(p,p)}=T_{(p+1,p+1)}={\cdots}=T_{(q,q)}$ and $T_{(i,j)}=0$, $p{\eqslantless}i{\eqslantless}q$ and i < $j{\eqslantless}q$ for all T in ${\mathcal{A}}$.

• 호남수학학술지
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• 제39권1호
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• pp.93-100
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• 2017

Let $\mathcal{H}$ be an infinite dimensional separable Hilbert space with a fixed orthonormal base $\{e_1,e_2,{\cdots}\}$. Let $\mathcal{L}$ be the subspace lattice generated by the subspaces $\{[e_1],[e_1,e_2],[e_1,e_2,e_3],{\cdots}\}$ and let $Alg{\mathcal{L}}$ be the algebra of bounded operators which leave invariant all projections in $\mathcal{L}$. Let p and q be natural numbers($p{\leqslant}q$). Let $\mathcal{B}_{p,q}=\{T{\in}Alg\mathcal{L}{\mid}T_{(p,q)}=0\}$. Let $\mathcal{A}$ be a linear manifold in $Alg{\mathcal{L}}$ such that $\{0\}{\varsubsetneq}{\mathcal{A}}{\subset}{\mathcal{B}}_{p,q}$. If $\mathcal{A}$ is an ideal in $Alg{\mathcal{L}}$, then $T_{(i,j)}=0$, $p{\leqslant}i{\leqslant}q$ and $i{\leqslant}j{\leqslant}q$ for all T in $\mathcal{A}$.

• Kyungpook Mathematical Journal
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• 제46권4호
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• pp.581-589
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• 2006

We characterize the linear operators which preserve the factor rank of integer matrices. That is, if $\mathcal{M}$ is the set of all $m{\times}n$ matrices with entries in the integers and min($m,n$) > 1, then a linear operator T on $\mathcal{M}$ preserves the factor rank of all matrices in $\mathcal{M}$ if and only if T has the form either T(X) = UXV for all $X{\in}\mathcal{M}$, or $m=n$ and T(X)=$UX^tV$ for all $X{\in}\mathcal{M}$, where U and V are suitable nonsingular integer matrices. Other characterizations of factor rank-preservers of integer matrices are also given.

• 대한전기학회논문지:시스템및제어부문D
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• 제52권5호
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• pp.295-304
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• 2003

In this paper, we proposed a hardware-oriented Genetic Algorithm Processor(GAP) based on subpopulation architecture for high-performance convergence and reducing computation time. The proposed architecture was applied to enhancing population diversity for correspondence to premature convergence. In addition, the crossover operator selection and linear ranking subpop selection were newly employed for efficient exploration. As stochastic search space selection through linear ranking and suitable genetic operator selection with respect to the convergence state of each subpopulation was used, the elapsed time of searching optimal solution was shortened. In the experiments, the computation speed was increased by over $10\%$ compared to survival-based GA and Modified-tournament GA. Especially, increased by over $20\%$ in the multi-modal function. The proposed Subpop GA processor was implemented on FPGA device APEX EP20K600EBC652-3 of AGENT 2000 design kit.

• 대한수학회지
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• 제56권6호
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• pp.1503-1514
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• 2019

A rank 1 matrix has a factorization as $uv^t$ for vectors u and v of some orders. The arctic rank of a rank 1 matrix is the half number of nonzero entries in u and v. A matrix of rank k can be expressed as the sum of k rank 1 matrices, a rank 1 decomposition. The arctic rank of a matrix A of rank k is the minimum of the sums of arctic ranks of the rank 1 matrices over all rank 1 decomposition of A. In this paper we obtain characterizations of the linear operators that strongly preserve the symmetric arctic ranks of symmetric matrices over nonnegative reals.