• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.623-630
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• 2017

For any nonzero elements x, y in a normed space X, the angular and skew-angular distance is respectively defined by ${\alpha}[x,y]={\parallel}{\frac{x}{{\parallel}x{\parallel}}}-{\frac{y}{{\parallel}y{\parallel}}}{\parallel}$ and ${\beta}[x,y]={\parallel}{\frac{x}{{\parallel}y{\parallel}}}-{\frac{y}{{\parallel}x{\parallel}}}{\parallel}$. Also inequality ${\alpha}{\leq}{\beta}$ characterizes inner product spaces. Operator version of ${\alpha}$ has been studied by $ Pe{\check{c}}ari{\acute{c}}$, $ Raji{\acute{c}}$, and Saito, Tominaga, and Zou et al. In this paper, we study the operator version of ${\beta}$ by using Douglas' lemma. We also prove that the operator version of inequality ${\alpha}{\leq}{\beta}$ holds for commutating normal operators. Some examples are presented to show essentiality of these conditions.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.311-317
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• 1998

For Hilbert spaces H, K, a compact operator T: H $\rightarrow$ K, and column, row, operator Hilbert spaces $H_c,\;K_c,\;H_r,\;K_r,\;H_o, K_o$,we show that ${\parallel}T_{co}{\parallel}_{cb}={\parallel}T_{ro}{\parallel}_{cb}={\parallel}T_{oc}{\parallel}_{cb}={\parallel}T_{or}{\parallel}_{cb}={\parallel}T{\parallel}_4$.

• The Transactions of the Korea Information Processing Society
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• v.4 no.11
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• pp.2903-2913
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• 1997

This paper describes the design and implementation of the ParaC language that supports parallel programming on the shared memory and distributed memory parallel machine. The ParaC language is designed for the effective use of system resources of scalable parallel systems. The goal is achieved by adding parallel and synchronization constructs for shared address spaces, and remote task constructs for distributed address spaces. This paper also shows the translation method, and we implement the translator and the run-time library for parallel execution of extended constructs.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.233-241
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• 2010

In this paper, we investigate the following functional inequality $${\parallel}f(\frac{x\;+\;y}{2}\;+\;z)\;+\;f(\frac{x\;+\;y}{2}\;+\;y)\;+\;f(\frac{y\;+\;z}{2}\;+\;x){\parallel\;\leq\;\parallel}2f(x\;+\;y\;+\;z)\parallel$$ in Banach modules over a $C^*$-algebra, and prove the generalized Hyers-Ulam stability of linear mappings in Banach modules over a $C^*$-algebra.

• Journal of Multimedia Information System
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• v.4 no.4
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• pp.219-224
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• 2017

This paper is to introduce an application of face recognition algorithm in parallel. We have experiments of 25 images with different motions and simulated the image recognitions; grouping of the image vectors, image normalization, calculating average image vectors, etc. We also discuss an analysis of the related eigen-image vectors and a parallel algorithm. To develop the parallel algorithm, we propose a new type of initial matrices for eigenvalue problem. If A is a symmetric matrix, initial matrices for eigen value problem are investigated: the "optimal" one, which minimize ${\parallel}C-A{\parallel}_F$ and the "super optimal", which minimize ${\parallel}I-C^{-1}A{\parallel}_F$. In this paper, we present a general new approach to the design of an initial matrices to solving eigenvalue problem based on the new optimal investigating C with preserving the characteristic of the given matrix A. Fast all resulting can be inverted via fast transform algorithms with O(N log N) operations.

• East Asian mathematical journal
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• v.19 no.1
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• pp.73-80
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• 2003

Let D be a bounded domain in $\mathbb{C}^n$ with $C^2$ boundary. In this paper, we prove the following inequality $${\parallel}u{\parallel}_{p_2,{\alpha}_2}{\lesssim}{\parallel}u{\parallel}_{p_1,{\alpha}_1}+{\parallel}\bar{\partial}u{\parallel}_{p_1,{\alpha}_1+p_1}/2$$, where $1{\leq}p_1{\leq}p_2<\infty,\;{\alpha}_j>0,(n+{\alpha}_1)/p_1=(n+{\alpha}_1)/p_1=(n+{\alpha}_2)/p_2$, and $1/p_2{\geq}1/p_1-1/2n$.

• Journal of the Korean Statistical Society
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• v.10
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• pp.122-127
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• 1981

A parallel flats fraction for the $3^n$ factorial is symbolically written as $At=C=(C_1 C_2 \cdots C_f)$ where C is a rxf matrix and A is rxn matrix with rank r. It is shown that the set of all possible parallel flats fraction C for a given A and given size can be partitioned into equivalence classes. The number of those classes are enumerated in general.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.587-601
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• 2022

We find the characterizations of the curvatures of Legendre curves and magnetic curves in Kenmotsu manifolds with C-parallel and C-proper mean curvature vector fields in the tangent and normal bundles. Finally, an illustrative example is presented.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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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.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.727-730
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• 1998

In this paper, we propose an implementation of an efficient parallel Radon transform on TMS320C80-based system. For an N$\times$N SAR image, we can obtain O(NM/p) of the conventional parallel Radon transform, by representing the projection patterns in Radon space variables instead of the image space variables, and pipelining the algorithm, where p is the number of processors and M is the number of projection angles. Also, we can reduce the time for the dynamic load distribution among the nodes and the communication overheads of accessing the global memories, by pipelining the memory and processing operations by using tripple buffer structure. Experimental results show an efficient parallel Radon transform of speedup Sp=3.9 and efficiency E=97.5% for 256$\times$256 image, when implemented on TMS320C80 composed of four parallel slave processors with three memory blocks.