• East Asian mathematical journal
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• v.27 no.1
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• pp.51-65
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• 2011

In the paper, we study questions on classical solvability of nonlocal problems for a third-order linear hyperbolic equation in a rectangular domain. The Riemann method is applied to the Goursat problem and solution is obtained in the integral form. Investigated problems are reduced to the uniquely solvable Volterra-type equation of second kind. Influence effects of coefficients at lowest derivatives on correctness of studied problems are detected.

• Journal of Integrative Natural Science
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• v.10 no.2
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• pp.110-114
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• 2017

The connected and simply connected four-dimensional matrix solvable Lie group $Sol^4_1$ is the four-dimensional geometry. A crystallographic group of $Sol^4_1$ is a discrete cocompact subgroup of $Sol^4_1{\rtimes}D(4)$. In this paper, we geometrically describe the crystallographic groups of $Sol^4_1$.

• 전기의세계
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• v.29 no.9
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• pp.599-603
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• 1980

Mathematically, the Electromagnetic phenomena can be represented by the Maxwell's equations, but it is very difficult to solve these equations, especially, having complex structural boundaries. By the way, the development of a computer system made us easy to solve these kind of partial differential equations. The Finite Element Method, one of the numerical methods, is very this. This paper shows the power of F.E.M. by examining, with an example of a hollow cylinder in a uniform magnetic field which is analytically solvable, the errors and the tendency of magnetic flux lines.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.735-750
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• 1995

We present a domain decomposition algorithm for solving large sparse linear systems of equations arising from queuing networks. Such techniques are attractive since the problems in subdomains can be solved independently by parallel processors. Many of the methods proposed so far use some form of the preconditioned conjugate gradient method to deal with one large interface problem between subdomains. However, in this paper, we propose a "nested" domain decomposition method where the subsystems governing the interfaces are small enough so that they are easily solvable by direct methods on machines with many parallel processors. Convergence of the algorithms is also shown.lso shown.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.91-95
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• 1984

Let D$^{p}$ be the space of distributions of $L^{p}$-growth and S the space of tempered destributions in $R^{n}$: D$^{p}$, 1.leq.P.leq..inf., is the dual of the space $D^{p}$ which we discribe later. We denote by O$_{c}$(S:S') the space of convolution operators in S. In [8] S. Sznajder and Z. Zielezny proved the following necessary conditions for convolution operators in O$_{c}$(S:S) to be solvable in S.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1659-1666
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• 2018

Let $P_r$ denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, it is proved that for every sufficiently large even integer N, the equation $$N=x^2+p_1^2+p_2^3+p_3^3+p_4^4+p_5^4$$ is solvable with x being an almost-prime $P_4$ and the other variables primes. This result constitutes an improvement upon that of $L{\ddot{u}}$ [7].

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.1047-1067
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• 1996

In this paper, we are interested in left invariant flat affine structures on Lie groups. These structures has been studied by many authors in different contexts. One of the fundamental questions is the existence of complete affine structures for solvable Lie groups G, raised by Minor [15]. But recently Benoist answered negatively even for the nilpotent case [1]. Also moduli space of such structures for lower dimensional cases has been studied by several authors, sometimes with compatible metrics [5,10,4,12].

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.309-317
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• 2016

Let V be a Euclidean Jordan algebra with a symmetric cone K. We show that for a Z-transformation L with the additional property L(K) ⊆ K (which we will call ’cone-preserving’), GUS ⇔ strictly copositive on K ⇔ monotone + P. Specializing the result to the Stein transformation S_A(X) := X - AXA^T on the space of real symmetric matrices with the property $S_A(S^n_+){\subseteq}S^n_+$, we deduce that S_A GUS ⇔ I ± A positive definite.

• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.909-919
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• 2020

The 4-dimensional solvable Lie group Sol₀⁴ does not admit a lattice. The purpose of this paper is two-fold. We study poly-crystallographic groups of Sol₀⁴, and then we study Nielsen fixed point theory on the spaces modeled on Sol₀⁴.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.1356-1359
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• 1996

The paper studies design of a decentralized supervisory controller with 2-level hierarchical structure for complex discrete event systems. Hierarchical structure with strict output-control-consistency(SOCC) gives a more abstract model for high-level control. The decentralized controller for a simple and abstract high-level system is designed more easily if the decentralized supervisory control problem in 2-level hierarchical structure systems(DSCP2) is solvable.