• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1345-1356
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• 2013

In this paper, we study rotational and helicoidal surfaces in Euclidean 3-space in terms of their Gauss map. We obtain a complete classification of these type of surfaces whose Gauss maps G satisfy $L_1G=f(G+C)$ for some constant vector $C{\in}\mathbb{E}^3$ and smooth function $f$, where $L_1$ denotes the Cheng-Yau operator.

• Bulletin of the Korean Mathematical Society
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• v.38 no.2
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• pp.413-425
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• 2001

We use the branching rules on SU(3) to show that if two Aloff-Wallach spaces $M_{k,l}\;and\;M_{k',l'}$ are isospectral for the Laplacian acting on smooth functions, they are isometric. We also show that 1 is the non-zero smallest eigenvalue among all Aloff-Wallach spaces and compute the multiplicities.

• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.43-65
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• 2015

We present a new convergence analysis of popular Broyden's method in the Banach/Hilbert space setting which is applicable to non-smooth operators. Moreover, we do not assume a priori solvability of the equation under consideration. Nevertheless, without these simplifying assumptions our convergence theorem implies existence of a solution and superlinear convergence of Broyden's iterations. To demonstrate practical merits of Broyden's method, we use it for numerical solution of three nontrivial infinite-dimensional problems.

• Proceedings of the IEEK Conference
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• 1999.06a
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• pp.1125-1128
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• 1999

This paper presents a speed controller for the Sinusoidal type BLDC motor using the sliding mode. Since the sliding mode control has some practical limitations such as the chattering phenomenon and reaching phase problems, the technique of overcoming these limitations is proposed in a practical realization. This proposed speed control technique is composed of an smooth integral variable structure control(IVSC), and chattering prediction method.

• Journal for History of Mathematics
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• v.20 no.4
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• pp.49-60
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• 2007

In this article, the concept of rigidity of smooth surfaces in the three dimensional Euclidean space which naturally arises in elementary geometry is introduced, and the natural process of the development of rigidity theory for compact surfaces and its generalizations are investigated.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1209-1220
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• 2014

We prove global gradient estimates in weighted Orlicz spaces for weak solutions of nonlinear elliptic equations in divergence form over a bounded non-smooth domain as a generalization of Calder$\acute{o}$n-Zygmund theory. For each point and each small scale, the main assumptions are that nonlinearity is assumed to have a uniformly small mean oscillation and that the boundary of the domain is sufficiently flat.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1699-1718
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• 2017

We give a construction of the second Chern number of a vector bundle over a smooth projective surface by means of adelic transition matrices for the vector bundle. The construction does not use an algebraic K-theory and depends on the canonical ${\mathbb{Z}}-torsor$ of a locally linearly compact k-vector space. Analogs of certain auxiliary results for the case of an arithmetic surface are also discussed.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.309-318
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• 1994

The approach presented in this paper is based on the transformation of the Stefan problem in one space dimension to an initial-boundary value problem for the heat equation in a fixed domain. Of course, the problem is non-linear. The finite element approximation adopted here is the standared continuous Galerkin method in time. In this paper, only the regular case is discussed. This means the error analysis is based on the assumption that the solution is sufficiently smooth. The aim of this paper is the existence of the solution in a finite Galerkin system of ordinary equations.

• Journal of applied mathematics & informatics
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• v.3 no.1
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• pp.47-54
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• 1996

We prove that if RUC(S) has a left invariant mean ${\rho}={T_{S} : s \;{\in}\; S}$ is a continuous repesentation of S as nonexpansive map-pings on a closed convex subset C of a p-uniformly convex and p-uniformly smooth Banach space and C contains an element of bounded orbit then C contains a common fixed point for ${\rho}$.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.375-385
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• 2014

We investigate strong convergence of Halpern's iteration for a countable family of strongly relatively nonexpansive mappings in the framework of uniformly convex and uniformly smooth Banach spaces. Our results extend those announced by many authors.