• Journal of the Chungcheong Mathematical Society
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• v.26 no.2
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• pp.351-356
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• 2013

In this article, we discuss the notions of chain prolongation functions on locally compact spaces and get some results for the concepts. We show that chain prolongation function is a cluster map.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.87-89
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• 1984

Let X be a Banach space, and let B(X) (resp. CB(X), K(X), CV(X)) denote the family of all nonvoid (resp. closed bounded, compact, convex) subsets of X. The Kuratowski measure of noncompactness is defined by the mapping .alpha.$_{k}$: B(X).rarw. $R_{+}$ with .alpha.$_{k}$(A) = inf {r>0 vertical bar A can be covered by a finite number of sets with diameter less than r}.an r}.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.575-585
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• 1996

Recently, existence theorems of coupled fixed points for mixed monotone operators have been considered by several authors (see [1]-[3], [6]). In this paper, we are continuously going to study the existence problems of coupled fixed points for two more general classes of mixed monotone operators. As an application, we utilize our main results to show thee existence of coupled fixed points for a class of non-linear integral equations.

• Journal of applied mathematics & informatics
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• v.5 no.2
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• pp.357-372
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• 1998

In this paper we introduce and study a new class of random completely generalized strongly nonlinear quasi -comple- mentarity problems with non-compact valued random fuzzy map-pings and construct some new iterative algorithms for this kind of random fuzzy quasi-complementarity problems. We also prove the existence of random solutions for this class of random fuzzy quasi-complementarity problems and the convergence of random iterative sequences generated by the algorithms.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.251-259
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• 2009

We investigate the multiple solutions for the nonlinear parabolic boundary value problem with jumping nonlinearity crossing two eigenvalues. We show the existence of at least four nontrivial periodic solutions for the parabolic boundary value problem. We restrict ourselves to the real Hilbert space and obtain this result by the geometry of the mapping.

• East Asian mathematical journal
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• v.26 no.1
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• pp.49-58
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• 2010

In this paper, we consider and study a new class of generalized vector quasi-variational type inequalities and obtain some existence theorems for both under compact and noncompact assumptions in topological vector spaces without using monotonicity. For the noncompact case, we use the concept of escaping sequences.

• Honam Mathematical Journal
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• v.20 no.1
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• pp.135-145
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• 1998

In this paper, we focus on the convex-valued selection theorem out of four main selection theorems; zero-dimensional, convex-valued, compact-valued, finite-dimensional theorems based on Michael's papers. We prove some theorems about lower semi-continuous set-valued mappings, and derive some applications to closed continuous set-valued mappings and to functional analysis. We also give a partial solution to the open problem posed by Engelking, Heath, and Michael.

• Journal of the Korean Society for Precision Engineering
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• v.25 no.3
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• pp.93-100
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• 2008

Laser interferometry is widely used as a measuring system in many fields because of its high resolution and ability to measure a broad area in real-time all at once. In conventional LASER interferometry, for example Out-of-plane ESPI(Electronic Speckle Pattern Interferometry), In plane ESPI, Shearography and Holography, it uses PZT or other components as a phase shift instrumentation to extract 3D deformation data, vibration mode and others. However, in most cases PZT has some disadvantages, which include nonlinear errors and limited time of use. In the present study, a new type of LASER interferometry using a laser diode is proposed. Using LASER Diode Sinusoidal Phase Modulating (LD-SPM) interferometry, the phase modulation can be directly modulated by controlling the LASER Diode injection current thereby eliminating the need for PZT and its components. This makes the interferometry more compact. This paper reports on a new approach to the LD Modulating interferometry that involves four-buckets phase shift method. This study proposes a four-bucket phase mapping algorithm, which was developed to have a guaranteed application, to stabilize the system in the field and to be a user-friendly GUI. In this paper, the theory for LD wavelength modulation and sinusoidal phase modulation of LD modulating interferometry is shown. Four-bucket phase mapping algorithm is then introduced.

• The Journal of Korea Robotics Society
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• v.3 no.3
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• pp.194-202
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• 2008

This paper describes a new method for indoor environment mapping and localization with stereo camera. For environmental modeling, we directly use the depth and color information in image pixels as visual features. Furthermore, only the depth and color information at horizontal centerline in image is used, where optical axis passes through. The usefulness of this method is that we can easily build a measure between modeling and sensing data only on the horizontal centerline. That is because vertical working volume between model and sensing data can be changed according to robot motion. Therefore, we can build a map about indoor environment as compact and efficient representation. Also, based on such nodes and sensing data, we suggest a method for estimating mobile robot positioning with random sampling stochastic algorithm. With basic real experiments, we show that the proposed method can be an effective visual navigation algorithm.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.401-408
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• 2014

If A is a unital Banach algebra, then the spectrum can be viewed as a function ${\sigma}$ : 𝕬 ${\rightarrow}$ 𝕾, mapping each T ${\in}$ 𝕬 to its spectrum ${\sigma}(T)$, where 𝕾 is the set, equipped with the Hausdorff metric, of all compact subsets of $\mathbb{C}$. This paper is concerned with the continuity of the spectrum ${\sigma}$ via Browder's theorem. It is shown that ${\sigma}$ is continuous when ${\sigma}$ is restricted to the set of essentially hyponormal operators for which Browder's theorem holds, that is, the Weyl spectrum and the Browder spectrum coincide.