• Journal of the Chungcheong Mathematical Society
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• v.18 no.1
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• pp.51-64
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• 2005

The object of this paper is to prove two unique common fixed point theorems for a pair of a set-valued map and a self map satisfying a general contractive condition using orbital concept and weak-compatibility of the pair. One of these results generalizes substantially, the result of Dhage, Jennifer and Kang [4]. Simultaneously, its implications for two maps and one map improves and generalizes the results of Dhage [3], and Rhoades [11]. All the results of this paper are new.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.807-816
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• 2007

For the stochastic differential inclusion on infinite dimensional space of the form $dX_t{\in}\sigma(X_t)dW_t+b(X_t)dt$, where ${\sigma}$, b are set-valued maps, W is an infinite dimensional Hilbert space valued Q-Wiener process, we prove the boundedness and continuity of solutions under the assumption that ${\sigma}$ and b are closed convex set-valued satisfying the Lipschitz property using approximation.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.55-60
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• 1984

In [2], D. Downing and W.A. Kirk obtained a number of fixed point theorems for set-valued maps in matric and Banach spaces. The authors considered maps which are more general than the contractions with nonempty and closed mapping values, and obtain results for maps satisfying certain "inwardness" conditions. A key aspect of their approach is the application of a general fixed point theorem due to Caristi [1]. On the other hand, in [6], the present author obtained a number of equivalent formulations of the well-known result of I. Ekeland [3, 4] on the variational principle for approximate solutions of minimization problems. Some of such formulations include sharpened forms of the Caristi theorem. In this paper, using one of such formulations, we show that Theorems 1-3 and Corollaries 1-5 of [2] are substantially improved by giving geometric estimations of fixed points.ed points.

• Kyungpook Mathematical Journal
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• v.10 no.1
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• pp.15-20
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• 1970

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.165-175
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• 1998

We give a generalization of the selection theorem of Ben-El-Mechaiekh and Oudadess to complete LD-metric spaces with the aid of the notion of n-connectedness. Our new selection theorem is used to obtain new results of fixed points and coincidence points for compact lower semicontinuous set-valued maps with closed values consisting of D-sets in a complete LD-metric space.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.73-90
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• 1998

In this paper we introduce and study a number of new classes of quasi variational inequalities. using essentially the projection technique and its variant forms we prove that the gen-eralized set-valued mixed quasivariational inequalities are equivalent to the fixed point problem and the Wiener-Hopf equations(normal maps). This equivalence enables us to suggest a number of iterative algorithms solving the generalized variational inequalities. As a special case of the generalized set-valued mixed quasi variational in-equalities we obtain a class of quasi variational inequalities studied by Siddiqi Husain and Kazmi [35] but there are several inaccuracies in their formulation of the problem the statement and the proofs of the problem the statement and the proofs of their results. We have removed these inaccuracies. The correct formulation of thir results can be obtained as special cases from our main results.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.135-144
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• 2005

We consider the stochastic differential inclusion of the form $dX_t{\in}{\sigma}(t, X_t)dB_t+b(t, X_t)dt$, where ${\sigma}$, b are set-valued maps, B is a standard Brownian motion. We prove that the set of solutions is closed.

• Bulletin of the Korean Mathematical Society
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• v.40 no.1
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• pp.159-165
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• 2003

We consider the stochastic differential inclusion of the form $dX_t\;\in\;\sigma(t,\;X_t)db_t+b(t,\;X_t)dt$, where $\sigma$, b are set-valued maps, B is a standard Brownian motion. We prove the boundedness of solutions under the assumption that $\sigma$ and b satisfy the local Lipschitz property and linear growth.

• Proceedings of the Korean Society of Crop Science Conference
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• 2017.06a
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• pp.117-117
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• 2017

The onion (Allium cepa L.) is the most widely cultivated species of the genus Allium, especially it has been valued because of the pungent flavor and aroma. Allium species including onion has very large genome sizes ranging from approximately 10 to 20 Gbp, which have complicated genomic studies and precluded genome sequencing until recently. A population of 186 F2 individuals derived from a cross of 'Umjinara' ${\times}$ 'Sinsunhwang' and the two parental lines were used for this study. For the development of framework map, various types of markers including SSRs, RAPD, SNPs, and CAPS makers have been used for polymorphism test. Especially, a lot of SNP and CAPS loci were developed from the onion transcriptome sequence by RNASEQ of two parental lines. The GBS libraries have been constructed based on a modified protocol from Poland Lab using a two-enzyme system. We have been developing markers showing polymorphism between two parental lines, and genotyping for all F2 individuals were finished for a number of polymorphic markers. For the construction of GBS libraries, a set of 192 barcoded adapters were generated from complementary oligonucleotides with XhoI overhang sequence and unique barcodes of length 4-8 bp and they have been tested using two parental linesto determine the optimum conditions for GBS analysis.

• Journal of the Korean Institute of Landscape Architecture
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• v.27 no.2
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• pp.41-50
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• 1999

The purpose of this study is to find out the changes in geomorphic characteristics of a small watershed when a golf course is constructed. The research site is a set of seven small watersheds including an 18-hole golf course that were randomly selected. The size, shape, and drainage network of watersheds were measured by using planimeter, watershed eccentricity, and stream order, respectively. In addition, a 25m$\times$25m mesh was used on topographic maps and grading plans in order to obtain the slope, elevation, and aspect of the watersheds. The major results of this research, while investigating of the changes in geomorphic characteristics of watersheds when a golf course is constructed, are as follows: 1. The size of watersheds is increased in accordance to the difference in elevation between the golf course site and the small watershed. 2. The watershed eccentricities are in general similar except for a few low-valued cases. 3. The changes in the average altitude and the gradient are more drastic with their bigger original values. 4. The aspects are changed more with decreasing elevation. 5. The stream order decreases in the case of a low watershed eccentricity. 6. The surface modification has a closer relationship to the slope rather than the size of effective use area. 7. With a steeper gradient and an excessively low gradient, the height of cutting/filling is increased.