• Title, Summary, Keyword: degree theory

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THE INDEX FOR A TOPOLOGICAL DEGREE THEORY FOR DENSELY DENIED OPERATORS OF TYPE ${S_+}_O,L$ IN BANACH SPACES

  • Kartsatos, Athanassios G.;Skrypnik, Igor V.
    • Journal of the Korean Mathematical Society
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    • v.37 no.6
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    • pp.901-913
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    • 2000
  • This is a summary of results involving the development of a theory of an index of an isolated critical point for densely defined nonlinear operators of type (S(sub)+)(sub)0,L. This index theory is associated with a degree theory, for such operators, whch has been recently developed by the authors.

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AN APPLICATION OF THE LERAY-SCHAUDER DEGREE THEORY TO THE VARIABLE COEFFICIENT SEMILINEAR BIHARMONIC PROBLEM

  • Choi, Q-Heung;Jung, Tacksun
    • Korean Journal of Mathematics
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    • v.19 no.1
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    • pp.65-75
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    • 2011
  • We obtain multiplicity results for the nonlinear biharmonic problem with variable coefficient. We prove by the Leray-Schauder degree theory that the nonlinear biharmonic problem has multiple solutions for the biharmonic problem with the variable coefficient semilinear term under some conditions.

INVARIANCE OF DOMAIN THEOREM FOR DEMICONTINUOUS MAPPINGS OF TYPE ( $S_+$)

  • Park, Jong-An
    • Bulletin of the Korean Mathematical Society
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    • v.29 no.1
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    • pp.81-87
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    • 1992
  • Wellknown invariance of domain theorems are Brower's invariance of domain theorem for continuous mappings defined on a finite dimensional space and Schauder-Leray's invariance of domain theorem for the class of mappings I+C defined on a infinite dimensional Banach space with I the identity and C compact. The two classical invariance of domain theorems were proved by applying the homotopy invariance of Brower's degree and Leray-Schauder's degree respectively. Degree theory for some class of mappings is a useful tool for mapping theorems. And mapping theorems (or surjectivity theorems of mappings) are closely related with invariance of domain theorems for mappings. In[4, 5], Browder and Petryshyn constructed a multi-valued degree theory for A-proper mappings. From this degree Petryshyn [9] obtained some invariance of domain theorems for locally A-proper mappings. Recently Browder [6] has developed a degree theory for demicontinuous mapings of type ( $S_{+}$) from a reflexive Banach space X to its dual $X^{*}$. By applying this degree we obtain some invariance of domain theorems for demicontinuous mappings of type ( $S_{+}$). ( $S_{+}$).

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THE PROOF OF THE EXISTENCE OF THE THIRD SOLUTION OF A NONLINEAR BIHARMONIC EQUATION BY DEGREE THEORY

  • Jung, Tacksun;Choi, Q.-Heung
    • Korean Journal of Mathematics
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    • v.16 no.2
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    • pp.165-172
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    • 2008
  • We investigate the multiplicity of solutions of the nonlinear biharmonic equation with Dirichlet boundary condition,${\Delta}^2u+c{\Delta}u=bu^{+}+s$, in ­${\Omega}$, where $c{\in}R$ and ${\Delta}^2$ denotes the biharmonic operator. We show by degree theory that there exist at least three solutions of the problem.

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LERAY-SCHAUDER DEGREE THEORY APPLIED TO THE PERTURBED PARABOLIC PROBLEM

  • Jung, Tacksun;Choi, Q-Heung
    • Korean Journal of Mathematics
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    • v.17 no.2
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    • pp.219-231
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    • 2009
  • We show the existence of at least four solutions for the perturbed parabolic equation with Dirichlet boundary condition and periodic condition when the nonlinear part cross two eigenvalues of the eigenvalue problem of the Laplace operator with boundary condition. We obtain this result by using the Leray-Schauder degree theory, the finite dimensional reduction method and the geometry of the mapping. The main point is that we restrict ourselves to the real Hilbert space instead of the complex space.

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MFSC: Mean-Field-Theory and Spreading-Coefficient Based Degree Distribution Analysis in Social Network

  • Lin, Chongze;Zheng, Yi
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.12 no.8
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    • pp.3630-3656
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    • 2018
  • Degree distribution can provide basic information for structural characteristics and internal relationship in social network. It is a critical procedure for social network topology analysis. In this paper, based on the mean-field theory, we study a special type of social network with exponential distribution of time intervals. First of all, in order to improve the accuracy of analysis, we propose a spreading coefficient algorithm based on intimate relationship, which determines the number of the joined members through the intimacy among members. Then, simulation show that the degree distribution of follows the power-law distribution and has small-world characteristics. Finally, we compare the performance of our algorithm with the existing algorithms, and find that our algorithm improves the accuracy of degree distribution as well as reducing the time complexity significantly, which can complete 29.04% higher precision and 40.94% lower implementation time.

Causes of high unemployment among the people with disabilities : productivity, or discrimination? (장애인 실업의 원인 : 생산성 또는 차별?)

  • Yu, Dong-Chul
    • Korean Journal of Social Welfare
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    • v.48
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    • pp.333-358
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    • 2002
  • The purpose of this study is to analyze empirically the causes of high unemployment among the people with disabilities, focused on productivity and discrimination. In order to pursue such goal this study adopts human capital theory, screening theory, job contest theory, taste theory and statistical discrimination theory as theoretical background. The major findings are: (1) Among the human capital variables Education degree and job training are not statistically significant on employment. Only degree of activity limit has significant effect. (2) Among the discrimination related variables only discrimination experiences variable has negative effect on employment. (3) Between degree of activity limit and discrimination experiences, both have similar effect on employment. But the degree of activity limit can be thought as discrimination related element. Because' not giving resonable accommodation' is regarded discrimination in ADA or DDA. These mean that it is important for society to compel the employment of the disabled and to put focus on eliminating prejudice rather than accomplishing education and job training programs to improve the employment of the disabled. In order to accomplish this it is necessary to increase the levy for disabled persons' employment promotion of the disabled persons' employment promotion act and to establish the disability discrimination act. Also, integrated education starting from infancy is necessary. Education system should be changed, and Job training must focused on industry which demand more labor force.

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EXISTENCE OF MULTIPLE SOLUTIONS OF A SEMILINEAR BIHARMONIC PROBLEM WITH VARIABLE COEFFICIENTS

  • Jung, Tacksun;Choi, Q-Heung
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.1
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    • pp.121-130
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    • 2011
  • We obtain multiplicity results for the biharmonic problem with a variable coefficient semilinear term. We show that there exist at least three solutions for the biharmonic problem with the variable coefficient semilinear term under some conditions. We obtain this multiplicity result by applying the Leray-Schauder degree theory.