• 대한수학회지
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• 제37권6호
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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.

• 대한수학회보
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• 제29권1호
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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 ( $S_{+}$). ( $S_{+}$).

• Korean Journal of Mathematics
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• 제17권2호
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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.

• Korean Journal of Mathematics
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• 제19권1호
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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.

• Korean Journal of Mathematics
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• 제16권2호
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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.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제12권8호
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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.

• 한국사회복지학
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• 제48권
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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.

• 대한수학회보
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• 제47권1호
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• pp.121-129
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• 2010

Using a degree theory for countably condensing multivalued maps, we show that under certain conditions an invariance of domain theorem holds for countably condensing or countably k-contractive multivalued vector fields.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권1호
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• pp.87-95
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• 2011

The existence of T-periodic solutions for a general class of p-Laplacian equations is investigated. By using coincidence degree theory, some existence and uniqueness results, which generalize some earlier works on this topic, are presented.

• 정보관리학회지
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• 제20권1호
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• pp.165-198
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• 2003

본 연구는 문헌정보학 분야 연구논문에서 저자들의 이론 활용 정도를 분석하기 위하여 한국문헌정보학회지와 정보관리학회지를 대상으로 지난 30년간 연구된 654편의 논문에 대한 내용분석이 이루어 졌다. 주요 연구내용은 연구논문의 연대별 생산성, 세부주제영역별 생산성, 연구에 활용된 이론의 유형과 근원, 개별 이론별 활용도, 세부주제 영역별 활용도, 학회지별 활용도 등에 대한 개념적 연구와 실증적 연구가 수행되었다. 이를 위하여 이론의 개념적 기준 설정과 문헌정보연구의 세부주제영역에 대한 새로운 분류 체계, 특히 이론의 활용성을 평가하기 위한 기준으로 ‘이론 활용 5단계’ 모델을 제시하였다.