• Journal of Korean Neurosurgical Society
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• v.30 no.11
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• pp.1263-1270
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• 2001

Objective : To analyze the radiosurgical results of intracranial meningiomas after Gamma Knife radiosurgery (GKS) and to assess the possible factors related to the outcome and complications in treating meningiomas. Patients and Methods : We retrospectively reviewed the clinical and radiological data in 179 patients(194 lesions) treated with GKS for intracranial meningiomas between May 1992 and October 2000. Radiosurgical responses were categorized as shrinkage, stasis and enlargement, and we defined the shrunken and static group as a radio-logical control. A Cox proportional hazards model was used to evaluate the correlation between the radiosurgical outcomes and various factors such as location and size of tumor, age and gender of patients, relation to venous sinus, pre-GKS degree of edema, treatment modality, radiosurgical parameters, and pathologic findings. Results : Patients were grouped into skull base meningiomas(57.7%), non-skull base tumor including convexity, parasagittal, and falx meningiomas(37.1%), and others(5.2%) according to the location of tumors. The mean maximum dose and the margin dose of tumor was 30.0Gy(19-45Gy) and 15.1Gy(9.5-24.5Gy), respectively. The mean volume of the tumors was 9.4cc(0.003-45.0cc). The radiologic control rate was 97.1%. The radiation induced imaging change with or without neurologic deficit was the most common complication(23.6%). There were seen mostly in convexity, parasagittal, and falx meningiomas which were deeply embedded in cortex. Conclusion : GKS for intracranial meningioma seems to be safe and effective treatments. However, GKS should be considered very cautiously in non-skull base tumor such as convexity, parasagittal, or falx meningiomas with regards to patient's age and general condition, size and location of tumor, pattern of embedding into cortex, presenting symptoms and patient's preference.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.425-434
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• 2007

We iteratively generate a sequence of measurable mappings and study necessary conditions for its convergence to a random fixed point of random nonexpansive operator. A random fixed point theorem for random nonexpansive operator, relaxing the convexity condition on the underlying space, is also proved. As an application, we obtained random fixed point theorems for Caristi type random operators.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.517-525
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• 2000

A constrained rational cubic spline with linear denominator was constructed in [1]. In the present paper, the sufficient condition for convex interpolation and some properties in error estimation are given.

• Honam Mathematical Journal
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• v.26 no.1
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• pp.77-83
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• 2004

A class of topological algebras, which we call it a fundamental one, has already been introduced generalizing the famous Cohen factorization theorem to more general topological algebras. To prove the generalized versions of Cohen's theorem to locally multilplicatively convex algebras, and finally to fundamental topological algebras, the completness of the background spaces is one of the main conditions. The local convexity of the completion of a locally convex space is a well known fact and here we have a discussion on the completness of fundamental metrizable topological vector spaces.

• International Journal of Control, Automation, and Systems
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• v.1 no.1
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• pp.156-161
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• 2003

An overview of our approach to autonomous navigation is presented showing how motion information can be integrated into existing navigation schemes. Particular attention is given to our short range motion estimation scheme which utilises a number of unique assumptions regarding the nature of the visual environment allowing a direct fusion of visual and range information. Graduated non-convexity is used to solve the resulting non-convex minimisation problem. Experimental results show the advantages of our fusion technique.

• Korean Journal of Mathematics
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• v.27 no.4
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• pp.879-898
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• 2019

In this paper we prove some interesting inclusions concerning the numerical range of some operators and the numerical range of theirs ranges with a convex function. Further, we prove some inequalities for the numerical radius. These inclusions and inequalities are based on some classical convexity inequalities for non-negative real numbers and some operator inequalities.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.9 no.13
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• pp.45-50
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• 1986

본 연구에서 고찰한 surrogate relaxation은 Lagrangian relaxation 방법과는 달리 제약식들을 선형조합으로 묶어 문제를 푼다. 수리계획 분계가 convexity를 만족하지 못하는 경우에는 Lagrangian의 경우와 마찬가지로 surrogate gap이 발생한다. Lagrangian 쌍대이론을 토대로 surrogate optimality condition을 알아보고 수리계획법의 특별 형태인 정수선형계획법에 적용해 보았다. 일반적으로 surrogate gap은 Lagrangian gap 보다 작기 때문에 좀더 근사하게 원 문제의 최적 목적 함수값에 접근할 수 있다. 따라서 branch and bound 알고리즘을 개발할 때 중요한 정보를 제공하는 것이다.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.433-446
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• 1997

In this paper we study an existence and the approxi-mation of the solution of the solution of the elliptic variational inequality from an abstract axiomatic point of view. We discuss convergence results and give an error estimate for the difference of the two solutions in an appropriate norm Also we present some computational results by using fixed point method.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1157-1165
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• 2011

The Karush-Kuhn-Tucker (KKT) necessary optimality conditions for nonlinear differentiable programming problems are also sufficient under suitable convexity assumptions. The KKT conditions in multiobjective programming problems with interval-valued objective and constraint functions are derived in this paper. The main contribution of this paper is to obtain the Pareto optimal solutions by resorting to the sufficient optimality condition.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.609-624
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• 1996

Recently, Giannessi [9] firstly introduced the vector-valued variational inequalities in a real Euclidean space. Later Chen et al. [5] intensively discussed vector-valued variational inequalities and vector-valued quasi variationl inequalities in Banach spaces. They [4-8] proved some existence theorems for the solutions of vector-valued variational inequalities and vector-valued quasi-variational inequalities. Lee et al. [14] established the existence theorem for the solutions of vector-valued variational inequalities for multifunctions in reflexive Banach spaces.