• KSII Transactions on Internet and Information Systems (TIIS)
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• 제15권7호
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• pp.2650-2667
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• 2021

In this paper, we derive the expression of the cache hitting probability with random caching policy and propose the joint optimization algorithm based on difference of convex algorithm (DCA) in the three-tier caching heterogeneous cellular network assisted by macro base stations, helpers and users. Under the constraint of the caching capacity of caching devices, we establish the optimization problem to maximize the cache hitting probability of the network. In order to solve this problem, a convex function is introduced to convert the nonconvex problem to a difference of convex (DC) problem and then we utilize DCA to obtain the optimal caching probability of macro base stations, helpers and users for each content respectively. Simulation results show that when the density of caching devices is relatively low, popular contents should be cached to achieve a good performance. However, when the density of caching devices is relatively high, each content ought to be cached evenly. The algorithm proposed in this paper can achieve the higher cache hitting probability with the same density.

• 한국음향학회지
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• 제41권6호
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• pp.637-646
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• 2022

임의의 곡면 배열에서 단위 빔 형성에 사용되는 부배열은 조향 방위마다 기하학적 형상이 다르다. 이 때문에 조향 방위 별 부배열의 빔 패턴은 항상 균일하지 않다. 본 논문에서는 볼록 최적화를 이용한 빔 형성 기법을 곡면 배열에 적용하고, 조향 방위별 빔 성능의 균일성이 향상되는 것을 보였다. 시뮬레이션은 절단 구면 형상의 곡면 배열에 대해 수행되었다. 고각 3 dB 빔 폭의 표준 편차가 크게 감소하였으나 반대급부로 지향 지수도 감소하는 것을 관찰했다. 이를 완화시키기 위한 하나의 방법으로 쉐이딩 함수를 이용한 최적화 기법을 제안한다.

• 대한수학회지
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• 제37권5호
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• pp.849-856
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• 2000

We give a new saddle point theorem for vector-valued functions on an admissible compact convex set in a topological vector space under weak condition that is the semicontinuity of two function scalarization and acyclicty of the involved sets. As application, we obtain the minimax theorem.

• 충청수학회지
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• 제21권3호
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• pp.321-326
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• 2008

In this note, using the separation theorem for convex sets, we will give a two functions version generalization of Fan's minimax theorem by relaxing the convexlike assumption to the weak convexlike condition.

• 대한수학회논문집
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• 제14권1호
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• pp.147-156
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• 1999

This paper deals with a class H(A,B,$\alpha$) of analytic functions and we obtain coefficient estimates and related results.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.461-466
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• 2006

In this paper, an algorithm with a new Armijo-type line search is proposed that ensure global convergence of a correlative Polak-Ribiere conjugate method for the unconstrained minimization of non-convex differentiable function.

• Kyungpook Mathematical Journal
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• 제47권3호
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• pp.393-401
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• 2007

In the present paper we introduce the subclass $S^{\lambda}_{a,c}(p,A,B)$ of analytic functions and then we investigate some interesting properties of functions belonging to this subclass. Our results generalize many results known in the literature and especially generalize some of the results obtained by Ling and Liu [5].

• 한국수학교육학회지시리즈A:수학교육
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• 제28권1호
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• pp.41-45
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• 1989

Subdifferentiability of a vector-valued set function is defined first. Then in terms of zero-like functions, a perperly efficient solution of a convex programming problem with set functions will be characterized.

• 대한수학회보
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• 제36권2호
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• pp.363-370
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• 1999

A new and simple estimate using a convex function for convergence factors of Schwarz algorithms orthogonal spline collocation method is presented. The estimated convergence factors in this context depend only on a way to split a given domain.

• 대한수학회논문집
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• 제37권2호
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• pp.567-574
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• 2022

We use convolution techniques to define certain classes of starlike functions which are associated with Lommel operator. Some inclusion results are investigated. It is also shown that these classes are invariant under Bernardi integral operator.