• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.7
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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.

• The Journal of the Acoustical Society of Korea
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• v.41 no.6
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• pp.637-646
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• 2022

Sub-arrays of arbitrary conformal array have different geometric shape through steering direction, thus the beam patterns of sub-arrays are always non-uniform. In this paper, we apply the beam pattern synthesis method using convex optimization into the conformal array, and shows the improvement of uniformity of beam performance. The simulation is performed with the conformal array of cut-sphere shape. As a result, the standard deviation of 3 dB beamwidth in elevation is greatly reduced but the directivity index is also reduced. To alleviate this trade-off, we propose a convex optimization using a shading function.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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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.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.3
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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.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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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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• v.22 no.1_2
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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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• v.47 no.3
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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].

• The Mathematical Education
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• v.28 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.37 no.2
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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.