• 한국IT서비스학회지
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• 제9권3호
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• pp.107-121
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• 2010

In this paper, we present a frequency reassignment problem (FRP) that arises when we install new base stations or reconfigure radio networks to increase the capacity or to expand service area. For this problem, we develop an integer programming (IP) model, and develop cutting planes to enhance the mathematical representation of the model. Also, we devise an effective tabu search algorithm to obtain tight upper bounds within reasonable time bounds. Computational results exhibit that the developed cutting planes are effective for reducing the computing time as well as for increasing lower bounds. Also, the proposed tabu search algorithm finds a feasible solution of good quality within reasonable time bound.

• 한국IT서비스학회지
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• 제10권1호
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• pp.117-133
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• 2011

In this paper, we present a frequency reassignment problem (FRP) arising from the reconfiguration of radio networks such as adding new base stations (BSs) and changing the number of frequencies assigned to BSs. For this problem, we develop an integer programming (IP) model that minimizes the sum of frequency reassignment cost and the cost for unsatisfied frequency demands, while avoiding interference among frequencies. To obtain tight lower bounds, we develop some valid inequalities and devise an objective function relaxation scheme. Also, we develop a simple but efficient heuristic procedure to solve large size problems. Computational results show that the developed valid inequalities are effective for improving lower bounds. Also, the proposed tabu search heuristic finds tight upper bounds with average optimality gap of 2.3%.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.785-800
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• 2021

In this paper, we obtain a new boundary version of the Schwarz lemma for analytic function. We give sharp upper bounds for |f'(0)| and sharp lower bounds for |f'(c)| with c ∈ ∂D = {z : |z| = 1}. Thus we present some new inequalities for analytic functions. Also, we estimate the modulus of the angular derivative of the function f(z) from below according to the second Taylor coefficients of f about z = 0 and z = z₀ ≠ 0. Thanks to these inequalities, we see the relation between |f'(0)| and 𝕽f(0). Similarly, we see the relation between 𝕽f(0) and |f'(c)| for some c ∈ ∂D. The sharpness of these inequalities is also proved.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.627-633
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• 2015

In this paper, we generalize the concept of the energy of Seidel matrix S(G) which denoted by S^α(G) and obtain some results related to this matrix. Also, we obtain an upper and lower bound for S^α(G) related to all of graphs with |detS(G)| ≥ (n - 1); n ≥ 3.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.39-46
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• 1997

Given to be the $m^{th}$ correlation coefficient of the Rudin-Shapiro polynomials of degrees $2^n-1$, $$\mid$a_m$\mid$ \leq C(2^n)^{\frac{3}{4}}$ and there exists $\kappa \neq 0$ such that $$\mid$a_{\kappa}$\mid$ ＞D(2^n)^{0.73}$ (C and D are universal constants). Here we show that the 0.73 is optimal in the upper vound case.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.332-332
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• 2000

In this paper, a novel sliding mode control with uncertainty adaptation is produced by introducing a virtual state. Because upper bounds of the uncertainty is difficult to know, we estimate these upper bound by using the simple adaptation law and design the novel sliding mode controller. The nominal controller is used the optimal controller to minimize cost function.

• 호남수학학술지
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• 제41권2호
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• pp.381-390
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• 2019

In this paper, we introduce interesting subclasses ${\mathcal{H}}^{p,q,{\beta},{\alpha}}_{{\sigma}B}$ and ${\mathcal{H}}^{p,q,{\beta}}_{{\sigma}B}({\gamma})$ of bi-univalent functions by (p, q)-derivative operator. Furthermore, we find upper bounds for the second and third coefficients for functions in these subclasses. The results presented in this paper would generalize and improve some recent works of several earlier authors.

• 한국정보통신학회논문지
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• 제20권12호
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• pp.2243-2251
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• 2016

본 연구에서는 트리구조를 가지는 네트워크의 [1,2]-지배집합에 대한 특성과 지배수의 상계 값에 대한 이론적 모형을 제시하였다. 구체적으로는 트리 네트워크가 가지는 몇 가지 전형적인 제약에 대해서 각 유형이 가지고 있는 지배집합의 지배수의 상계 값을 도출하였다. 본 논문에서는 트리구조의 네트워크에 대한 특성을 해석함에 있어서 그래프이론을 적용하였다. 노드집합 V와 링크집합 E으로 구성되는 그래프 G=(V,E)에 대해서 노드집합 V의 부분 집합 D를 가정한다. 이때 집합 V에 속하면서 집합 D에 속하는 않는 임의의 노드 ${\upsilon}$가 D에 속하는 노드와 1개 이상 2개 이하로만 인접하여 있으면 D를 [1,2]-지배집합이라 한다. 그리고 그래프 G의 [1,2]-지배집합 중 최소 농도를 [1,2]-지배 수라 하고 ${\gamma}_{[1,2]}(G)$로 표시한다. 본 논문에서는 트리(tree)의 [1,2]-지배 수에 대한 특성과 이의 새로운 상계 값을 증명하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제2권2호
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• pp.49-56
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• 1998

In this paper, by the use of an Ostrowski type integral inequality for double integrals, we establish an upper bound for the estimation error variance of a continuous stream with stationary variogram.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2000년도 추계학술발표회 논문집
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• pp.115-118
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• 2000

In this paper we establish limit results on the increments of (N, d)-Gaussian processes with independent components, via estimating upper bounds of large deviation probabilities on the suprema of (N, d)-Gaussian processes.