• Journal of Communications and Networks
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• v.18 no.2
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• pp.182-189
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• 2016

The focus in this paper is on obtaining tight, simple algebraic-form bounds and invertible expressions for the average symbol error probability (ASEP) of M-ary phase shift keying (MPSK) in a class of composite fading channels. We employ the mixture gamma (MG) distribution to approximate the signal-to-noise ratio (SNR) distributions of fading models, which include Nakagami-m, Generalized-K ($K_G$), and Nakagami-lognormal fading as specific examples. Our approach involves using the tight upper and lower bounds that we recently derived on the Gaussian Q-function, which can easily be averaged over the general MG distribution. First, algebraic-form upper bounds are derived on the ASEP of MPSK for M > 2, based on the union upper bound on the symbol error probability (SEP) of MPSK in additive white Gaussian noise (AWGN) given by a single Gaussian Q-function. By comparison with the exact ASEP results obtained by numerical integration, we show that these upper bounds are extremely tight for all SNR values of practical interest. These bounds can be employed as accurate approximations that are invertible for high SNR. For the special case of binary phase shift keying (BPSK) (M = 2), where the exact SEP in the AWGN channel is given as one Gaussian Q-function, upper and lower bounds on the exact ASEP are obtained. The bounds can be made arbitrarily tight by adjusting the parameters in our Gaussian bounds. The average of the upper and lower bounds gives a very accurate approximation of the exact ASEP. Moreover, the arbitrarily accurate approximations for all three of the fading models we consider become invertible for reasonably high SNR.

• Journal of Information Technology Services
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• v.10 no.1
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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%.

• Journal of Information Technology Services
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• v.9 no.3
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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.

• Journal of the Korean Ceramic Society
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• v.28 no.11
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• pp.878-884
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• 1991

The mobility and diffusivity in an edge dislocation in an FCC crystal formed by the removal of one half of a (100) plane were evaluated in an applied field by analyzing a vacancy tight binding model using Stark's matrix technique. A model of an edge dislocation in an FCC crystal was constructed for a [100] Burgers vector where vacancy transport along the edge dislocation in an FCC crystal was constructed for a [100] Burgers vector where vacancy transport along the edge of the extrac half plane of ions was considered. The model considered a tight binding approximation of the vacancy to the compressed region of the core and carried the calculation to the limit of an infinite length of dislocation. The diffusivity and the ratio of mobility to diffusivity were found to increase without bounds in the limit where the correlation factor becomes zero. In contrast, as the correlation factor became unity, the diffusivity became zero and the ratio of mobility to diffusivity became unity associated with the uncorrelated limit of 1/kT. This implied that the phenomenon was not unique to the crystal structure but was unique to edge dislocations with vacancy tight binding.

• Journal of the Korean Operations Research and Management Science Society
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• v.36 no.2
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• pp.1-14
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• 2011

In this paper, we deal with an access network design problem of fiber-to-the-home passive optical network (FTTH-PON). The FTTH-PON network design problem seeks to minimize the total cost of optical splitters and cables that provide optical connectivity between central office and subscribers. We develop a flow-based mixed integer programming (MIP) model with nonlinear link cost. By developing valid inequalities and preprocessing rules, we enhance the strength of the proposed MIP model in generating tight lower bounds for the problem. We develop an effective Tabu Search (TS) heuristic algorithm that provides good quality feasible solutions to the problem. Computational results demonstrate that the valid inequalities and preprocessing rules are effective for improving the LP-relaxation lower bound and TS algorithm finds good quality solutions within reasonable time bounds.

• Bulletin of the Korean Mathematical Society
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• v.57 no.2
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• pp.355-369
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• 2020

In the present investigation, by applying two different normalizations of the Jackson's second and third q-Bessel functions tight lower and upper bounds for the radii of convexity of the same functions are obtained. In addition, it was shown that these radii obtained are solutions of some transcendental equations. The known Euler-Rayleigh inequalities are intensively used in the proof of main results. Also, the Laguerre-Pólya class of real entire functions plays an important role in this work.

• Journal of the Korean Operations Research and Management Science Society
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• v.20 no.3
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• pp.31-41
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• 1995

The maximum Origin-Destination Flow Path Problem (MODFP) in an Acyclic Network has known as NP-hard. K. S. Sung has suggested on Optimal Algorithm for MODFP based on the Pseudo flo or arc and the K-th shortest path algorithm. When we try to solve MODFP problem by general Branch and Bound Method (BBM), the upper and lower bounds of subproblems are so weak that the BBM become very inefficient. Here we utilized the Pseudo flow of arc' for the tight bounds of subproblems so that it can produce an efficient BBM for MODFP problem.

• Journal of Korean Institute of Industrial Engineers
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• v.24 no.4
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• pp.571-578
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• 1998

In this paper, we deal with a node weighted Steiner Ring Problem (SRP) arising from the deployment of Synchronous Optical Networks (SONET), a standard of transmission using optical fiber technology. The problem is to find a minimum weight cycle (ring) covering a subset of nodes in the network considering node and link weights. We have developed two mathematical models, one of which is stronger than the other in terms of LP bounds, whereas the number of constraints of the weaker one is polynomially bounded. In order to solve the problem optimally, we have developed some preprocessing rules and valid inequalities. We have also prescribed an effective heuristic procedure for providing tight upper bounds. Computational results show that the stronger model is better in terms of computation time, and valid inequalities and preprocessing rules are effective for solving the problem optimally.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.29 no.6
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• pp.1259-1270
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• 2019

The upper bound of differential characteristic probability is mainly used to determine the number of rounds when constructing a block cipher. As the number of rounds affects the performance of block cipher, it is critical to evaluate the tight upper bound in the constructing process. In order to calculate the upper bound of differential characteristic probability, the previous searching methods for minimum number of active S-boxes constructed constraint equations for non-linear operations and linear operations, independently. However, in the case of BOGI design strategy, where linear operation is dependent on non-linear operation, the previous methods may present the less tight upper bound. In this paper, we exploit the properties of BOGI strategy to propose a new method to evaluate a tighter upper bound of differential characteristic probability than previous ones. Additionally, we mathematically proved the validity of our method. Our proposed method was applied to GIFT-64 and GIFT-128, which are based on BOGI strategy, and the upper bounds of differential characteristic probability were derived until 9 round. Previously, the upper bounds of differential characteristic probability for 7-round GIFT-64 and 9-round GIFT-128 were 2^-18.395 and 2^-26.885, respectively, while we show that the upper bounds of differential characteristic probability are more tight as 2^-19.81 and 2^-28.3, respectively.

• Journal of Communications and Networks
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• v.16 no.1
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• pp.67-80
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• 2014

Spectrum sensing is vital for secondary unlicensed nodes to coexist and avoid interference with the primary licensed users in cognitive wireless networks. In this paper, we develop models for bounding interference levels from secondary network to the primary nodes within a spectrum sensing framework. Instead of classical stochastic approaches where Poisson point processes are used to model transmitters, we consider a more practical model which takes into account the medium access control regulations and where the secondary Poisson process is judiciously thinned in two phases to avoid interference with the secondary as well as the primary nodes. The resulting process will be a modified version of the Mat$\acute{e}$rn point process. For this model, we obtain bounds for the complementary cumulative distribution function of interference and present simulation results which show the developed analytical bounds are quite tight. Moreover, we use these bounds to find the operation regions of the secondary network such that the interference constraint is satisfied on receiving primary nodes. We then obtain theoretical results on the primary and secondary throughputs and find the throughput limits under the interference constraint.