• 충청수학회지
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• 제17권1호
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• pp.47-56
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• 2004

The nonlinearity of a Boolean function f on $GF(2)^n$ is the minimum hamming distance between f and all affine functions on $GF(2)^n$ and it measures the ability of a cryptographic system using the functions to resist against being expressed as a set of linear equations. Finding out the exact value of the nonlinearity of given Boolean functions is not an easy problem therefore one wants to estimate the nonlinearity using extra information on given functions, or wants to find a lower bound or an upper bound on the nonlinearity. In this paper we extend the notion of auto-correlations of Boolean functions to vector Boolean functions and obtain upper bounds and a lower bound on the nonlinearity of vector Boolean functions in the context of their auto-correlations. Also we can describe avalanche characteristics of vector Boolean functions by examining the extended notion of auto-correlations.

• Structural Engineering and Mechanics
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• 제31권1호
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• pp.113-116
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• 2009

• 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%.

• 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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• 제8권3호
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• pp.881-888
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• 2001

Recently, Hooda and Ram [7] have proposed and characterized a new generalized measure of R-norm entropy. In the present communication we have studied its application in coding theory. Various mean codeword lengths and their bounds have been defined and a coding theorem on lower and upper bounds of a generalized mean codeword length in term of the generalized R-norm entropy has been proved.

• 한국경영과학회지
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• 제17권2호
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• pp.123-130
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• 1992

The model of k-out-of n : G repairable system with identical components is extended to a repairable system with n different components. The objective is to analytically derive the mean time of the busy period for a k-out-of-n : G system with unrestricted repair. Then, the lower and upper bounds on the average time of the busy period of the n-component system with restricted repair are also shown.

• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.319-330
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• 2016

The hyper-Zagreb index HM(G) of a simple graph G is defined as the sum of the terms (d_u+d_v)² over all edges uv of G, where d_u denotes the degree of the vertex u of G. In this paper, we present several upper and lower bounds on the hyper-Zagreb index in terms of some molecular structural parameters and relate this index to various well-known molecular descriptors.

• 대한수학회지
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• 제42권6호
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• pp.1215-1230
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• 2005

In this paper we establish some results on the increments of a d-dimensional Gaussian process with the usual Euclidean norm. In particular we obtain the law of iterated logarithm and the Book-Shore type theorem for the increments of ad-dimensional Gaussian process, via estimating upper bounds and lower bounds of large deviation probabilities on the suprema of the d-dimensional Gaussian process.

• 한국경영과학회지
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• 제34권4호
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• pp.113-121
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• 2009

In this paper, we consider the departure process from the open and nested tandem Queueing network with population constraint and constant service times. It is known that the Queueing network can be transformed into a simple Queueing network which can be easy to analyze. Using this simple Queueing network, upper and lower bounds on the interdeparture time are obtained. We prove that the variance of the interdeparture time is bounded within these two bounds. Validation against simulation data is shown that how it works the variance of the interdeparture time within two bounds. These bounds can be applied to obtain the better variance of the interdeparture time using a suitable method.

• 대한수학회보
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• 제60권2호
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• pp.389-404
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• 2023

We prove sharp bounds for Hankel determinants for starlike functions f with respect to symmetrical points, i.e., f given by $f(z)=z+{\sum{_{n=2}^{\infty}}}\,{\alpha}_nz^n$ for z ∈ 𝔻 satisfying $$Re{\frac{zf^{\prime}(z)}{f(z)-f(-z)}}>0,\;z{\in}{\mathbb{D}}$$. We also give sharp upper and lower bounds when the coefficients of f are real.