• Structural Engineering and Mechanics
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• 제13권3호
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• pp.299-312
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• 2002

In this paper, a new method to solve the dynamic response problem for structures with interval parameters is presented. It is difficult to obtain all possible solutions with sharp bounds even an optimum scheme is adopted when there are many interval structural parameters. With the interval algorithm, the expressions of the interval stiffness matrix, damping matrix and mass matrices are developed. Based on the matrix perturbation theory and interval extension of function, the upper and lower bounds of dynamic response are obtained, while the sharp bounds are guaranteed by the interval operations. A numerical example, dynamic response analysis of a box cantilever beam, is given to illustrate the validity of the present method.

• 한국통신학회:학술대회논문집
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• 한국통신학회 1991년도 추계종합학술발표회논문집
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• pp.145-149
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• 1991

In this paper, an algorithm is proposed to analyze the approximating reliability of the capacity considered communication networks. In the case ofthe former methods to evaluate the source-to-termianl node reliability, it is very difficult to contract and delete the jointed terms in the simple path group. Therefore, the reliability bounds are used and compared to the exact reliability by TURBO PROLOG, the natural lanquage of artficial intelligence. In the reliability bounds, the upper bound used the valid cutset that isthe group of simple path and the lower bound used the minimal cutset by complement operation and the esact reiability is compared to this reliability bounds.

• Journal of the Korean Data and Information Science Society
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• 제16권1호
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• pp.1-11
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• 2005

A network consisting of a set of N nodes and a set of links is considered. The nodes are assumed to be perfect and the states of links to be binary and associated to each other. After defining a network structure function, which represents the state of network as a function of the states of links, we obtain some lower and upper bounds on the network reliability by adopting minmax principle and minimal path and cut set arguments. These bounds are given as functions of the reliabilities of links. The bridge network is considered as an example.

• 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.

• 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.

• 대한수학회보
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• 제44권1호
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• pp.103-108
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• 2007

In this paper, we obtain some lower bounds for area of non-simply connected compact singular surfaces of nonpositive curvature. One inequality involves systole and area of the surface.

• 대한수학회보
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• 제54권6호
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• pp.2149-2154
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• 2017

In this paper, we obtain a simple lower bound for the number of positive (resp. negative) crossings in oriented link diagrams in terms of the maximal (resp. minimal) degree of the Jones polynomial.

• 대한수학회지
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• 제33권3호
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• pp.513-525
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• 1996

Let the operator A be self-adjoint with domain, Dom(A), dense in $(H)$ which is a separable Hilbert space with norm $\left\$\mid$ \cdot \right\$\mid$$ and inner product $<\cdot, \cdot>$.

• 호남수학학술지
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• 제45권1호
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• pp.82-91
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• 2023

In this paper, we study the nonlinear eigenvalue problem for some of the (p, q)-Laplacian on compact Finsler manifolds with zero boundary condition, and estimate the lower bound of the first eigenvalues for (p, q)-Laplace operators on Finsler manifolds.

• 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.