• 호남수학학술지
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• 제39권4호
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• pp.617-635
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• 2017

By applying a classical approach for scalar rational interpolation problem, certain type of minimal interpolation problem for rational matrix functions is solved. It is shown that an appropriately defined matrix plays a key role in solving the minimal problem.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.159-169
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• 2005

An algorithmic approach to degree reduction of rational Bezier curves is presented. The algorithms are based on the degree reduction of polynomial Bezier curves. The method is introduced with the following steps: (a) convert the rational Bezier curve to polynomial Bezier curve by using homogenous coordinates, (b) reduce the degree of polynomial Bezier curve, (c) determine weights of degree reduced curve, (d) convert the Bezier curve obtained through step (b) to rational Bezier curve with weights in step (c).

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제8권1호
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• pp.1-17
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• 2014

Cooperative spectrum sensing (CSS) is considered as a powerful approach to improve the utilization of scarce radio spectrum resources. However, most of CSS schemes assume all secondary users (SU) are honest, and thus offering opportunities for malicious SUs to launch the spectrum sensing data falsification attack (SSDF attack). To combat such misbehaved behaviors, recent efforts have been made to trust schemes. In this paper, we argue that powering CSS with traditional trust schemes is not enough. The rational SSDF attack is found in this paper. Unlike the simple SSDF attack, rational SSDF attackers send out false sensing data on a small number of interested primary users (PUs) rather than all PUs. In this case, rational SSDF attackers can keep up high trustworthiness, resulting in difficultly detecting malicious SUs in the traditional trust schemes. Meanwhile, a defense scheme using a novel trust approach is proposed to counter rational SSDF attack. Simulation results show that this scheme can successfully reduce the power of rational SSDF, and thus ensure the performance of CSS.

• International Journal of Control, Automation, and Systems
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• 제5권1호
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• pp.1-7
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• 2007

In this paper, the necessary and sufficient conditions for strict positive realness of the rational transfer functions directly from basic definitions in the frequency domain are studied. A new frequency domain approach is used to check if a rational transfer function is a strictly positive real or not. This approach is based on the Taylor expansion and the Maximum Modulus Principle which are the fundamental tools in the complex functions analysis. Four related common statements in the strict positive realness literature which is appeared in the control theory are discussed. The drawback of these common statements is analyzed through some counter examples. Moreover a new necessary condition for strict positive realness is obtained from high frequency behavior of the Nyquist diagram of the transfer function. Finally a more simplified and completed conditions for strict positive realness of single-input single-output linear time-invariant systems are presented based on the complex functions analysis approach.

• 한국구조물진단유지관리공학회 논문집
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• 제2권4호
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• pp.159-171
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• 1998

This study attempts to develop a rational approach to flexural concrete beam analysis with crack growth. In order to develope analytical solutions, several simplification and assumption are made and the Hillerborg fictitious crack model is adapted for new rational approach to the flexural concrete beam. To provide desired results, the concrete beams with various conditions(more than 126 beam conditions) are analyzed. Before producing the results, these assumptions are founded to be justified by comparison with a FE analysis. The results for each condition of the beams are presented in terms of crack lengths, the strength and cracking stability of concrete beams. And also size effects in a flexural concrete beam is studied using a new flexural cracking model.

• Journal of Mechanical Science and Technology
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• 제20권5호
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• pp.658-667
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• 2006

Fractional derivative models, which are used to describe the viscoelastic behavior of material, have received considerable attention. Thus it is necessary to put forward the analysis solutions of dynamic systems containing a fractional derivative. Although previously reported such kind of fractional calculus-based constitutive models, it only handles the particularity of rational number in part, has great limitation by reason of only handling with particular rational number field. Simultaneously, the former study has great unreliability by reason of using the complementary error function which can't ensure uniform real number. In this paper, a new approach is proposed for an analytical scheme for dynamic system of a spring-mass-damper system of single-degree of freedom under general forcing conditions, whose damping is described by a fractional derivative of the order $0<{\alpha}<1$ which can be both irrational number and rational number. The new approach combines the fractional Green's function and Laplace transform of fractional derivative. Analytical examples of dynamic system under general forcing conditions obtained by means of this approach verify the feasibility very well with much higher reliability and universality.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1999년도 학회창립 10주년 기념 1999년도 가을 학술발표회 논문집
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• pp.445-448
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• 1999

The minimum shear and torsional reinforcement provisions in ACI 318-95 are still empirical. This paper describes the derivation of a rational approach for minimum shear and torsional reinforcement in beams so as to preclude brittle failure in shear and torsion. This is ensured by specifying that the beam's ultimate capacity of shear and torsion should be greater than its cracking shear and torsion. The formula presented herein for computing minimum shear and torsional reinforcement shows the need for modification of current provision for the minimum shear and torsion reinforcement.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1995년도 가을 학술발표회 논문집
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• pp.312-316
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• 1995

Flat-plate buildings are commonly modeled as two-dimensional frames to calculate lateral drift, unbalanced moments, and shear at slab-column connections. For gravity loads. the slab-column frames are analyzed using equivalent column approach, while equivalent beam approach is typical for lateral loads. The equivalent beam approach is convenient for computer analysis, but no rational procedure exists for determining the effective width of foor slabs. At present, the determination of the equivalent slab width and its stiffness is a matter of engineering judgement. To account for cracking, overly conservative assumptions are made regarding the stiffness of the slab. A rational approach is therefore needed to realistically estimate the equivalent slab width and its stiffness for unbalanced moment and lateral drift calculations. Based on the test results of 8 interior slab-column connections, an equivalent beam model is proposed in which columns are modeled conventionally as a function of column and slab aspect ratios and the magnitude of the gravity load. the proposed approach is verified with selected experimental results and is founded to be practical and convenient for analyzing flat-plate buildings subjected to gravity and lateral loading.

• Wind and Structures
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• 제16권6호
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• pp.561-577
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• 2013

Rational Functions are used to express the self-excited aerodynamic forces acting on a flexible structure for use in time-domain flutter analysis. The Rational Function Approximation (RFA) approach involves obtaining of these Rational Functions from the frequency-dependent flutter derivatives by using an approximation. In the past, an algorithm was developed to directly extract these Rational Functions from wind tunnel section model tests in free vibration. In this paper, an algorithm is presented for direct extraction of these Rational Functions from section model tests in forced vibration. The motivation for using forced-vibration method came from the potential use of these Rational Functions to predict aerodynamic loads and response of flexible structures at high wind speeds and in turbulent wind environment. Numerical tests were performed to verify the robustness and performance of the algorithm under different noise levels that are expected in wind tunnel data. Wind tunnel tests in one degree-of-freedom (vertical/torsional) forced vibration were performed on a streamlined bridge deck section model whose Rational Functions were compared with those obtained by free vibration for the same model.

• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.151-165
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• 2002

An a1gorithmic approach to degree elevation of NURBS curves is presented. The new algorithms are based on the weighted blossoming process and its matrix representation. The elevation method is introduced that consists of the following steps: (1) decompose the NURBS curve into piecewise rational Bezier curves, (b) elevate the degree of each rational Bezier piece, and (c) compose the piecewise rational Bezier curves into NURBS curve.