• Advances in materials Research
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• 제1권4호
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• pp.285-297
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• 2012

The present study addresses the problem of quantitative prediction of effective complex relative permittivity of Barium Titanate/Polyvenylidene Fluoride (PVDF) and $(Bi_{0.5}Na_{0.5})_{0.94}Ba_{0.06}TiO_3$/Poly(VDF-TrFE) biphasic ceramic-polymer composites. Theoretical results for effective relative permittivity derived from several dielectric mixture equations were fitted to the experimental data taken from the works of Prasad et al. (2010), Wang et al. (2004), Takenaka et al. (1991) and Yamada et al. (1982). The study revealed that out of the different test equations, only a few equations like modified Rother-Lichtenecker equation, Dias-Dasgupta equation or Rao equation for the real part and Bruggeman equation for the imaginary part of complex permittivity well fitted the corresponding experimental results. In the present study, some of the equations were used in their original forms, while some others were modified by choosing suitable shape-dependent parameters in order to get reasonably good agreement with experimental results. Besides, the experimental results have been proposed in the form of a mathematical model using first order exponential growth, which provided excellent fits.

• Structural Engineering and Mechanics
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• 제19권3호
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• pp.281-295
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• 2005

An analytical method is presented to solve the elastodynamic problem of finitely long hollow cylinder subjected to torsional impact often occurs in engineering mechanics. The analytical solution is composed of a solution of quasi-static equation satisfied with the non-homogeneous boundary condition and a solution of dynamic equation satisfied with homogeneous boundary condition. The quasi-static solution is obtained directly by solving the quasi-static equation satisfied with the non-homogeneous boundary condition. The solution of the non-homogeneous dynamic equation is obtained by means of finite Hankel transform on the radial variable, r, Laplace transform on time variable, t, and finite Fourier transform on axial variable, z. Thus, the solution for finitely long, hollow cylinder subjected to torsion impact is obtained. In the calculating examples, the response histories and distributions of shear stress in the finitely long hollow cylinder subjected to an exponential decay torsion load are obtained, and the results have been analyzed and discussed. Finally, a dynamic finite element for the same problem is carried out by using ABAQUS finite element analysis. Comparing the analytical solution with the finite element solution, it can be found that two kinds of results obtained by means of two different methods agree well. Therefore, it is further concluded that the analytical method and computing process presented in the paper are effective and accurate.

• 호남수학학술지
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• 제41권2호
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• pp.403-420
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• 2019

The Helmholtz equation represents acoustic or electromagnetic scattering phenomena. The Method of Lines are known to have many advantages in simulation of forward and inverse scattering problems due to the usage of angle rays and Bessel functions. However, the method does not account for the jump phenomena on obstacle boundary and the approximation includes many high order Bessel functions. The high order Bessel functions have extreme blow-up or die-out features in resonance region obstacle boundary. Therefore, in particular, when we consider shape reconstruction problems, the method is suffered from severe instabilities due to the logical confliction and the severe singularities of high order Bessel functions. In this paper, two approximation formulas for the Helmholtz equation are introduced. The formulas are new and powerful. The derivation is based on Method of Lines, Huygen's principle, boundary jump relations, Addition Formula, and the orthogonality of the trigonometric functions. The formulas reduce the approximation dimension significantly so that only lower order Bessel functions are required. They overcome the severe instability near the obstacle boundary and reduce the computational time significantly. The convergence is exponential. The formulas adopt the scattering jump phenomena on the boundary, and separate the boundary information from the measured scattered fields. Thus, the sensitivities of the scattered fields caused by the boundary changes can be analyzed easily. Several numerical experiments are performed. The results show the superiority of the proposed formulas in accuracy, efficiency, and stability.

• 생태와환경
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• 제57권2호
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• pp.111-122
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• 2024

Zooplankton biomass is essential for understanding the quantitative structure of lake food webs and for the functional assessment of biotic interactions. In this study, we aimed to propose a biomass (dry weight) estimation method using the body length of cyclopoid copepods. These copepods play an important role as omnivores in lake zooplankton communities and contribute significantly to biomass. We validated several previously proposed estimation equations against direct measurements and compared the suitability of prosomal length versus total length of copepods to suggest a more appropriate estimation equation. After comparing the regression analysis results of various candidate equations with the actual values measured on a microbalance-using the coefficient of variation, mean absolute error, and coefficient of determination-it was determined that the Total Length-DW exponential regression equation [W=0.7775×e^2.0183L; W (㎍), L (mm)] could be used to calculate biomass with higher accuracy. However, considering practical issues such as the morphological similarity between species and genera of copepods and the limitations of classifying copepodid stages, we derived a general regression equation for the pooled copepod community rather than a species-specific regression equation.

• Korean Journal of Mathematics
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• 제19권2호
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• pp.171-180
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• 2011

In this paper, we study the superstability problem bounded by two-variables of Th. M. Rassias type for the generalized sine functional equations $$g(x+y)f(x-y)=f(x)^2-f(y)^2 \\ f(x+y)g(x-y)=f(x)^2-f(y)^2 \\ g(x+y)g(x-y)=f(x)^2-f(y)^2$$, which does not use his iteration method.

• 대한산업공학회지
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• 제5권2호
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• pp.2-7
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• 1979

The fundamental stochastic duel of Williams and Ancker is combined with the probabilistic linear, square and mixed laws of Brown and Smith when the battle time is limited and interfiring times are continuous. The Probability of a given side's winnig or a draw is derived in a recursive equation with Laplace transforms. Examples with negative exponential firing times are given. In linear law an exact closed form solution is obtained, whereas for square and mixed laws only square ($2{\times}2$) duels are considered.

• 아시안잔디학회지
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• 제9권2호
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• pp.119-129
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• 1995

Decomposition rates of glucose, starch, spinach leaves and litters in forests are calculated by equation dC dt=-kC(Co-1nC), dC- dt=$-kC^2$, and Olson's negative exponential decay model.dC dt = - kC =-kC(Co - InC) showed a very close fit to decomposition of the organic matters in cultural media by purified microorganisms and dC dt=$-kC^2$ to decomposition of the litters in forests. Key words: Organic matters, Cultural media, Glucose, Starch, Leaves, Litters.

• 한국미생물·생명공학회지
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• 제17권2호
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• pp.170-172
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• 1989

It is preyed that marine algae, Chlorella pyrenoidosa can synthesize about 3.52% of eicosapentaenoic (EPA) of dry cell weight at the light intensity of 10 W/$\m^2$ which is optimal light intensity of producing EPA at $25^{\circ}C$. An equation to predict the amounts of EPA in the culture broth is derived as an exponential form with 0.91 of the correlation factor. The behavior of cell growth follows a photo-inhibition model by showing 12 W/$\m^2$ of saturation light intensity.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1994년도 Proceedings of the Korea Automatic Control Conference, 9th (KACC) ; Taejeon, Korea; 17-20 Oct. 1994
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• pp.168-172
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• 1994

This paper shows that the GPC with exponential weighting(GPCEW) can be applied to Electric furnace system which has large time delay. Stability of GPCEW can be guarantee from monotonically non-increasing property of Riccati difference equation. We show that the performance of GPCEW versus GPC and auto-tuning PID control is better than that of GPC or atito-tuning PID.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권3호
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• pp.231-244
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• 2011

We prove the Hyers-Ulam stability for trigonometric type functional inequalities in restricted domains with time variables. As consequences of the result we obtain asymptotic behaviors of the inequalities and stability of related functional inequalities in almost everywhere sense.