• Structural Engineering and Mechanics
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• v.23 no.5
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• pp.525-542
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• 2006

On the basis of equilibrium equations for static electric and magnetic fields, two unknown functions related to electric and magnetic fields were firstly introduced to rewrite the governing equations, boundary conditions and initial conditions for mechanical field. Then by introducing a dependent variable and a special function satisfying the inhomogeneous mechanical boundary conditions, the governing equation for a new variable with homogeneous mechanical boundary conditions is obtained. By using the separation of variables technique as well as the electric and magnetic boundary conditions, the dynamic problem of a functionally graded magneto-electro-elastic hollow sphere under spherically symmetric deformation is transformed to two Volterra integral equations of the second kind about two unknown functions of time. Cubic Hermite polynomials are adopted to approximate the two undetermined functions at each time subinterval and the recursive formula for solving the integral equations is derived. Transient responses of displacements, stresses, electric and magnetic potentials are completely determined at the end. Numerical results are presented and discussed.

• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.869-878
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• 2016

This paper presents an ecient fractional shifted Legendre polynomial method to solve the fractional Volterra's model for population growth model. The fractional derivatives are described based on the Caputo sense by using Riemann-Liouville fractional integral operator. The theoretical analysis, such as convergence analysis and error bound for the proposed technique has been demonstrated. In applications, the reliability of the technique is demonstrated by the error function based on the accuracy of the approximate solution. The numerical applications have provided the eciency of the method with dierent coecients of the population growth model. Finally, the obtained results reveal that the proposed technique is very convenient and quite accurate to such considered problems.

• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.441-457
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• 2005

An analytical method is presented to solve the problem of transient wave propagation in a transversely isotropic piezoelectric hollow sphere subjected to thermal shock and electric excitation. Exact expressions for the transient responses of displacements, stresses, electric displacement and electric potentials in the piezoelectric hollow sphere are obtained by means of Hankel transform, Laplace transform, and inverse transforms. Using Hermite non-linear interpolation method solves Volterra integral equation of the second kind involved in the exact expression, which is caused by interaction between thermo-elastic field and thermo-electric field. Thus, an analytical solution for the problem of transient wave propagation in a transversely isotropic piezoelectric hollow sphere is obtained. Finally, some numerical results are carried out, and may be used as a reference to solve other transient coupled problems of thermo-electro-elasticity.

• International Journal of Automotive Technology
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• v.2 no.1
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• pp.17-23
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• 2001

Measurements of the initial values lead to an inverse and mathematically unprecisely formulated problem. A precise definition of an inverse problem is possible. It is to state a mathematical model of a physical process with clearly defined initial and exit values for the system behind the process. One can grasp the idea of an inverse problem by considering the tire as a copy of the objects of nature in a room with observations. Interpretation of nature is generally a result of an inverse problem. On one hand, the tire may be represented through the sensory organs and the nervous system as well as the experiences of the developer's existing apparatus of the projection of reality. On the other hand, it may be represented by a physical law or a model that can be confirmed or is to be refuted with the help of suitable measurements. During reconstruction of a measuring signal and the identification of a black box that can be assumed to be linear and causal, the tire becomes a first type Volterra integral equation of the convolution type. But measurements of the initial values are always fuzzy, the errors grow and the system behavior can no longer be forecasted. Thus, we have to deal with a chaotic system. This chaos produces fractals in a natural way. These are self-similar geometric structures. This self-similarity is clearly visible in the design.

• Korean journal of applied entomology
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• v.61 no.4
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• pp.549-554
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• 2022

Life table-related studies in insect ecology have been an interesting topic for insect researchers. Two calculation methods are commonly applied to estimate the intrinsic rate of natural increase (r_m) in the life table statistics. The first method is to estimate an approximate r_m by dividing the natural logarithm of the net reproductive rate (R₀) by mean generation time (T) (namely mean generation time-based method). Another approach is to apply the Lotka-Euler equation derived from the population growth equation of Lotka-Volterra to estimate accurate r_m using the maximum likelihood method (Lotka-Euler equation-based method). In the latter case, there is a difference in the estimated r_m value when the initial age class of the target cohort was set to "0" or "1", which confused the application. In this short review, a brief history of the calculation process of the life table was reviewed. It was again confirmed in the Lotka-Euler equation-based method that the form of $\sum\limits_{x=1}^{w}e^{-rx}l_xm_x=1$ should be applied to estimate r_m when the first age class was set to zero, while the form of $\sum\limits_{x=0}^{w}e^{-r(x+1)}l_xm_x=1$ when set to one.

• Korean Journal of Environmental Agriculture
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• v.32 no.4
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• pp.294-303
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• 2013

BACKGROUND: It is well known that rice-fields can provide excellent foraging places for birds including seasonal migrants, wintering, and breeding and hence the high biodiversity of rice-fields may be expected. However, how environmental change including climate-changes on life-history and population dynamics in birds on rice-fields has not been fully understood. In order to investigate how climate-change affects population migratory patterns and migration timing, I modeled a population dynamics of birds in rice-fields over a whole year. METHODS AND RESULTS: I applied the Lotka-Volterra equation to model the population dynamics of birds that have been foraging/visiting rice-fields in Korea. The simple model involves the number of interspecific individuals and temperature, and the model parameters are periodic in time as the biological activities related to the migration, wintering and reproduction are seasonal. As results, firstly there was a positive relationship between the variation of seasonal population sizes and temperature change. Secondly, the reduced lengths of season were negatively related to the population size. Overall, the effects of the difference of lengths of season on seasonal population dynamics were higher than the effects of seasonal temperature change. CONCLUSION(S): Climate change can alter population dynamics of birds in rice-fields and hence the variation may affect the fitness, such as reproduction, survival and migration. The unstable balances of population dynamics in birds using paddy rice field as affected by climate change can reduce the population growth and species diversity in rice fields. The results suggest that the agricultural production is partly affected by the unstable balance of population in birds using rice-fields.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.19 no.11
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• pp.1254-1264
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• 2008

This paper suggests an extended memory polynomial model that improves accuracy in modeling memory effects of RF power amplifiers(PAs), and verifies effectiveness of the suggested method. The extended memory polynomial model includes cross-terms that are products of input terms that have different delay values to improve the limited accuracy of basic memory polynomial model that includes the diagonal terms of Volterra kernels. The complexity of the memoryless model, memory polynomial model, and the suggested model are compared. The extended memory polynomial model is represented with a matrix equation, and the Volterra kernels are extracted using least square method. In addition, the structure of digital predistorter and digital signal processing(DSP) algorithm based on the suggested model and indirect learning method are proposed to implement a digital predistortion linearization. To verify the suggested model, the predicted output of the model is compared with the measured output for a 10W GaN HEMT RF PA and 30 W LDMOS RF PA using 2.3 GHz WiBro input signal, and adjacent-channel power ratio(ACPR) performance with the proposed digital predistortion is measured. The proposed model increases model accuracy for the PAs, and improves the linearization performance by reducing ACPR.