• Structural Engineering and Mechanics
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• v.77 no.4
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• pp.535-547
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• 2021

This paper concerns with free torsional vibration analysis of size dependent circular nanobars with von kármán type nonlinearity. Although review of the literature suggests several studies employing nonlocal elasticity theory to investigate linear torsional behavior, linear/nonlinear transverse vibration and buckling of the nanoscale structures, so far, no study on the nonlinear torsional behavior of the nanobars, considering the size effect, has been reported. This study employs nonlocal elasticity theory along with a variational approach to derive nonlinear equation of motion of the nanobar. Then, the nonlinear equation is solved using the elliptic functions to extract the natural frequencies of the structure under fixed-fixed and fixed-free end conditions. Finally, the natural frequencies of the nanobar under different nanobar lengths, diameters, nonlocal parameters, and amplitudes of vibration are reported to illustrate the effect of these parameters on the vibration characteristics of the nanobars. In addition, the phase plane diagrams of the nanobar for various cases are reported.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.391-398
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• 2024

This article explains how solitons propagate when there is a detuning factor involved. The explanation is based on the nonlinear complex Ginzburg-Landau equation, and we first consider this equation before systematically deriving its solutions using Jacobian elliptic functions. We illustrate that one specific ellipticity modulus is on the verge of occurring. The findings from this study can contribute to the understanding of previous research on the Ginzburg-Landau equation. Additionally, we utilize Jacobi's elliptic functions to define specific solutions, especially when the ellipticity modulus approaches either unity or zero. These solutions correspond to particular periodic wave solitons, which have been previously discussed in the literature.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.1
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• pp.139-146
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• 2008

We investigate the uniqueness and multiplicity of solutions for the nonlinear elliptic system with Dirichlet boundary condition $$\{-{\Delta}u+g_1(u,v)=f_1(x){\text{ in }}{\Omega},\\-{\Delta}v+g_2(u,v)=f_2(x){\text{ in }}{\Omega},$$ where ${\Omega}$ is a bounded set in $R^n$ with smooth boundary ${\partial}{\Omega}$. Here $g_1$, $g_2$ are nonlinear functions of u, v and $f_1$, $f_2$ are source terms.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.1-10
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• 2009

Main purpose of this paper is to define an elliptic analogue of the Hardy sums. Some results, which are related to elliptic analogue of the Hardy sums, are given.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.442-445
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• 1997

We present a hybrid self-tuning method of fuzzy inference systems with hyper elliptic Gaussian membership functions using genetic algorithm(GA) and back-propagation algorithm. The proposed self-tuning method has two phases : one is the coarse tuning process based on GA and the other is the fine tuning process based on back-propagation. But the parameters which is obtained by a GA are near optimal solutions. In order to solve the problem in GA applications, it uses a back-propagation algorithm, which is one of learning algorithms in neural networks, to finely tune the parameters obtained by a GA. We provide Box-Jenkins time series to evaluate the advantage and effectiveness of the proposed approach and compare with the conventional method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.2
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• pp.143-159
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• 2020

We propose a consistent numerical method for elliptic interface problems with nonhomogeneous jumps. We modify the discontinuous bubble immersed finite element method (DB-IFEM) introduced in (Chang et al. 2011), by adding a consistency term to the bilinear form. We prove optimal error estimates in L² and energy like norm for this new scheme. One of the important technique in this proof is the Bramble-Hilbert type of interpolation error estimate for discontinuous functions. We believe this is a first time to deal with interpolation error estimate for discontinuous functions. Numerical examples with various interfaces are provided. We observe optimal convergence rates for all the examples, while the performance of early DB-IFEM deteriorates for some examples. Thus, the modification of the bilinear form is meaningful to enhance the performance.

• Journal of the Korean Institute of Telematics and Electronics
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• v.23 no.1
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• pp.74-82
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• 1986

The elliptic functions have a set of zeros on the jw axis. In acitve realization we decompose a function into product of biquads. In this paper, a simple method of pole-zero pairing is proposed for the enhancement of overall dynamic range. Secondly, the optimum sequencing of individual biquads is developed and it is demonstrated that the commonly accepted sequencing technique does not hold in the case of elliptic functions. This work is an approximation for Leuder's(1970)method.

• Structural Engineering and Mechanics
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• v.53 no.2
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• pp.337-354
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• 2015

In this article, free vibration of functionally graded (FG) elliptic plates subjected to various classical boundary conditions has been investigated. Literature review reveals no study has been performed based on functionally graded elliptic plates till date. The mechanical kinematic relations are considered based on classical plate theory. Rayleigh-Ritz technique is used to obtain the generalized eigenvalue problem. The material properties of the FG plate are assumed to vary along thickness direction of the constituents according to power-law form. Trial functions denoting the displacement components are expressed in simple algebraic polynomial forms which can handle any edge support. The objective is to study the effect of geometric configurations and gradation of constituent volume fractions on the natural frequencies. New results for frequency parameters are incorporated after performing a test of convergence. A comparison study is carried out with existing literature for validation in special cases. Three-dimensional mode shapes for circular and elliptic FG plates are also presented with various boundary conditions at the edges.

• The KIPS Transactions:PartB
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• v.9B no.5
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• pp.599-608
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• 2002

This paper proposes DIT (Digital Investment Trust) agent based on ECSSL (Elliptic Curve SSL). This DIT agent is a banking project using IT (Investment Trust) conception based on EC (Electronic Commerce) and can manage micro payment, account opening and account transferring. In addition, ECSSL (Elliptic Curve SSL) protocol is implemented which consists of much better encryption functions than existing SSL (Secure Socket Layer) Protocol. Therefore, This DIT agent based on ECSSL protocol protects a customer's information and asset from third party.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.11 no.5
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• pp.315-322
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• 1986

In this paper, we have studied on the IIR digital filters design using Elliptic functions. In process of transformation to digital fouctions from analos Elliptic functions, Bilinear z transformation method has been silized. Designing of digital filter using the Bilinear z transformation the problems of aliasing can be avoidedm whereas the frequency distrotion is generated. The transformation form analog function to digital function is not equal in the region of the cut off frequency response caused by this effect. Avoiding the problem of this effect, we have used proewarping method. Finally, the magnitude characteristics of digital filters are compared with its of analog filters by computer simulation. The results have shown that the magnitude characteristics of digital filters by the prewarping method have made more remarkable improvement than its of analog filters.