• Structural Engineering and Mechanics
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• 제77권4호
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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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• 제42권2호
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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.

• 충청수학회지
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• 제21권1호
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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.

• 대한수학회보
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• 제46권1호
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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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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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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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• 제24권2호
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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.

• 대한전자공학회논문지
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• 제23권1호
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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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• 제53권2호
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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.

• 정보처리학회논문지B
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• 제9B권5호
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• pp.599-608
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• 2002

본 논문에서 제안하는 DIT(Digital Investment Trust) 에이전트는 전자상거래에 투자 신탁의 개념을 도입한 인터넷 기반의 은행업무 프로젝트로서, 소액지불뿐만 아니라, 계좌 생성 및 계좌 이체를 할 수 있으며, 또한 여기서 사용되는 인터넷 보안 프로토콜로는 기존의 SSL(Secure Socket Layer)보다 보안 기능을 강화한 ECSSL(Elliptic Curve SSL)이라는 프로토콜을 구축하여, 이를 기반으로 개발한 DIT 에이전트를 이용하여 고객의 정보와 자산을 제 3자로부터 보호하고자 한다.

• 한국통신학회논문지
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• 제11권5호
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• pp.315-322
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• 1986

本 論文은 　圓函數를 利用한 IIR digital 필터 設計에 關하여 硏究한 것이다. Digital 　圓函數는 analog 　圓函數로부터 Bilinear z 變換에 依하여 求하였다. Bilinear z 變換된 函數로 digital필터를 設計하면 aliasing 現象은 避할 수 있으나 周波數歪曲이 發生한다. Analog函數를 digital函數로 變換하면 이러한 影響으로 遮斷周波數 領域이 不一致하므로 이것을 避하기 爲하여 prewarping法을 利用하였다. 마지막으로, 컴퓨터 simulation에 依하여 analog 크기 特性과 digital 크기 特性을 比較한 結果, prewarping을 한 digital 크기特性이 analog 크기 特性에 比하여 改善되었음을 確認할 수 있었다.