• Structural Engineering and Mechanics
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• 제3권2호
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• pp.121-133
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• 1995

It is well known that two-dimensional simplified third-order theories satisfy the layer interface continuity of transverse shear strains, thus these theories violate the continuity of transverse shear stresses when two consecutive layers differ either in fibre orientation or material. The third-order theories considered herein involve four/or five dependent unknowns in the displacement field and satisfy the condition of vanishing of transverse shear stresses at the bounding planes of the plate. The objective of this investigation is to examine (i) the flexural response prediction accuracy of these third-order theories compared to exact elasticity solution (ii) the effect of layer interface continuity conditions on the flexural response. To investigate the effect of layer interface continuity conditions, three-dimensional elasticity solutions are developed by enforcing the continuity of different combinations of transverse stresses and/or strains at the layer interfaces. Three dimensional twenty node solid finite element (having three translational displacements as degrees of freedom) without the imposition of any of the conditions on the transverse stresses and strains is also employed for the flexural analysis of the laminated plates for the purposes of comparison with the above theories. These shear deformation theories and elasticity approaches in terms of accuracy, adequacy and applicability are examined through extensive numerical examples.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.791-805
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• 2014

In this article, we investigate third order three-point fuzzy boundary value problem to using a generalized differentiability concept. We present the new concept of solution of third order three-point fuzzy boundary value problem. Some illustrative examples are provided.

• 한국광학회지
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• 제2권1호
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• pp.31-35
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• 1991

The third-order nonlinear optical susceptibilities of $\beta$-carotene, retinal and retinol have been measured using self-induced ellipse rotation and dc-Kerr effects. The strengths of $\chi$1221(-$\omega$, $\omega$, -$\omega$, $\omega$) and $\chi$1221(-$\omega$, $\omega$, 0, 0) measured by the two different methods are not different each other significantly. And it is observed that the strength of the third order nonlinear optical susceptibility is relatively insensitive to the conformational difference between retinal and retinol. It is also demonstrated that the third order nonlinear optical susceptibility of long-chained organic molecules is dependent upon the number of the double-bonds.

• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.61-76
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• 2015

In this paper, a fifth order extension of Potra's third order iterative method is proposed for solving nonlinear equations. A convergence theorem along with the error bounds is established. The method takes three functions and one derivative evaluations giving its efficiency index equals to 1.495. Some numerical examples are also solved and the results obtained are compared with some other existing fifth order methods. Next, the interval extension of both third and fifth order Potra's method are developed by using the concepts of interval analysis. Convergence analysis of these methods are discussed to establish their third and fifth orders respectively. A number of numerical examples are worked out using INTLAB in order to demonstrate the efficacy of the methods. The results of the proposed methods are compared with the results of the interval Newton method.

• 한국정보과학회논문지:소프트웨어및응용
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• 제31권5호
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• pp.577-585
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• 2004

인식기와 클래스 레이블로 구성된 고차 확률 분포를 가정이나 근사 없이 저장하고, 평가하는 것은 기하급수적으로 복잡하고 관리하기 어렵다. 따라서, 의존관계를 이용한 근사 방법에 의존하게 된다. 본 논문에서는 기존의 2차 의존관계에 기반 한 곱 근사 방법을 확장하여, 이 확률 분포를 3차 의존관계에 의해 최적으로 곱 근사 하는 방법을 제안하고자 한다. 제안된 3차 의존관계에 기반 한 곱 근사 방법은 Concordia 대학과 UCI(University of California, Irvine) 대학으로부터 얻은 필기 숫자를 인식하는 실험에서 다수 인식기의 결합 방법에 적용되었고, 실험을 통하여 제안된 방법의 유용성을 살펴보았다.

• Journal of applied mathematics & informatics
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• 제36권1_2호
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• pp.135-154
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• 2018

In this paper, an almost second order overlapping Schwarz method for singularly perturbed third order convection-diffusion type problem is constructed. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region we use the combination of classical finite difference scheme and central finite difference scheme on a uniform mesh while on the non-layer region we use the midpoint difference scheme on a uniform mesh. It is shown that the numerical approximations which converge in the maximum norm to the exact solution. We proved that, when appropriate subdomains are used, the method produces convergence of second order. Furthermore, it is shown that, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantages of this method used with the proposed scheme are it reduce iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.

• 한국항만학회지
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• 제8권1호
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• pp.41-47
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• 1994

The present paper discusses the nonlinear wave deformation due to a submerged coastal structure. Theory is based on the frequency-domain method using the third order perturbation and boundary integral method. Theoretical development to the second order perturbation and boundary integral method. Theoretical development to the second order Stokes wave for a bottom-seated submerged breakwater to the sea floor is newly expanded to the third order for a submerged coastal structure shown in Figure 1. Validity is demonstrated by comparing numerical results with the experimental ones of a rectangular air chamber structure, which has the same dimensions as that of this study. Nonlinear waves become larger and larger with wave propagation above the crown of the structure, and are transmitted to the onshore side of the structure. These characteristics are shown greatly as the increment of Ursell number on the structure. The total water profile depends largely on the phase lag among the first, second and third order component waves.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권4호
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• pp.307-319
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• 2022

The present paper deals with the upper bound of third order Hankel determinant for a certain subclass of analytic functions associated with Cardioid domain in the open unit disc E = {z ∈ ℂ : |z| < 1}. The results proved here generalize the results of several earlier works.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1988년도 한국자동제어학술회의논문집(국제학술편); 한국전력공사연수원, 서울; 21-22 Oct. 1988
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• pp.1018-1021
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• 1988

This study is concerned with modeling an elastomer constitutive relation by utilizing the truncated Volterra series. Actual experimental data from the Instron Tester are obtained for combined input, i.e. constant strain rate followed by a constant strain input. These data are then estimated for step inputs and utilized for the truncated Volterra series models. One second order and one third order truncated Volterra series models have been employed to estimated the force-displacement relation which is one of the prominent properities to characterize the viscoelastic material. The third order Volterra series model has better results, compared with those of the second order Volterra series model.

• 전자공학회논문지A
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• 제31A권5호
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• pp.18-26
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• 1994

We express fundamental second-order and third- order harmonic distortions and intermodulation distortions in terms of the laser parameters. Compared to the Darcie `s result only limited to the high frequency (f >1GHz), these expression are quite valid in the entire modulation frequency region. It is found that the fundamental nonlinear distortions are strongly effected by the spontaneous emission to lasing mode as well as the gain compresion damping in the low frequency region.