• Structural Engineering and Mechanics
• /
• v.3 no.2
• /
• pp.121-133
• /
• 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
• /
• v.32 no.5_6
• /
• pp.791-805
• /
• 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.

• Korean Journal of Optics and Photonics
• /
• v.2 no.1
• /
• pp.31-35
• /
• 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
• /
• v.33 no.1_2
• /
• pp.61-76
• /
• 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.

• Journal of KIISE:Software and Applications
• /
• v.31 no.5
• /
• pp.577-585
• /
• 2004

Storing and estimating the high order probability distribution of classifiers and class labels is exponentially complex and unmanageable without an assumption or an approximation, so we rely on an approximation scheme using the dependency. In this paper, as an extended study of the second-order dependency-based approximation, the probability distribution is optimally approximated by the third-order dependency. The proposed third-order dependency-based approximation is applied to the combination of multiple classifiers recognizing handwritten numerals from Concordia University and the University of California, Irvine and its usefulness is demonstrated through the experiments.

• Journal of applied mathematics & informatics
• /
• v.36 no.1_2
• /
• pp.135-154
• /
• 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.

• Journal of Korean Port Research
• /
• v.8 no.1
• /
• pp.41-47
• /
• 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.

• The Pure and Applied Mathematics
• /
• v.29 no.4
• /
• pp.307-319
• /
• 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
• /
• 1988.10b
• /
• pp.1018-1021
• /
• 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.

• Journal of the Korean Institute of Telematics and Electronics A
• /
• v.31A no.5
• /
• pp.18-26
• /
• 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.