scholarly journals A THEORETICAL METHOD TO OBTAIN THE SECOND ORDER PARTIAL DERIVATIVE OF SHEAR MODU LUS WITH RESPECT TO PRESSURE

2000 ◽  
Vol 49 (12) ◽  
pp. 2443
Author(s):  
HUA JING-SONG ◽  
JIN FU-QIAN ◽  
TAN HUA
Keyword(s):  
Partial Derivative ◽  
Theoretical Method ◽  
Second Order ◽  
Order Partial Derivative

scholarly journals A Method for Rapid Matching Based on Second Order Partial Derivative

2010 ◽  
Vol 02 (01) ◽  
pp. 37-42 ◽  
Author(s):  
Haiyan YU ◽  
Zhiquan ZHOU ◽  
Zhanfeng ZHAO ◽  
Xiaolin QIAO
Keyword(s):  
Partial Derivative ◽  
Second Order ◽  
Order Partial Derivative

Statistical Analysis of Second-Order Response of Marine Structures

1985 ◽  
Vol 29 (04) ◽  
pp. 270-284 ◽  
Author(s):  
Arvid Naess
Keyword(s):  
Volterra Series ◽  
Theoretical Method ◽  
Problem Formulation ◽  
Second Order ◽  
Quadratic Term ◽  
Closed Form Solutions ◽  
Marine Structure ◽  
Asymptotic Expressions ◽  
The Mean ◽  
Extreme Responses

A theoretical method is presented for estimating the response statistics of a marine structure that can be modeled as a second-order dynamic system subjected to a stationary, Gaussian sea. The method is particularly suitable for predicting extreme responses. The problem formulation expresses the response in terms of a second-order Volterra series, that is, including a linear and a quadratic term. For this response process the mean upcrossing frequency is found and asymptotic expressions are established that can be used to obtain closed-form solutions to the extreme-value problem.

Second-order piezomagnetism in polychromatic crystals

1990 ◽  
Vol 46 (2) ◽  
pp. 130-133
Author(s):  
K. Rama Mohana Rao
Keyword(s):  
Point Group ◽  
Physical Property ◽  
Theoretical Method ◽  
Second Order ◽  
Acta Cryst ◽  
Theoretical Methods ◽  
Group Theoretical Method ◽  
Group 4 ◽  
Independent Number

The group-theoretical method established for obtaining the non-vanishing independent number of constants required to describe a magnetic/physical property in respect of the 18 polychromatic crystal classes [Rama Mohana Rao (1987). J. Phys. A, 20, 47-57] has been explored to enumerate the second- order piezomagnetic coefficients (n i ′) for the same classes. The advantage of Jahn's method [Jahn (1949). Acta Cryst. 2, 30-33] is appreciated in obtaining these n i ′ through the reduction of a representation. The different group-theoretical methods are illustrated with the help of the point group 4. The results obtained for all 18 classes are tabulated and briefly discussed.

Using Maple to Study the Partial Differential Problems

2013 ◽  
Vol 479-480 ◽  
pp. 800-804 ◽  
Author(s):  
Chii Huei Yu
Keyword(s):  
Infinite Series ◽  
Partial Derivative ◽  
Higher Order ◽  
The Other ◽  
Mathematical Software ◽  
Partial Differential ◽  
Differential Problem ◽  
Partial Derivatives ◽  
Order Partial Derivative ◽  
Derivatives Of

This paper uses the mathematical software Maple for the auxiliary tool to study the partial differential problem of two types of multivariable functions. We can obtain the infinite series forms of any order partial derivatives of these two types of multivariable functions by using differentiation term by term theorem, and hence greatly reduce the difficulty of calculating their higher order partial derivative values. On the other hand, we propose two examples of multivariable functions to evaluate their any order partial derivatives, and some of their higher order partial derivative values practically. At the same time, we employ Maple to calculate the approximations of these higher order partial derivative values and their infinite series forms for verifying our answers.

scholarly journals Fractional Rogue Waves with Translational Coordination, Steep Crest, and Modified Asymmetry

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Bo Xu ◽  
Yufeng Zhang ◽  
Sheng Zhang
Keyword(s):  
Partial Derivative ◽  
Wave Solution ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Second Order ◽  
Coordinate Plane ◽  
Nls Equation ◽  
Wave Solutions ◽  
Rogue Wave Solution ◽  
Rogue Wave Solutions

To construct fractional rogue waves, this paper first introduces a conformable fractional partial derivative. Based on the conformable fractional partial derivative and its properties, a fractional Schrödinger (NLS) equation with Lax integrability is then derived and first- and second-order fractional rogue wave solutions of which are finally obtained. The obtained fractional rogue wave solutions possess translational coordination, providing, to some extent, the degree of freedom to adjust the position of the rogue waves on the coordinate plane. It is shown that the obtained first- and second-order fractional rogue wave solutions are steeper than those of the corresponding NLS equation with integer-order derivatives. Besides, the time the second-order fractional rogue wave solution undergoes from the beginning to the end is also short. As for asymmetric fractional rogue waves with different backgrounds and amplitudes, this paper puts forward a way to construct them by modifying the obtained first- and second-order fractional rogue wave solutions.

Sign in / Sign up

Export Citation Format

Share Document