ﻻ يوجد ملخص باللغة العربية
In this work we obtain an approximate solution of the strongly nonlinear second order differential equation $frac{d^{2}u}{dt^{2}}+omega ^{2}u+alpha u^{2}frac{d^{2}u}{dt^{2}}+alpha uleft( frac{du}{dt}right)^{2}+beta omega ^{2}u^{3}=0$, describing the large amplitude free vibrations of a uniform cantilever beam, by using a method based on the Laplace transform, and the convolution theorem. By reformulating the initial differential equation as an integral equation, with the use of an iterative procedure, an approximate solution of the nonlinear vibration equation can be obtained in any order of approximation. The iterative approximate solutions are compared with the exact numerical solution of the vibration equation.
In this paper, we develop a method for obtaining the approximate solution for the evolution of single-step transformations under non-isothermal conditions. We have applied it to many reaction models and obtained very simple analytical expressions for
In this paper, we investigate tree-level scattering amplitude relations in $U(N)$ non-linear sigma model. We use Cayley parametrization. As was shown in the recent works [23,24] both on-shell amplitudes and off-shell currents with odd points have to
Since the first reports of oscillations in prominences in 1930s there have been major theoretical and observational advances to understand the nature of these oscillatory phenomena leading to a whole new field of so called prominence seismology. Ther
We apply moment methods to obtaining an approximate analytical solution to Knudsen layers. Based on the hyperbolic regularized moment system for the Boltzmann equation with the Shakhov collision model, we derive a linearized hyperbolic moment system
This analysis paper presents previously unknown properties of some special cases of the Wright function whose consideration is necessitated by our work on probability theory and the theory of stochastic processes. Specifically, we establish new asymp