This paper investigates the instability of an isotropic, homogeneous, simply supported rectangular plate subjected to a prescribed periodic in-plane load. The material is assumed to be viscoelastic and obey the Leaderman nonlinear constitutive relation. The equation of motion is derived as a nonlinear integro-partial-differential equation, and is simplified into a nonlinear integro-differential...

A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method provides a more systematical and convenient handling of the solution process of nonlinear equations, unifying the tanhfunction type methods, the homogeneous balance method, the exp-function method, the mapping method, and the F-expansion type m...

We extend the definition of Walsh’s martingale measure stochastic integral so as to be able to solve stochastic partial differential equations whose Green’s function is not a function but a Schwartz distribution. This is the case for the wave equation in dimensions greater than two. Even when the integrand is a distribution, the value of our stochastic integral process is a real-valued martinga...

In [26], Olofsson introduced a kind of second order homogeneous partial differential equation. We call the solution this equation real kernel ?-harmonic mappings. paper, we study some geometric properties give univalence criteria and sufficient coefficient conditions for mappings that are fully starlike or convex ?, ? [0, 1). Furthermore, establish Landau type theorem

NDIR-based CO2 sensor is commonly used in the field of environmental monitoring due to relatively high accuracy compared with that of a chemical CO2 gas sensor. This paper presents a wireless sensing system with a low-cost Non-Dispersive InfraRed (NDIR) sensor module used to determine gas concentration in a remote air quality monitoring system. Unlike the chemical CO2 gas sensor, the proposed s...

In this paper we investigate the following question: under what conditions can a second-order homogeneous ordinary differential equation (spray) be the geodesic equation of a Finsler space. We show that the EulerLagrange partial differential system on the energy function can be reduced to a first order system on this same function. In this way we are able to give effective necessary and suffici...

In atmospheric dynamics, the governing equations are usually non-linear partial differential equations. Some knowledge of finite-difference approximations to ordinary differential equations (especially first order) is needed, however. In fact, if we linearize a governing partial differential equation and assume a wave form for the solution, the equation simply reduces to an ordinary differentia...