“Painlevé 34” equation: Equivalence test

We give the complete solution of the Equivalence Problem for “Painlevé 34” equation.     

NONLINEAR DYNAMICS AND SYNCHRONIZATION OF TWO COUPLED PIPES CONVEYING PULSATING FLUID

In this paper, the nonlinear dynamical behavior of two coupled pipes conveying pulsating fluid is studied. The connection between the two pipes is considered as a distributed linear spring. Based on this consideration, the equations of motion of the coupled two-pipe system are obtained. The two coupled nonlinear partial differential equations, discretized using the fourth- order Galerkin method, are solved by a fourth-order Runge-Kutta integration algorithm. Results show that the connection stiffness has a significant effect on the dynamical behavior of the coupled system. It is found that for some parameter values the motion types of the two pipes might be synchronous.     

三阶柯西差分方程在几类群上的解

在几类群上讨论了三阶柯西差分方程解的存在性问题,将二阶柯西差分方程的已有结论进一步推广到三阶的情况,并给出在不同群上的一般解.     

LIMIT CYCLES OF THE GENERALIZED POLYNOMIAL LINARD DIFFERENTIAL EQUATION

We investigate the generalized polynomial Linard differential equations. Using the averaging theory of first and second order, we obtain the maximum number of limit cycles of the system.     

A general poisson approximation theorem

We study the rate of convergence in a limit theorem due to Kabanov-Liptser-Shiryayev. We show how the probabilities P(N _t= k) can be computed from the compensator, when it is deterministic.     

Dark solitons of the Biswas–Milovic equation by the first integral method

This paper studies the Biswas–Milovic equation that is a generalized version of the familiar nonlinear Schrodinger's equation describing the propagation of solitons through optical fibers for trans-continental and trans-oceanic distances with Kerr law nonlinearity by the aid of the first integral method. The dark 1-soliton solution is retrieved by the aid of this method and a couple of other singular periodic solutions are also obtained.     

Temperature dependence of the properties of ternary systems ethanol + water + an aliphatic alkane (C6-C9)

The measures and calculation of different properties such as refractive index, density, speed of sound, excess molar volume, and isentropic compressibility of the ternary heterogeneous compounds by ethanol + water + (n-hexane, n-heptane, n-octane, n-nonane) have been performed in the range 288.15–323.15 K and atmospheric pressure. Attending to the accurate results of these models, the equation of state enclosing mixing rules is indicated as a simple estimation of the procedures of these properties for this kind of multicomponent systems.     

Nonexistence of global solutions to new ordinary differential inequality and applications to nonlineardispersive equations

A new ordinary differential inequality without global solutions is proposed. Comparison with similar differential inequalities in the well‐known concavity method is performed. As an application, finite time blow up of the solutions to nonlinear Klein–Gordon equation and generalized Boussinesq equation is proven. The initial energy is arbitrary high positive. The structural conditions on the initial data generalize the assumptions used in the literature for the time being. Copyright © 2015 John Wiley & Sons, Ltd.     

The gas phase oxidation of HCOOH by Cl and NH2 radicals. Proton coupled electron transfer versus hydrogen atom transfer*

ABSTRACT

The reaction of formic acid (HCOOH) with chlorine atom and amidogen radical (NH₂) have been investigated using high level theoretical methods such BH&HLYP, MP2, QCISD, and CCSD(T) with the 6–311?+?G(2df,2p), aug-cc-pVTZ, aug-cc-pVQZ and extrapolation to CBS basis sets. The abstraction of the acidic and formyl hydrogen atoms of the acid by the two radicals has been considered, and the different reactions proceed either by a proton coupled electron transfer (pcet) and hydrogen atom transfer (hat) mechanisms. Our calculated rate constant at 298?K for the reaction with Cl is 1.14?×?10^?13?cm³?molecule^?1?s^?1 in good agreement with the experimental value 1.8?±?0.12/2.0?×?10^?13?cm³?molecule^?1?s^?1 and the reaction proceeds exclusively by abstraction of the formyl hydrogen atom, via hat mechanism, producing HOCO+ClH. The calculated rate constant, at 298?K, for the reaction with NH₂ is 1.71?×?10^?15?cm³?molecule^?1?s^?1, and the reaction goes through the abstraction of the acidic hydrogen atom, via a pcet mechanism, leading to the formation of HCOO+NH₃.