Bäcklund transformations and abundant exact explicit solutions of the Sharma-Tasso-Olver equation

By using an extension of the homogeneous balance method and Maple, the Bäcklund transformations for the Sharma-Tasso-Olver equation are derived. The connections between the Sharma-Tasso-Olver equation and some linear partial differential equations are found. With the aid of the transformations given here and the computer program Maple 12, abundant exact explicit special solutions to the Sharma-Tasso-Olver equation are constructed. In addition to all known solutions re-deriving in a systematic way, several entirely new and more general exact explicit solitary wave solutions can also be obtained. These solutions include (a) the algebraic solitary wave solution of rational function, (b) single-soliton solutions, (c) double-soliton solutions, (d) N-soliton solutions, (e) singular traveling solutions, (f) the periodic wave solutions of trigonometric function type, and (g) many non-traveling solutions. By using the Airy’s function and the Bäcklund transformations obtained here, the exact explicit solution of the initial value problem for the STO equation is presented. The variety of the structure of the solutions for the Sharma-Tasso-Olver equation is illustrated.     

关于负超几何分布期望与方差算法的注记

研究了非还原取样模型中负超几何随机变量的联合分布,得到了若干有用的推论.据此给出了负超几何分布的期望和方差的一种分解算法.     

An asymptotic Reissner–Mindlin plate model

A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner–Mindlin plate model.     

Near-field-smoothing of periodic chirped pulse with applied angular dispersion

Periodic chirped pulse (PCP) with applied angular dispersion has been approved to be an efficient beam smoothing method in inertial confinement fusion. In this paper, the propagation characteristics of dispersed PCP in near field is analyzed theoretically and calculated numerically, and the results indict dispersed PCP is a motion beam, which can be applied to improve beam uniformity in near field. An experiment is carried out to validate the near-field-intensity smoothing effect of PCP.     

Young measures generated by a class of integrands: a narrow epicontinuity and applications to Homogenization

Given a subset E of convex functions from into which satisfy growth conditions of order p>1 and an open bounded subset of , we establish the continuity of a map μΦ_μ from the set of all Young measures on equipped with the narrow topology into a set of suitable functionals defined in and equipped with the topology of Γ-convergence. Some applications are given in the setting of periodic and stochastic homogenization.     

Electronic effects of heterocyclic ring systems as evaluated with the aid of 13C and 15N NMR chemical shifts and NBO analysis

The electronic effects of the 5‐ and 6‐membered heterocyclic rings on the C?N? N unit of five different hydrazone derivatives of pyridine‐2‐, ‐3‐ and ‐4‐carbaldehydes, pyrrole‐2‐carbaldehyde, furan‐2‐ and ‐3‐carbaldehydes and thiophene‐2‐ and ‐3‐carbaldehydes have been studied with the aid of ¹³C and ¹⁵N NMR measurements together with the natural bond orbital (NBO) analysis. As model compounds are used the corresponding substituted benzaldehyde derivatives. The polarization of the C?N unit of the hydrazone functionality of the heteroaryl derivatives occurs in an analogous manner with that of phenyl derivatives. The electron‐withdrawing heteroaryl groups destabilize and the electron‐donating groups stabilize the positive charge development at the C?N carbon while the effect on the negative charge development is opposite. The ¹⁵N NMR chemical shift of the C?N and C?N? N nitrogens and the NBO charges at C?N? N unit can be correlated with the replacement substituent constants σ of the heteroaryl groups. ¹³C NMR shifts of the C?N carbon of N,N‐dialkylhydrazones of the heteroarenecarbaldehydes can be correlated with a dual parameter equation possessing the polar substituent constant σ* of the heteroaryl group and the electronegativity of the heteroatom as variables. Copyright © 2008 John Wiley & Sons, Ltd.     

ON THE EXISTENCE THEOREMS OF NONTRIVIAL PERIODIC SOLUTIONS TOA CLASS OF NONLINEAR NON－AUTONOMOUS SYS

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