同分布的NA序列加权和的强大数律

讨论了同分布NA随机变量序列加权和的强大数律,所得结果推广了Z．D．Bai和P．E．Cheng及S．H．Sung的结果．     

Conservation Laws and Exact Solutions for some Nonlinear Partial Differential Equations

An effective algorithmic method (Anco, S. C. and Bluman, G. (1996). Journal of Mathematical Physics 37, 2361; Anco, S. C. and Bluman, G. (1997). Physical Review Letters 78, 2869; Anco, S. C. and Bluman, G. (1998). European Journal of Applied Mathematics 9, 254; Anco, S. C. and Bluman, G. (2001). European Journal of Applied Mathematics 13, 547; Anco, S. C. and Bluman, G. (2002). European Journal of Applied Mathematics 13, 567 is used for finding the local conservation laws for some nonlinear partial differential equations. The method does not require the use or existence of a variational principle and reduces the calculation of conservation laws to solving a system of linear determining equations similar to that of finding symmetries. An explicit construction formula is derived which yields a conservation law for each solution of the determining system. Different methods to construct new exact solution classes for the same nonlinear partial differential equations are also presented, which are named hyperbolic function method and the Bäcklund transformations. On the other hand, other methods and transformations are developed to obtain exact solutions for some nonlinear partial differential equations.     

Multi-dimensional liquid chromatography in proteomics—A review

Proteomics is the large-scale study of proteins, particularly their expression, structures and functions. This still-emerging combination of technologies aims to describe and characterize all expressed proteins in a biological system. Because of upper limits on mass detection of mass spectrometers, proteins are usually digested into peptides and the peptides are then separated, identified and quantified from this complex enzymatic digest. The problem in digesting proteins first and then analyzing the peptide cleavage fragments by mass spectrometry is that huge numbers of peptides are generated that overwhelm direct mass spectral analyses. The objective in the liquid chromatography approach to proteomics is to fractionate peptide mixtures to enable and maximize identification and quantification of the component peptides by mass spectrometry. This review will focus on existing multidimensional liquid chromatographic (MDLC) platforms developed for proteomics and their application in combination with other techniques such as stable isotope labeling. We also provide some perspectives on likely future developments.     

Application of the homotopy perturbation method to the modified regularized long‐wave equation

In this article, the homotopy perturbation method (HPM) is used to implement the modified regularized long‐wave (MRLW) equation with some initial conditions. The method is very efficient and convenient and can be applied to a large class of problems. In the last, three invariants of the motion are evaluated to determine the conservation properties of the system. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Quasi-potentials of the entropy functionals for scalar conservation laws

We investigate the quasi-potential problem for the entropy cost functionals of non-entropic solutions to scalar conservation laws with smooth fluxes. We prove that the quasi-potentials coincide with the integral of a suitable Einstein entropy.     

Unsteady state mathematical model of chemically reactive pollutants from an instantaneous line source into a stable atmospheric boundary layer

A time dependent atmospheric model represented for chemically reactive primary pollutants emitted from an elevated line source into a stable atmospheric boundary layer over a surface terrain. The model obtained from an analytical solution of the atmospheric diffusion equation with the quadratic diffusion coefficient (exchange coefficient) and the variable wind velocity taken to be of three different types’ viz. constant, constant shear and parabolic functions of vertical height. The pollutants considered to be of chemically reactive primary pollutants emitted from a time-dependent line source of Instantaneous type. In order to facilitate the application of the model the results for the general situation that includes chemical reaction rate & time dependent source incorporated in the model.     

Geometric singular perturbation analysis of oxidation heat pulses for two-phase flow in porous media

When air or oxygen is injected into a petroleum reservoir, and oxidation or combustion is induced, a combustion front forms if heat loss to the surrounding rock formation is negligible. Here, we employ a simple model for combustion, which takes into account oil viscosity reduction, but neglects gas density dependence on temperature and uses a simplified oxidation reaction. We show that for small heat loss, this combustion front is actually the lead part of a pulse, while the trailing part of the pulse is a slow cooling process. If the heat loss is too large, we show that such a pulse does not exist. The proofs use geometric singular perturbation theory and center manifold reduction.Dedicated to Constantine Dafermos on his 60^th birthdayThis work was supported in part by: CNPq under Grant 300204/83-3; CNPq/NSF under Grant 91.0011/99-0; MCT under Grant PCI 650009/97-5; FINEP under Grant 77.97.0315.00; FAPERJ under Grants E-26/150.936/99 and E-26/151.893/2000; NSF under Grant DMS-9973105.     

Essential Conservation Laws for Equations with Infinite Symmetries

We consider partial differential equations of variational problems with infinite symmetry groups. We study local conservation laws associated with arbitrary functions of one variable in the group generators. We show that only symmetries with arbitrary functions of dependent variables lead to an infinite number of conservation laws. We also calculate local conservation laws for the potential Zabolotskaya-Khokhlov equation for one of its infinite subgroups.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 1, pp. 190–198, July, 2005.     

Formulation of the problem of sonic boom by a maneuvering aerofoil as a one-parameter family of Cauchy problems

For the structure of a sonic boom produced by a simple aerofoil at a large distance from its source we take a physical model which consists of a leading shock (LS), a trailing shock (TS) and a one-parameter family of nonlinear wavefronts in between the two shocks. Then we develop a mathematical model and show that according to this model the LS is governed by a hyperbolic system of equations in conservation form and the system of equations governing the TS has a pair of complex eigenvalues. Similarly, we show that a nonlinear wavefront originating from a point on the front part of the aerofoil is governed by a hyperbolic system of conservation laws and that originating from a point on the rear part is governed by a system of conservation laws, which is elliptic. Consequently, we expect the geometry of the TS to be kink-free and topologically different from the geometry of the LS. In the last section we point out an evidence of kinks on the LS and kink-free TS from the numerical solution of the Euler’s equations by Inoue, Sakai and Nishida [5].