ENTROPY CONSISTENCY OF LARGE TIME STEP SCHEMES FOR ISENTROPIC EQUATIONS OF GAS DYNAMICS

In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entropy solution in the limit if Courant number is less than or equal to 1.

A CONTINUUM DAMAGE MODEL OF AGING CONCRETE

There is up to now no constitutive model in the current theoriesof CDM that could give a description for the degradation of agingconcrete. The two internal state variable β and ω are intro- ducedin this paper β is called cohesion variable as an additionalkinematic parameter, reflecting the cohesion state among materialparticles. ω is called damage factor for micro-defects such s voids.Then a damage model and a series of constitutive equations aredeveloped on Continuum Mechanics. The model proposed could give avalid description for the whole-course-degradation of aging concretedue to chemical and mechanical actions. Finally, the validity of themodel is evaluated by an example and experimental results.

Consistent Burgers equation expansion method and its applications to high-dimensional Burgers-type equations

In this paper,a novel method,named the consistent Burgers equation expansion(CBEE)method,is proposed to solve nonlinear evolution equations(NLEEs)by the celebrated Burgers equation.NLEEs are said to be CBEE solvable if they are satisfied by the CBEE method.In order to verify the effectiveness of the CBEE method,we take(2+1)-dimensional Burgers equation as an example.From the(1+1)-dimensional Burgers equation,many new explicit solutions of the(2+1)-dimensional Burgers equation are derived.The obtained results illustrate that this method can be effectively extended to other NLEEs.

Conservation laws of some lattice equations

We derive infinitely many conservation laws for some multi- dimensionally consistent lattice equations from their Lax pairs. These lattice equations are the Nijhoff-Quispel-Capel equation, lattice Boussinesq equation, lattice nonlinear SchrSdinger equation, modified lattice Boussinesq equation, Hietarinta＇s Boussinesq-type equations, Schwarzian lattice Boussinesq equation, and Toda-modified lattice Boussinesq equation.

Asymptotically efficient parameter estimation for ordinary differential equations

Parameter estimation for ordinary differential equations arises in many fields of science and engineering. To be the best of our knowledge, traditional methods are often either computationally intensive or inaccurate for statistical inference. Ramsay et al.(2007) proposed a generalized profiling procedure. It is easily implementable and has been demonstrated to have encouraging numerical performance. However, little is known about statistical properties of this procedure. In this paper, we provide a theoretical justification of the generalized profiling procedure. Under some regularity conditions, the procedure is shown to be consistent for a broad range of tuning parameters. When the tuning parameters are sufficiently large, the procedure can be further shown to be asymptotically normal and efficient.

Various Kinds Waves and Solitons Interaction Solutions of Boussinesq Equation Describing Ultrashort Pulse in Quadratic Nonlinear Medium

The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves.