Positive solutions of m-point boundary value problems

The second-order m-point boundary value problem

     

A limit-point criterion for a class of Sturm-Liouville operators defined in spaces

Using a recent result of Chernyavskaya and Shuster we show that the maximal operator determined by on , -\infty$">, where and the mean value of computed over all subintervals of of a fixed length is bounded away from zero, shares several standard ``limit-point at " properties of the case. We also show that there is a unique solution of that is in all , .

     

Nonconforming elements in least-squares mixed finite element methods

In this paper we analyze the finite element discretization for the first-order system least squares mixed model for the second-order elliptic problem by means of using nonconforming and conforming elements to approximate displacement and stress, respectively. Moreover, on arbitrary regular quadrilaterals, we propose new variants of both the rotated nonconforming element and the lowest-order Raviart-Thomas element.

     

一维对流扩散方程CRANK—NICOLSON特征差分格式

本文针对一维线性和非线性对流扩散方程提出一种Crank-Nicolson类型的特征差分格式,给出了该格式形成的线性代数方程组可解的一个充条件,证明了该格式按离散L^2模是收敛的,且其收敛阶为O（△t^ h^2).     

W型单模单偏振光纤基模截止的条件

给出了 W型单模单偏振光纤基模截止的必要条件。通过对基模截止波长的数值计算 ,分析了这个必要条件的充分性。结论是 :对于圆形内包层 W型光纤来说 ,这是必要的而又充分的条件 ;对于低椭圆度内包层 W型单模单偏振光纤来说 ,它可以在较高的精度上近似作为充分条件 ,而对于高椭圆度内包层 W型单模单偏振光纤来说 ,它仅仅只是必要条件而非充分条件     

Non-linear filtering for a dust-perturbed two-body model

In standard textbooks on classical mechanics, the two-body central forcing problem is formulated as a system of the coupled non-linear second-order deterministic differential equations. Uncertainties, introduced by the astronomical ‘dust’, are not assumed in the orbit dynamics. The dust population produces an additional random force on the orbiting particle. This work is a continuation of the paper (Sharma and Parthasarathy, Proc. R. Soc. A: Math. Phys. Eng. Sci. 463:979–1003, [2007]) in which the authors developed and analyzed the dust-perturbed two-body model, which accounts for the dust perturbation felt by the orbiting particle. The theory of the dust-perturbed stochastic system was developed using the Fokker–Planck equation. This paper discusses the problem of realizing non-linear stochastic filters for estimating the states of the dust-perturbed planar two-body stochastic system, especially from noisy observations. This paper utilizes the Kushner’s theory of non-linear filtering, which involves stochastic observation term in the evolution of conditional probability density, for deriving the stochastic evolutions of the conditional mean and conditional covariance. The effectiveness of the non-linear filters of this paper is examined on the basis of their ability to preserve the perturbation effect, less random fluctuations in the mean trajectory and stability characteristics in the mean and variance trajectories. Most notably, this paper reveals the efficacy of the second-order approximate Kushner filter for the estimation procedure in contrast to the first-order approximate filter. Simulation results are introduced to demonstrate the usefulness of an analytic theory developed in this paper.     

Recurrence Relations for Chebyshev-Type Methods

The convergence of new second-order iterative methods are analyzed in Banach spaces by introducing a system of recurrence relations. A system of a priori error bounds for that method is also provided. The methods are defined by using a constant bilinear operator A , instead of the second Fréchet derivative appearing in the defining formula of the Chebyshev method. Numerical evidence that the methods introduced here accelerate the classical Newton iteration for a suitable A is provided. Accepted 23 October 1998     

Modélisation de la turbulence en déclin avec rotation

The study presented in the present paper deals with the modeling of the rotation effects on a homogeneous turbulence evolving without a mean velocity gradient. The developed model results from a modification of the second order model of Haworth and Pope. This modification is expressed as a function of the rotation rate, of the component of the Reynolds tensor and of the characteristic length scale in the direction of the rotation axis. The obtained results have evidenced the great capacity of the present model to describe the rotation effects on the time evolution of the homogeneous decaying turbulence.     

A nonlinear kp-εp particle two-scale turbulence model and its application

A particle nonlinear two-scale turbulence model is proposed for simulating the anisotropic turbulent two-phase flow. The particle kinetic energy equation for two-scale fluctuation, particle energy transfer rate equation for large-scale fluctuation, and particle turbulent kinetic energy dissipation rate equation for small-scale fluctuation are derived and closed. This model is used to simulate gas–particle flows in a sudden-expansion chamber. The simulation is compared with the experiment and with those obtained by using another two kinds of tow-phase turbulence model, such as the single-scale two-phase turbulence model and the particle two-scale second-order moment (USM) two-phase turbulence model. It is shown that the present model gives simulation in much better agreement with the experiment than the single-scale two-phase turbulence model does and is almost as good as the particle two-scale USM turbulence model. The project supported by China Postdoctoral Science Foundation (2004036239).     

Singularities in the lineshape of a second-order perturbed quadrupolar nucleus. The magic-angle spinning case

For a nucleus with a half-integral spin and a strong quadrupole coupling, the central transition (from magnetic quantum number −1/2 to +1/2) in the spectrum shows a characteristic lineshape. By strong coupling, we mean an interaction strong enough so that second-order perturbation theory is needed, yet still sufficient. The spectrum of a static sample is well-known and the magic-angle-spinning (MAS spectrum) is different, but still can be calculated. The important features of both these spectra are singularities and steps in the lineshape, since these are the main tools in fitting the calculated spectrum to experimental data. A useful tool in this investigation is a plot of the frequency as a function of orientation over the surface of the unit sphere. These plots have maxima, minima and saddle points, and these correspond to the features of the spectrum. We used these plots to define both the positions and derive new formulae for the heights of the features and we now extend this to the magic-angle spinning case. For the first time, we identify the orientations corresponding to the features of the MAS spectra and derive formulae for the heights. We then compare the static and MAS cases and show the relationships between the features in the two spectra.