Error analysis of the L2 least‐squares finite element method for incompressible inviscid rotational flows

In this article we analyze the L² least‐squares finite element approximations to the incompressible inviscid rotational flow problem, which is recast into the velocity‐vorticity‐pressure formulation. The least‐squares functional is defined in terms of the sum of the squared L² norms of the residual equations over a suitable product function space. We first derive a coercivity type a priori estimate for the first‐order system problem that will play the crucial role in the error analysis. We then show that the method exhibits an optimal rate of convergence in the H¹ norm for velocity and pressure and a suboptimal rate of convergence in the L² norm for vorticity. A numerical example in two dimensions is presented, which confirms the theoretical error estimates. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004     

Structure of multiple solutions for nonlinear differential equations

Based on the eigensystem {λj,φj}of -Δ, the multiple solutions for nonlinear problem Δu f(u) =0 in Ω, u=0 on Ω are approximated. A new search-extension method (SEM), which consists of three steps in three level subspaces, is proposed. Numerical simulations for several typical nonlinear cases, i.e. f(u) = u~3,u~2(u-p),u~2(u~2 -p),     

微粒群算法及其在热轧生产调度中的应用

针对整数规划问题的特点,提出了一种在整数空间中进行进化计算的PSO算法,使微粒群的进化限于整数空间。给出了热轧生产调度问题的最优轧制单元数学规划模型。并将该方法成功应用于最优轧制单元求解。     

Congratulations to Professor K. Itô

In this paper we describe a story how a Moscow mathematician solved an important problem in ergodic theory using It? multiple stochastic integrals.     

Regularized product expressions of higher Riemann zeta functions

As a generalization of recent work by Kurokawa, Matsuda, and Wakayama (2004) we introduce a higher Riemann zeta function for an abstract sequence. Then we explicitly determine its regularized product expression.

     

A differential geometric setting for BRS transformations and anomalies I

The Becchi-Rouet-Stora relations and the cohomological construction of anomalies of gauge fields are described within the theory of principal connections of smooth vector bundles.     

Ultrasonic velocity hydration numbers of polyamines

Ultrasonic velocity hydration numbers of diamines, triamines and tetraamines and hydrochlorides of these amines were determined by measuring the maximum velocity of ultrasound in aqueous-ethanolic solutions. The results are interpreted on the basis of the hydrogen-bonded framework model of the water structure.     

Non-classicality of photon added coherent and thermal radiations

Production and analysis of non-Gaussian radiation fields has evinced a lot of attention recently. Simplest way of generating such non-Gaussians is through adding (subtracting) photons to Gaussian fields. Interestingly, when photons are added to classical Gaussian fields, the resulting states exhibit non-classicality. Two important classical Gaussian radiation fields are coherent and thermal states. Here, we study the non-classical features of such states when photons are added to them. Non-classicality of these states shows up in the negativity of the Wigner function. We also work out the entanglement potential, a recently proposed measure of non-classicality for these states. Our analysis reveals that photon added coherent states are non-classical for all seed beam intensities; their non-classicality increases with the addition of more number of photons. Thermal state exhibits non-classicality at all temperatures, when a photon is added; lower the temperature, higher is their non-classicality.     

一种新型全光纤速度干涉仪

 基于传统速度干涉仪(VISAR)和光纤速度干涉仪(AFVISAR)的特点，提出了一种由光纤和光纤耦合器组成的工作波长为532 nm的新型全光纤速度干涉仪（NAFVISAR）。该干涉仪采用多模光纤器件构成分离系统,单模光纤器件组成核心部分。由于有两路携带不同信息的光束经不同路径传输到耦合器中，当这两路光束满足干涉条件时，可利用它们的干涉场信息来调解出被测靶的信息，从而区分波面的加减速变化。用该系统进行了Hopkinson森杆一维应力加载下的入射杆端面的速度剖面测试，实测速度最大值为49.36 m/s，与理论速度的最大值50.16 m/s基本符合，实现了全光纤速度干涉仪的实用化。     

The Stripping Voltammetry In High Frequency Electromagnetic Field

The effectiveness of high frequency electromagnetic field influence on the analytical signal value in the stripping voltammetry method depending on such factors as the nature and concentration of the defined element, nature and concentration of the supporting electrolyte and agitation velocity has been studied. It has been demonstrated that an analytical signal increase may be achieved that allows one to lower a detection limit and to reduce the time of individual definition. The highest peak current is observed at some definite frequencies of the exterior field depending on the nature of the element and on the supporting electrolyte as well.