Refinement of a criterion for superfluidity of a classical liquid in a nanotube

The problem has a large parameter, the number N of particles (outside the condensate), and a small parameter, Planck’s constant ħ (more precisely, a dimensionless parameter containing ħ in the numerator). They turn out to be interrelated for Bose particles. Using the exact solution of the variational equation for a bosonic system in a capillary, we can obtain precise criteria restricting the superfluidity of a classical liquid in the capillary. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 524–528, June, 2008.     

A Step-Function Approximation in the Theory of Critical Fluctuations

We consider fluctuations near the critical point using the step-function approximation, i.e., the approximation of the order parameter field f(x) by a sequence of step functions converging to f(x). We show that the systematic application of this method leads to a trivial result in the case where the fluctuation probability is defined by the Landau Hamiltonian: the fluctuations disappear because the measure in the space of functions that describe the fluctuations proves to be supported on the single function f0. This can imply that the approximation of the initial smooth functions by the step functions fails as a method for evaluating the functional integral and for defining the corresponding measure, although the step-function approximation proves to be effective in the Gaussian case and yields the same result as alternative methods do.     

Superfluidity of classical liquid in a nanotube for even and odd numbers of neutrons in a molecule

We show that the superfluidity phenomenon occurs for classical liquids in nanotubes. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 3, pp. 388–408, December, 2007.     

进化泛函网络多维函数逼近理论及学习算法

提出了一种用于多维函数逼近的进化策略修正泛函网络基函数系数的新算法,并给出了其算法学习过程.利用进化策略的自适应性来确定基函数前的系数,改进了泛函网络的参数通过解方程组来得到这一传统方法.仿真结果表明,这种新的逼近算法简单可行,能够逼近给定的函数到预先给定的精度,具有较快的收敛速度和良好的逼近性能.     

Calculating a minimal sphere containing a polytope defined by a system of linear inequalities

We will propose an algorithm for calculating a minimal sphere containing a polytope defined by a system of linear inequalities in low dimensional Euclidean space. This algorithm is a straightforward application of the algorithm for maximizing a convex quadratic function over a polytope. It will be shown that this algorithm successfully generates a minimal sphere when the dimensions of the underlying space is up to five.International Digital Communication Inc.     

On a modification of the Clenshaw-Curtis quadrature formula

In this paper we discuss a modification of the Clenshaw-Curtis quadrature formula. It is shown that for integrals, where the integrand may be expanded in a sufficiently rapid convergent Chebyshev series, we may split the sequence of calculated approximations into two sequences, one which approximates the integral from above and one which approximates it from below. Thus, at any step during the calculation we obtain both upper and lower bounds for the true value of the integral.Work performed while the author was working as a visiting scientist at CERN/Geneve.     

Gravitational Effects on Light Rays and Binary Pulsar Energy Loss in a Scalar Theory of Gravity

We summarize a scalar bimetric theory of gravity with a preferred reference frame. The dynamics are governed by an extension of Newton's second law. We recover geodesic motion together with Newton's attraction field in the static case and find Schwarzschild's metric in the static spherical case. We build asymptotic schemes of post-Newtonian (PN) and post-Minkowskian (PM) approximations, each based on associating a conceptual family of systems with the given system. At the 1PN approximation, there is no preferred-frame effect for photons, and we hence obtain the standard predictions of GR for photons. At the 0PM approximation, an isolated system loses energy by quadrupole radiation without any monopole or dipole term. Inserting this loss into the Newtonian two-body problem gives the Peters–Mathews coefficients of the theory.     

W_2~1[a,b]中的最佳逼近泛函及应用

1 引言 线性泛函的逼近问题有着十分广泛的应用背景,本文在具有再生核的W_2~1[a,b]空间中讨论线性泛函L(f)的形如 L_n(f)=sum from i=1 to n(i/1)w_if(x_i) (1)的逼近问题,其中{w_i}_1~n是待定系数,如果存在一组常数{w_i~x}_1~n使 L_n~x=sum from i=1 to n(i/1)w_i~xf(x_i) (2)满足||L—L_n~x||=inf||L—L_n||,则称L_n~x是L的最佳逼近,记 w_i E_n=L—L_n, E_n~3=L—L_n~x,则称E_n~x是最佳逼近误差泛函。 本文在§1中给出L_n~x的表达式及L_(n+1)~x与L_n~x之间的递推公式。并证明L_n~x的收敛性。§3中讨论了上L_n~x(f)在数值积分及常微分方程数值解中的应用,并给出数值算例。     

湍流流场中激光传输的积分法研究

采用Born近似的Maxwell(麦克斯韦)方程组的积分解形式较少用于气动光学数值计算,其困难在于对该方程组的离散化数值计算.结合广义卷积-快速Fourier变换(GCV-FFT)方法,对在自由空间传播的Rayleigh-Sommerfeld衍射方程进行数值计算,可以达到比较高的精度.通过对Green函数及采样系数的修正,可以得到对气动光学现象进行数值仿真的积分解算方法;而用修正GCV-FFT结合数值积分的方法,对超声速湍流边界层中传输的激光光束进行数值计算,可以很好地对一些气动光学现象,如光束偏移、破碎等,进行数值模拟.由于这种积分方法不依赖傍轴近似条件,故给出的计算结果能够更接近问题的物理本质.     

Existence and uniqueness for a mathematical model in superfluidity

In this paper we propose a model to study superfluidity by considering as state variables the order parameter, describing the concentration of the superfluid phase, the velocity of the superfluid and the absolute temperature. We assume that the order parameter satisfies a Ginzburg–Landau equation and that the velocity is decomposed as the sum of a normal and a superfluid component. The heat equation provides the evolution equation for the temperature. We prove that this model is consistent with the principles of thermodynamics. Well‐posedness of the resulting initial and boundary value problem is shown. Copyright © 2008 John Wiley & Sons, Ltd.     

Exceptional units in a family of quartic number fields

We determine all exceptional units among the elements of certain groups of units in quartic number fields. These groups arise from a one-parameter family of polynomials with two real roots.

     

Dynamic approximation of a random information functional

Using the probabilistic evaluation of the Marcovian diffusion process by a functional of action, the paper introduces a dynamic approximation of a random information functional defined on the process trajectories and determined by the parameters of a controlled stochastic equation. The developed mathematical formalism is aimed toward a dynamic modeling of a random object.     

Dynamic approximation of a random information functional

Using the probabilistic evaluation of the Marcovian diffusion process by a functional of action, the paper introduces a dynamic approximation of a random information functional defined on the process trajectories and determined by the parameters of a controlled stochastic equation. The developed mathematical formalism is aimed toward a dynamic modeling of a random object.     

Quasi-steady-state approximation for a reaction-diffusion system with fast intermediate

We consider a prototype reaction-diffusion system which models a network of two consecutive reactions in which chemical components A and B form an intermediate C which decays into two products P and Q. Such a situation often occurs in applications and in the typical case when the intermediate is highly reactive, the species C is eliminated from the system by means of a quasi-steady-state approximation. In this paper, we prove the convergence of the solutions in L², as the decay rate of the intermediate tends to infinity, for all bounded initial data, even in the case of initial boundary layers. The limiting system is indeed the one which results from formal application of the QSSA. The proof combines the recent L²-approach to reaction-diffusion systems having at most quadratic reaction terms, with local L^∞-bounds which are independent of the decay rate of the intermediate. We also prove existence of global classical solutions to the initial system.     

一类反射型非线性倒向随机微分方程的适应解

本文研究了反射型非线性倒向随机微分方程yt=ξ ∫Ttf(s,ys,zs)ds-∫Ttg(s,ys,zs)dws KT-Kt,t∈[0,T],在非Lipschitz条件下,给出了其解的存在唯一性定理.文中所使用的主要方法是罚则函数法,主要工具是Bihari不等式的一个推广形式及凸函数次微分算子的Yosida逼近.     

W_2~m[a,b]空间中线性泛函最佳逼近的深入讨论

本文基础上给出了Wm2(a,b)空间再生核构造的普遍方法,并利用再生核讨论算于插值样条的投影性质及最佳数值逼近问题     

Improving projection‐based eigensolvers via adaptive techniques

We consider subspace iteration (or projection‐based) algorithms for computing those eigenvalues (and associated eigenvectors) of a Hermitian matrix that lie in a prescribed interval. For the case that the projector is approximated with polynomials, we present an adaptive strategy for selecting the degree of these polynomials such that convergence is achieved with near‐to‐optimum overall work without detailed a priori knowledge about the eigenvalue distribution. The idea is then transferred to the approximation of the projector by numerical integration, which corresponds to FEAST algorithm proposed by E. Polizzi in 2009. [E. Polizzi: Density‐matrix‐based algorithm for solving eigenvalue problems. Phys. Rev. B 2009; 79 :115112]. Here, our adaptation controls the number of integration nodes. We also discuss the interaction of the method with search space reduction methods.