一种求解Robin反问题的边界型无网格方法

给出一种求解非齐次稳态热传导方程Robin反问题的边界型无网格方法. 该方法首先利用Newton法则将Robin反问题转化为Cauchy问题,然后用边界粒子法处理非齐次项以避免区域内部的离散节点,并结合基本解方法分别求得近似特解以及相应齐次问题的近似解. 鉴于所考虑问题的不适定性,引入截断奇异值分解和L-曲线准则来求解离散后得到的高度病态的线性方程组. 最后给出数值例子说明该方法的稳定性和有效性.     

A Boundary Meshless Method for Solving Heat Transfer Problems Using the Fourier Transform

Fourier transform is applied to remove the time-dependent variable in the diffusion equation. Under non-harmonic initial conditions this gives rise to a non-homogeneous Helmholtz equation, which is solved by the method of fundamental solutions and the method of particular solutions. The particular solution of Helmholtz equation is available as shown in [4, 15]. The approximate solution in frequency domain is then inverted numerically using the inverse Fourier transform algorithm. Complex frequencies are used in order to avoid aliasing phenomena and to allow the computation of the static response. Two numerical examples are given to illustrate the effectiveness of the proposed approach for solving 2-D diffusion equations.     

Influence of spherical aberrations on fundamental mode beam quality under different laser resonators

Spherical aberrations of the thermal lens of the active media are severe when solid state lasers are strongly pumped. The fundamental mode profile deteriorates due to the aberrations. Self-consistent modes of a resonator with aberrations are calculated by using the Fox--Li diffraction iterative algorithm. Calculation results show that the aberration induced fundamental mode beam quality deterioration depends greatly on the resonator design. The tolerance of a flat--flat resonator to the aberration coefficient is about 30λ in the middle of stability, where λ is the wavelength of laser beam. But for a dynamically stable resonator, 2λ of spherical aberration will create diffraction loss of more than 40%, if inappropriate design criteria are used. A birefringence compensated laser resonator with two Nd:YAG rods is experimentally studied. The experimental data are in quite good agreement with simulation results.     

Pseudospin symmetry as an accidental symmetry in the relativistic framework

We analyse the arguments used in the relativistic context to base the quasi-degeneracy of pseudospin doublets (PSDs) observed in atomic nuclei on the smallness of the single-particle central potential (Σ _S + Σ₀), discussing, especially, the implications of the results obtained in the limit (Σ _S + Σ₀ = 0. We study also the transition from a relativistic model, where Σ _S + Σ₀ is a harmonic-oscillator potential and exhibits degenerate PSDs, to a more realistic one with broken pseudospin symmetry. We examine, in particular, the effect of the corresponding pseudospin symmetry-breaking term on the Dirac spinors of the PSDs. An extension of the Nilsson model to the relativistic case is also considered. Communicated by V. Vento     

Temperature dependence of optical absorption in In1‐xGaxAs solid solutions

Absorption spectra near the fundamental absoption edge of n‐type of In_1‐xGa_xAs are studied. The temperature coefficient of the In_1‐xGa_xAs energy gap, dE_g/dT, has been obtained and compared with calculated data. An exponential dependence of the absorption coefficient on photon energy has been found. The slope of the exponential absorption curve is discussed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Differential Forms and Smoothness of Quotients by Reductive Groups

Let :XY be a good quotient of a smooth variety X by a reductive algebraic group G and 1k dim (Y) an integer. We prove that if, locally, any invariant horizontal differential k-form on X (resp. any regular differential k-form on Y) is a Kähler differential form on Y then codim(Y _sing)>k+1. We also prove that the dualizing sheaf on Y is the sheaf of invariant horizontal dim(Y)-forms.     

A New Construction of Central Relative (p a , p a , p a , 1)-Difference Sets

Semiregular relative difference sets (RDS) in a finite group E which avoid a central subgroup C are equivalent to orthogonal cocycles. For example, every abelian semiregular RDS must arise from a symmetric orthogonal cocycle, and vice versa. Here, we introduce a new construction for central (p ^a , p ^a , p ^a , 1)-RDS which derives from a novel type of orthogonal cocycle, an LP cocycle, defined in terms of a linearised permutation (LP) polynomial and multiplication in a finite presemifield. The construction yields many new non-abelian (p ^a , p ^a , p ^a , 1)-RDS. We show that the subset of the LP cocycles defined by the identity LP polynomial and multiplication in a commutative semifield determines the known abelian (p ^a , p ^a , p ^a , 1)-RDS, and give a second new construction using presemifields.We use this cohomological approach to identify equivalence classes of central (p ^a , p ^a , p ^a , 1)-RDS with elementary abelian C and E/C. We show that for p = 2, a 3 and p = 3, a 2, every central (p ^a , p ^a , p ^a , 1)-RDS is equivalent to one arising from an LP cocycle, and list them all by equivalence class. For p = 2, a = 4, we list the 32 distinct equivalence classes which arise from field multiplication. We prove that, for any p, there are at least a equivalence classes of central (p ^a , p ^a , p ^a , 1)-RDS, of which one is abelian and a – 1 are non-abelian.     

The Maximum Tension Principle in General Relativity

I suggest that classical General Relativity in four spacetime dimensions incorporates a Principal of Maximal Tension and give arguments to show that the value of the maximal tension is . The relation of this principle to other, possibly deeper, maximal principles is discussed, in particular the relation to the tension in string theory. In that case it leads to a purely classical relation between G and the classical string coupling constant and the velocity of light c which does not involve Planck's constant.     

Nonlinearity of strong interaction and doorway states for one-nucleon transfer reactions

The experimental data on the doorway states for one-nucleon transfer reactions permit to reveal the many-particle nucleon-nucleon forces resulting from the nonlinearity of strong interaction. The three-particle and four-particle forces are found to be of the same magnitude as the two-particle ones in contrast to the finding from the few-nucleon systems. The origin of this difference is explained. Received: 14 May 2002 / Accepted: 4 June 2002 / Published online: 19 November 2002 RID="a" ID="a"e-mail: birbrair@thd.pnpi.spb.ru Communicated by V.V. Anisovich     

Phonational profiles of female professional singers and nonsingers

Measures of the SFF, vocal intensity, phonational range, and habitualpitch level are reported for 39 professional singer and 39 nonsinger females, who were divided into three age groups (young, middle, and old age), with the professionals further divided into sopranos and altos. Each read the “Rainbow Passage” and spoke extemporaneously, from which measures of the SFF and vocal intensity were calculated; phonational range and habitual pitch levels were also determined. No significant differences were noted between the reading and speaking tasks. The SFF and intensity levels were significantly higher for the professionals in comparison to the nonsingers, but only for certain age groups. Moreover, whereas the nonsinger SFF levels varied significantly as a function of age, those for the professional singers did not. Although trends occurred, no significant differences were found for the mean phonational range or habitual pitch levels when the professionals and nonsingers were compared.