Semigroups of matrices of intermediate growth

Finitely generated linear semigroups over a field K that have intermediate growth are considered. New classes of such semigroups are found and a conjecture on the equivalence of the subexponential growth of a finitely generated linear semigroup S and the nonexistence of free noncommutative subsemigroups in S, or equivalently the existence of a nontrivial identity satisfied in S, is stated. This ‘growth alternative’ conjecture is proved for linear semigroups of degree 2, 3 or 4. Certain results supporting the general conjecture are obtained. As the main tool, a new combinatorial property of groups is introduced and studied.     

Mathematical modelling and analytical solution for workpiece temperature in grinding

This paper deals with modelling the workpiece temperature field produced during the grinding process. The proposed model is given in terms of a two-dimensional boundary-value problem where the interdependence among the grinding wheel, the workpiece and the coolant is described by two variable functions in the boundary condition. An explicit integral form solution is constructed using the Laplace and Fourier transforms and the Green’s function method.     

Comment on “The Free Will Theorem”

In a recent paper Conway and Kochen, Found. Phys. 36, 2006, claim to have established that theories of the Ghirardi-Rimini-Weber (RW) type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRW-type theories have already been presented, in my recent paper, J. Stat. Phys. 125, 2006, and by Dowker and Henson, J. Stat. Phys. 115, 2004. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen.      

Neutral Community Theory: How Stochasticity and Dispersal-Limitation Can Explain Species Coexistence

Neutral community theory explains biodiversity, i.e. the coexistence of several species, as the result of a stochastic balance between immigration and extinction on a local level, and between speciation and extinction on a regional level. The most popular model, presented by Hubbell in 2001, has seen many analytical developments in recent years, which can be used in model analysis, model testing and model comparison. We review these developments here, and present alternative derivations and shine previously unnoticed lights on them.     

关于p-叶星形性和强星形性的充分条件 (英)

本文利用微分从属的方法得到了单位圆盘内p-叶星形函数和强星形函数的某些充分条件．     

Deconvolution of very low primary energy SIMS depth profiles

In this paper, the deconvolution of SIMS profiles analysed at very low primary energy (0.5 keV/O₂⁺) is addressed. The depth resolution function (DRF) of the SIMS analysis in presence of roughness is established and a deconvolution procedure is implemented without or in presence of roughness on samples containing delta-doped layers of boron in silicon. It is shown that the deconvolution procedure can lead to a great improvement of the full width at half maximum (FWHM) of the measured peaks in the case where no roughness in detected in the crater bottom. In the case where it is present, the conditions required to use a deconvolution procedure are discussed, and the deconvolution is implemented using precise and restrictive assumptions.     

Fourth-order problems with fully nonlinear boundary conditions

Differential inequality method, bounding function method and topological degree are applied to obtain the existence criterions of at least one solution for the general fourth-order differential equations under nonlinear boundary conditions, and many existing results are complemented.     

p+209Bi核反应微观数据的理论计算

利用光学模型、激光模型、蒸发模型及扭曲波玻恩近似理论,对入射能量从阈能到300MeV,p+²⁰⁹Bi的中子反应截面、剩余核截面、出射粒子的多重数进行了理论计算及分析,并将计算结果与实验数据进行了比较.同时得到一组能量到50?0MeV与实验数据符合很好的光学势参数.     

X分形晶格上Gauss模型的临界性质

采用实空间重整化群变换的方法,研究了2维和d(d>2)维X分形晶格上Gauss模型的临界性质.结果表明:这种晶格与其他分形晶格一样,在临界点处,其最近邻相互作用参量也可以表示为K=bqiqi(qi是格点i的配位数,bqi是格点i上自旋取值的Gauss分布常数)的形式;其关联长度临界指数v与空间维数d(或分形维数df)有关.这与Ising模型的结果存在很大的差异. 关键词： X分形晶格 重整化群 Gauss模型 临界性质