On bounded time-dependent perturbations of operator cosine functions

In this note it is shown that the Cauchy problem associated with the infinitesimal generatorA of a strongly continuous operator cosine function remains uniformly well-posed under bounded time-dependent perturbations ofA.     

Cellularity in polyhedra

A compact subset X of a polyhedron P is cellular in P if there is a pseudoisotropy of P shrinking precisely X to a point. A proper surjection between polyhedra f:P→Q is cellular if each point inverse of f is cellular in P. It is shown that if f:P→Q is a cellular map and either P or Q is a generalized n-manifold, n≠4, then f is approximable by homeomorphisms. Also, if P or Q is an n-manifold with boundary, n≠4, 5, then a cellular map f:P→Q is approximable by homeomorphisms. A cellularity criterion for a special class of cell-like sets in polyhedra is established.     

On the representations of quantum oscillator algebra

It is shown that for q<1, the quantum oscillator algebra has a supplementary family of representations inequivalent to the usual q-Fock representation, with no counterpart at the limit q=1. They are used to build representations of SU _q (1,1) and E(2) in Schwinger's way.     

Mapping properties of wave and scattering operators for two-body Schrödinger operators

The modified wave and scattering operators are shown to be bounded between weighted L ²-spaces for two-body Schrödinger operators with long range potentials.     

Solution of a diffusion equation of smoke molecules due to constant point source in gravitational field

From both the Langevin equation, including a gravitational term, the Fokker-Planck equation based on the dynamical behavior of Brownian particles, and equation of smoke molecular diffusion due to a constant point source is introduced and is solved by applying the Laplace transformation with the convolution theorem.The solution is expressed by the complementary error function with a mean pathway of smoke molecules affected by gravity and is proved to be reduced to conventional forms by a certain restriction neglecting gravity without any forced term.     

The two-dimensional quantum Euclidean algebra

The algebra dual to Woronowicz's deformation of the two-dimensional Euclidean group is constructed. The same algebra is obtained from SU _q (2) via contraction on both the group and algebra levels.     

锰结核中硅,铝,铁,镁,磷,钾,锰,钛的XRFA

本文叙述了用XRF分析锰结核中Si、Al、Fe、Mg、P、K、Mn和Ti的方法。按照通常锰结核的主次成分制备6个人工合成标准,根据Sherman方程计算了已知成分(二元系统)的相对强度。用L-T方求得了互致元素校正的理论α系数(基本的、混合的、修正的),用DATAFLEX151B计算机以BASIC语言汇了“PRA,APU”计算机程序。然后进行非线性回归分析了锰结核样品得到了满意的结果。     

Serre-type relations for special linear Lie superalgebras

It is pointed out that, for m, n 2, the naive Serre presentation corresponding to the simplest Cartan matrix of sl(m, n) does not define the Lie superalgebra sl(m, n) but a larger algebra s(m, n) of which sl(m, n) is a nontrivial quotient. The supplementary relations for the generators are found and the definition of the q-deformed universal enveloping algebra of sl(m, n) is modified accordingly.     

Surface free energies of electroless Ni–P based composite coatings

Surface free energy of a solid surface gives a direct measure of intermolecular interactions at interfaces and has a strong influence on adsorption and adhesion behaviour. However few data are available for the surface free energies of electroless Ni–P based composition coatings. In this paper, the electroless Ni–P, Ni–P-surfactant, Ni–Cu–P, Ni–P–PTFE and Ni–Cu–P–PTFE composite coatings were prepared under various coating conditions. The chemical compositions, surface morphology and thickness of the coatings were measured using an energy dispersive X-ray microanalysis (EDX), a scanning electron microscope (SEM) and a digital micrometer respectively. The contact angles of water, diiodomethane and ethylene glycol on the coatings were measured automatically using dataphysics OCA-20 contact angle analyser. The surface free energy of the coatings and their components (e.g. dispersion, polar or acid/base portions) were calculated using various methods. The experimental results showed that the incorporation of surfactant or PTFE particles into Ni–P matrixes has a significant influence on the surface free energy of the coatings, while the incorporation of copper into Ni–P matrixes has no significant influence on the surface free energy of the coatings.