The conjugacy problem for Dehn twist automorphisms of free groups

A Dehn twist automorphism of a group G is an automorphism which can be given (as specified below) in terms of a graph-of-groups decomposition of G with infinite cyclic edge groups. The classic example is that of an automorphism of the fundamental group of a surface which is induced by a Dehn twist homeomorphism of the surface. For , a non-abelian free group of finite rank n, a normal form for Dehn twist is developed, and it is shown that this can be used to solve the conjugacy problem for Dehn twist automorphisms of . Received: February 12, 1996.     

Spectroscopic Ellipsometry Characterisation and Estimation of the Hamaker Constant of Cellulose

Calculations of Hamaker constants using Lifshitz theory require the availability of accurate dielectric data, especially in the visible-ultraviolet region. We present spectroscopic ellipsometry data on well-defined cellulose films of a limited thickness range (100–140 layers) deposited on an oxidised and hydrophobised silicon substrate. The spectral data, representing measurements from a perpendicular orientation to the fibre deposition direction, was used for estimates of the necessary spectral parameters, i.e. the oscillator strengths and characteristic frequencies in the UV-range. Our calculations show that cellulose has a relatively low Hamaker constant in air (58 zJ) and water (8.0 zJ). The implications for the surface energy estimates of cellulose and colloidal interactions between cellulose and various types of fillers and coating colours are indicated.     

Pore Network Analysis of Resistivity Index for Water-Wet Porous Media

Pore network analysis is used to investigate the effects of microscopic parameters of the pore structure such as pore geometry, pore-size distribution, pore space topology and fractal roughness porosity on resistivity index curves of strongly water-wet porous media. The pore structure is represented by a three-dimensional network of lamellar capillary tubes with fractal roughness features along their pore-walls. Oil-water drainage (conventional porous plate method) is simulated with a bond percolation-and-fractal roughness model without trapping of wetting fluid. The resistivity index, saturation exponent and capillary pressure are expressed as approximate functions of the pore network parameters by adopting some simplifying assumptions and using effective medium approximation, universal scaling laws of percolation theory and fractal geometry. Some new phenomenological models of resistivity index curves of porous media are derived. Finally, the eventual changes of resistivity index caused by the permanent entrapment of wetting fluid in the pore network are also studied.Resistivity index and saturation exponent are decreasing functions of the degree of correlation between pore volume and pore size as well as the width of the pore size distribution, whereas they are independent on the mean pore size. At low water saturations, the saturation exponent decreases or increases for pore systems of low or high fractal roughness porosity respectively, and obtains finite values only when the wetting fluid is not trapped in the pore network. The dependence of saturation exponent on water saturation weakens for strong correlation between pore volume and pore size, high network connectivity, medium pore-wall roughness porosity and medium width of the pore size distribution. The resistivity index can be described succesfully by generalized 3-parameter power functions of water saturation where the parameter values are related closely with the geometrical, topological and fractal properties of the pore structure.     

胺、醇和醚类化合物电离能的估算

脂肪族胺、醇、醚、硫醇和硫醚的第一电离能Ip与N、O、S原子的电负性X~Z^O、分子中N、O、S原子的部分电荷q~z以及烷基的极化效应指数PEI的关系可以表示为:Ip(eV)=4.4851+3.0727X~Z~O+7.1702q~z-1.3949∑PEI上式较好地表达了脂肪族胺、醇、醚、硫醇和硫醚的第一电离能变化的共同规律。     

Electronic structure of C60 films

A complete set of fundamental optical functions of fullerite (C₆₀) films in energy ranges of 2.5–5.0 and 4.0–9.0 eV is calculated using the known spectra of the imaginary and real parts of the dielectric constant. An integrated spectrum of the dielectric constant is decomposed into elementary components. Three basic parameters of each component (the maximum and halfwidth energies and oscillator strength) are determined. Based on the known theoretical calculations of fullerite zones, a scheme of the nature of these components of the dielectric constant is suggested. Udmurt State University, 71, Krasnogeroiskaya Str., Izhevsk, 426034, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 2, pp. 227–232, March–April, 1999.     

Quantum Phase and Phase Difference for Fermion

In this paper, from the index theorem, we present the Hermitian phase operator for fermion, give its eigenvalues and orthogonal, normalized and complete eigenstates. Furthermore, we also get the phase difference operator for two fermions and discuss its quantum properties.     

Hybrid paper sheets with improved barrier properties

Hybrid paper sheets were prepared by applying a thin coating layer of cross-linked polydimethylsiloxane (PDMS) and inorganic particles onto Whatman Grade 1 filter paper substrates. Several coatings with different inorganic particle contents and types were applied onto the paper substrates to investigate the effect of the variation in the coating formulation on the (i) wetting, (ii) water barrier properties, (iii) air barrier properties, (iv) surface roughness, and (v) mechanical properties of the samples. It was revealed that the superhydrophobic hybrid paper sheets with significantly low air permeability and high water barrier properties could be prepared which is an indication that the method proposed can be used for the preparation of packaging materials.     

Characterization of Annealed, Proton Exchange Optical Waveguides in Y-cut MgO∶LiNbO3 Crystal

It is reported the results of a systematic study on planar waveguides fabricated in Y-cut MgO∶LiNbO3 crystal. The index profile of the as-exchanged waveguide can be modeled as a step-like one. It is deduced the diffusion coefficient and the activation energy for the proton exchange process. The surface index increases Δne of around 0.127 after proton exchange can be reduced by post thermal annealing. The effects of the annealing on the index profile and guide depth were found not as fast as it does on a pure LiNbO3 crystal.     

Lie-optics, geometrical phase and nonlinear dynamics of self-focusing and soliton evolution in a plasma

It is useful to state propagation laws for a self-focusing laser beam or a soliton in group-theoretical form to be called Lie-optical form for being able to predict self-focusing dynamics conveniently and amongst other things, the geometrical phase. It is shown that the propagation of the gaussian laser beam is governed by a rotation group in a non-absorbing medium and by the Lorentz group in an absorbing medium if the additional symmetry of paraxial propagation is imposed on the laser beam. This latter symmetry, however, needs care in its implementation because the electromagnetic wave of the laser sees a different refractive index profile than the laboratory observer in this approximation. It is explained how to estimate this non-Taylor paraxial power series approximation. The group theoretical laws so-stated are used to predict the geometrical or Berry phase of the laser beam by a technique developed by one of us elsewhere. The group-theoretical Lie-optic (or ABCD) laws are also useful in predicting the laser behavior in a more complex optical arrangement like in a laser cavity etc. The nonlinear dynamical consequences of these laws for long distance (or time) predictions are also dealt with. Ergodic dynamics of an ensemble of laser beams on the torus during absorptionless self-focusing is discussed in this context. From the point of view of new physics concepts, we introduce a stroboscopic invariant torus and a stroboscopic generating function in classical mechanics that is useful for long-distance predictions of absorptionless self-focusing.     

人工神经网络法鉴别红外光谱

本文将反向传播人工神经网络（ＢＰ－ＡＮＮ）用于ＦＴＩＲ,鉴别未知化合物。结果表明,当训练集样本不含噪声时,纯光谱的预测结果很好。而当训练集样本有少量噪声干扰时,预测结果随预测集样本的不同,而得到不同的改善。