Isospectrality and galois projective geometries

We construct a series of pairs of domains in the plane and pairs of surfaces with boundary that are isospectral but not isometric. The construction is based on the existence of finite transformation groups that are spectrally equivalent but not isomorphic. Translated fromMatematicheskie Zametki, Vol. 63, No. 5, pp. 660–664, May, 1998. This research was partially supported by the Russian Foundation for Basic Research and by INTAS under joint grant No. 96-01-00043.     

k-order Slant Toeplitz Operators on the Bergman Space

In this paper κ-order slant Toeplitz operator on the Bergman space is defined. Some properties like spectrum, commuting are discussed.     

Literal‐paraconsistent and literal‐paracomplete matrices

We introduce a family of matrices that define logics in which paraconsistency and/or paracompleteness occurs only at the level of literals, that is, formulas that are propositional letters or their iterated negations. We give a sound and complete axiomatization for the logic defined by the class of all these matrices, we give conditions for the maximality of these logics and we study in detail several relevant examples. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A procedure for measuring the flexibility of single wood-pulp fibres

A way of determining the flexibility of wood-pulp fibres is developed, which involves i) a precise measurement of the topology of single-fibres by using a confocal laser scanning microscope and ii) the measurement of the elastic modulus of the fibres by using a single-fibre fatigue cell. Reported in this paper are the initial results of tests carried out on black spruce fibres, which have been subjected to three different levels of mechanical refining energy, namely ∼1100, 2300, and 3500 kWh/t. It is found that the fibre flexibility rises significantly between the first and second energy levels, but it does not change to the same degree between the second and third ones. The described procedure of measuring the flexibility of fibres may be used to establish the appropriate refiner energy necessary for the production of a specific grade of paper. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 115–128, January–February, 2006.     

On error operators related to the arbitrary functions principle

The error on a real quantity Y due to the graduation of the measuring instrument may be asymptotically represented, when the graduation is regular and fines down, by a Dirichlet form on R whose square field operator does not depend on the probability law of Y as soon as this law possesses a continuous density. This feature is related to the “arbitrary functions principle” (Poincaré, Hopf). We give extensions of this property to Rd and to the Wiener space for some approximations of the Brownian motion. This gives new approximations of the Ornstein-Uhlenbeck gradient. These results apply to the discretization of some stochastic differential equations encountered in mechanics.     

Multi‐dimensional combustion waves for Lewis number close to one

This paper is devoted to the study of multi‐dimensional travelling wave solution for a thermo‐diffusive model, describing the propagation of curved flames in an infinite cylinder. The linear dependence of the components of the reaction rate together with the existence of an ignition temperature ensure that the corresponding linearized operator does not satisfy the Fredholm property. A direct consequence is that solvability conditions for the linearized operator are not known and classical methods of nonlinear analysis cannot be directly applied. We prove in this paper existence results of such travelling waves, by first introducing a suitable re‐formulation of the equations and then by choosing suitable weighted spaces that allows us to move the essential spectrum away from zero. Copyright © 2006 John Wiley & Sons, Ltd.     

球上加权Bergman空间上的Schatten类Hankel算子

本文给出了超球上加权Ｂｅｒｇｍａｎ空间上Ｈａｎｋｅｌ算子属于Ｓｃｈａｔｔｅｎｐ－类（２≤ｐ＜＋∞）的一个充要条件，推广了文［１０］中的主要结果。     

制备高比表面积碳化硅的几种影响因素

采用溶胶凝胶法，以蔗糖和正硅酸乙酯(TEOS)为原料，草酸为TEOS水解的催化剂，制备均相碳化硅前驱体，在氩气氛和高温条件下(1 350～1 600 ℃)将碳化硅先驱体进行碳热还原，制备出高比表面积的SiC。考察了水/TEOS物质的量的比、碳/硅物质的量的比及镍盐等因素对碳化硅比表面积的影响。结果表明，当n_water/n_TEOS=7.5，n_C/n_Si=4时，适宜的镍催化剂(n_Ni/n_TEOS=0.005)，凝胶形成的时间最短，镍盐的加入可使碳热还原温度降低200 ℃。