Isoperimetric Constants of Infinite Plane Graphs

   Abstract. Let G be an infinite locally finite plane graph with one end and let H be a finite plane subgraph of G . Denote by a(H) the number of finite faces of H and by l(H) the number of the edges of H that are on the boundary of the infinite face or a finite face not in H . Define the isoperimetric constant h (G) to be inf _H l(H) / a(H) and define the isoperimetric constant h (δ) to be inf _G h (G) where the infimum is taken over all infinite locally finite plane graphs G having minimum degree δ and exactly one end. We establish the following bounds on h (δ) for δ ≥ 7 :

The Probability Content of Cones in Isotropic Random Fields

This paper provides computable representations for the evaluation of the probability content of cones in isotropic random fields. A decomposition of quadratic forms in spherically symmetric random vectors is obtained and a representation of their moments is derived in terms of finite sums. These results are combined to obtain the distribution function of quadratic forms in spherically symmetric or central elliptically contoured random vectors. Some numerical examples involving the sample serial covariance are provided. Ratios of quadratic forms are also discussed.     

La densité de la loi-limite d'un processus en cascade expansif

Sans résumé     

Non-quasi-stationary state pyrolysis of ethane

An induction period has been observed in the pyrolysis of ethane in a continuous-flow stirred tank reactor at 530°C. The rate constants of the initiation, determining propagation and termination steps, have been determined.     

Inductive (direct) limits in the categories of heterogeneous algebras and of abstract automata

In our preceding paper [2], we have studied the fundamental properties of the heterogeneous algebras, and constructed the projective limits in the category of these algebras and in the category of abstract automata. The present article is devoted to the study ofdirect limits in the same categories.     

Anisotropy profiles of optical fibers and preforms

An experimental method to measure the optical anisotropy profiles of optical fibers and preforms is presented. The local values of n_z?n_r and n_z?n_?, (r,?,z) being a cylindrical coordinate system associated with the fiber or preform, are obtained.     

How to reduce the experimental time in isotopic 2H NMR using the ERETIC method

Deuterium site-specific natural isotope abundance (Ai) is routinely measured by NMR spectroscopy and quantified using an internal reference peak. This study demonstrates that the substitution of the chemical compound used as internal reference by an electronically generated signal (the ERETIC method) allows a dramatic reduction of the experimental time. Measurements of Ai on eight samples of methylsalicylate have been performed using either an internal reference (TMU) or ERETIC. No significant difference in accuracy or precision had been found between the two methods. However, because the method is applicable in partially saturated conditions, the experiment time was divided by a factor of 4 and the drawbacks associated with an internal chemical reference were avoided when ERETIC was used.