Displacement discontinuity method for modeling axisymmetric cracks in an elastic half-space

This paper describes a displacement discontinuity method for modeling axisymmetric cracks in an elastic half-space or full space. The formulation is based on hypersingular integral equations that relate displacement jumps and tractions along the crack. The integral kernels, which represent stress influence functions for ring dislocation dipoles, are derived from available axisymmetric dislocation solutions. The crack is discretized into constant-strength displacement discontinuity elements, where each element represents a slice of a cone. The influence integrals are evaluated using a combination of numerical integration and a recursive procedure that allows for explicit integration of hyper- and Cauchy singularities. The accuracy of the solution at the crack tip is ensured by adding corrective stresses across the tip element. The method is validated by a comparison with analytical and numerical reference solutions.     

Noise-induced outer synchronization between two different complex dynamical networks

In this paper, based on the theory of stochastic differential equations, we study the outer synchronization between two different complex dynamical networks with noise coupling. The theoretical result shows that two different complex networks can achieve generalized outer synchronization only with white-noise-based coupling. Numerical examples further verify the effectiveness and feasibility of the theoretical results. Numerical evidence shows that the synchronization rate is proportional to the noise intensity.     

Cellular covers of groups

In this paper we discuss the concept of cellular cover for groups, especially nilpotent and finite groups. A cellular cover is a group homomorphism c:G→M such that composition with c induces an isomorphism of sets between and . An interesting example is when G is the universal central extension of the perfect group M. This concept originates in algebraic topology and homological algebra, where it is related to the study of localizations of spaces and other objects. As explained below, it is closely related to the concept of cellular approximation of any group by a given fixed group. We are particularly interested in properties of M that are inherited by G, and in some cases by properties of the kernel of the map c.     

Multivariate Cramér-Rao inequality for prediction and efficient predictors

We derive and discuss a matricial Cramér-Rao type inequality for the quadratic prediction error matrix. A study of the attainment of the bound follows. Then we introduce an unbiased predictor for a bivariate Poisson process and prove that it is efficient, i.e. its quadratic error attains the Cramér-Rao bound.     

Intramolecular homolytic substitution at the sulfur atom: an alternative way to generate phosphorus- and sulfur-centered radicals

Two efficient procedures involving tin hydride or thiophenol-mediated intramolecular homolytic substitution at the sulfur atom are reported. They lead to the generation of varied P(V)-centered radicals from the corresponding aryl or alkyne thiophosphorus substrates. The radical formed can be trapped by an olefin via an intermolecular addition, leading to the construction of C-P bonds. Thiophosphination of triple bonds was also achieved using a radical cycloisomerization process. Extension of the methodology to sulfur-containing species was examined.     

A short and efficient synthesis of the NMDA glycine site antagonist: (3R,4R)-3-amino-1-hydroxy-4-methyl pyrrolidin-2-one (L-687,414)

A short and efficient synthesis of the NMDA glycine site antagonist: (3R,4R)-3-amino-1-hydroxy-4-methyl pyrrolidin-2-one (L-687,414) is described.     

Measures on double or resonant eigenvalues for linear Schrödinger operator

In this paper we consider linear Schrödinger operator with double or resonant eigenvalues. The main result is the bound of the measure (in a suitable space of functions) of the potentials leading to such double or resonant eigenvalues. Namely we present measure type estimates evaluating neighborhoods of the so-called double or resonant set.     

Induction period in the low‐temperature thermal oxidation of saturated hydrocarbons: Example of polyethylene

Thermal oxidation of hydrocarbon substrates at low‐to‐moderate temperature, typically T ≤ 150^°C, results from a radical chain process initiated by hydroperoxide decomposition and displays an induction period. A reliable model exists to simulate oxidation kinetics, but an incertitude remains on initial steps because they are out of reach of all available analytical methods. This work is aimed to have a kinetic approach of the problem, by comparing various mechanisms, i.e., (A) bimolecular decomposition of initially present hydroperoxides; (B) combined uni‐ and bimolecular decomposition of hydroperoxides; (C) the presence of radicals at the beginning of the exposure; and (D) radicals generation at (low) constant rate from irradiation, for instance by ionizing radiation linked to natural radioactivity or from a direct oxygen–substrate reaction. Scheme A is not realistic at low initial hydroperoxide concentrations. All the other mechanisms generate similar behaviors: the induction time tends toward a constant value almost independent of the nature of initial steps, when the concentration of precursors (initially present hydroperoxides or radicals) or the rate of their initial production (from species other than hydroperoxides) tends toward zero. © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 769–777, 2008