Stereo- and Regiochemical Effect of N,N-Dialkylamide Extractants on the Speciation of Pu Complexes

The relationship between extractant stereochemistry and their extraction performance has only poorly been established. In order to address a part of this concern, we investigated the Pu(IV) liquid-liquid extraction (LLE) by using the N,N-di-(2-ethylhexyl)butyramide (DEHBA), as well as those of its position isomers. DEHBA (ββ-isomer) and N-(2-ethylhexyl)-N-(oct-3-yl)butyramide (EHOBA or αβ-isomer) were synthesized as a mixture of stereoisomer or stereoenriched (R,S)- and (S,S)-diastereoisomers, and were all assessed for Pu^IV LLE. The results showed that both the position and the stereoisomerism of the aliphatic substituents affect Pu^IV complexation and extraction. We found that Pu extraction is lowered by factor 2 to 4 when the ethyl branching group is closer to the complexing site. UV-vis spectroscopy showed that this extraction decrease was affected by steric hindrance inducing a deprivation of Pu inner sphere complex. Effect of stereoisomerism is highlighted for branching closer to the complexing site (α-position). Enantiopure DEHBA stereoisomers provided similar Pu extraction, whereas a slight decrease could be noticed for the more cluttered stereoenriched (αβ)-isomers, which was also concomitant with a smaller population of inner sphere complex. In contrast, the stereoisomers mixture led to a strong decrease of Pu extraction because of an antagonistic association in the mixed complexes.     

Cycle-maximal triangle-free graphs

We conjecture that the balanced complete bipartite graph _{K⌊n/2⌋,⌈n/2⌉}$K_{\lfloor n/2\rfloor ,\lceil n/2\rceil }$ contains more cycles than any other n$n$-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small fixed graphs; and use the bounds to show that among regular graphs, the conjecture holds. We also consider graphs that are close to being regular, with the minimum and maximum degrees differing by at most a positive integer k$k$. For k=1$k=1$, we show that any such counterexamples have n≤91$n\le 91$ and are not homomorphic to _C5$C_5$; and for any fixed k$k$ there exists a finite upper bound on the number of vertices in a counterexample. Finally, we describe an algorithm for efficiently computing the matrix permanent (a #P$\#P$-complete problem in general) in a special case used by our bounds.     

Existence of strong minimizers for the Griffith static fracture model in dimension two

We consider the Griffith fracture model in two spatial dimensions, and prove existence of strong minimizers, with closed jump set and continuously differentiable deformation fields. One key ingredient, which is the object of the present paper, is a generalization to the vectorial situation of the decay estimate by De Giorgi, Carriero, and Leaci. This is based on replacing the coarea formula by a method to approximate $SB{D}^p$ functions with small jump set by Sobolev functions, and is restricted to two dimensions. The other two ingredients will appear in companion papers and consist respectively in regularity results for vectorial elliptic problems of the elasticity type and in a method to approximate in energy $GSB{D}^p$ functions by $SB{V}^p$ ones.     

Nilmanifolds with a calibrated G2-structure

We introduce obstructions to the existence of a calibrated G₂-structure on a Lie algebra g of dimension seven, not necessarily nilpotent. In particular, we prove that if there is a Lie algebra epimorphism from g to a six-dimensional Lie algebra h with kernel contained in the center of g, then h has a symplectic form. As a consequence, we obtain a classification of the nilpotent Lie algebras that admit a calibrated G₂-structure.     

Radial Solutions of¶Superlinear Equations on ℝN¶Part II: The Forced Case

We study the effect of a forcing term in the context of the search of multiple nodal solutions u∈h ¹(? ^N ) to a class of elliptic equations of type¶?Δu(x)=f(|x|,u(x))+h(|x|), x∈? ^N ,¶where f(|x|≡0 and f is superlinear but subcritical at infinity.     

Regularity of multivariate vector subdivision schemes

In this paper we discuss methods for investigating the convergence of multivariate vector subdivision schemes and the regularity of the associated limit functions. Specifically, we consider difference vector subdivision schemes whose restricted contractivity determines the convergence of the original scheme and describes the connection between the regularity of the limit functions of the difference subdivision scheme and the original subdivision scheme.     

Long‐range dependence and performance in telecom networks

Telecommunications systems have recently undergone significant innovations. These call for suitable statistical models that can properly describe the behaviour of the input traffic in a network. Here we use fractional Brownian motion (FBM) to model cumulative traffic network, thus taking into account the possible presence of long‐range dependence in the data. A Bayesian approach is devised in such a way that we are able to: (a) estimate the Hurst parameter H of the FBM; (b) estimate the overflow probability which is a parameter measuring the quality of service of a network: (c) develop a test for comparing the null hypothesis of long‐range dependence in the data versus the alternative of short‐range dependence. In order to achieve these inferential results, we elaborate an MCMC sampling scheme whose output enables us to obtain an approximation of the quantities of interest. An application to three real datasets, corresponding to three different levels of traffic, is finally considered. Copyright © 2004 John Wiley & Sons, Ltd.     

Concerning Order of Convergence for Subdivision

We discuss order of convergence for subdivision algorithms, in the scalar-valued and the vector-valued case. In order to find the generic order, the usual definition of convergence order is extended, refering to a proper quasi interpolant operator whose representation on polynomial spaces can be constructively determined with recourse to properties of the subdivision mask. Assuming stability and smoothness of the limit functions, the approximation order of the quasi interpolant operator determines the order of convergence of subdivision.