An analysis of over-relaxation in a kinetic approximation of systems of conservation laws

The over-relaxation approach is an alternative to the Jin–Xin relaxation method in order to apply the equilibrium source term in a more precise way. This is also a key ingredient of the lattice Boltzmann method for achieving second-order accuracy. In this work, we provide an analysis of the over-relaxation kinetic scheme. We compute its equivalent equation, which is particularly useful for devising stable boundary conditions for the hidden kinetic variables.     

A brittle material with tunable elasticity: Crêpe paper

We study the mechanical response, and tearing features of crêpe paper, a two-dimensional, very anisotropic material, with one direction much less stiff than the other one. Depending on how the soft direction has been pre-stretched or not, the apparent Young modulus of the material can be varied over a broad range, while its fracture energy remains unaltered. The classical tearing concertina problem shows that a macroscopic measurement (the shape of the teared region) provides a direct access to the fracture properties of the material (effective Young's modulus, and fracture energy). The overall discussion is conducted in the frame of Griffith's theory of fracture.     

Reactivity of B‐Xanthyl N‐Heterocyclic Carbene‐Boranes

The synthesis and reactivity of mono‐ and bis‐S‐xanthyl NHC‐boranes is reported. The new NHC‐boranes are prepared through nucleophilic exchange at boron from either mono‐ or bis‐triflyl NHC‐boranes, themselves obtained by protolysis of the NHC‐BH₃ starting compounds. The B?H bond of the S‐xanthyl NHC‐boranes can be cleaved both homolytically and heterolytically, albeit the latter is more synthetically useful. The S‐xanthyl NHC‐boranes can reduce both aldehydes and imines. The B?S bond can also be cleaved homolytically. Under UV irradiation, the S‐xanthyl NHC‐boranes generate NHC‐boryl radicals that can initiate radical polymerizations of acrylates.     

Environmentally Compatible Access to α-Trifluoromethylseleno-Enones

α-Trifluoromethylselenolated enones constitute valuable building-blocks for further synthesis of innovative fluorinated compounds. Herein, we described an easy access to such compounds in green conditions through a Morita-Baylis-Hillman like reaction. These conditions have also been extended to higher fluorinated homologs.     

The conformational search,the stability,fragment interaction and resistance to acidic attack of epoxyl-polyurethanes in different solvent media

Structural Chemistry - Natural-based polyols are seen by polyurethane industries as an alternative to the petroleum-based polyols because of increasing challenges due to the oil crisis and global...     

Multidimensional Scaling With Very Large Datasets

Multidimensional scaling has a wide range of applications when observations are not continuous but it is possible to define a distance (or dissimilarity) among them. However, standard implementations are limited when analyzing very large datasets because they rely on eigendecomposition of the full distance matrix and require very long computing times and large quantities of memory. Here, a new approach is developed based on projection of the observations in a space defined by a subset of the full dataset. The method is easily implemented. A simulation study showed that its performance are satisfactory in different situations and can be run in a short time when the standard method takes a very long time or cannot be run because of memory requirements.     

Constructive Approximation in de Branges–Rovnyak Spaces

In most classical holomorphic function spaces on the unit disk in which the polynomials are dense, a function f can be approximated in norm by its dilates \(f_r(z):=f(rz)~(r<1)\). We show that this is not the case for the de Branges–Rovnyak spaces \(\mathcal{H}(b)\). More precisely, we exhibit a space \(\mathcal{H}(b)\) in which the polynomials are dense and a function \(f\in \mathcal{H}(b)\) such that \(\lim _{r\rightarrow 1^-}\Vert f_r\Vert _{\mathcal{H}(b)}=\infty \). On the positive side, we prove the following approximation theorem for Toeplitz operators on general de Branges–Rovnyak spaces \(\mathcal{H}(b)\). If \((h_n)\) is a sequence in \(H^\infty \) such that \(\Vert h_n\Vert _{H^\infty }\le 1\) and \(h_n(0)\rightarrow 1\), then \(\Vert T_{\overline{h}_n}f-f\Vert _{\mathcal{H}(b)}\rightarrow 0\) for all \(f\in \mathcal{H}(b)\). Using this result, we give the first constructive proof that, if b is a nonextreme point of the unit ball of \(H^\infty \), then the polynomials are dense in \(\mathcal{H}(b)\).     

Controlled Markov processes on the infinite planning horizon: Weighted and overtaking cost criteria

Stochastic control problems for controlled Markov processes models with an infinite planning horizon are considered, under some non-standard cost criteria. The classical discounted and average cost criteria can be viewed as complementary, in the sense that the former captures the short-time and the latter the long-time performance of the system. Thus, we study a cost criterion obtained as weighted combinations of these criteria, extending to a general state and control space framework several recent results by Feinberg and Shwartz, and by Krass et al. In addition, a functional characterization is given for overtaking optimal policies, for problems with countable state spaces and compact control spaces; our approach is based on qualitative properties of the optimality equation for problems with an average cost criterion.Research partially supported by the Engineering Foundation under grant RI-A-93-10, in part by the National Science Foundation under grant NSF-INT 9201430, and in part by a grant from the AT&T Foundation.Research partially supported by the Air Force Office of Scientific Research under Grant F49620-92-J-0045, and in part by the National Science Foundation under Grant CDR-8803012.     

Separating Market Efficiency from Profitability and its Implications for Planning

This paper discusses the practical usefulness of separating market efficiency from profitability when assessing the comparative performance of private sector organizational units. The market efficiency of a unit reflects its ability to attract custom. The paper shows how data envelopment analysis can be used to assess market efficiency and it illustrates the usefulness of this measure in managing the public houses of a brewery.     

Design Adaptive Nearest Neighbor Regression Estimation

This paper deals with nonparametric regression estimation under arbitrary sampling with an unknown distribution. The effect of the distribution of the design, which is a nuisance parameter, can be eliminated by conditioning. An upper bound for the conditional mean squared error of k−NN estimates leads us to consider an optimal number of neighbors, which is a random function of the sampling. The corresponding estimate can be used for nonasymptotic inference and is also consistent under a minimal recurrence condition. Some deterministic equivalents are found for the random rate of convergence of this optimal estimate, for deterministic and random designs with vanishing or diverging densities. The proposed estimate is rate optimal for standard designs.