High asymmetric induction in diels-alder additions of cyclopentadiene to acrylates derived from isoborneol

Starting from (R)-(+)- and from (S)-(?)-camphor the chiral alcohols $\text{1}$, $\text{2}$ and $\text{3}$ have been prepared; their acrylates II underwent TiCl₂(OR)₂-promoted Diels-Alder additions to cyclopentadiene giving efficiently in a predictable manner either the (2R)- or the (2S)-adducts III with up to virtually quantitative asymmetric induction.     

Central limit theorem for the heat kernel measure on the unitary group

We prove that for a finite collection of real-valued functions f₁,…,fn on the group of complex numbers of modulus 1 which are derivable with Lipschitz continuous derivative, the distribution of under the properly scaled heat kernel measure at a given time on the unitary group U(N) has Gaussian fluctuations as N tends to infinity, with a covariance for which we give a formula and which is of order N−1. In the limit where the time tends to infinity, we prove that this covariance converges to that obtained by P. Diaconis and S.N. Evans in a previous work on uniformly distributed unitary matrices. Finally, we discuss some combinatorial aspects of our results.     

W01,1 solutions in some borderline cases of Calderon–Zygmund theory

In this paper we study the existence of $W_0^{1,1}(\Omega )$ distributional solutions of Dirichlet problems whose simplest example is$\{\begin{array}{cc}?\mathrm{div}\left({|\mathrm{?}u|}^{p?2}\mathrm{?}u\right)=f(x),\hfill & \text{in}\Omega ;\hfill \\ u=0,\hfill & \text{on}?\Omega .\hfill \end{array}$     

Evidential reasoning in large partially ordered sets

The Dempster-Shafer theory of belief functions has proved to be a powerful formalism for uncertain reasoning. However, belief functions on a finite frame of discernment Ω are usually defined in the power set 2^Ω, resulting in exponential complexity of the operations involved in this framework, such as combination rules. When Ω is linearly ordered, a usual trick is to work only with intervals, which drastically reduces the complexity of calculations. In this paper, we show that this trick can be extrapolated to frames endowed with an arbitrary lattice structure, not necessarily a linear order. This principle makes it possible to apply the Dempster-Shafer framework to very large frames such as the power set, the set of partitions, or the set of preorders of a finite set. Applications to multi-label classification, ensemble clustering and preference aggregation are demonstrated.     

LocalSolver 1.x: a black-box local-search solver for 0-1 programming

This paper introduces LocalSolver 1.x, a black-box local-search solver for general 0-1 programming. This software allows OR practitioners to focus on the modeling of the problem using a simple formalism, and then to defer its actual resolution to a solver based on efficient and reliable local-search techniques. Started in 2007, the goal of the LocalSolver project is to offer a model-and-run approach to combinatorial optimization problems which are out of reach of existing black-box tree-search solvers (integer or constraint programming). Having outlined the modeling formalism and the main technical features behind LocalSolver, its effectiveness is demonstrated through an extensive computational study. The version 1.1 of LocalSolver can be freely downloaded at and used for educational, research, or commercial purposes.     

Backscatter factor and absorption ratio of fibrous zirconia media in the visible

Fibrous thermal insulations are widely used to conserve energy in ambient to high temperature applications including buildings, solar collectors, heat exchangers, furnaces and thermal protection systems of reusable launch vehicles. It has long been recognised that zirconia has the lowest thermal conductivity of commercial refractories. The thermal conductivity of a zirconia fibrous medium is strongly dependent of its bulk density; high bulk densities of zirconia fibers provide the most effective insulation at high temperatures. Lee's theory for radiative transfer through fibrous media is used in this paper. The two-flux model is applied to determine the backward and forward parameters of a medium of zirconia fibers oriented in parallel planes. Theoretical calculations of the backscatter factor and absorption ratio of this medium are carried out in the visible spectrum for different size parameters of the fibers and for three different temperatures. Our results show that the backscatter factor of zirconia fibrous insulations is maximum, and therefore the heat transfer by the fibrous medium is the lowest, for a size parameter of 0.45 for all the temperatures studied. We also observed that the backscatter factor decreases with increasing temperature.     

How to Mask the Structure of Codes for a Cryptographic Use

In this paper we show how to strengthen public-key cryptosystems against known attacks, together with the reduction of the public-key. We use properties of subcodes to mask the structure of the codes used by the conceiver of the system. We propose new parameters for the cryptosystems and even a modified Niederreiter cryptosystem in the case of Gabidulin codes, with a public-key size of less than 4000 bits.Communicated by: P. WildAMS Classification: 11T71     

On the Convergence of Time Splitting Methods for Quantum Dynamics in the Semiclassical Regime

Foundations of Computational Mathematics - By using the pseudo-metric introduced in Golse and Paul (Arch Ration Mech Anal 223:57–94, 2017), which is an analogue of the Wasserstein distance of...