Quantum Transport in Crystals: Effective Mass Theorem and K·P Hamiltonians

In this paper the effective mass approximation and the k·p multi-band models, describing quantum evolution of electrons in a crystal lattice, are discussed. Electrons are assumed to move in both a periodic potential and a macroscopic one. The typical period e{\epsilon} of the periodic potential is assumed to be very small, while the macroscopic potential acts on a much bigger length scale. Such homogenization asymptotic is investigated by using the envelope-function decomposition of the electron wave function. If the external potential is smooth enough, the k·p and effective mass models, well known in solid-state physics, are proved to be close (in the strong sense) to the exact dynamics. Moreover, the position density of the electrons is proved to converge weakly to its effective mass approximation.     

Asymmetric Cycloaddition: An Efficient Synthesis of Enantiopure Isoxazolines Substituted with Carbohydrate Analogues

A simple and convenient method for the synthesis of heterocycles substituted with carbohydrate analogs is described. The chiral optically pure five‐membered glycoconjugates containing the isoxazoline unit were obtained by an aromatic nitrile oxides cycloaddition with 1‐phenyl‐1,2‐dihydro‐pyridazine‐3,6‐dionyl N‐glycoside derivatives.     

Time averaging for the strongly confined nonlinear Schrödinger equation, using almost-periodicity

We study the limiting behavior of a nonlinear Schrödinger equation describing a 3-dimensional gas that is strongly confined along the vertical, z direction. The confinement induces fast oscillations in time, that need to be averaged out. Since the Hamiltonian in the z direction is merely assumed confining, without any further specification, the associated spectrum is discrete but arbitrary, and the fast oscillations induced by the nonlinear equation entail countably many frequencies that are arbitrarily distributed. For that reason, averaging cannot rely on small denominator estimates or like.To overcome these difficulties, we prove that the fast oscillations are almost-periodic in time, with values in a Sobolev-like space that we completely identify. We then exploit the existence of long-time averages for almost-periodic functions to perform the necessary averaging procedure in our nonlinear problem.     

A mathematical model for the transient evolution of a resonant tunneling diodeModélisation d'une diode à effet tunnel résonant en régime transitoire

A mathematical model of quantum transient transport is derived and analyzed. The model describes the evolution of electrons injected into the “device” by reservoirs having a stationary statistics. The electrostatic potential in the device is modified by electron presence through electrostatic interaction. The wave functions are computed in the device region and satisfy non homogeneous open boundary conditions at the device edges. A priori estimates are deduced from the “dissipative properies” of the boundary conditions and from the repulsive character of the electrostatic interaction. To cite this article: N. Ben Abdallah, O. Pinaud, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 283–288.     

Chemo- and Regioselective 1,3-Dipolar Cycloaddition of 2-Diazopropane over 1,4-Benzoquinone: Synthesis of New Pyrazoloquinones

Abstract

1,3-Dipolar cycloaddition reaction of 2-diazopropane 1 with 1,4-benzoquinone 2 carried out at ?20 °C led to a minor mono-cycloadduct 4 and mixture of bis-cycloadducts 6 and 7. The same addition realized with 3H-pyrazole 7 at ?60 °C for 2 h yields a mixture of compounds 8 and 9 and results in O-alkylation. The reaction of 3H-pyrazoles 4 and 7 with dimethylsulfoxide and oxalyl chloride under Swern conditions led to pyrazolenines 11 and 12.     

Synthesis of New Spirocyclopropane and Oxadiazole Products

In explorations of synthesis and chemistry of spiroheterocycles, we found that the reaction of 2‐diazopropane with arylidene‐benzofuran‐2(3H)‐one and arylidene‐benzofuran‐3(2H)‐one derivatives generated the spirocyclopropane products. In addition to the expected cycloadducts, an unexpected oxadiazole was formed in some cases. The structures of the obtained adducts have been assigned by means of spectroscopic methods.     

1,3-dipolar cycloadditions of arylnitrile oxides and 2-diazopropane with 5-hydroxy-3-methyl-1,5-dihydropyrrol-2-one derivatives

The reactions of arylnitrile oxides 2 and 2-diazopropane 5 with 5-hydroxy-3-methyl-1,5-dihydropyrrol-2-one derivatives 1 have been studied. 1,3-dipolar cycloaddition of arylnitrile oxides and 2-diazopropane with 5-hydroxy-3-methyl-1,5-dihydropyrrol-2-one derivatives is taking place regiospecifically. The asymmetric induction expected by the chiral centre of the 5-hydroxy-3-methyl-1,5-dihydropyrrol-2-one derivatives was very effective, diastereoisomers 3 and 4 were formed in an approximate 90:10 ratio. The stereoselectivity of the 1,3-dipolar cycloaddition of the 2-diazopropane with the 5-hydroxy-3-methyl-1,5-dihydropyrrol-2-one derivatives are investigated. The attack of the 1,3-dipole occurred from the less hindered face of the dipolarophile, giving the isomer 6.     

A rewarding-punishing coordination mechanism based on Trust in a divergent supply chain

Coordination of decentralized supply chains using contract design is a problem that has been widely addressed in the literature. We consider a divergent supply chain including a supplier and several retailers producing fashion products with short sale seasons. The retailers cooperate with the supplier as sales agents; i.e., they work in the framework of revenue sharing contracts. Because of their proximity to the market, retailers can provide more accurate demand forecasts to the supplier that is used to decide on issues such as capacity building and market prices with regard to retailers stiff due dates, different lead times and different price-dependent demand functions. To ensure abundant supply and cope with the demand variability, the retailers have an incentive to exaggerate their private forecast information. In this study, we propose a new rewarding-punishing coordination mechanism based on trust between supply chain tiers, considered as a differentiation factor between honest and deceptive partners. An optimization model is developed as a building block of this mechanism. An approximation method is used to simplify and solve the problem. The model is then implemented using Monte-Carlo simulation in four different situations, according to 10 different strategies for forecast information sharing. The findings from the tests show that the mechanism including trust as a decisional factor performs better than ‘No Trust’ mechanism in all situations. These results suggest that taking into account Trust in designing coordination mechanism may have significant influence on the financial performance of the supply chain.     

Recent Advances on Electrochemical Sensors Based on Electroactive Bacterial Systems for Toxicant Monitoring: A Minireview

In recent years, there have been advancements in the development of bacterial electrochemical sensors for toxicity monitoring, especially through utilization of electroactive bacteria. Accordingly, this mini review summarizes the recent advances in the design of bacterial-based electrochemical sensors with a specific discussion of main methodologies used for preparation of bioelectrodes based on electroactive bacteria. Additionally, current trends in the design of efficient and high performing bacterial electrochemical sensors for toxicity monitoring are presented. An overview of the most relevant findings and challenges of this technology for practical are provided and might serve as a general outlook for planning further research.     

Synthesis and reactivity of N-sugar-maleimides: an access to novel highly substituted enantiopure pyrazolines

Two diastereomeric isoxazolines were synthesized in a stereoselective manner with 6.64–20.36% diastereoisomeric excess. The cycloaddition of N-sugar-maleimide in the presence of MgBr₂ afforded isoxazolines with high diasterioselectivities (76–84% de). The 1,3-dipolar cycloaddition reaction was diastereospecific and enantiomerically pure (3R,4S,5S,6S,3aR,6aS)-pyrazolines were obtained from N-sugar-maleimides via 1,3-proton migration.