A Brownian Particle in a Microscopic Periodic Potential

We study a model for a massive test particle in a microscopic periodic potential and interacting with a reservoir of light particles. In the regime considered, the fluctuations in the test particle’s momentum resulting from collisions typically outweigh the shifts in momentum generated by the periodic force, so the force is effectively a perturbative contribution. The mathematical starting point is an idealized reduced dynamics for the test particle given by a linear Boltzmann equation. In the limit that the mass ratio of a single reservoir particle to the test particle tends to zero, we show that there is convergence to the Ornstein–Uhlenbeck process under the standard normalizations for the test particle variables. Our analysis is primarily directed towards bounding the perturbative effect of the periodic potential on the particle’s momentum.     

Multiplicity of positive solutions for a critical quasilinear elliptic system with concave and convex nonlinearities

In this paper, by using the Lusternik–Schnirelmann category, we obtain a multiplicity result for a quasilinear elliptic system with both concave and convex nonlinearities and critical growth terms in bounded domains.     

New eco-friendly animal bone meal catalysts for preparation of chalcones and aza-michael adducts

ABSTRACT: Two efficient reactions were successfully carried out using Animal Bone Meal (ABM) and potassium fluoride or sodium nitrate doped ABMs as new heterogeneous catalysts under very mild conditions. After preparation and characterization of the catalysts, we first report their use in a simple and convenient synthesis of various chalcones by Claisen-Schmidt condensation and then in an aza-Michael addition involving several synthesized chalcones with aromatic amines. All the reactions were carried out at room temperature in methanol; the chalcone synthesis was also achieved in water environment under microwave irradiation. Doping ABM enhances the rate and yield at each reaction. Catalytic activities are discussed and the ability to re-use the ABM is demonstrated. RESULTS: For Claisen-Schmidt the use of ABM alone, yields never exceeded 17%. In each entry, KF/ABM and NaNO3/ABM (79-97%) gave higher yields than using ABM alone under thermic condition. Also the reaction proceeded under microwave irradiation in good yields (72-94% for KF/ABM and 81-97% for NaNO3/ABM) and high purity. For aza-Michael addition the use of ABM doped with KF or NaNO3 increased the catalytic activity remarkably. The very high yields could be noted (84-95% for KF/ABM and 81-94% for NaNO3/ABM). CONCLUSION: The present method is an efficient and selective procedure for the synthesis of chalcones anaaza-Michael adducts. The ABM and doped ABMs are a new, inexpensive and attractive solid supports which can contribute to the development of catalytic processes and reduced environmental problems.     

Chemical Preparation,Thermal Behavior,Kinetic, and IR Studies of MnK4(P3O9)2.2H2O,Crystallographic Data of a New Cyclotriphosphate MnK4(P3O9)2, and Quantum Chemical Calculations for the P3O3− 9 Ion

Abstract

Chemical presparation, thermal behavior, and infrared (IR) studies are discussed for the cyclotriphosphate MnK₄(P₃O₉)₂.2H₂O and its anhydrous form MnK₄(P₃O₉)₂. The total dehydration of MnK₄(P₃O₉)₂.2H₂O, between 200 and 550 °C, leads to its anhydrous form MnK₄(P₃O₉)₂. MnK₄(P₃O₉)₂ is a new cyclotriphosphate crystallizing in the rhombohedral system and is stable until its melting point at 560 °C. The thermal behavior of MnK₄(P₃O₉)₂.2H₂O has been investigated and interpreted by comparison with IR absorption spectrometry and X-ray diffraction experiments. Two different methods, Ozawa and KAS (Kissinger-Akahira-Sunose), were selected in studying the kinetics of thermal behavior of the title compound. Quantum chemical calculations were made for the P₃O ^3? ₉ ion.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.

GRAPHICAL ABSTRACT     

Design,Synthesis and Structural Analysis of New Macrocycles Containing Dispiro-1,3-dioxane Units

The synthesis and the structure of new macrocycles containing semiflexible dispiro-1,3-dioxane units is reported. The structural analysis of the compounds is performed by high field NMR spectra, mass spectrometry investigations (MALDI, ESI-MS) and the solid state molecular structure obtained for two compounds by single crystal X-ray diffractometry. The dynamics of the macrocycles promoted by the flipping of the middle cyclohexane ring of the dispirane units is investigated using low temperature NMR experiments.

New macrocycles containing dispiro-1,3-dioxane units were investigated by NMR, X-ray diffractometry and mass spectrometry     

Synthesis,Photophysics and Nonlinear Optical Properties of Stilbenoid Pyrimidine‐Based Dyes Bearing Methylenepyran Donor Groups

The nonlinear properties and the photophysical behavior of two π‐conjugated chromophores that incorporate an electron‐deficient pyrimidine core (A) and γ‐methylenepyrans as terminal donor (D) groups have been thoroughly investigated. Both dipolar and quadrupolar branching strategies are explored and rationalized on the basis of the Frenkel exciton model. Even though a cooperative effect is clearly observed if the dimensionality is increased, the nonlinear optical (NLO) response of this series is moderate if one considers the nature of the D/A couple and the size of the chromophores (as measured by the number of π electrons). This effect was attributed to a disruption in the electronic conjugation within the dyes’ scaffold for which the geometry deviates from planarity owing to a noticeable twisting of the pyranylidene end‐groups. This latter structural parameter also has a strong influence on the excited‐state dynamics, which leads to a very efficient fluorescence quenching.     

Theoretical Design of Strong Neutral Radical–Boron Adducts: Trisubstituted Boranes as Potential Radical Scavengers

The conditions of formation of strong two‐center one‐electron bonds in neutral compounds are discussed. Both molecular orbital and valence bond analyses show that good candidates are adducts of radicals ^.AR₃ (A=C, Si, Ge) of low ionization energy (IE) with boranes BX₃ of high electron affinity (EA). This is confirmed by ab initio calculations. The bond energy of adducts of B(CF₃)₃ with various radicals ranges from 18 kcal mol^?1 for ^.CH₃ to approximately 40 kcal mol^?1 for Me₃Si^., and a clear correlation with IE–EA difference is found. This allows one to expect B(CF₃)₃, among other fluoroboranes, to be an efficient radical scavenger.     

Identification and functional characterization of a novel α-conotoxin (EIIA) from Conus ermineus

Nicotinic acetylcholine receptors (nAChRs) are one of the most important families in the ligand-gated ion channel superfamily due to their involvement in primordial brain functions and in several neurodegenerative pathologies. The discovery of new ligands which can bind with high affinity and selectivity to nAChR subtypes is of prime interest in order to study these receptors and to potentially discover new drugs for treating various pathologies. Predatory cone snails of the genus Conus hunt their prey using venoms containing a large number of small, highly structured peptides called conotoxins. Conotoxins are classified in different structural families and target a large panel of receptors and ion channels. Interestingly, nAChRs represent the only subgroup for which Conus has developed seven distinct families of conotoxins. Conus venoms have thus received much attention as they could represent a potential source of selective ligands of nAChR subtypes. We describe the mass spectrometric-based approaches which led to the discovery of a novel α-conotoxin targeting muscular nAChR from the venom of Conus ermineus. The presence of several posttranslational modifications complicated the N-terminal sequencing. To discriminate between the different possible sequences, analogs with variable N-terminus were synthesized and fragmented by MS/MS. Understanding the fragmentation pathways in the low m/z range appeared crucial to determine the right sequence. The biological activity of this novel α-conotoxin (α-EIIA) that belongs to the unusual α4/4 subfamily was determined by binding experiments. The results revealed not only its selectivity for the muscular nAChR, but also a clear discrimination between the two binding sites described for this receptor.