Synthesis and characterization of twin mesogens containing siloxane units as central spacers

A mesogenic ester, 4-hexyloxyphenyl 4-vinyl benzoate was synthesized and studied. The synthesis and characterization of bimesogenic molecules employing this ester with oligosiloxane spacers of different lengths are described. The compounds were characterized by IR ¹H NMR, elemental and thermal analysis, and polarized light microscopy.     

Sufficiency conditions with minimal regularity assumptions

The aim of this article is to provide second-order sufficiency criteria that extend known ones in [6] and [7] to the case where the control candidate and some of the data are merely essentially bounded, and/or the control setU is any convex subset of ^m . In the classical setting, where a restriction on the velocity is imposed , it is shown that whenU is compact the known strengthened Weierstrass condition is equivalent to the Weierstrass condition with strict inequality.The research was supported by an NSERC Grant and by GNAFA of CNR, which are gratefully acknowledged.     

Homoanomeric effects in six-membered heterocycles

Structural and energetic consequences of homoanomeric n(X) --> beta-sigma(C-Y) interactions in saturated six-membered heterocycles where X = O, N, S, Se and Y = H, Cl were studied computationally using a combination of density functional theory (B3LYP) and Natural Bond Orbital (NBO) analysis. Unlike the classic anomeric effect where the interacting donor and acceptor orbitals are parallel and overlap sidewise in a pi-fashion, orbital interactions responsible for homoanomeric effects can follow different patterns imposed by the geometric restraints of the respective cyclic moieties. For the equatorial beta-C-Y bonds in oxa-, thia- and selena-cyclohexanes, only the homoanomeric n(X)(ax) --> sigma(C-Y)(eq) interaction (the Plough effect) with the axial lone pair of X is important, whereas the n(X)(eq) --> sigma(C-Y)(eq) interaction (the W-effect) is negligible. On the other hand, the W-effect is noticeably larger than the n(X)(ax) --> sigma(C-Y)(eq) interaction in azacyclohexanes. Hyperconjugation is a controlling factor which determines relative trends in the equatorial beta-C-H bonds in heterocycloxanes. In contrast, all homoanomeric interactions are weak for the respective axial bonds where relative lengths are determined by intramolecular electron transfer through exchange interactions and polarization-induced rehybridization. Although the homoanomeric effects are considerably weaker than the classic vicinal anomeric n(X)(ax)-->alpha-sigma(C-Y)(ax) interactions, their importance increases significantly when the acceptor ability of sigmaorbitals increases as a result of bond stretching and/or polarization. Depending on the number of electrons and the topology of interactions, homoconjugation interactions can be cooperative (enhance each other) or anticooperative (compete with each other). Such effects reflect symmetry of the wave function and can be considered as weak manifestations of sigma homoaromaticity or homoantiaromaticity.     

Biomimetic approach to communesin B (a.k.a. nomofungin)

The development of an approach to the alkaloid communesin B (2) is presented. The approach is based on considerations of a possible biosynthetic sequence involving an oxidative coupling of tryptamine with a derivative of the ergot alkaloid aurantioclavine. Structure revision is also suggested for the recently isolated microfilament disrupting alkaloid nomofungin.     

A modified Hamilton-Jacobi approach in the generalized problem of Bolza

We are concerned with developing sufficiency criteria for the generalized problem of Bolza, where the Hamiltonian is neither concave-convex nor differentiable. The core of the approach is the modified Hamilton-Jacobi inequality which leads to a new type of sufficient conditions. This latter is then used to derive new first order and known second order sufficient conditions.The publication of this report has been made possible due to a grant of the Fonds FCAC for the help and support of research.     

Triplet acetylenes as synthetic equivalents of 1,2-bicarbenes, part II: new supramolecular scaffolds from photochemical cycloaddition of diarylacetylenes to 1,4-cyclohexadienes

1,5-Diaryl substituted homoquadricyclanes which are readily available through cascade photocycloaddition of diarylacetylenes to 1,4-cyclohexadienes are useful supramolecular scaffolds with an angle of about 60 degrees formed by the two aromatic rings defining a hydrophobic cavity. These structural features of pyridinyl homoquadricyclanes were applied to the design of composite organic/inorganic materials with topologies depending on the ratio of ligand to metal. The crystal structure of complex 1 (L1/AgNO(3) in a 1:1 ratio) shows an alternating ligand-metal polymer in which each of the silver ions in its linear coordination geometry is shared between two L1 molecules. A small change in the crystallization method yields a supramolecular rhomboid (complex 2, L1/AgNO(3) 3:2 ratio) which has two ligands that occupy opposite corners of the rhomboid and two silver atoms occupy the other two corners. Connection of the rhomboids units through a third molecule forms unique "beads on a string" polymeric chains. In complex 2, the silver ions adopt a distorted tetrahedral geometry with the nitrate anion occupying one of the vertices of the tetrahedron. The crystal packing of the chain of rhomboids generates cavities which are filled with disordered solvent molecules. Non-symmetrical homoquadricyclane L3 coordinates with silver only through the nitrogen of the pyridine ring but not through the nitrogen of the tetrafluoropyridine ring in which the electron density of the nitrogen lone-pair is very low. The substituents on the polycyclic moiety of the homoquadricyclane cause restricted rotation of the pyridine rings which suggests that the flexibility of such systems can be fine-tuned to create a family of supramolecular scaffolds of controlled rigidity.     

The Riemann problem for a hyperbolic model of two-phase flow in conservative form

This article is to continue the present author's work (International Journal of Computational Fluid Dynamics (2009) 23 (9), 623–641) on studying the structure of solutions of the Riemann problem for a system of three conservation laws governing two-phase flows. While existing solutions are limited and found quite recently for the Baer and Nunziato equations, this article presents the first instance of an exact solution of the Riemann problem for two-phase flow in gas–liquid mixture. To demonstrate the structure of the solution, we use a hyperbolic conservative model with mechanical equilibrium and without velocity equilibrium. The Riemann problem solution for the model equations comprises a set of elementary waves, rarefaction and discontinuous waves of various types. In particular, such a solution treats both the wave structure and the intermediate states of the two-phase gas–liquid mixture. The resulting exact Riemann solver is fully non-linear, direct and complete. On this basis then, we use locally the exact Riemann solver for the two-phase flow in gas–liquid mixture within the framework of finite volume upwind Godunov methods. In order to demonstrate the effectiveness and accuracy of the proposed solver, we consider a series of test problems selected from the open literature and compare the exact and numerical results by using upwind Godunov methods, showing excellent oscillation-free results in two-phase fluid flow problems.     

Nonlinear friction dynamics on fibrous materials,application to the characterization of surface quality. Part I: global characterization of phase spaces

The diversity and the complexity of fibrous materials (woven fabrics, nonwovens or knitted fabrics) make the control of surface qualities very difficult. The control and the comprehension of the tribological phenomena generated by a dynamic friction are of major importance. Whereas the traditional investigations such as measurements of average parameters like roughness or friction coefficient quickly find their limits on such deformable, heterogeneous and flexible fibrous surfaces with very heterogeneous relief, this series of two publications proposes a new manner of observing the interactions of friction. Our laboratory has developed a patented method of measurements, called MODALSENS, which aims at rubbing a very fine and flexible blade on the analyzed surface. Dynamic friction with the contact generates nonlinear vibrations, and the response of the sensor is analyzed in its phase space using the tools of nonlinear analysis of time series. Then, when the evaluated surfaces change, this first part endeavors to characterize the portraits of phases related to the nonlinear vibrations of MODALSENS in a global way, by quantifying its invariants such as dimensions, Shannon entropies, diameters of attractors and largest Lyapunov exponents. From this first part, a classification of studied fibrous surfaces is built and is expected to give rise to new estimators for the surface quality analysis of fibrous media.     

Cooperative catalysis by silica-supported organic functional groups

Hybrid inorganic-organic materials comprising organic functional groups tethered from silica surfaces are versatile, heterogeneous catalysts. Recent advances have led to the preparation of silica materials containing multiple, different functional groups that can show cooperative catalysis; that is, these functional groups can act together to provide catalytic activity and selectivity superior to what can be obtained from either monofunctional materials or homogeneous catalysts. This tutorial review discusses cooperative catalysis of silica-based catalytic materials, focusing on the cooperative action of acid-base, acid-thiol, amine-urea, and imidazole-alcohol-carboxylate groups. Particular attention is given to the effect of the spatial arrangement of these organic groups and recent developments in the spatial organization of multiple groups on the silica surface.