On Legendre curves in contact 3-manifolds

It is first observed that on a 3-dimensional Sasakian manifold the torsion of a Legendre curve is identically equal to +1. It is then shown that, conversely, if a curve on a Sasakian 3-manifold has constant torsion +1 and satisfies the initial conditions at one point for a Legendre curve, it is a Legendre curve. Furthermore, among contact metric structures, this property is characteristic of Sasakian metrics. For the standard contact structure onR ³ with its standard Sasakian metric the curvature of a Legendre curve is shown to be twice the curvature of its projection to thexy-plane with respect to the Euclidean metric. Thus this metric onR ³ is more natural for the study of Legendre curves than the Euclidean metric.This work was done while the first author was a visiting scholar at Michigan State University.     

Optimal Lot-sizing and Machining Economics

This paper presents a queueing model with the service station subject to breakdown while it is busy, in order to determine analytically the optimal batch size in a machining economics problem. It is shown that departures from the optimal batch size result in moderate waiting-time increases when the batch size is scaled up and in significant waiting-time increases when the batch size is scaled down. It is also shown, through the use of a simulation model with normally distributed tool lives, that the analytical results obtained with exponentially distributed tool lives are quite robust. In the multiple-item case, simulation results show that the time in the system for each item and the average time in the system across all items behave exactly like the time in the system in the single-item case.     

Development of an optimised, standard-compliant procedure to calculate sound transmission loss: design of transmission rooms

A numerical procedure to estimate the transmission loss of sound insulating structures is proposed based upon the technology of acoustic measurements and standards. A virtual laboratory (VL), namely, a numerical representation of a real laboratory consisting of two reverberation rooms meeting certain sound field quality criteria is designed. VL is to be used for the numerical simulation of standardised measurements under predefined, controlled, acoustic conditions. In this paper, the design and optimisation of VL is investigated. The geometry of the transmission rooms is designed following first principles, in order for diffuse field conditions and sufficiently smooth primary mode distribution in the low frequency to be achieved. A finite element-based optimisation procedure, introduced by the author in previous work, is extended to arbitrarily shaped rooms. It is used to predict the appropriate local geometric modifications so as for improved mode distribution and smoother sound pressure fluctuations of the transmission rooms in the low-frequency range to be achieved and low-frequency measurement reproducibility and accuracy to be increased. Steady-state acoustic response analysis is performed in order to quantify the acoustic field quality of the virtual transmission rooms in the frequency range of measurements. A method to calculate the total absorption, A, of the receiving room is introduced by simulation of the reverberation time measurement procedure using Transient acoustic response analysis. The acoustic performance of VL is overall considered and is shown to meet in a sufficient degree, relative laboratory measurement standards in the frequency range of 100÷704 Hz.     

Rheological behavior of concentrated suspensions as affected by the dynamics of the mixing process

The rheological characterizations of concentrated suspensions are generally carried out assuming “well-mixed” suspensions. However, the variation of the concentration distributions of the ingredients of the formulation, i.e., the “goodness of mixing”, the size and shape distributions of the particle clusters and the rheological behavior of the suspension all depend on the thermo-mechanical history that the suspension is exposed to during the mixing process. Here, various experimental tools are used for the characterization of the degree of mixedness (concentration distributions) of various ingredients along with the characterization of rheological material functions, wall slip behavior and the maximum packing fraction of a graphite/elastomer suspension. The degree of mixedness values of the ingredients of the suspensions processed using batch and continuous processes and under differing operating conditions were characterized quantitatively using wide-angle X-ray diffraction and thermo gravimetric analysis and were elucidated under the light of the electrical properties of the suspension as affected by the mixing process. Upon achieving better homogeneity of the graphite particles and the binder and decreases in the size and breadth of the size distributions of particle clusters (as inferred from electrical measurements and maximum packing fraction values), the elasticity (storage modulus) and the shear viscosity (magnitude of the complex viscosity from small-amplitude oscillatory shear and shear viscosity from steady torsional and capillary rheometry) of the suspension decreased significantly and the wall slip velocity values increased. These findings demonstrate the intimate relationships that exist between the rheological behavior of concentrated suspensions and the thermo-mechanical history that they are exposed to during the processing stage and suggest that the preparation conditions for suspensions should be carefully selected and well documented to achieve reproducible characterization of rheological material functions.     

Interfacial impregnation chemistry in the synthesis of nickel catalysts supported on titania

The interfacial chemistry of the impregnation step involved in the preparation of nickel catalysts supported on titania is presented. Several methodologies based on deposition data, pH measurements, potentiometric mass titrations, and microelectrophoresis have been used in conjunction with diffuse reflectance UV/Vis/NIR spectroscopy, simulations, and semiempirical quantum chemical calculations. Three mononuclear inner-sphere complexes were formed at the compact layer of the "titania/electrolyte solution" interface: A monosubstituted, dihydrolyzed complex above a terminal oxo group, a disubstituted, dihydrolyzed complex above two terminal adjacent oxo groups, and a disubstituted, nonhydrolyzed complex above one terminal and one bridging adjacent oxo groups. The monosubstituted, dihydrolyzed complex predominates. The contribution of the disubstituted configurations is also important at very low Ni(II) surface concentration, but it decreases as the Ni(II) surface concentration increases. In addition, bi- and trinuclear inner-sphere complexes were formed. The receptor site involves one bridging and two terminal oxo groups in the first case and two bridging and three terminal oxo groups in the second case. The relative surface concentrations of these configurations increase initially with Ni(II) surface concentration and then remain practically constant. The understanding of these interfacial processes at a molecular level is very important to shift the catalytic synthesis from an art to a science as well as to obtain strict control of the impregnation step and, to some extent, of the whole preparative sequence. This study is very relevant to the synthesis of submonolayer/monolayer nickel catalysts supported on TiO(2) following equilibrium deposition filtration (otherwise called equilibrium adsorption).     

Technetium dichloride: a new binary halide containing metal-metal multiple bonds

Technetium dichloride has been discovered. It was synthesized from the elements and characterized by several physical techniques, including single crystal X-ray diffraction. In the solid state, technetium dichloride exhibits a new structure type consisting of infinite chains of face sharing [Tc(2)Cl(8)] rectangular prisms that are packed in a commensurate supercell. The metal-metal separation in the prisms is 2.127(2) ?, a distance consistent with the presence of a Tc≡Tc triple bond that is also supported by electronic structure calculations.     

Ruthenium-catalyzed selective hydrogenation of bis-arylidene tetramic acids. Application to the synthesis of novel structurally diverse pyrrolidine-2,4-diones

Catalytic hydrogenation of 3,5-bis-arylidenetetramic acids, known for their biological activity, has been developed. The chemoselective ruthenium-catalyzed reduction of the exocyclic carbon-carbon double bonds on pyrrolidine-2,4-dione ring system, containing other reducible functions, has been investigated. Depending on the substrate the yield of the hydrogenation process can reach up to 95%. The structural elucidation has been established using NMR and HRMS spectral data.     

Synthesis of novel PPARα/γ dual agonists as potential drugs for the treatment of the metabolic syndrome and diabetes type II designed using a new de novo design program PROTOBUILD

Peroxisome proliferator activated receptors (PPARs) have been shown to have critical roles in fatty acid oxidation, triglyceride synthesis, and lipid metabolism - making them an important target in drug discovery. Here we describe the in silico design, synthesis and in vitro characterisation of a novel series of 2,5-disubstituted indoles as PPARα/γ dual agonists. PPAR activation assays are performed with known agonists diazabenzene (WY14.643), aminopyridine (BRL49653) and bisaryl (L165.041), as positive controls. All the indole compounds synthesized are found to be active PPARα and PPARγ agonists, with particular efficacy from those with 2-naphthylmethyl substitution. This is a useful demonstration of a new de novo design methodology implemented by the protobuild program and its ability to rapidly produce novel modulators for a well characterized drug target.     

Palladium catalyzed C-C coupling reactions of 3,5-dichloro-4H-1,2,6-thiadiazin-4-one

Palladium catalyzed Suzuki-Miyaura, Stille, and Sonogashira coupling reactions are reported for the electron-deficient heterocyclic scaffold 3,5-dichloro-4H-1,2,6-thiadiazin-4-one (1). Furthermore, 3,5-di(thien-2-yl)-4H-1,2,6-thiadiazin-4-one (7m) is further elaborated to afford the tetrathienyl 3,5-bis[(2,2'-bithien)-5-yl]-4H-1,2,6-thiadiazin-4-one (9). All compounds are fully characterized.     

Crystal structures, EPR and magnetic properties of 2-ClC6H4CNSSN˙ and 2,5-Cl2C6H3CNSSN˙

The β-sheet structure associated with chlorinated aromatics (d(Cl···Cl)≈ 4.0 ?) has been implemented to drive formation of π-stacked structures of dithiadiazolyl radicals. Both title compounds exhibit an increase in paramagnetism above 150 K but solid-state EPR studies indicate that the origin of the paramagnetism in these two systems is different.