Multi-valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems

Multi-valued solutions are constructed for 2 × 2 first-order systems using a generalization of the hodograph transformation. The solution is found as a complex analytic function on a complex Riemann surface for which the branch points move as part of the solution. The branch point singularities are envelopes for the characteristics and thus move at the characteristic speeds. We perform an analysis of stability of these singularities with respect to perturbations of the initial data. The generic singularity types are folds, cusps, and nondegenerate umbilic points with non-zero 3-jet. An isolated singularity is generically a square root branch point corresponding to a fold. Two types of collisions between singularities are generic: At a “tangential” collision between two singularities moving at the same characteristic speed, a cube root branch point is formed, corresponding to a cusp. A “non-tangential” collision, between two square root branch points moving at different characteristic speeds, remains a square root branch point at the collision and corresponds to a nondegenerate umbilic point. These results are also valid for a diagonalizable n-th order system for which there are exactly two speeds. © 1993 John Wiley & Sons, Inc.     

Theoretical study on the hydrogen migration reactions in ground state vinyl fluoride: Basis set and correlation energy effects

We performed ab initio molecular orbital (MO) calculations using Hartree—Fock SCF, and second- and fourth-order Møller—Plesset perturbation theory for hydrogen migration reactions on the singlet vinyl fluoride potential energy surface. We used different basis sets and polarization functions to obtain the stationary point geometries and activation barriers. Basis set and the polarization function extension have small effects, while the correlation energy evaluation leads to new conclusions for one of the studied reactions: the product singlet CHCH₂F is not a true local minimum on the potential energy surface.     

Computational combinatorial ligand design: Application to human α-thrombin

Summary A new method is presented for computer-aided ligand design by combinatorial selection of fragments that bind favorably to a macromolecular target of known three-dimensional structure. Firstly, the multiple-copy simultaneous-search procedure (MCSS) is used to exhaustively search for optimal positions and orientations of functional groups on the surface of the macromolecule (enzyme or receptor fragment). The MCSS minima are then sorted according to an approximated binding free energy, whose solvation component is expressed as a sum of separate electrostatic and nonpolar contributions. The electrostatic solvation energy is calculated by the numerical solution of the linearized Poisson-Boltzmann equation, while the nonpolar contribution to the binding free energy is assumed to be proportional to the loss in solvent-accessible surface area. The program developed for computational combinatorial ligand design (CCLD) allows the fast and automatic generation of a multitude of highly diverse compounds, by connecting in a combinatorial fashion the functional groups in their minimized positions. The fragments are linked as two atoms may be either fused, or connected by a covalent bond or a small linker unit. To avoid the combinatorial explosion problem, pruning of the growing ligand is performed according to the average value of the approximated binding free energy of its fragments. The method is illustrated here by constructing candidate ligands for the active site of human -thrombin. The MCSS minima with favorable binding free energy reproduce the interaction patterns of known inhibitors. Starting from these fragments, CCLD generates a set of compounds that are closely related to high-affinity thrombin inhibitors. In addition, putative ligands with novel binding motifs are suggested. Probable implications of the MCSS-CCLD approach for the evolving scenario of drug discovery are discussed.     

Synthetic entries to 6-fluoro-7-substituted indole derivatives

Three practical synthetic entries of functionalized 6-fluoro-7-substituted indole derivatives were developed in connection with the preparation of 7-fluoro-8-substituted-1,3,4,9-tetrahydropyrano[3,4-b]indole-1-acetic acid derivatives 11 . The first route, which permits group modification about position 8 of the pyranoindole skeleton, employs 2-bromo-3-fluoroaniline ( 18 ) as a key intermediate, the preparation of which was achieved by either a novel ortho metalation of 15 or via the intermediacy of 22 . The second route utilizes 32 to append a terminally functionalized three carbon side chain onto the indole template and in addition leads to 43 from 40 . The third route to the 7-fluoro-8-substituted-pyranoindole skeleton complements route two in that the synthetic pathway exploits 32 in a nucleophilic fashion to construct a terminally functionalized two carbon appendage onto the indole nucleus.     

Hexasulfanyl analogues of cyclotriveratrylene

The synthesis of four 3,4-di(alkylsulfanyl)benzyl alcohol derivatives is described, in five steps from methyl 3,4-di(hydroxy)benzoate via a Newman–Kwart rearrangement. Incubation of these derivatives in formic acid affords 2,3,7,8,12,13-hexakis(alkylsulfanyl)-10,15-dihydro-5H-tribenzo[a,d,g]cyclononene products, which are hexa-sulfanyl analogues of the well-known supramolecular cavitand host, cyclotriveratrylene (CTV). The yield of this cyclization depends strongly on the alkylsulfanyl substituents present, in the order SMe > SEt ≈ SiPr ? SBn. A crystal structure determination of one of the cyclotrimers shows a mode of self-association that is commonly exhibited by CTV itself.     

Effect of Metal Ions in Organic Synthesis. part XVI. Knoevenagel Condensations of Aldehydes and Tosylhydrazones with 2,4-Pentanedione by Copper (II) Chloride-Catalyzed Reaction

Based on some of our previous findings on the activity of some metal ions in certain organic reactivities,¹ we have now studied the Knoevenagel condensations of aliphatic and aromatic aldehydes or their tosylhydrazone derivatives with 2,4-pentanedione. In the presence of catalytic amounts of anhydrous copper (II) chloride, these compounds react in tetrahydrofuran at room temperature, affording the corresponding alkylidene or arylidene compounds in 48–98% yields.     

Biosensors based on gold nanoelectrode ensembles and screen printed electrodes

Gold nanowires were synthesized within polycarbonate membranes according to an electroless deposition method, obtaining nanoelectrode ensembles (NEEs) with special electrochemical features. NEEs were coupled with home-produced carbon graphite screen printed electrodes and the electrochemical properties of the original nanoelectrode ensemble on screen printed substrate (NEE/SPS) assembly has been tested for sensors application. Glucose oxidase has been used as model enzyme in order to verify the feasibility of disposable gold NEE/SPS biosensors. Finally, different immobilisation and electrochemical deposition techniques based on either self assembled monolayers of cysteamine (CYS) or amino-propyl-triethoxysilane (APTES) and conductive polyaniline (PANI) molecular wires were used. Spatial patterning of the enzyme on the polycarbonate surface and of PANI wires on gold nanoelectrodes was obtained. Possible direct electron transfer between the enzyme and the PANI modified gold nanoelectrodes has been evaluated.     

Probenecid and benzamide: DSC applied to the study of an “impossible” pharmaceutical system

Journal of Thermal Analysis and Calorimetry - The study of the binary system probenecid–benzamide is an excellent example of the power and the limits of thermal analysis applied to the...     

The Physico-Chemical Properties of Glipizide: New Findings

The present work is a concrete example of how physico-chemical studies, if performed in depth, are crucial to understand the behavior of pharmaceutical solids and constitute a solid basis for the control of the reproducibility of the industrial batches. In particular, a deep study of the thermal behavior of glipizide, a hypoglycemic drug, was carried out with the aim of clarifying whether the recognition of its polymorphic forms can really be done on the basis of the endothermic peak that the literature studies attribute to the melting of the compound. A number of analytical techniques were used: thermal techniques (DSC, TGA), X-ray powder diffraction (XRPD), FT-IR spectroscopy and scanning electron microscopy (SEM). Great attention was paid to the experimental design and to the interpretation of the combined results obtained by all these techniques. We proved that the attribution of the endothermic peak shown by glipizide to its melting was actually wrong. The DSC peak is no doubt triggered by a decomposition process that involves gas evolution (cyclohexanamine and carbon dioxide) and formation of 5-methyl-N-[2-(4-sulphamoylphenyl) ethyl] pyrazine-2-carboxamide, which remains as decomposition residue. Thermal treatments properly designed and the combined use of DSC with FT-IR and XRPD led to identifying a new polymorphic form of 5-methyl-N-[2-(4-sulphamoylphenyl) ethyl] pyrazine-2-carboxamide, which is obtained by crystallization from the melt. Hence, our results put into evidence that the check of the polymorphic form of glipizide cannot be based on the temperature values of the DSC peak, since such a peak is due to a decomposition process whose Tonset value is strongly affected by the particle size. Kinetic studies of the decomposition process show the high stability of solid glipizide at room temperature.