Numerical method for a model of inhomogeneous muscle fibers

The numerical solution of a nonlinear and nonlocal system of integro-differential equations that models the contraction of a single heterogeneous muscle fiber is studied. The method proposed is a form of the finite difference method of characteristics. Optimal error bounds are established for the resulting approximation. © 1993 John Wiley & Sons, Inc.     

Fluoride effect on the palladium–phenanthroline catalyzed carbonylation of nitroarenes to carbamates

Fluorides promote the palladium–phenanthroline catalyzed carbonylation of nitroarenes to carbamates. The effect is more evident on the rate of the reaction at short reaction times, but a positive effect on selectivity is also observed under certain conditions. The effect is observed even under conditions under which chloride inhibits the reaction. Tetraethylammonium is a better countercation than sodium. Copyright © 2007 John Wiley & Sons, Ltd.     

ON THE INADEQUACY OF THE RELATIONAL SEMANTIC FOR THE “UNTIL” OPERATOR

Modal logics with the binary operator Until are considered. It is shown that there exists a continuum of consistent U-logics without Kripke frames, and that each U-logic whose class of order does not have the finite frame property.     

Reaction kinetics and pathway of hydrothermal decomposition of aspartic acid

The kinetics and pathway of hydrothermal decomposition of aspartic acid were studied using a continuous‐flow tubular reactor. The reaction was carried out in the temperature range of 200–260°C and at a pressure of 20 MPa. Deamination was the primary reaction, indicated by the presence of significant amount of ammonia, fumaric acid, or maleic acid in the products. Other reaction products were pyruvic acid, malic acid, and traces of succinic and lactic acid. Traces of alanine were also detected, showing the possibility of decomposing high‐molecular weight amino acids to obtain simple amino acids such as glycine or alanine. Results on the effect of reaction parameters demonstrated that decomposition of aspartic acid is highly temperature dependent under hydrothermal conditions. For a slight temperature difference of 60°C (from 200 to 260°C), the first‐order reaction rate constants of 0.003 significantly increased to 0.231 s^?1. The activation energy was 144 kJ/mol, as calculated by the Arrhenius equation. No significant effect was exhibited by other reaction parameters such as pH and pressure. The results are useful in controlling the hydrolysis of proteinaceous materials toward high yield of aspartic acid under hydrothermal conditions. © 2007 Wiley Periodicals, Inc. 39: 175–180, 2007     

Crystal and molecular structure of thiamine monochloride

The crystal and molecular structure of thiamine monochloride (C₁₂H₁₇N₄OSCl) was determined by X-ray diffraction and refined to a finalR value of 0.042. The compound crystallizes in the monoclinic system, space groupP2₁/a, with cell constantsa=18.929(4),b=11.663(2),c=6.376(2) Å and=96.72(8)°. The thiamine molecule is anhydrous and unprotonated, and the torsion angles at the methylene carbon show that it possesses anF conformation. The dihedral angle value of 84.16(6)° between thiazolium and pyrimidine rings is in the normal range found for the thiamine withF conformation, protonated or not, hydrated or not. Thiamine therefore has the same conformation notwithstanding protonation or hydration, with the rings similarly oriented in all the crystal structures containing thiamine.     

Reduction of cyclohexanone 2-nitrophenylhydrazone. Formation of cyclohexane-3-spiro-3,4-dihydro-1,2,4-benzotriazine

The structure of compound C₁₂H₁₅N₃, obtained by Perkin and Riley in 1923, through the reduction of cyclohexanone 2-nitrophenylhydrazone, was reexamined. This compound, considered originally as 3,4-cyclotetramethylene-4,5-dihydro-1,2,5-benzotriazepine (I) and later as 2-aminophenylazocyclohexene (II), is now defined through the nmr spectrum and chemical behaviour as cyclohexane-3-spiro-3,4-dihydro-1,2,4-benzotriazine (V). It is formed by spontaneous oxidation of the cyclic form of cyclohexanone 2-aminophenylhydrazone (namely, cyclohexane-3-spiro-1,2,3,4-tetrahydro-1,2,4-benzotriazine) obtained through amino group addition on the hydrazone double bond.     

Intercalation of α,ω-alkyldiamines in layered α-zirconium phosphate and the inclusion behaviour of some of the intercalates obtained

The paper reports a study on the intercalation mechanism of NH₂(CH₂) _n NH₂ (withn=2, 4, 6, 8, 10) diamines in layered Zr(HOPO₃)₂·H₂O, performed by titrating the host with aqueous solutions of amines at 80°C. The intercalation reactions occur stepwise according to the ‘moving boundary’ model, with the formation of a number of intermediate intercalation compounds of formula Zr(HOPO₃)₂·xNH₂(CH₂) _n NH₂ (0<x<1) before obtaining the fully intercalated ones (x=1). For each diamine the batch titration curve and a diagram of the phases involved in the interaclation reaction are reported. Twenty-two intercalation compounds have been isolated and characterized by their composition, XRD patterns and thermal behaviour, and information on the disposition of the guests within the interlayer region have been derived. At full intercalation the diamines form a monolayer of extended molecules with their axis inclined at 58° to the plane of the sheet. The terminal amino groups are protonated by the —POH groups of the host, thus each diamine binds adjacent layers and, in a sense, transforms a layered structure into a framework structure that may have an accessible or potentially accessible porosity. The intercalation compound Zr(HOPO₃)₂·0.5NH₂(CH₂)₈NH₂ is indeed able to include polar molecules such as water and short chain alkanols.     

Nonsteady-state flow in gas chromatography during fast changes in inlet pressure

The steady-state assumption for describing the flow in a capillary gas chromatography column fails when changes in inlet pressure are introduced at a fast rate. To accommodate the possibility of nonsteady-state conditions, or a transient behavior, a second-order nonlinear differential equation for the pressure is suggested. Good agreement between the new theoretical model and representative experimental results is shown when the inlet pressure is increased at a rate of several hundred kPa per minute; in contrast, predictions from traditional steady-state calculations are relatively poor.     

Bile acids LXIX. Selective K-Selectride reduction of 3,7-diketo steroids

The K-Selectride reduction at low temperature (-45°C) of 7-oxo-5α-holestan-3β-yl acetate and methyl 7-oxo-3α-hydroxy-5(β-cholanoate resulted in almost quantitative yield of the 7α-alcohol in the 5α-compound but only moderate yield of the 5β-analog. The simultaneous reduction of two carbonyl groups in the 3 and 7 positions afforded good to excellent yields of the diaxial diol in planar steroids (methyl 3,7-dioxo-5α-cholanoate, 3,7-dioxo-5α-cholestane and methyl 3,7-dioxo-5α-cholestan-27-oate) and only 14% of 3α,7α-(OH)₂ from methyl 3,7-dioxo-5β-cholanoate.