On stability of stationary motion of a nonconservative nonholonomic rheonomic system

One considers, in this paper, the motion of a mechanical system in a nonstationary field of potential and positional forces, subject to the action of rheonomic holonomic and nonholonomic linear homogeneous constraints. Assuming that differential equations of motion of the system considered satisfy the conditions for the existence of Painlevé's integral of energy, formulated in [Painlevé, P., 1897. Leçons sur l'intégration des équations de la Mécanique, Paris] and [Appell, P., 1911. Traité de mécanique rationnelle, T. II, Dynamique des systémes – Mécanique analitique, Gauthier-Villars, Paris] and generalized in [Čović, V., Vesković, M., 2004. On stability of motion of a rheonomic system in the field of potential and positional forces, BAMM-1720/2004, No-2233, 93–100] and [Čović, V., Vesković, M., 2005. Hagedorn's theorem in some special cases of rheonomic systems. Mechanics Research Communications 32 (3), 265–280], the original mechanical system is substituted by an equivalent one whose Lagrangian function, nontransformed with respect to nonholonomic constraints, does not depend on time explicitly. Using the properties of the equivalent system, which, in contrast to the original one, moves in a stationary field of potential forces and in a nonstationary field of gyroscopic forces, the definition of cyclic coordinates is generalized, as well as sufficient conditions for the existence of (cyclic) first integrals, corresponding to coordinates mentioned and linear in velocities are established. Further, the conditions for the existence of steady motion of the system considered are found. In the case of existence of such a motion of the system, the Theorem of Routh's type on stability of that motion, based on the minimum of reduced potential for which it is shown that, in contrast to known cases (see, for example, [Gantmacher, F., 1975. Lectures in Analytical Mechanics. Mir Publisher, Moscow; Neimark, J., Fufaev, N., 1972. Dynamics of Nonholonomic Systems. Amer. Math. Soc., Providence, RI; Pars, L., 1962. An Introduction to Calculus of Variations. Heinemann, London; Karapetyan, A., Rumyantsev, V., 1983. Stability of conservative and dissipative systems. In: Itogi Nauki I Tekhniki: Obschaya Mekh., vol. 6, VINITI, Moscow, pp. 3–128 (in Russian)]), it includes the influence of the positional forces field, is formulated. Thus, the Routh's Theorem on stability of steady motion of a conservative mechanical system is extended to the case of a nonconservative system.     

Design and construction of an quasi-adiabatic dissolution calorimeter with a novel dosing apparatus and a low heat capacity

A quasi-adiabatic calorimeter for determining the molar solution enthalpies (Δ_sol H) of non-volatile solids was constructed. The design of the instrument was adjusted to allow the determination of solution enthalpies of small amounts of solids. For that purpose, the novel apparatus for sample dosage with virtually negligible “blank heat” was built. The rather low heat capacity of the calorimeter was achieved by reducing the volume of the reaction cell (20 mL), the dosing unit, and electric elements (the thermistor and the heater). Good thermal isolation of the reaction cell from the surroundings was accomplished by placing the cell into an evacuated polypropylene vessel. A computer program for processing the calorimetric data according to modified Regnault–Pfaundler method was written. The performance of the calorimeter was tested by determining the heats of the reactions serving as thermochemical standards at 25 °C (the dissolution of KCl and NaCl in water and the dissolution of tris(hydroxymethyl)-aminomethane in 0.1 mol dm^?3 HCl(aq)). The obtained data were in very good agreement with the literature values.     

alpha-phenylpropionic acid derivatives. Synthesis and dethiation of 5-benzoylbenzo[b]thiophene-3-carboxylic acid

The total synthesis of the title compound 8 started with p-thiocresol which was acylated with oxalyl chloride to give compound 1 . This product underwent a condensation reaction with chloroacetic acid under basic conditions yielding compound 2 . Two different synthetic pathways were used to convert compound 2 into the title compound 8 . The first consisted in decarboxylation of 2 to 3 , which was then converted to the ester 4 , which was brominated and the product 5 was subjected to a Friedel-Craft's reaction with benzene. The resulting benzyl derivative 6 was oxidized to the benzoyl stage i.e. compound 7 , which was finally hydrolyzed to 8 . The second pathway was similar to the first one so that the steps of esterification, bromination, Friedel-Craft's alkylation and oxidation started with the dicarboxylic acid 2 . Thus compounds 12–16 were obtained, and the last product was decarboxylated to 8 . The yields in both procedures were similar. Finally, the dethiation of compound 8 with Raney nickel afforded compounds 18, 19 and 20 .     

Maps serving the combined coupling for use in environmental models and their behaviour in the presence of dynamical noise

Many physical, biological as well as the environmental problems, can be described by the dynamics of driven coupled oscillators. In order to study their behaviour as a function of coupling strength and nonlinearity, we considered dynamics of two maps serving the combined coupling (diffusive and linear) in the above fields. Firstly, we have considered a logistic difference equation on extended domain that is a part of the maps, that is discussed using its bifurcation diagram, Lyapunov exponent, sample as well as the permutation entropy. Secondly we have performed the dynamical analysis of the coupled maps using Lyapunov exponent and cross sample entropy in dependence on two coupling parameters. Further, we investigated how dynamical noise can affects the structure of their bifurcation diagrams. It was done (i) by the noise entering in two specific ways, that disturbs either the logistic parameter on extended domain or (ii) by an additive “shock” to the state variables. Finally, we demonstrated the effect of forcing by parametric noise, introduced in all maps’ parameter, on Lyapunov exponent of coupled maps.     

Stereoselective in-vitro aromatic-ring oxygenations of chiral 1,4-benzodiazepin-2-ones

Biological N(1)-demethylation and C(3)-hydroxylation of two enantiomeric 1,4-benzodiazepin-2-ones 1 and 2 (cf. scheme 2) were found to be nonstereoselective. Aromatic-ring hydroxylation, however, took place in the (S)-series only, leading to 3′- and 4′-hydroxylated, N(1)-demethylated, metabolites ( 54 and 56 , cf. scheme 5: these structures were unambiguously confirmed by comparing their UV., CD., and mass spectra with those of authentic specimens). Several compounds, theoretically conceivable as products of hydroxylation in the aromatic A-ring of 1 and 2 by mechanisms including the NIH-shift (cf. scheme 3), were synthesized but none of these compounds was yet isolated from in vitro incubation mixtures.