Group analysis and constitutive laws for fluid filled elastic tubes

The group properties are investigated for the non-linear mathematical model describing thin walled elastic tubes filled with incompressible fluid. The analysis developed for determining the generators of the group provides a mathematical approach for characterizing classes of constitutive laws for internal area, outflow and viscous retarding force. Thus integration of a system of (non-linear) ordinary differential equations gives rise to several classes of invariant solutions for non-linear arterial flow problems. Some features of these solutions are also discussed.     

Complete exceptionality, constitutive laws and symmetric form for a non-linear inelastic rod

In this paper we consider quasilinear constitutive laws characterizing ‘Maxwellian Materials’ in the case of a one-dimensional inelastic rod. By using the complete exceptionality condition, we are able to determine the most general class of quasilinear constitutive relations by which a weak discontinuity wave propagating along characteristics cannot evolve into a non- linear shock. The last part of the paper is devoted to point out some properties connected with the special class of constitutive relations where the material functions do not depend on the strain. In such a case by means of a field variables transformation, we are able to reduce the fundamental system of equations to a symmetric hyperbolic system where the coefficient of the field spatial derivative is a constant matrix. This special symmetric form is very useful to study shocks.     

Group analysis for a linear hyperbolic equation arising from a quasilinear reducible system

The aim of this paper is to carry out infinitesimal group analysis for a second order linear hyperbolic equation in canonical form. To such a kind of equation one could be led in considering the hodograph transformation for a first order reducible system. In the first part of the paper we characterize the most general expression for the generator of the Lie group, which has an infinite dimensional algebra. Then we calculate the invariant surfaces in some special cases of interest, and point out the corresponding ordinary differential equations whose integration allows us to determine possible classes of solutions for the equation we are considering.     

Partial regularity of minimizers of quasiconvex integrals with subquadratic growth

We prove partial regularity for minimizers of quasiconvex integrals of the form dx where the integral F() has subquadratic growth, ie .Research supported by MURST, Gruppo Nazionale 40%.     

Computing nonperforming loan prices in banking efficiency analysis

Within the framework of banking efficiency analysis, we propose a methodology for computing unobservable shadow prices for nonperforming loans (NPL). Our approach is to include NPL as an undesirable output variable in a distance function stochastic frontier analysis. We conduct a panel study of US and European banks during the most recent financial crisis by adopting a semi-nonparametric Fourier specification, which ensures convergence to the true values of both the estimated function and the related efficiency. Computing NPL prices has several advantages, such as identifying approaching crises, quantifying the responsibilities of governments and banks for credit risk and determining appropriate regulatory interventions.

     

Fischer synthesis of indoles from 2,6-disubstituted arylhydrazones

A review of the literature data on the Fischer synthesis of indoles from 2,6-disubstituted arylhydrazones is given. As a result of their own experimental studies of the indolization of hydrazones from 8-R-N-amino-1,2,3,4-tetrahydroquinolines the authors established that no less than five different transformations of the cyclohexadienoneimine intermediate, including 1,2 and 1,4 shifts and splitting out of the substituent, may follow attack on the 8 position of the tetrahydroquinoline ring. Attack in the 10 position of the tetrahydroquinoline ring leads to another cyclohexadienoneimine, which undergoes indolization with the loss of apropylamine chain via a different mechanism. It was proved by experiments with labeled compounds that 1,3 migration of the methyl group (R=CH₃) is the result of a double 1,2 shift, while the 1,4 shift is a direct reaction.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 200–216, February, 1978.     

Oxyfunctionalization of non-natural targets by dioxiranes. 5. Selective oxidation of hydrocarbons bearing cyclopropyl moieties

The powerful methyl(trifluoromethyl)dioxirane (1b) was employed to achieve the direct oxyfunctionalization of 2,4-didehydroadamantane (5), spiro[cyclopropane-1,2'-adamantane] (9), spiro[2.5]octane (17), and bicyclo[6.1.0]nonane (19). The results are compared with those attained in the analogous oxidation of two alkylcyclopropanes, i.e., n-butylcyclopropane (11) and (3-methyl-butyl)-cyclopropane (14). The product distributions observed for 11 and 14 show that cyclopropyl activation of alpha-C-H bonds largely prevails when no tertiary C-H are present in the open chain in the tether; however, in the oxyfunctionalixation of 14 cyclopropyl activation competes only mildly with hydroxylation at the tertiary C-H. The application of dioxirane 1b to polycyclic alkanes possessing a sufficiently rigid framework (such as 5 and 9) demonstrates the relevance of relative orientation of the cyclopropane moiety with respect to the proximal C-H undergoing oxidation. At one extreme, as observed in the oxidation of rigid spiro compound 9, even bridgehead tertiary C-H's become deactivated by the proximal cyclopropyl moiety laying in the unfavorable "eclipsed" (perpendicular) orientation; at the other end, a cyclopropane moiety constrained in a favorable "bisected" orientation (as for didehydroadamantane 5) can activate an "alpha" methylene CH2 to compete effectively with dioxirane O-insertion into tertiary C-H bonds. Comparison with literature reports describing similar oxidations by dimethyldioxirane (1a) demonstrate that methyl(trifluoromethyl)dioxirane (1b) presents similar selectivity and remarkably superior reactivity.     

Non-conventional syntheses of heterocyclic compounds: a new synthesis of 1,3,4-benzotriazepine derivatives

4,5-Dihydro-1,3,4-benzotriazepines were obtained in good yields by intramolecular thermal cyclization of arylazoanils with methyl or ethyl groups in the ortho positions of the aromatic ring on the imine nitrogen.