Exact solutions for a semilinear hyperbolic system with general quadratic interactions

Summary The approximate conservation laws for a binary gas mixture with quadratic interactions can be written as a system of two semilinear hyperbolic equations. By using the method of characteristics the study of this system is reduced to the study of a system of nonlinear ordinary differential equations, for which we find several classes of exact solutions. Exact integrability conditions are found for ODE systems of generalized Lotka-Volterra type. Some situations are also considered, in which the characteristic method cannot be applied and exact solutions are obtained via an operator method.     

Homotopy equivalence of two families of complexes

An explicit homotopy equivalence is established between two families of complexes, both of which generalize the classical Koszul complex.

     

On a 3×3 semilinear hyperbolic system arising in extended kinetic theory

Summary A 3×3 semi-linear hyperbolic system arising in extended kinetic theory is studied. Direct solutions to such system are discussed in a systematic way, and for various physical situations.     

Charge exchange in the final state of direct (γ, n) reactions

The two-step charge-exchange contribution coming from a direct (γ, p) reaction followed by a (p, n) transition due to isospin dependence of the optical-model potential is studied for photonuclear reactions. The charge-exchange mechanism appears to be substantial: its contribution is strongly dependent on the rather uncertain isospin term in the phenomenological optical-model potential, but is still insufficient to make the size of the (γ, n) cross section comparable with the (γ, p) one as found experimentally.     

Nonlinear hyperbolicity in kinetic theory of a gas mixture

Summary A system of nonlinear hyperbolic conservation equations, arising in the study of an evolution problem of a mixture of gases of interacting particles in the presence of only removal effects, is illustrated. Explicit analytical solutions to such system are obtained and commented on both mathematical and physical grounds.

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Riassunto Nel presente lavoro si illustra un sistema di equazioni iperboliche non lineari di conservazione, che si incontra nello studio di un problema di evoluzione per una miscela di gas di particelle interagenti in presenza di soli effetti di rimozione. Soluzioni analitiche esplicite di tale sistema sono costruite e commentate su base sia matematica che fisica.

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Резюме Рассматривается система нелинейных гиперболических уравнений сошранения, возникающих при исследовании проблемы эволюции смеси газов взаимодействующих частиц в присутствии зффектов удаления. Получаются точные аналитические решения для такой системы. Проводится обсуждение полученных результатов с математической и физической точек зрения

     

On the treatment of the Δ-contributions in electromagnetic pp-knockout reactions

The treatment of the Δ-current and its contribution in the exclusive ¹⁶O (e, e'pp)¹⁴C and ¹⁶O (γ, pp)¹⁴C knockout reactions are investigated in combination with the effects of correlations. Different parametrizations of the effective Δ-current and different treatments of correlations in the two-nucleon overlap function are considered. The results are presented and discussed for a suitable choice of kinematics. It is found that the investigation of different mutually supplementing kinematics is necessary to resolve the uncertainties in the theoretical ingredients and extract clear and unambiguous information on correlations.     

A quasi-Newton method for solving fixed point problems in Hilbert spaces

Summary We study the convergence properties of a projective variant of Newton's method for the approximation of fixed points of completely continuous operators in Hilbert spaces. We then discuss applications to nonlinear integral equations and we produce some numerical examples.     

Non-steroidal antiinflammatory agents. VI. Synthesis of 10-oxo-5H-pyrrolo[1,2-b]isoquinoline-3-acetic Acid,a conformationally restricted analogue of tolmetin

The synthesis of 10-oxo-5H-pyrrolo[1,2-b]isoquinoline-3-acetic acid 4 , a tricyclic analogue of tolmetin which might show significant analgesic-antiinflammatory activity, has been accomplished in four steps. Alkylation of ethyl 2-pyrrolylglyoxylate ( 15 ) with 2-cyanobenzyl bromide afforded derivative 16 , which was transformed by the Huang-Minion reaction into the dicarboxylic acid 6 . Cyclization of this key intermediate to 17 , followed by alkaline hydrolysis, afforded 10-oxo-5H-pyrrolo[1,2–6]isoquinoline-3-acetic acid ( 4 ). Various attempted syntheses of 6 are also discussed.     

Integral transform method in radiative transfer

A method based on integral Fourier transform technique is proposed for obtaining the radiation intensity in a nonconservative, isotropically scattering, finite slab with a general internal isotropic source and with general transparent boundary conditions. The theory of the method is first presented and it is shown to provide an exact analytical solution for the problem. Numerical results for various physical situations are then reported and compared with previous other results wherever possible. The case of the universal functions Θ(τ) and Θ_g(τ) is also considered.