Existence results for forced nonlinear periodic BVPs at resonance

Sunto In questo lavoro si presentano alcuni risultati riguardanti l'esistenza di soluzioni p-periodiche per sistemi di equazioni differenziali non lineari in risonanza, del tipo x+ Dx + + Ag(t, x)=h(t), ove D ed A sono matrici m×m, con D di tipo diagonale, h è un termine forzante p-periodico e g è un campo vettoriale, non necessariamente limitato. In particolare, viene esteso ai sistemi, in ipotesi più generali, un classico teorema dovuto a Lazer e Leach. Le dimostrazioni sono basate sull'uso del grado topologico (teorema di continuazione di Mawhin).     

Convergence of a singular Euler-Poisson approximation of the incompressible Navier-Stokes equations

In this note, we rigorously justify a singular approximation of the incompressible Navier-Stokes equations. Our approximation combines two classical approximations of the incompressible Euler equations: a standard relaxation approximation, but with a diffusive scaling, and the Euler-Poisson equations in the quasineutral regime.

     

How parabolic free boundaries approximate hyperbolic fronts

A rather complete study of the existence and qualitative behaviour of the boundaries of the support of solutions of the Cauchy problem for nonlinear first-order and second-order scalar conservation laws is presented. Among other properties, it is shown that, under appropriate assumptions, parabolic interfaces converge to hyperbolic ones in the vanishing viscosity limit.

     

On a relaxation approximation of the incompressible Navier-Stokes equations

We consider a hyperbolic singular perturbation of the incompressible Navier Stokes equations in two space dimensions. The approximating system under consideration arises as a diffusive rescaled version of a standard relaxation approximation for the incompressible Euler equations. The aim of this work is to give a rigorous justification of its asymptotic limit toward the Navier Stokes equations using the modulated energy method.

     

Indole and quinoline derivatives of 2,3-dihydro-l-benzothiepin-4(5H) one

By application of the Friedlander synthesis on 2,3-dihydro-l-benzothiepin-4(5H) one (4), the corresponding [4,5-b]quinoline derivatives 5a and 5b were obtained. Starting from the ketone (4) and by application of the Fischer indole synthesis, 1-benzolhiepino[4,5-b ]indole (6) and 1-benzothiepino[4,5-b]benzo[g]indole (7) were obtained. When β-naphthylhydrazine was used in the indolisation reaction, a mixture of 1-benzothiepino[4,5-b]benzo[e]indole ( 8 ) and 1-benzothiepino[4,3-b]benzo[e] indole (9) was obtained.     

The proficiency testing programme for trace elements of the CORILA project

Harmonised quality schemes are being implemented in the framework of the thematic area Organization and Dissemination of Data of the Consorzio per la Gestione del Centro di Coordinamento delle Attività di Ricerca Inerenti il Sistema Lagunare di Venezia (Consortium for the Management of the Coordination Centre of Research Activities on the Venice Lagoon System, CORILA). Over the last 2 years, two proficiency tests were completed at the time of writing (while a third one is still in progress) to assess the capabilities of the analytical laboratories involved in the determination of trace elements in environmental inorganic matrices from the Lagoon of Venice.Both interlaboratorial trials were based on the determination of As, Cd, Cr, Cu, Fe, Hg, Pb and Zn in aqueous acidic, matrix-enriched solutions at concentrations within the ranges generally found in marine water and in sediment after chemical digestion, respectively. The proficiency of participants was assessed on the basis of the z score criterion (|z|≤2, acceptable results; 2<|z|<3, questionable results; |z|≥3, unacceptable results). In the two trials, the relevant percentages for the laboratories scoring |z|≤2 and |z|<3 were 61% and 71% and 65% and 77%, respectively. These first two proficiency tests, on the one hand, clearly pointed to the benefits the laboratories had from their participation in these exercises, and on the other hand, provided sound evidence of the need for further trials based on real environmental matrices.     

Correction to: Numerical evaluation of entropy generation in isolated airfoils and Wells turbines

Meccanica - In the original publication of the article, Eqs. (26)–(28) are incorrect due to a missing ρ symbol, inadvertently omitted when reporting the equations in the article.     

Convergence to equilibrium for the relaxation approximations of conservation laws

We study the Cauchy problem for 2 × 2 semilinear and quasilinear hyperbolic systems with a singular relaxation term. Special comparison and compactness properties are established by assuming the subcharacteristic condition. Therefore we can prove the convergence to equilibrium of the solutions of these problems as the singular perturbation parameter tends to 0. This research was strongly motivated by the recent numerical investigations of S. Jin and Z. Xin on the relaxation schemes for conservation laws. © 1996 John Wiley & Sons, Inc.     

Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy

We study the asymptotic time behavior of global smooth solutions to general entropy, dissipative, hyperbolic systems of balance laws in m space dimensions, under the Shizuta‐Kawashima condition. We show that these solutions approach a constant equilibrium state in the L^p‐norm at a rate O(t^{? (m/2)(1 ? 1/p)}) as t → ∞ for p ∈ [min{m, 2}, ∞]. Moreover, we can show that we can approximate, with a faster order of convergence, the conservative part of the solution in terms of the linearized hyperbolic operator for m ≥ 2, and by a parabolic equation, in the spirit of Chapman‐Enskog expansion in every space dimension. The main tool is given by a detailed analysis of the Green function for the linearized problem. © 2007 Wiley Periodicals, Inc.