Hyperbolic Principal Subsystems: Entropy Convexity and Subcharacteristic Conditions

We consider a system of N balance laws compatible with an entropy principle and convex entropy density. Using the special symmetric form induced by the main field, we define the concept of principal subsystem associated with the system. We prove that the 2 ^N −2 principal subsystems are also symmetric hyperbolic and satisfy a subentropy law. Moreover we can verify that for each principal subsystem the maximum (minimum) characteristic velocity is not larger (smaller) than the maximum (minimum) characteristic velocity of the full system. These are the subcharacteristic conditions. We present some simple examples in the case of the Euler fluid. Then in the case of dissipative hyperbolic systems we consider an equilibrium principal subsystem and we discuss the consequences in the setting of extended thermodynamics. Finally in the moments approach to the Boltzmann equation we prove, as a consequence of the previous result, that the maximum characteristic velocity evaluated at the equilibrium state does not decrease when the number of moments increases. (Accepted October 6, 1995)     

Surface-enhanced fluorescence and surface-enhanced Raman scattering of push–pull molecules: sulfur-functionalized 4-amino-7-nitrobenzofurazan adsorbed on Ag and Au nanostructured substrates

We investigated the chemisorption of self-assembled monolayers of sulfur-functionalized 4-amino-7-nitrobenzofurazan on gold and silver nanoisland films (NIFs) by means of surface-enhanced fluorescence (SEF) and surface-enhanced Raman scattering (SERS). The ligand is a push–pull molecule, where an intramolecular charge transfer occurs between an electron-donor and an electron-acceptor group, thus exhibiting nonlinear optical properties that are related to both SERS and SEF effects. The presence of different heteroatoms in the molecule ensures the possibility of chemical interaction with both silver and gold substrates. The SERS spectra suggest that furazan is bound to silver via lone pairs of the nitrogen atoms, whereas the ligand is linked to gold via a sulfur atom. Silver NIFs provide more efficient enhancement of both fluorescence and Raman scattering in comparison with gold NIFs. The present SEF and SERS investigation could provide useful information for foreseeing changes in the nonlinear responses of this push–pull molecule.     

Local estimates for parabolic equations with nonlinear gradient terms

In this paper we deal with local estimates for parabolic problems in ${\mathbb{R}^N}$ with absorbing first order terms, whose model is $$\left\{\begin{array}{l@{\quad}l}u_t- \Delta u +u |\nabla u|^q = f(t,x) \quad &{\rm in}\, (0,T) \times \mathbb{R}^N\,,\\u(0,x)= u_0 (x) &{\rm in}\, \mathbb{R}^N \,,\quad\end{array}\right.$$ where ${T >0 , \, N\geq 2,\, 1 < q \leq 2,\, f(t,x)\in L^1\left( 0,T; L^1_{\rm loc} \left(\mathbb{R}^N\right)\right)}$ and ${u_0\in L^1_{\rm loc}\left(\mathbb{R}^{N}\right)}$ .     

The continuous-flow cycloaddition of azomethine ylides to carbon nanotubes

This communication demonstrates a straightforward continuous-flow method for efficient exohedral functionalisation of carbon nanotubes which affords soluble samples in a much shorter time over conventional batch processing.     

On the complexity of the Leibniz hierarchy

We prove that the problem of determining whether a finite logical matrix determines an algebraizable logic is complete for EXPTIME. The same result holds for the classes of order algebraizable, weakly algebraizable, equivalential and protoalgebraic logics. Finally, the same problem for the class of truth-equational logic is shown to be hard for EXPTIME.     

Numerical solution of the optimized random phase approximation

An accurate, efficient and robust numerical method for the solution of the optimized random phase approximation (ORPA) of classical liquids is presented. The uniqueness of the solution of the ORPA is proved rigorously. The method, hinging on the characterization of the generating functional, improves significantly on previous algorithms. Higher accuracy is obtained by using the values of the unknown functions on the grid points as independent variables instead of the usual coefficients of an expansion in orthogonal polynomials. It is shown that minimizing a suitably modified functional with a conjugate-gradient algorithm results in a very efficient and robust algorithm.     

Uncertainty principle and quantum Fisher information

A family of inequalities, related to the uncertainty principle, has been recently proved by S. Luo, Z. Zhang, Q. Zhang, H. Kosaki, K. Yanagi, S. Furuichi and K. Kuriyama. We show that the inequalities have a geometric interpretation in terms of quantum Fisher information. Using this formulation one may naturally ask if this family of inequalities can be further extendend, for example to the RLD quantum Fisher information. We show that this is impossible by producing a family of counterexamples.