The Well-Posedness Issue in Sobolev Spaces for Hyperbolic Systems with Zygmund-Type Coefficients

In this paper we study the well-posedness of the Cauchy problem for first order hyperbolic systems with constant multiplicities and with low regularity coefficients depending just on the time variable. We consider Zygmund and log-Zygmund type assumptions, and we prove well-posedness in H^∞ respectively without loss and with finite loss of derivatives. The key to obtain the results is the construction of a suitable symmetrizer for our system, which allows us to recover energy estimates (with or without loss) for the hyperbolic operator under consideration. This can be achievied, in contrast with the classical case of systems with smooth (say Lipschitz) coefficients, by adding one step in the diagonalization process, and building the symmetrizer up to the second order.     

Bicomplex holomorphic functional calculus

In this paper we introduce and study a functional calculus for bicomplex linear bounded operators. The study is based on the decomposition of bicomplex numbers and of linear operators using the two nonreal idempotents. We show that, due to the presence of zero divisors in the bicomplex numbers, the spectrum of a bounded operator is unbounded. We therefore introduce a different spectrum (called reduced spectrum) which is bounded and turns out to be the right tool to construct the bicomplex holomorphic functional calculus. Finally we provide some properties of the calculus.     

Realisations of Non v-Sufficient Jets with value in Rp, p > 1

The purpose of this paper is to show that if a jet cue oJ^r(n,p), n p, p > 1, is not v-sufficient in C^r+1, there existsan infinite sequence (f_i)_iN^* of realisations of o with mutuallynon-homeomorphic germs of varieties . Bochnak and Kuo [2, 5] showed it when p = 1 and thought thatthe same argument slightly modified can be used in the casep 2 [7, p. 225]. But when n p + 2, p > 1, we have to proceeddifferently. Moreover, it is necessary to prove separately theresult when n = p and n = p + 1. About C⁰-sufriciency and p> 1, Brodersen [3, p. 168] showed a similar theorem.     

General infinite dimensional duality and applications to evolutionary network equilibrium problems

In this paper the authors present an infinite dimensional duality theory for optimization problems and evolutionary variational inequalities where the constraint sets are given by inequalities and equalities. The difficulties arising from the structure of the constraint set are overcome by means of generalized constraint qualification assumptions based on the concept of quasi relative interior of a convex set. An application to a general evolutionary network model, which includes as special cases traffic, spatial price and financial equilibrium problems, concludes the paper.     

A FPTAS for a class of linear multiplicative problems

In this paper we consider the problem of minimizing the product of two affine functions over a polyhedral set. An approximation algorithm is proposed and it is proved that it is a Fully Polynomial Time Approximation Scheme. We will also present and computationally investigate an exact version of the algorithm.     

Supporting reliability engineers in exploiting the power of Dynamic Bayesian Networks

In this paper, we present an approach to reliability modeling and analysis based on the automatic conversion of a particular reliability engineering model, the Dynamic Fault Tree (DFT), into Dynamic Bayesian Networks (DBN). The approach is implemented in a software tool called RADYBAN (Reliability Analysis with DYnamic BAyesian Networks). The aim is to provide a familiar interface to reliability engineers, by allowing them to model the system to be analyzed with a standard formalism; however, a modular algorithm is implemented to automatically compile a DFT into the corresponding DBN. In fact, when the computation of specific reliability measures is requested, classical algorithms for the inference on Dynamic Bayesian Networks are exploited, in order to compute the requested parameters. This is performed in a totally transparent way to the user, who could in principle be completely unaware of the underlying Bayesian Network. The use of DBNs allows the user to be able to compute measures that are not directly computable from DFTs, but that are naturally obtainable from DBN inference. Moreover, the modeling capabilities of a DBN, allow us to extend the basic DFT formalism, by introducing probabilistic dependencies among system components, as well as the definition of specific repair policies that can be taken into account during the reliability analysis phase. We finally show how the approach operates on some specific examples, by describing the advantages of having available a full inference engine based on DBNs for the requested analysis tasks.     

Inverse compton scattering on laser beam and monochromatic isotropic radiation

Most of the known literature on inverse compton scattering (ICS) is based on earliest theoretical attempts and later approximations led by F.C. Jones and J.B. Blumenthal. We found an independent and more general analytical procedure which provide both relativistic and ultrarelativistic limits for ICS. These new analytical expressions can be derived in a straightforward way and they contain the previously reminded Jones’ results. Our detailed solutions may be probed by already existing as well future ICS experiments.     

Cross‐linked resins functionalized with triorganotin carboxylates: synthesis,characterization and preliminary catalytic screening in transesterification

Cross‐linked polymers containing triorganotin carboxylate functionalities were synthesized from ionic exchange resins bearing carboxylic groups. The organic tin substituents selected were methyl and butyl in order to ensure different accessibility at the metal centre. The functionalization degree depends on the different substituents and strongly affects the thermal stability of the final product. Catalytic screenings were performed in order to assess the activity of the above resins in transesterification reactions, using ethyl acetate as a substrate, together with differently hindered alcohols. The results obtained point to a negligible role of the bulkiness of tin substituents with a small contribution of the metal atom Lewis acidity in the conversion of the primary alcohol, whereas with secondary and tertiary alcohols the steric hindrance of the reagent strongly affects the conversion of the reacting alcohol. The transesterification process takes place at the liquid–solid interface, so that the catalyst grafted to an insoluble solid support can be completely removed by simple filtration. Copyright © 2005 John Wiley & Sons, Ltd.     

A practical entry to C18-constrained-E-ring analogues of methyllycaconitine (MLA): a concise new stereoselective approach to 8-oxa-decahydroisoquinolines accompanied by a simple microwaves-assisted synthesis of the succinimidobenzoate appendage of MLA

A Mannich-type intramolecular cyclization afforded access to a 8-oxa-decahydroisoquinoline heterocyclic system. Good stereoselectivity was observed. A promising microwave-assisted synthesis of the methylsuccinimidobenzoate moiety of methyllycaconitine has also been carried out.