Some observations about the extreme points of the Generalized Cardinality-Constrained Shortest Path Problem polytope

The Generalized Cardinality-Constrained Shortest Path Problem (GCCSPP) consists in finding the minimum cost path in a digraph, using at most r arcs in a subset F of the arc set. We propose an algebraic characterization of the extreme points of the associated polytope, and then we show that it is equivalent to the geometric one, obtained extending to the GCCSPP some known results for the cardinality-constrained shortest path problem.     

The weight-decay technique in learning from data: an optimization point of view

The technique known as “weight decay” in the literature about learning from data is investigated using tools from regularization theory. Weight-decay regularization is compared with Tikhonov’s regularization of the learning problem and with a mixed regularized learning technique. The accuracies of suboptimal solutions to weight-decay learning are estimated for connectionistic models with a-priori fixed numbers of computational units. The Authors were partially supported by a PRIN grant from the Italian Ministry for University and Research, project “Models and Algorithms for Robust Network Optimization”.     

A hard ferromagnetic and elastic beam-plate sandwich structure

In this paper, the deformation of a composite hard ferromagnetic-elastic beam-plate structure is investigated. A sandwich structure, composed of two thin hard ferromagnetic layers, with a linear elastic layer in between, is considered. The deformation is due to the self generated magnetic field (magnetostriction). The aim is to assess the interaction forces among the perfectly bonded layers, through a consistent application of the classical nonlinear magneto-elastic theory. Once the general mechanical model is stated, the analysis is specialized to study longitudinal elongation, given its great relevance in technical applications. Owing to the non-local character of the magnetic action, a nonlinear integro-differential equation is derived. Some qualitative properties of the solution are pointed out and the asymptotic behavior near the end sections is examined in detail. A finite differences approach allows writing an approximating nonlinear system of equations in the non asymptotic part of the solution, which is solved through a Newton’s iterative scheme. The numerical results are discussed and it is shown how the asymptotic part of the solution well approximates the full behavior of the structure. Furthermore, the longitudinal interaction force density is found to be singular at the end cross-sections, regardless of the assumed bonding type.     

Finite homogeneous deformations of symmetrically loaded compressible membranes

The equilibrium problem of nonlinear, isotropic and hyperelastic square membranes, stretched by a double symmetric system of dead loads, is investigated. Depending on the form of the stored energy function, the problem considered may admit asymmetric solutions in addition to the expected symmetric solutions. For compressible materials, the mathematical condition allowing the computation of these asymmetric solutions is given. Moreover, explicit expressions for evaluating critical loads and bifurcation points are derived. Results and basic relations obtained for general isotropic materials are then specialized for a compressible Mooney–Rivlin material and a broad numerical analysis is performed. The qualitatively more interesting branches of asymmetric equilibrium are shown and the influence of the material parameters is discussed. Finally, using the energy criterion, some stability considerations are made.     

The vibrational spectroscopy of indigo: A reassessment

We report the neutron vibrational spectra of indigo and its model compounds thioindigo and isatin. The neutron data extend the low energy range of the vibrational spectra of these molecules. The assignments, made with the help of ab-initio calculations, give convincing fits between the observed and scaled calculated results, and correct errors in the published literature. The indigo eigenvectors are described in terms of those of its model compound isatin. Finally, candidate modes, that could be used to study indigoids in matices (e.g. ‘Maya Blue’), are selected.     

On the production of \pi^{+}_{} \pi^{+}_{} pairs in pp collisions at 0.8 GeV

Data accumulated recently for the exclusive measurement of the pp $ \rightarrow$ pp $ \pi^{+}_{}$ $ \pi^{-}_{}$ reaction at a beam energy of 0.793GeV using the COSY-TOF spectrometer have been analyzed with respect to possible events from the pp $ \rightarrow$ nn $ \pi^{+}_{}$ $ \pi^{+}_{}$ reaction channel. The latter is expected to be the only $ \pi$ $ \pi$ production channel, which contains no major contributions from resonance excitation close to threshold and hence should be a good testing ground for chiral dynamics in the $ \pi$ $ \pi$ production process. No single event has been found, which meets all conditions for being a candidate for the pp $ \rightarrow$ nn $ \pi^{+}_{}$ $ \pi^{+}_{}$ reaction. This gives an upper limit for the cross-section of 0.16μb (90% C.L.), which is more than an order of magnitude smaller than the cross-sections of the other two-pion production channels at the same incident energy.     

李群流形中的扩散方程

为了描述对称空间中的无规运动,建立了群流形中的扩散方程,给出了紧致黎曼空间中扩散方程的一种具体形式,并进一步讨论了紧致黎曼空间中量子扩散运动.     

NMR Characterization of Ethylene/Propylene Copolymers and Propylene Impact Copolymers from MgCl2/TiCl4/ID+AlR3/ED Catalytic Systems

Summary: The aim of this work was to study the comonomer distribution and the chemical composition distribution generated by different Ziegler-Natta (ZN) systems (different internal donors, ID, dicyclopentadienyl-dimethoxy silane, D donor, as the external donor) and to define the potentialities of different IDs to produce improved heterophasic copolymers (HECO). A methodology to quantify the amount of ethylene-propylene copolymer (EP) portion in ZN-HECO and ethylene content of the EP portion by ¹³C-NMR was established. By using this method, it was possible to analyze the composition of ZN-HECO obtaining results comparable to those obtained with a more complex fractionation technique.