Quasilinear degenerate evolution equations in Banach spaces

The quasilinear degenerate evolution equation of parabolic type 0< t T considered in a Banach space X is written, putting Mv = u, in the from 0< t T, where A(u)=L(u)M^–1 are multivalued linear operators in X for u K, K being a bounded ball ||u||_Z<R in another Banach space Z continuously embedded in X. Existence and uniqueness of the local solution for the related Cauchy problem are given. The results are applied to quasilinear elliptic-parabolic equations and systems.     

On the structure of 3‐acetylamino‐5‐methyl‐1,2,4‐oxadiazole and on the fully degenerate rearrangements (FDR) of its anion: a stimulating comparison between the results of ‘in‐silicon chemistry’ and ‘laboratory chemistry’

An accurate crystal structure determination has provided evidence for a planar conformation for 3‐acetylamino‐5‐methyl‐1,2,4‐oxadiazole ( 5 ), in agreement with quantum‐mechanical calculations in the gas phase. In the crystal, a series of strong intermolecular N7H7^….O9 hydrogen bonds link the amido groups of different molecules, causing the formation of infinite parallel ordered chains. The effect of the DMSO solvent on the energy and charge distribution of compound 5 and on its relevant 5 ^? anion, involved in a fully degenerate rearrangement (FDR), has been deepened by quantum‐mechanical DFT calculations. The calculated energy barrier for the FDR increases in going from in vacuo to DMSO, in agreement with previsions based on the Hughes and Ingold rules concerning the nucleophilic substitution of an anionic reagent (the deprotonated amido group in the side chain) on a neutral substrate (the 1,2,4‐oxadiazole ring). Copyright © 2009 John Wiley & Sons, Ltd.     

Dynamic Analysis of Linear and Nonlinear Oscillations of a Beam Under Axial and Transversal Random Poisson Pulses

This paper proposes an approximate explicit probability density function for the analysis of external and parametric oscillation of a simply supported beam driven by random pulses. The impulsive loading model adopted is Poisson white noise, which is a process having Dirac delta occurrences with random intensity distributed in time according to Poisson's law. The response probability density function can be obtained by solving the related Kolmogorov–Feller integro-differential equation. An approximate solution is derived by transforming this equation to a first-order partial differential equation. The method of characteristics is then applied to obtain an explicit solution. The theory has been validated through numerical simulations.     

Constitutive branching analysis of cylindrical bodies under in-plane equibiaxial dead-load tractions

Finite homogeneous deformations of hyperelastic cylindrical bodies subjected to in-plane equibiaxial dead-load tractions are analyzed. Four basic equilibrium problems are formulated considering incompressible and compressible isotropic bodies under plane stress and plane deformation condition. Depending on the form of the stored energy function, these plane problems, in addition to the obvious symmetric solutions, may admit asymmetric solutions. In other words, the body may assume an equilibrium configuration characterized by two unequal in-plane principal stretches corresponding to equal external forces. In this paper, a mathematical condition, in terms of the principal invariants, governing the global development of the asymmetric deformation branches is obtained and examined in detail with regard to different choices of the stored energy function. Moreover, explicit expressions for evaluating critical loads and bifurcation points are derived. With reference to neo-Hookean, Mooney-Rivlin and Ogden-Ball materials, a broad numerical analysis is performed and the qualitatively more interesting asymmetric equilibrium branches are shown. Finally, using the energy criterion, a number of considerations are put forward about the stability of the computed solutions.     

Parametric, external and self-excitation of a tower under turbulent wind flow

In this paper the analysis of a self-excited tower under turbulent wind flow is carried out. The structure is considered as a one dof nonlinear system, and the implications of this modeling are deeply discussed. The stationary wind is responsible for self-excitation, while the turbulent part provides both parametric and external excitations. The simultaneous presence of those excitations is taken into account in a specific resonance condition. The periodic and quasi-periodic solutions are studied by means of a perturbation method and the effects of the turbulence on the dynamics of the structure are analyzed.     

Fast perturbation Monte Carlo method for photon migration in heterogeneous turbid media

We present a two-step Monte Carlo (MC) method that is used to solve the radiative transfer equation in heterogeneous turbid media. The method exploits the one-to-one correspondence between the seed value of a random number generator and the sequence of random numbers. In the first step, a full MC simulation is run for the initial distribution of the optical properties and the "good" seeds (the ones leading to detected photons) are stored in an array. In the second step, we run a new MC simulation with only the good seeds stored in the first step, i.e., we propagate only detected photons. The effect of a change in the optical properties is calculated in a short time by using two scaling relationships. By this method we can increase the speed of a simulation up to a factor of 1300 in typical situations found in near-IR tissue spectroscopy and diffuse optical tomography, with a minimal requirement for hard disk space. Potential applications of this method for imaging of turbid media and the inverse problem are discussed.     

Community structure and modularity in networks of correlated brain activity

Functional connectivity patterns derived from neuroimaging data may be represented as graphs or networks, with individual image voxels or anatomically-defined structures representing the nodes, and a measure of correlation between the responses in each pair of nodes determining the edges. This explicit network representation allows network-analysis approaches to be applied to the characterization of functional connections within the brain. Much recent research in complex networks has focused on methods to identify community structure, i.e. cohesive clusters of strongly interconnected nodes. One class of such algorithms determines a partition of a network into 'sub-networks' based on the optimization of a modularity parameter, thus also providing a measure of the degree of segregation versus integration in the full network. Here, we demonstrate that a community structure algorithm based on the maximization of modularity, applied to a functional connectivity network calculated from the responses to acute fluoxetine challenge in the rat, can identify communities whose distributions correspond to anatomically meaningful structures and include compelling functional subdivisions in the brain. We also discuss the biological interpretation of the modularity parameter in terms of segregation and integration of brain function.     

Interplay of information quantifiers and the modified Jaynes-Cummings model

The dynamics of the Buck and Sukumar model (B. Buck and C. V. Sukumar, Phys. Lett. A 81, 132 (1981)) is investigated using different semi-classical information-theory tools. Their interplay reveals somewhat unexpected features. A new signature for the classical-quantum barrier is encountered thereby.     

Synthesis of side‐chain‐substituted ifosfamide analogs

Three analogs of the cytostatic drug ifosfamide incorporating 1‐methyl‐2‐chloroethyl side chains were designed and prepared as an attempt to obtain drugs of lower toxicity.