On the decay of solutions for a class of quasilinear hyperbolic equations with non‐linear damping and source terms

In this paper, we consider the non‐linear wave equation a,b>0, associated with initial and Dirichlet boundary conditions. Under suitable conditions on α, m, and p, we give precise decay rates for the solution. In particular, we show that for m=0, the decay is exponential. This work improves the result by Yang (Math. Meth. Appl. Sci. 2002; 25 :795–814). Copyright © 2005 John Wiley & Sons, Ltd.     

13C NMR study of N-unsubstituted aziridines: I—steric effects,pseudoconjugation

¹³C chemical shifts for twenty-nine alkyl and phenyl substituted N-unsubstituted aziridines have been measured. Additivity parameters for methyl, phenyl and aziridyl carbons have been derived with the aim of testing the consistency of the assignments made on the basis of chemical shift considerations and off-resonance decoupling information. The observed chemical shifts are discussed in terms of steric and pseudoconjugation effects.     

‘All‐supramolecular’ Nanocapsules from Low‐Molecular Weight Ureas Through Interfacial Addition Reaction in Miniemulsion

This contribution presents a new strategy for preparing nanocapsules with a shell made of a supramolecular polymer which repeating units are held together by reversible interactions rather than covalent bonds. These nanocapsules were prepared in classical miniemulsion through interfacial addition reaction of a diisocyanate (IPDI) and a monoamine (iBA), forming low‐molecular weight bis‐ureas moieties which are strong self‐complementary interacting molecules through hydrogen‐bonding. The nanocapsules present a diameter around 100 nm, and MALDI‐TOF MS and ¹H NMR analyses confirm the expected molecular characteristics for the shell. This strategy opens the scope of a new type of nanomaterials exhibiting stimuli‐responsiveness due to the reversible interaction linking the repeating units.

     

Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation

In this paper, we consider the nonlinear viscoelastic equation

with initial conditions and Dirichlet boundary conditions. For nonincreasing positive functions g and for p>m, we prove that there are solutions with positive initial energy that blow up in finite time.     

A semiparametric test of independence in copula models for censored data

We propose a semiparametric test of independence in copula models for bivariate survival censored data. We give the limit laws of the estimate of the parameter and the proposed test statistic under the null hypothesis of independence.     

Global Existence,Decay, and Blow up of Solutions of a Singular Nonlocal Viscoelastic Problem

In this work we consider a nonlinear hyperbolic one-dimensional viscoelastic nonlocal problem with a nonlocal boundary condition. We establish a blow up result for large initial data and a decay result for small enough initial data.     

The Exchange Property in Grothendieck Categories: Applications

We introduce the concept of an object with the (finite) exchange property in an arbitrary Grothendieck category, and we present the basic properties of such an object. Applications are given for categories of graded modules and for categories of comodules over a coalgebra. Among other results, it is proved that an arbitrary coalgebra 𝒞 over a field has the finite exchange property.     

A cryptosystem based on elementary cellular automata

Based on elementary cellular automata, a new image encryption algorithm is proposed in this paper. In this algorithm, a special kind of periodic boundary cellular automata with unity attractors is used. From the viewpoint of security, the number of cellular automata attractor states are changed with respect to the encrypted image, and different key streams are used to encrypt different plain images. The cellular neural network with chaotic properties is used as the generator of a pseudo-random key stream. Theoretical analysis and experimental results have both confirmed that the proposed algorithm possesses high security level and good performances against differential and statistical attacks. The comparison with other existing schemes is given, which shows the superiority of the proposal scheme.     

First principle calculation of the electronic and magnetic properties of Mn-doped 6H-SiC

The electronic and magnetic properties of 6H-SiC with Mn impurities have been calculated using GGA formalism. Various configurations of Mn sites were considered. It was found that 6H-SiC doped with Mn atoms possess a moment for both types of substitution. The Mn atom at Si site possesses larger magnetic moment than Mn atom at C site. The energy levels appearing in the band gap due to vacancies and due to Mn impurities are determined and the calculated densities of states (DOSs) are used to analyse the different value of the magnetic moments for different types of substitution. A model that explains the magnetic moment at Mn site is proposed.