Structure of \mathrm {Gal}(\mathbb {k}_2^{(2)}/\mathbb {k}) for some fields \mathbb {k}=\mathbb {Q}(\sqrt{2p_1p_2},i) with \mathbf {C}l_2(\mathbb {k})\simeq (2, 2, 2)

Let \(p_1 \equiv p_2 \equiv 5\pmod 8\) be different primes. Put \(i=\sqrt{-1}\) and \(d=2p_1p_2\) , then the bicyclic biquadratic field \(\mathbb {k}=\mathbb {Q}(\sqrt{d},i)\) has an elementary abelian 2-class group of rank \(3\) . In this paper we determine the nilpotency class, the coclass, the generators and the structure of the non-abelian Galois group \(\mathrm {Gal}(\mathbb {k}_2^{(2)}/\mathbb {k})\) of the second Hilbert 2-class field \(\mathbb {k}_2^{(2)}\) of \(\mathbb {k}\) . We study the capitulation problem of the 2-classes of \(\mathbb {k}\) in its seven unramified quadratic extensions \(\mathbb {K}_i\) and in its seven unramified bicyclic biquadratic extensions \(\mathbb {L}_i\) .     

An Efficient Algorithm for the Knapsack Sharing Problem

The Knapsack Sharing Problem (KSP) is an NP-Hard combinatorial optimization problem, admitted in numerous real world applications. In the KSP, we have a knapsack of capacity c and a set of n objects, namely N, where each object j, j = 1,...,n, is associated with a profit p _j and a weight w _j. The set of objects N is composed of m different classes of objects J _i, i = 1,...,m, and N = ^m _i=1 J _i. The aim is to determine a subset of objects to be included in the knapsack that realizes a max-min value over all classes.In this article, we solve the KSP using an approximate solution method based upon tabu search. First, we describe a simple local search in which a depthparameter and a tabu list are used. Next, we enhance the algorithm by introducing some intensifying and diversifying strategies. The two versions of the algorithm yield satisfactory results within reasonable computational time. Extensive computational testing on problem instances taken from the literature shows the effectiveness of the proposed approach.     

Semilinear evolution inclusions with nonlocal conditions

We discuss conditions for the existence of at least one solution of semilinear evolution inclusions with a nonlocal condition and a nonconvex right-hand side. Our technique is based on fixed point theorems for multivalued maps.     

Decay rates at low and high frequencies for a plate equation with feedback concentrated in interior curves

In this paper we study the stabilization of plate vibrations by means of piezoelectric actuators. In this situation the geometric control condition of Bardos, Lebeau and Rauch [6] is not satisfied. We prove that we have exponential stability for the low frequencies but not for the high frequencies. We give an explicit decay rate for regular initial data at high frequencies while clarifying the behavior of the constant which intervenes in this estimation there function of the frequency of cut n. The method used is based on some trace regularity which reduces stability to some observability inequalities for the corresponding undamped problem. Moreover, we show numerically at low frequencies, that the optimal location of the actuator is the center of the domain Ω. Research supported by the RIP program of Oberwolfach Institut and by the Tunisian Ministry for Scientific Research and Technology (MRST) under Grant 02/UR/15-01. Research supported by the RIP program of Oberwolfach Institut. (Received: September 17, 2003; revised: February 26, 2004)     

Numerical modelling of twin helical spring under tensile loading

This paper presents a 3D geometric modelling of a twin helical spring and its finite element analysis to study the spring mechanical behaviour under tensile axial loading. The spiralled shape graphic design is achieved through the use of Computer Aided Design (CAD) tools, of which a finite element model is generated. Thus, a 3D 18-dof pentaedric elements are employed to discretise the complex “wired-shape” of the spring, allowing the analysis of the mechanical response of the twin spiralled helical spring under an axial load. The study provides a clear match between the evolution of the theoretical and the numerical tensile and compression normal stresses, being of sinusoidal behaviour. The overall equivalent stress isovalues increases radially from 0° to 180°, being maximal on the internal radial zone at the section 180°. On the other hand, the minimum stress level is located in the centre of the filament cross section.     

Nanostructured layered double hydroxide aerogels with enhanced adsorption properties

Aerogels of layered double hydroxides were prepared by a simple and eco-friendly method involving a quick coprecipitation followed by supercritical CO(2) drying. Such aerogels display high surface areas and enhanced adsorption behavior.     

Experimental and theoretical study of AC electrical conduction mechanisms of semicrystalline parylene C thin films

The electrical conduction mechanisms of semicrystalline thermoplastic parylene C (-H(2)C-C(6)H(3)Cl-CH(2)-)(n) thin films were studied in large temperature and frequency regions. The alternative current (AC) electrical conduction in parylene C is governed by two processes which can be ascribed to a hopping transport mechanism: correlated barrier hopping (CBH) model at low [77-155 K] and high [473-533 K] temperature and the small polaron tunneling mechanism (SPTM) from 193 to 413 K within the framework of the universal law of dielectric response. The conduction mechanism is explained with the help of Elliot's theory, and the Elliot's parameters are determined. From frequency- and temperature-conductivity characteristics, the activation energy is found to be 1.27 eV for direct current (DC) conduction interpreted in terms of ionic conduction mechanism. The power law dependence of AC conductivity is interpreted in terms of electron hopping with a density N(E(F)) (~10(18) eV cm(-3)) over a 0.023-0.03 eV high barrier across a distance of 1.46-1.54 ?.