A generalizaton of Hardy’s uncertainty principle on compact extensions of \mathbb R ^n

Let \(K\) be a compact subgroup of automorphisms of \(\mathbb R ^n\) . We prove in this paper a generalization of Hardy’s uncertainty principle on the semi-direct product \(K\ltimes \mathbb R ^n\) , and we solve the sharpness problem. As a consequence, a complete analogue of classical Hardy’s theorem is obtained. The representation theory and the Plancherel formula play an important role in the proofs.     

Effects of the molecular properties of mixed solvents on the elution of alkyl benzoates in RPLC.

The retention behavior and mechanism of methyl, ethyl, propyl, isopropyl, buthyl and isobuthyl benzoates have been studied at different eluent compositions of aqueous mixtures with water-soluble organic solvents (methanol, ethanol, 1-propanol, 2-propanol, acetonitrile (AN), 1,4-dioxane and tetrahydrofuran (THF)) in RPLC. The retention of the solutes is discussed based on the solvent composition, solvent polarity (ETN value), preferential solvation, hydrogen bonding and solvent clusters of the eluents. The smaller ETN values and the larger preferential solvation of the mixed solvent eluted the solutes faster. The IR spectra of HDO suggested that the solvents, except for methanol and ethanol, break the hydrogen bonding between water molecules, resulting in fast elution of the solutes. Based upon the results, we chose an optimum solvent composition for the separation of benzoates and applied it to the determination of the benzoates in clove.     

A hybrid rank-based evolutionary algorithm applied to multi-mode resource-constrained project scheduling problem

We consider the multi-mode resource-constrained project scheduling problem (MRCPSP), where a task has different execution modes characterized by different resource requirements. Due to the nonrenewable resources and the multiple modes, this problem is NP-hard; therefore, we implement an evolutionary algorithm looking for a feasible solution minimizing the makespan.     

Chemical composition and antioxidant activity of Borago officinalis L. leaf extract growing in Algeria

The aqueous and hydroalcoholic extracts of borage (Borago officinalis) leaves from Annaba region (Algeria) were preliminary analyzed for their phenolic profile (total phenolics, total flavonoids, total flavonols, total tannins and total anthocyanins). These extracts were evaluated for their antioxidant properties by different methods such as DPPH radical scavenging, test NBT and total antioxidant activity. The two extracts have exhibited a high antiradical capacity. Indeed, the ethanolic extract showed the lower IC50 values and the highest amount of phenolics (94.09 ± 1.72 mg gallic acid/g dry extract). Using LC-MS/MS analysis, it was possible to identify phenolic acids, flavonoids, sterol and for the first time oleuropein was identified in the aqueous extract of the plant. The obtained results have demonstrated that phenolic compounds are the major contributor to the antioxidant activity of plants.     

An efficient compact quadratic convex reformulation for general integer quadratic programs

We address the exact solution of general integer quadratic programs with linear constraints. These programs constitute a particular case of mixed-integer quadratic programs for which we introduce in Billionnet et al. (Math. Program., 2010) a general solution method based on quadratic convex reformulation, that we called MIQCR. This reformulation consists in designing an equivalent quadratic program with a convex objective function. The problem reformulated by MIQCR has a relatively important size that penalizes its solution time. In this paper, we propose a convex reformulation less general than MIQCR because it is limited to the general integer case, but that has a significantly smaller size. We call this approach Compact Quadratic Convex Reformulation (CQCR). We evaluate CQCR from the computational point of view. We perform our experiments on instances of general integer quadratic programs with one equality constraint. We show that CQCR is much faster than MIQCR and than the general non-linear solver BARON (Sahinidis and Tawarmalani, User??s manual, 2010) to solve these instances. Then, we consider the particular class of binary quadratic programs. We compare MIQCR and CQCR on instances of the Constrained Task Assignment Problem. These experiments show that CQCR can solve instances that MIQCR and other existing methods fail to solve.     

Analogues of Miyachi, cowling-price and Morgan theorems for compact extensions of ℝ n

Let K be a compact subgroup of automorphisms of ? ⁿ . We formulate and prove an analogue of Miyachi’s theorem for the semi-direct product K ? ? ⁿ . This allows us to solve the sharpness problems in the theorem of Cowling-Price and in the L ^p ? L ^q analogue of Morgan theorem for any compact extension of ? ⁿ . These upshots are proved using the representations theory and the Plancherel formula for the group Fourier transform.     

Time-dependent behavior of a pulsed high power xenon flashlamp. Application to the Mega-Joule laser pumping

A numerical model has been developed for studying the time-dependent behavior of cylindrical high power xenon flashlamp. The equations of local energy conservation and mass conservation are solved using the finite volume method to give plasma parameters such as radial temperature profiles, instantaneous emission spectra, pressure, velocity, arc conductance, etc. In a first approximation the plasma is described under local thermodynamic equilibrium, LTE. The results are given as a function of time over the pulse and for several nodes in the cross section. Then the detailed spectral and temporal calculations of the output radiation from xenon flashlamp and radiation efficiencies are provided.     

Closed-form solutions of the frictional sliding contact problem for a magneto-electro-elastic half-plane indented by a rigid conducting punch

This paper focuses on the study of a frictional sliding contact problem between a homogeneous magneto-electro-elastic material (MEEM) and a perfectly conducting rigid flat punch subjected to magneto-electro-mechanical loads. The problem is formulated under plane strain conditions. Using Fourier transform, the resulting plane magneto-electro-elasticity equations are converted analytically into three coupled singular integral equations in which the main unknowns are the normal contact stress, the electric displacement and the magnetic induction. An analytical closed-form solution is obtained for the normal contact stress, electric displacement and magnetic induction distributions. The main objective of this paper is to study the effect of the friction coefficient and the elastic, electric and magnetic coefficients on the surface contact pressure, electric displacement and magnetic induction distributions for the case of flat stamp profile.     

Decomposition and Linearization for 0-1 Quadratic Programming

This paper presents a general decomposition method to compute bounds for constrained 0-1 quadratic programming. The best decomposition is found by using a Lagrangian decomposition of the problem. Moreover, in its simplest version this method is proved to give at least the bound obtained by the LP-relaxation of a non-trivial linearization. To illustrate this point, some computational results are given for the 0-1 quadratic knapsack problem.     

Extending the QCR method to general mixed-integer programs

Let (MQP) be a general mixed integer quadratic program that consists of minimizing a quadratic function subject to linear constraints. In this paper, we present a convex reformulation of (MQP), i.e. we reformulate (MQP) into an equivalent program, with a convex objective function. Such a reformulation can be solved by a standard solver that uses a branch and bound algorithm. We prove that our reformulation is the best one within a convex reformulation scheme, from the continuous relaxation point of view. This reformulation, that we call MIQCR (Mixed Integer Quadratic Convex Reformulation), is based on the solution of an SDP relaxation of (MQP). Computational experiences are carried out with instances of (MQP) including one equality constraint or one inequality constraint. The results show that most of the considered instances with up to 40 variables can be solved in 1?h of CPU time by a standard solver.