Test d'hétéroscédasticité quand les covariables sont fonctionnelles

We present in this paper a consistent nonparametric test for heteroscedasticity when data are of functional kind. The latter is constructed by evaluating the difference between the conditional and unconditional variances. We show the asymptotic normality of the statistical test under the null hypothesis. In addition, we prove that this test is consistent against all deviations from homoscedasticity condition.     

Theoretical spectroscopy and metastability of BeS and its cation

Multiconfiguration self-consistent field and multiconfiguration reference interaction including the Davidson’s correction techniques were employed to calculate the potential energy curves (PECs) of the BeS/BeS⁺ electronic states correlating to the 4/5 lowest dissociation limits. After nuclear motion treatment, we deduced reliable spectroscopic data for the neutral and cationic bound states. For BeS, the transition moments and spin-orbit couplings were also evaluated and used later with the PECs to deduce the rovibronic transition probabilities and the radiative lifetimes in the low-lying states, and to investigate the unimolecular decomposition processes of BeS (X¹Σ⁺, A¹Π, ³Σ⁺ and B¹Σ⁺) leading to Be(¹S_g) + S(³P_g). The prominent mechanism is a spin-orbit induced predissociation via the repulsive BeS(1³Σ⁻) state. Finally, we give the single ionization spectrum of BeS (X¹Σ⁺) populating the BeS⁺ (X²Π, 1²Σ⁻, 1²Σ⁺, 1²Δ, 2²Σ⁺, 2²Π and 3²Π) electronic states. The adiabatic ionisation energy of BeS is estimated to be ∼9.15 eV.     

SAXS studies of blends of high- and low-density polyethylene

It is shown that in blends of PE having different melting temperatures the morphology depends drastically on the cooling rate. In these heterogeneous PE, the correlation relationship L = r between the long period L of the solid state and the dimension of the coils r in the liquid state is observed only in rapidly quenched materials. In slowcooled materials the SAXS spectra are interpreted in terms of segregation of two types of PE, on a scale of the order of the dimension of the coils, the arrangement of the crystalline lamellae being paracrystalline and statistical.     

Identification of internal cracks in a three-dimensional solid body via Steklov–Poincaré approaches

This Note deals with the identification of internal planar cracks inside a three-dimensional elastic body via two approaches relying on domain decomposition using elastostatic measurements. These approaches consist in recasting the problem in terms of primal or dual Steklov–Poincaré equations. The primal approach is a straightforward continuation to the elastic Cauchy problem of the work presented in J. Ben Abdallah (2007) [1] which is devoted to the Cauchy problem for the scalar Laplace equation. The numerical performances of these formulations are compared.     

A cell cycle model and translation semigroups

First are given results on the norm-continuity of translation semigroups and their asymptotic behavior. Secondly a cell cycle model is studied from the point of view of linear translation semigroups theory. Existence and norm-continuity of the solution semigroup and the property of exponential asynchronous growth are established for this model.     

Compactness properties of operators dominated by AM-compact operators

We study several properties about the problem of domination in the class of positive AM-compact operators, and we obtain some interesting consequences on positive compact operators. Also, we give a sufficient condition under which a Banach lattice is discrete.

     

Synthesis of new spiro‐[isothiochromene‐3,5′‐isoxazolidin]‐4(1H)‐ones

A series of seven new 2′,3′,4′‐substituted spiro[isothiochromene‐3,5′‐isoxazolidin]‐4(1H)‐ones ( 7‐13 ) has been prepared in the reaction of benzylidene(phenyl)azane oxide ( 5 ) or benzylidene(methyl)azane oxide ( 6 ) with (3Z)‐3‐(4‐substituted‐benzylidene)‐1H‐isothio‐ chromen‐4(3H)‐one ( 1‐4 ). The reaction occurs by a 1,3‐dipolar cycloaddition mechanism that leads to the regiospecific formation of various spiroisoxazolidines ( 7‐13 ).     

Effects of blowing through a porous strip in a turbulent channel flow

An experimental investigation is performed on a fully developed turbulent channel flow with local injection through a porous strip. The Reynolds number based on the channel half-width was set to 5000. In addition to the no blowing case, measurements are made for three different blowing rates σ = 0.22, 0.36 and 0.58 (where σ is the ratio of momentum flux gain due to the blowing and momentum flux of the incoming channel flow). Measurements carried out with hot-wire anemometry reveal that injection strongly affects both the velocity profiles and the turbulence characteristics. The injection decreases the skin friction coefficient and increases all the Reynolds stresses downstream the blowing strip. The turbulence structure and the bursting phenomena were examined using space-time correlations measurements and conditional analysis. It is found that the injection increases the frequency of occurrence of the bursts.     

Compactness of positive semi-compact operators on Banach lattices

We study Banach lattices on which each positive semi-compact operator is compact.     

Non standard weak bosons at HERA collider

We compare the effects of non-standard weak bosons (NSB) expected fromE ₆-superstrings (Z′), strong Higgs (V ₀) and composite (spin 0, 1, 2) models by using the classical inclusive deep-inelastic “ep” scattering at HERA energies. TheX ² associated to polarized and unpolarized cross-sections, as well as the six combinations of asymmetries, allow us to derive significant bounds on the masses of the new bosons of various spins associated to some composite models with exception of the excitedZ ^*. We have also obtained some lower bounds for spin one bosons of different models (Z′,V ₀,Z ^*) which are stronger than the present experimental limits.