Some properties of pseudo-almost automorphic functions and applications to abstract differential equations

This paper is concerned with some properties of pseudo-almost automorphic functions, which are more general and complicated than pseudo-almost periodic functions. Using these properties, we establish an existence and uniqueness theorem for pseudo-almost automorphic mild solutions to semilinear differential equations in a Banach space.     

非自治中立型无穷时滞泛函微分方程的加权伪概自守解

首先引入h型Stepanov 加权伪概自守函数和∞型Stepanov加权伪概自守函数的概念, 接着建立了其函数空间的完备性以及相应组合定理, 最后证明了一类非自治无穷时滞偏中立型泛函微分方程在S^p-加权伪概自守系数下加权伪概自守解的存在唯一性.     

Three-point function in perturbed Liouville gravity

Three-point correlation function in perturbed conformal field theory coupled to two-dimensional quantum gravity (perturbed Liouville gravity) is explicitly computed by using the free field approach. The representation considered here is the one recently proposed in [G. Giribet, Nucl. Phys. B 737 (2006) 209] to describe the string theory in AdS₃${\mathit{AdS}}_3$ space. Consequently, this computation extends previous results which presented free field calculations of particular cases of string amplitudes, and confirms that the free field approach leads to the exact result. Remarkably, this representation allows to compute winding violating three-point functions without making use of the spectral flow operator.     

Gain characteristics of a 210 km hybrid Raman/erbium-doped fiber amplified loop

As an alternative to using gain flattening filters or other optical devices that add attenuation to balance the gain in the optical spectrum, we have studied the effects of combining gain from Raman amplifiers and erbium-doped fiber amplifiers (EDFAs) in a fiber recirculating loop. We have shown a parameter range for which the gain profile is flat, and have analyzed the variation of the gain tilt as a function of the individual contributions of the Raman and EDFA amplifiers.     

Cation π interaction between acetylcholine and the benzene ring

 Ab initio self-consistent-field second-order M?ller–Plesset perturbation theory computations including basis set superposition error and zero-point vibrational energy corrections have been performed on the complexation of benzene with the polar head of acetylcholine (ACh). The ACh–benzene complex is about 0.5 kcal/mol less stable than the corresponding tetramethylammonium (TMA)–benzene complex, with a structure a little distorted with respect to the latter. The electronic structure of ACh is little modified by the ligand. Overall, the replacement of one methyl group of TMA by the acetyl tail of ACh does not affect strongly the complexation to benzene, as far as the main interaction is concerned. Received: 1 April 1999 / Accepted: 19 October 1999 / Published online: 14 March 2000     

Points invariants dans le produit de quatre inversions de centres non coplanaires

We study in the spaceE _n(n≥3) a special case in order to simplify long calculus. IfS ₁,S ₂,S ₃,S ₄ are centers of inversion’s spheres, then the straight lineS ₁ S ₄ is the common perpendicular to straight linesS ₁ S ₂ andS ₃ S ₄ which are orthogonal. But then we show that there exist invariant points ifn>3 in the subspace orthogonal to the centers’ subspace and if the powerk of four inversions is upper to 3a ²/₄ by supposing that lenghts ofS ₁ S ₂,S ₁ S ₄,S ₃ S ₄ are all equal toa. Ifk=3a ²/₄ it exists in the centers’ subspace an invariant point which is equidistant of four centers and which is common to four inversions’ spheres. Ifk<3a ²/₄ there is not any invariant point.      

Achieving second order advantage with multi-way partial least squares and residual bi-linearization with total synchronous fluorescence data of monohydroxy–polycyclic aromatic hydrocarbons in urine samples

An attractive approach to handle matrix interference in samples of unknown composition is to generate second- or higher-order data formats and process them with appropriate chemometric algorithms. Several strategies exist to generate high-order data in fluorescence spectroscopy, including wavelength time matrices, excitation–emission matrices and time-resolved excitation–emission matrices. This article tackles a different aspect of generating high-order fluorescence data as it focuses on total synchronous fluorescence spectroscopy. This approach refers to recording synchronous fluorescence spectra at various wavelength offsets. Analogous to the concept of an excitation–emission data format, total synchronous data arrays fit into the category of second-order data. The main difference between them is the non-bilinear behavior of synchronous fluorescence data. Synchronous spectral profiles change with the wavelength offset used for sample excitation. The work presented here reports the first application of total synchronous fluorescence spectroscopy to the analysis of monohydroxy-polycyclic aromatic hydrocarbons in urine samples of unknown composition. Matrix interference is appropriately handled by processing the data either with unfolded-partial least squares and multi-way partial least squares, both followed by residual bi-linearization.     

Abel inversion of axially-symmetric shock wave flows

Finite-fringe interferograms produced for axisymmetric shock wave flows are analyzed by Fourier transform fringe analysis and an Abel inversion method to produce density field data for the validation of numerical models. For the Abel inversion process, we use basis functions to model phase data from axially-symmetric shock wave structure. Steady and unsteady flow problems are studied, and compared with numerical simulations. Good agreement between theoretical and experimental results is obtained when one set of basis functions is used during the inversion process, but the shock front is smeared when another is used. This is because each function in the second set of basis functions is infinitely differentiable, making them poorly-suited to the modelling of a step function as is required in the representation of a shock wave.Received: 12 November 2003, Accepted: 21 October 2004, Published online: 31 March 2005[/PUBLISHED]PACS: 47.40.-x, 42.40.Kw, 02.30.Zz     

Sur les logarithmes dans les algèbres de Clifford deR(n, 0)

We prove that the use of logarithms in Clifford AlgebrasCL (n, 0) forn≥3 brings not any advantage but only inevitable complications.