Abdellatif Ghendir Aoun

In this paper, we study a fractional differential equation $$^{c}D^{\alpha}_{0^{+}}u(t)+f(t,u(t))=0,\quad t\in(0, +\infty)$$ satisfying the boundary conditions: $$u^{\prime}(0)=0,\quad \lim_{t\rightarrow +\infty}\,^{c}D^{\alpha-1}_{0^{+}}u(t)=g(u),$$ where $1<\alpha\leqslant2$, $^{c}D^{\alpha}_{0^{+}}$ is the standard Caputo fractional derivative of order $\alpha$. The main tools used in the paper is contraction principle in the Banach space and the fixed point theorem due to D. O''Regan. Some the compactness criterion and existence of solutions are established.     

The Generalised Dyson Circular Unitary Ensemble: Asymptotic Distribution of the Eigenvalues at the Origin of the Spectrum

The first part of this paper is devoted to the study of F_N{\Phi_N} the orthogonal polynomials on the circle, with respect to a weight of type f = (1 − cos θ) ^α c where c is a sufficiently smooth function and ${\alpha > -\frac{1}{2}}${\alpha > -\frac{1}{2}}. We obtain an asymptotic expansion of the coefficients F^*(p)_N(1){\Phi^{*(p)}_{N}(1)} for all integer p where F^*_N{\Phi^*_N} is defined by F^*_N (z) = z^N [`(F)]_N(\frac1z) (z 1 0){\Phi^*_N (z) = z^N \bar \Phi_N(\frac{1}{z})\ (z \not=0)}. These results allow us to obtain an asymptotic expansion of the associated Christofel–Darboux kernel, and to compute the distribution of the eigenvalues of a family of random unitary matrices. The proof of the results related to the orthogonal polynomials are essentially based on the inversion of the Toeplitz matrix associated to the symbol f.     

Analytical formulas for calculation of K X-ray production cross sections by alpha ions

In the present study, different procedures are followed to deduce the semi-empirical and the empirical K X-rayX-ray production cross sections induced by alpha ions from the available experimental data and the theoretical results of the ECPSSR model for elements with 20≤Z≤30. The deduced K X-ray production cross sections are compared with predictions from ECPSSR model and with other earlier works. Generally, the deduced K X-ray production cross sections obtained by fitting the available experimental data for each element separately give the most reliable values than those obtained by a global fit.     

Computation of the infrared active modes in single-walled boron nitride nanotube bundles

In this work, the infrared active modes are computed for homogeneous bundles of single-walled boron nitride nanotubes (BBNNTs), using the so-called spectral moments method. The dependence of the wavenumber on these modes in terms of diameters, lengths, and numbers of tubes, is investigated. To this end, use is made of a Lennard-Jones potential for describing the van der Waals interactions between tubes in a bundle. We find that, for a finite homogeneous bundle, additional modes appear as a specific signature. Finally, these results are useful for the interpretation of the experimental infrared spectra of BBNNTs.     

A cellular automata traffic flow modeling of desired speed variability

The satisfaction rate of desired velocity in the case of a mixture of fast and slow vehicles is studied by using a cellular automaton method. It is found that at low density the satisfaction rate depends on the maximal velocity. However, the behavior of the satisfaction rate as a function of the coefficient of variance is independent of the maximal velocity. This is in good agreement with empirical results obtained by Lipshtat [Phys. Rev. E 79 066110 (2009)]. Furthermore, our numerical result demonstrates that at low density the satisfaction rate takes higher values, whereas the coefficient of variance is close to zero. The coefficient of variance increases with increasing density, while the satisfaction rate decreases to zero. Moreover, we have also shown that, at low density the coefficient variance depends strongly on the probability of overtaking.     

Integral inequalities related to the Tchebychev semigroup

We study the semigroup (P _t ) _t≥0 generated by the operator