Synthesis and characterisation of polypyrrole–indium phosphide composite film

Polypyrrole (PPy)–indium phosphide (InP) composite material was electrochemically prepared by the incorporation of InP into a PPy matrix during electrochemical synthesis (cycling) under magnetic stirring from the acetonitrile/LiClO4 electrolyte containing the Py and InP particles. The PPy–InP composite material was designed to explore new approaches to improve light-collection efficiency in polymer photovoltaic. The samples were characterised by cyclic voltammetry, impedance spectroscopy measurement, scanning electron microscopy, energy dispersive X-ray spectroscopy, UV–visible and photoelectrochemical measurements. It was observed that the photocurrent of the composites was higher than that of the single PPy films and increased with InP concentration. The study showed that the presence of InP particles in the polymeric film improves the optical and the photovoltaic properties of PPy and give information on the use possibility of these films for photovoltaic cells' application.     

Photoluminescence and energy transfer of Tm doped LiIn (WO4)2 blue phosphors

Room temperature steady and time resolved emission spectra of LiIn_1−xTm_x(WO4)2 (where thulium concentration is 0, 0.5, 1, 5 and 10 at%) blue phosphors, under UV excitation energy have been investigated. The concentration quenching effect on the blue emission, due to the (WO₄)⁻² groups and ¹G₄→³H₆ emission transition of Tm³⁺ were studied. Two energy transfer mechanisms are shown. The first takes place between excited (WO₄)⁻² groups and the ¹G₄ energy level of Tm³⁺, and is mainly analyzed by phonon-assisted energy transfer. The second mechanism is due to an energy transfer from the excited Tm³⁺ ions to the surrounding ground state Tm³⁺ ions. The non-exponential decay curves of the ¹G₄ level observed for higher concentrations are analyzed by the Inokuti–Hirayama model. We think that the quenching effect between Tm³⁺ ions is mainly linked to the dipole–dipole interactions.     

Optimization and limits of optical nonlinear measurements using imaging technique

We report on analytical calculations for a 4f coherent imaging system in presence of a phase object at the entry of the set-up. We give the results of the optimized parameters to be used in this system so as to increase the sensitivity of the measurement of the nonlinear refraction coefficient. Analytical and previously reported simulated image profiles are compared here. Our study also gives the limits of the nonlinear imaging technique with a phase object for relatively high nonlinear phase shifts.     

Le nombre des diviseurs unitaires d'un entier dans les progressions arithmétiques

Let the functions $d_{k\text{,}l}^{*}(n)$ and $d_{k\text{,}l}(n)$ be number of unitary divisors (see below) and number of divisors n in arithmetic progressions $\{l+mk\}$; k and l are integers relatively prime such that $1?l?k$ and let, for $n?2$

$F(n\text{;}k\text{,}l)=\frac{\ln (d_{k\text{,}l}(n))\ln (\phi (k)\ln n)}{\ln n}\text{,}{F}^{*}(n\text{;}k\text{,}l)=\frac{\ln (d_{k\text{,}l}^{*}(n))\ln (\phi (k)\ln n)}{\ln n}\text{and}$

$D^{*}(n\text{;}k\text{,}l)=\frac{\ln (d_{k\text{,}l}(n)/d_{k\text{,}l}^{*}(n))\ln (\phi (k)\ln n)}{\ln n}\text{,}$

where $\phi (k)$ is Euler's totient. The function $F(n\text{;}k\text{,}l)$ has been studied in [A. Derbal, A. Smati, C. A. Acad. Sci. Paris, Ser. I 339 (2004) 87–90]. In this Note we study the functions $F^{*}(n\text{;}k\text{,}l)$ and $D^{*}(n\text{;}k\text{,}l)$. We give explicitly their maximal orders and we compute effectively the maximum of $F^{*}(n\text{;}k\text{,}l)$ for $k=1\text{,}2\text{,}3$ and that of $D^{*}(n\text{;}k\text{,}l)$ for $k=1\text{,}3\text{,}5\text{,}7\text{,}8\text{,}9\text{,}10\text{,}11\text{,}13$. To cite this article: A. Derbal, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

Behaviour at the non-positive integers of Dirichlet series associated to polynomials of several variables

In this paper, we relate the special values at a non-positive integer \({\underline{\mathbf{s}}=(s_{1},\ldots, s_{r})= -\underline{\mathbf{N}}= (-N_{1},\ldots, -N_{r})}\) obtained by meromorphic continuation of the multiple Dirichlet series \({{Z(\underline{\mathbf{P}}, \underline{\mathbf{s}})=\sum_{\underline{m}\in {\mathbb{N}}^{*n}}{\frac{1}{\prod_{i=1}^{r}{P_{i}^{ s_{i}}(\underline{m})}}}}}\) to special values of the function \({Y(\underline{\mathbf{P}}, \underline{\mathbf{s}})=\int_{[1, +\infty[^{n}} {\prod_{i=1}^{r}{P_{i}^{- s_{i}}(\underline{\mathbf{x}})}\; d{\underline{\mathbf{x}}}}}\) where \({\underline{\mathbf{P}}=(P_{1},..., P_{r}),\; (r\geq 1)}\) are elliptic polynomials in “\({n}\) ” variables. We prove a simple relation between \({Z(\underline{\mathbf{P}}_{\underline{\mathbf{a}}}, -\underline{\mathbf{N}})}\) and \({Y(\underline{\mathbf{P}}_{\underline{\mathbf{a}}}, -\underline{\mathbf{N}})}\), such that for all \({\underline{\mathbf{a}} \in {\mathbb{R}}^{n}_{+}}\), we denote \({\underline{\mathbf{P}}_{\underline{\mathbf{a}}}:=(P_{1 \underline{\mathbf{a}}},\ldots, P_{r \underline{\mathbf{a}}})}\), where \({P_{i\;\underline{\mathbf{a}}}(\underline{\mathbf{x}}):= P_i(\underline{\mathbf{x}}+ \underline{\mathbf{a}})\; (1\leq i\leq r)}\) is the shifted polynomial.     

An Efficient Parameterized Logarithmic Kernel Function for Semidefinite Optimization

Acta Mathematicae Applicatae Sinica, English Series - In this paper, we present a primal-dual interior point algorithm for semidefinite optimization problems based on a new class of kernel...     

La somme des diviseurs unitaires d'un entier dans les progressions arithmétiques (σk,l*(n))

Soit ${\sigma }_{k,l}^{*}(n)$ la fonction somme des diviseurs unitaires du nombre entier n dans la progression arithmétique $\{l+mk\}$ définie, pour $n={\prod }_{p^{\alpha }\parallel n}{p}^{\alpha }$, par : ${\sigma }_{k,l}^{*}(n)={\prod }_{p^{\alpha }\parallel n,p\equiv l(k)}(1+p^{\alpha }),{\sigma }_{1,1}^{*}(n)={\sigma }^{*}(n)={\sum }_{d|n,(d,n/d)=1}d$. Dans cette Note nous établissons un théorème sur le comportement relatif de cette fonction et de son ordre maximal qui sera explicitement déterminé et nous donnons des majorations effectives de ${\sigma }_{3,l}^{*}(n)$. Pour citer cet article : A. Derbal, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Le nombre des diviseurs d'un entier dans les progressions arithmétiques

Let d_k,?(n) be the function number of divisors of the integer n?1, in arithmetic progressions {?+mk}, with 1???k and ?,k coprime, and let F(n;k,?) defined as follows:

$\text{F(n;k,?)=}\text{ln}\text{d}{}_{\mathrm{k,?}}\text{(n)}\text{ln}\text{(?(k)}\text{ln}\text{n)}\text{ln}\text{2}\text{ln}\text{n}\text{.}$

In this Note, we study and give the structure of d_k,?-superior, highly composite numbers, which generalize those defined by S. Ramanujan. We prove that F(n;k,?) reaches its maximum among these numbers. We give it explicitly for k=2,…,13. This generalizes the study of Nicolas and Robin, in which the case k=1 is treated. To cite this article: A. Derbal, A. Smati, C. R. Acad. Sci. Paris, Ser. I 339 (2004).