Applications purement semi-affines et tressages

In this Note, we show essentially two results which complete the article by Ait Mokhtar et al., 2008. The first one, having defined the maps purement semi-affines, consists in looking the writing clarify of the compound of these maps. The second result, having defined the tressage, consists in showing that the compound of two tressages is also a tressage.     

Kinetics and mechanism of oxidation of N,N-bis(salicylaldehyde-1,2-diaminoethane) cobalt(II) by N-bromosuccinimide in aqueous acidic medium

The kinetics of oxidation of N,N-bis(salicylaldehyde-1,2-diaminoethane) cobalt(II) complex by N-bromosuccinimide (NBS) in aqueous acid and H₂O–MeOH solvent mixtures were studied spectrophotometrically over the 20–40 °C range, 0.1–0.5 mol dm^?3 ionic strength, 2.2–2.8 pH range and 0–40 wt% MeOH–H₂O solvent mixtures for a range of NBS and complex concentrations. The rate shows first-order dependence on both [NBS] and [complex] and decreases with pH over the range studied. The protonated form of N-bromosuccinimide was identified as the main reactive species. An inner-sphere mechanism involving free radicals is proposed.     

Why Is the Spontaneous Deprotonation of [Cu(uracil)2]2+ Complexes Accompanied by Enolization of the System?

The reaction‐force formalism is applied to carry out a detailed analysis of the mechanisms behind the enolization processes undergone by the complexes formed on interaction of uracil dimers with Cu²⁺ ions after spontaneous deprotonation of the resulting complexes. These enolization processes apparently involve a single proton transfer (PT) from an NH group to a carbonyl group of the same uracil moiety, which should involve a rather high activation barrier that prevents the process occurring. However, the reaction‐force, chemical‐potential, and electronic‐flux profiles unambiguously indicate that the actual mechanism involves three low‐barrier elementary steps, and this explains why enolization of the [Cu(uracil?H)(uracil)]⁺ complexes is a highly facile, assisted PT process. All of the observed PT processes show a typical profile for both the chemical potential and the electronic flux associated with the bond‐breaking and the bond‐formation processes.     

Development and application of a validated stability-indicating high-performance liquid chromatographic method using photodiode array detection for simultaneous determination of granisetron, methylparaben, propylparaben, sodium benzoate, and their main degradation products in oral pharmaceutical preparations

A simple, rapid, and sensitive RP-HPLC method using photodiode array detection was developed and validated for the simultaneous determination of granisetron hydrochloride, 1-methyl-1H-indazole-3-carboxylic acid (the main degradation product of granisetron), sodium benzoate, methylparaben, propylparaben, and 4-hydroxybenzoic acid (the main degradation product of parabens) in granisetron oral drops and solutions. The separation of the compounds was achieved within 8 min on a SymmetryShield RP18 column (100 x 4.6 mm id, 3.5 microm particle size) using the mobile phase acetonitrile--0.05 M KH2PO4 buffered to pH 3 using H3PO4 (3+7, v/v). The photodiode array detector was used to test the purity of the peaks, and the chromatograms were extracted at 240 nm. The method was validated, and validation acceptance criteria were met in all cases. The robust method was successfully applied to the determination of granisetron and preservatives, as well as their degradation products in different batches of granisetron oral drops and solutions. The method proved to be sensitive for determination down to 0.04% (w/w) of granisetron degradation product relative to granisetron and 0.03% (w/w) 4-hydroxybenzoic acid relative to total parabens.     

A derivative concept with respect to an arbitrary kernel and applications to fractional calculus

In this paper, we propose a new concept of derivative with respect to an arbitrary kernel function. Several properties related to this new operator, like inversion rules and integration by parts, are studied. In particular, we introduce the notion of conjugate kernels, which will be useful to guaranty that the proposed derivative operator admits a right inverse. The proposed concept includes as special cases Riemann‐Liouville fractional derivatives, Hadamard fractional derivatives, and many other fractional operators. Moreover, using our concept, new fractional operators involving certain special functions are introduced, and some of their properties are studied. Finally, an existence result for a boundary value problem involving the introduced derivative operator is proved.     

On an inverse problem of reconstructing a subdiffusion process from nonlocal data

We consider a problem of modeling the thermal diffusion process in a closed metal wire wrapped around a thin sheet of insulation material. The layer of insulation is assumed to be slightly permeable. Therefore, the temperature value from one side affects the diffusion process on the other side. For this reason, the standard heat equation is modified, and a third term with an involution is added. Modeling of this process leads to the consideration of an inverse problem for a one‐dimensional fractional evolution equation with involution and with periodic boundary conditions with respect to a space variable. This equation interpolates heat equation. Such equations are also called nonlocal subdiffusion equations or nonlocal heat equations. The inverse problem consists in the restoration (simultaneously with the solution) of the unknown right‐hand side of the equation, which depends only on the spatial variable. The conditions for overdefinition are initial and final states. Existence and uniqueness results for the given problem are obtained via the method of separation of variables.     

Multiaccess in all-optical networks with wavelength and code concurrency

A major obstacle in realizing fast packet switching in all-optical networks is the large tuning delays of tunable optical devices. This article proposes a multiaccess scheme for all-optical local area networks that employs both wavelength and code concurrency. In this scheme, several users share a wavelength channel through code multiplexing. The delay performance of hybrid wavelength/code division multiaccess is obtained under a simple, suboptimal access protocol based on cyclic search. Due to the reduction in the number of wavelength channels without an associated reduction in transmission concurrency, hybrid multiaccess is robust against tuning delays. At a given network throughput, the hybrid scheme achieves considerably lower delays than that of Wavelength Division Multiple Access even with a small amount of code concurrency. Conversely, the hybrid network can support a higher load when there is a maximum allowable value for the average packet delay.     

Blowing‐up solutions to two‐times fractional differential equations

Nonexistence results for a class of two‐times differential equations with fractional derivatives of orders between zero and one are presented. Furthermore, the result is extended to a two‐times system of two differential equations with fractional derivatives of orders between zero and one.     

On necessary and sufficient conditions for near-optimal singular stochastic controls

In this paper we discuss the necessary and sufficient conditions for near-optimal singular stochastic controls for the systems driven by a nonlinear stochastic differential equations (SDEs in short). The proof of our result is based on Ekeland’s variational principle and some delicate estimates of the state and adjoint processes. It is well known that optimal singular controls may fail to exist even in simple cases. This justifies the use of near-optimal singular controls, which exist under minimal conditions and are sufficient in most practical cases. Moreover, since there are many near-optimal singular controls, it is possible to choose suitable ones, that are convenient for implementation. This result is a generalization of Zhou’s stochastic maximum principle for near-optimality to singular control problem.