Synthesis of compact multidentate ligands to prepare stable hydrophilic quantum dot fluorophores

We describe a simple and versatile scheme to prepare an array of heterofunctional multidentate ligands that permit strong and stable interactions with colloidal semiconductor nanocrystals (quantum dots, QDs) and render them soluble in aqueous environments. These ligands were synthesized by reacting various chain length poly(ethylene glycols) with thioctic acid, followed by ring opening of the dithiolane moiety, creating a bidentate thiol motif with enhanced affinity for CdSe-ZnS core-shell QDs. Functionalization with these ligands permits processability of the nanocrystals not only in aqueous but also in many other polar solvents. These ligands provide a straightforward means of preparing QDs that exhibit greater resistance to environmental changes, making them more amenable for use in live cell imaging and other biotechnological applications.     

Theoretical studies of vibrational spectra of [N(CH3)4]2ZnCl4−yBry compounds with y = 0, 2 and 4

The infrared and Raman spectra of [N(CH₃)₄]₂ZnCl_4?yBr_y, where y = 0, 2 and 4, have been analyzed with ab initio calculations of the vibrational characteristics of constitutive polyhedra, tetramethylammonium [N(CH₃)₄]⁺ and [ZnCl_4?xBr_x]^2? (x = 0, 1, 2, 3 and 4) tetrahedra. The optimized geometries, calculated vibrational frequencies, infrared intensities and Raman activities are calculated using Hartree–Fock and density functional theory B3LYP methods with 3-21G, 6-31G(d) and 6-311G⁺(d,p) basis sets. Calculation of the root mean square difference δ_rms between the observed and calculated frequencies allows to give scaling factors and to deduce that the best agreements are obtained by B3LYP/6-311G⁺(d,p) for [N(CH₃)₄]⁺ and B3LYP/3-21G for [ZnCl_4?xBr_x]^2?. The present study establishes a strongly reliable assignment of the vibrational modes of [ZnCl_4?xBr_x]^2? tetrahedra based on comparison between experimental and ab initio calculations, both of the frequencies and the intensities of the Raman signals.     

Martingale measures and partially observable diffusions

In this paper, we solve the problem of existence of an optimal control based on partial observations in the general case where the observation process depends on the control. The method of solution is based on the use of relaxed controls and martingales measures: we associate a martingale problem with the filter and we prove that this problem is equivalent to the initial one     

Sensitivity analysis to perturbations of the weight of a subset of items: The knapsack case study

In this paper, we study the sensitivity of the optimum to perturbations of the weight of a subset of items of both the knapsack problem (denoted KP) and knapsack sharing problem (denoted KSP). The sensitivity interval of the weight associated to an item is characterized by two limits, called lower and upper values, which guarantee the optimality of the solution at hand whenever the new weight’s value belongs to such an interval. For each perturbed weight, we try to establish approximate values of the sensitivity interval whenever the original problem is solved. We do it by applying a dynamic programming method where all established results require a negligible runtime. First, two cases are studied when considering an optimal solution of KP: (i) the case in which all perturbations are (non)negatives and (ii) the general case in which the set of the perturbed items is divided into two disjoint subsets (the first subset contains the nonnegative perturbations and the second one represents the subset of negative perturbations). Second, we show how we can adapt the results of KP to the KSP. All established results require a negligible runtime which grows the interest of such a study. Finally, for each of these problems, we will see the impact of the established results on an example while considering the various cases.     

Weight-based Heuristics for Constraint Satisfaction and Combinatorial Optimization Problems

In this paper, we propose mechanisms to improve instantiation heuristics by incorporating weighted factors on variables. The proposed weight-based heuristics are evaluated on several tree search methods such as chronological backtracking and discrepancy-based search for both constraint satisfaction and optimization problems. Experiments are carried out on random constraint satisfaction problems, car sequencing problems, and jobshop scheduling with time-lags, considering various parameter settings and variants of the methods.The results show that weighting mechanisms reduce the tree size and then speed up the solving time, especially for the discrepancy-based search method.     

Représentation de Feynman–Kac dans des domaines temps–espace et sensibilité par rapport au domaine

We consider the solution X=(X_t)_t?0 of a time-inhomogeneous stochastic differential equation and the exit time τ by (t,X_t)_t?0 of the time–space domain $\text{D}$. We prove the differentiability of expectations of functionals of X stopped at τ, with respect to the domain $\text{D}$: these results extend those in the literature, known in particular by the analysts for the issues of shape optimization. However from the probabilistic point of view, this is not standard. To cite this article: C. Costantini et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Synthesis and structure of 5,5-diethoxycarbonyl-1-pyrroline N-oxide (DECPO). Application to superoxide radical trapping

DECPO, a new analogue of EMPO was synthesized through a two-step synthetic pathway. Its structure and its application to trap superoxide were investigated. The ESR detection of the DECPO-OOH spin adduct is easy even at low concentration of superoxide. In comparison with DEPMPO, the trapping of superoxide with DECPO is faster and the detection of DECPO-OOH can be performed using a very low nitrone concentration (0.5 mM).     

Explicit upper bounds for exponential sums over primes

We give explicit upper bounds for linear trigonometric sums over primes.