High pressure X-ray diffraction experiments on NpS and PUS up to 60 GPa

Abstract

Neptunium and plutonium monosulfides were studied under high pressure up to ～60 GPa using a diamond anvil cell in an energy dispersive X-ray diffraction facility. The compounds, of cubic rock salt structure type at ambient pressure, do not show any crystallographic phase transition in the domain of investigation. From the pressure-volume relationship, we determined bulk moduli of 92 and 120 GPa with pressure derivatives of 4.6 and 4.1 for NpS and PUS respectively.     

Markov Chain Approximations to Nonsymmetric Diffusions with Bounded Coefficients

We consider a certain class of nonsymmetric Markov chains and obtain heat kernel bounds and parabolic Harnack inequalities. Using the heat kernel estimates, we establish a sufficient condition for the family of Markov chains to converge to nonsymmetric diffusions. As an application, we approximate nonsymmetric diffusions in divergence form with bounded coefficients by nonsymmetric Markov chains. This extends the results by Stroock and Zheng to the nonsymmetric divergence forms. © 2012 Wiley Periodicals, Inc.     

On Inverse Optimal Control Problems of Human Locomotion: Stability and Robustness of the Minimizers

In recent papers, models of human locomotion by means of optimal control problems have been proposed. In this paradigm, the trajectories are assumed to be solutions of an optimal control problem whose cost has to be determined. The purpose of the present paper is to analyze the class of optimal control problems defined in this way. We prove strong convergence results for their solutions, on the one hand, for perturbations of the initial and final points (stability), and, on the other hand, for perturbations of the cost (robustness).     

Convex underestimators of polynomials

Convex underestimators of a polynomial on a box. Given a non convex polynomial ${f\in \mathbb{R}[{\rm x}]}$ and a box ${{\rm B}\subset \mathbb{R}^n}$ , we construct a sequence of convex polynomials ${(f_{dk})\subset \mathbb{R}[{\rm x}]}$ , which converges in a strong sense to the “best” (convex and degree-d) polynomial underestimator ${f^{*}_{d}}$ of f. Indeed, ${f^{*}_{d}}$ minimizes the L ₁-norm ${\Vert f-g\Vert_1}$ on B, over all convex degree-d polynomial underestimators g of f. On a sample of problems with non convex f, we then compare the lower bounds obtained by minimizing the convex underestimator of f computed as above and computed via the popular α BB method and some of its other refinements. In most of all examples we obtain significantly better results even with the smallest value of k.     

Ultrafast nanoporous silica formation driven by femtosecond laser irradiation

A type of glass modifications occurring after femto‐second laser irradiation gives rise to strong (10⁻²) from birefringence. This form birefringence is thought to be related to index nanostructure (called nanogratings). Analyzing induced tracks in fused silica using scanning electron microscopy (SEM) with nm resolution shows that nanostructures are porous nanoplanes with an average index lower than typical silica (Δn ∼ –0.20). Their origin is explained as arising from fast decomposition of the glass under localized, high‐intensity femtosecond laser radiation where strong nonlinear, multiphoton‐induced photoionization leads to plasma generation. Mechanistic details include Coulombic explosions characteristic of strong photoionization and the production of self‐trapped exciton (STE). Rapid relaxation of these STE prevents recombination and dissociated atomic oxygen instead recombines with each other to form molecular oxygen pointed out using Raman microscopy. Some of it is dissolved in the condensed glass whilst the rest is trapped within nanovoids. A chemical recombination can only occur at 1200 °C for many hours. This explains the thermal stability of such a nanostructure. Precise laser translation and control of these birefringent nanoporous structures allo arbitrarily tuning and positioning within the glass, an important tool for controlling optical properties for photonic applications, catalysts, molecular sieves, composites and more.     

Strict Monotonicity of Eigenvalues and Unique Continuation

In this paper, we show that the strict mononicity of the eigen-values of an uniformly elliptic operator of second order is equivalent to a unique continuation property.     

Recovering an Homogeneous Polynomial from Moments of Its Level Set

Let $\mathbf{K }:=\left\{ \mathbf{x }: g(\mathbf{x })\le 1\right\} $ K : = x : g ( x ) ≤ 1 be the compact (and not necessarily convex) sub-level set of some homogeneous polynomial $g$ g . Assume that the only knowledge about $\mathbf{K }$ K is the degree of $g$ g as well as the moments of the Lebesgue measure on $\mathbf{K }$ K up to order $2d$ 2 d . Then the vector of coefficients of $g$ g is the solution of a simple linear system whose associated matrix is nonsingular. In other words, the moments up to order $2d$ 2 d of the Lebesgue measure on $\mathbf{K }$ K encode all information on the homogeneous polynomial $g$ g that defines $\mathbf{K }$ K (in fact, only moments of order $d$ d and $2d$ 2 d are needed).     

Synthesis and Structure of a Copper Complex of a Macrocyclic Ligand with Dissimilar HN+N(Amino)O2 and N2(Imino)O2 Inners

Abstract The copper complex [Cu(C₂₃H₂₇Br₂N₄O₂)(H₂O)(NO₃)]₂ was synthesized and characterized by X-ray diffraction. The complex crystallizes in the triclinic system with space group P-1, lattice parameters: a = 13.2293(18) (?), b = 14.184(20) (?), c = 16.522(23) (?), α = 91.923(2)°, β = 111.777(2)°, γ = 111.259(2)°, V = 2632.0(6) ?³, Z = 4, D _c = 0.88 Mg m⁻³. In the title compound [Cu(C₂₃H₂₇Br₂N₄O₂)(H₂O)(NO₃)]₂, the coordination polyhedron of the Cu atom is a square-planar environment. The structure consists of mononuclear units in which the copper(II) ions are linked in the plane by N, N′ iminato and O, O′ phenoxo atoms. In addition the crystal lattice contains one water molecule per unit. Graphical Abstract Dissymmetric ligand was efficiently synthesized and used to prepfsare a copper(II) complex which was characterized by X-ray diffraction      

A simple and versatile method to synthesize N-acyl-benzotriazoles

An efficient method for the synthesis of N-acyl-benzotriazoles from a wide variety of protected amino acids, as well as from compounds frequently used in drug discovery such as biotin and N-Fmoc polyethylene glycol, has been developed. The reaction of carboxylic acid derivatives with benzotriazole in the presence of T3P® yielded the corresponding N-acyl-benzotriazoles, which were obtained in high purity following a simple work-up procedure, in most cases via precipitation of the desired product in water.