Detecting discontinuity points from spectral data with the quotient-difference (qd) algorithm

This paper introduces a new technique for the localization of discontinuity points from spectral data. Through this work, we will be able to detect discontinuity points of a 2π-periodic piecewise smooth function from its Fourier coefficients. This could be useful in detecting edges and reducing the effects of the Gibbs phenomenon which appears near discontinuities and affects signal restitution. Our approach consists in moving from a discontinuity point detection problem to a pole detection problem, then adapting the quotient-difference (qd) algorithm in order to detect those discontinuity points.     

A combined Mössbauer spectroscopy and x-ray diffraction operando study of Sn-based composite anode materials for Li-ion accumulators

The reaction mechanisms of Li with Sn/BPO₄ composites to be used as negative electrode materials for Li-ion batteries were studied during electrochemical cycling by operando Mössbauer spectroscopy and X-ray diffraction using a specifically conceived in situ electrochemical cell. The starting composites consist of three main components: β-Sn particles as the electrochemically active species, an inactive matrix of BPO₄ and an amorphous Sn^II-borophosphate interfacial phase linking the two former components and improving the cohesion of the composite. During the first discharge, the latter Sn(II) species are first reduced to zerovalent tin forming Li-poor Li–Sn alloys. After its complete reduction, the reaction of Li continues with β-Sn leading to Li–Sn alloys increasingly rich in Li, with a final composition between those of Li₇Sn₂ and Li₁₃Sn₅. X-ray diffraction shows a progressive loss of long range order of the composites with the suppression of the diffraction peaks of the initial β-Sn and the formation of an ill-defined mixture of Li–Sn alloys. The evolution of this mechanism is investigated on going from a reference Sn/BPO₄ composite prepared by conventional ceramic methods with common micrometric BPO₄ to a new improved material prepared by carbothermal synthesis starting from nanometric BPO₄. With the new composite prepared by carbothermal synthesis, a significant improvement of the reversible capacity at the first cycle is obtained together with a slight improvement of the cycling behaviour. An additional improvement can be obtained by increasing the rate of the first discharge, and thus hampering the formation of the thermodynamically stable LiSn intermetallic.     

Finite time stability and stabilization of a class of continuous systems

Finite time stability is investigated for continuous system which satisfies uniqueness of solutions in forward time. A necessary and sufficient condition for finite time stability is given for this class of systems using Lyapunov functions. Then, a necessary and sufficient condition is developed for finite time stabilization of class CLk-affine systems involving a class CL⁰-settling-time function for the closed-loop system. Finally an explicit feedback control is addressed by using a control Lyapunov function verifying a certain inequality.     

Perturbation of spectra of operator matrices and local spectral theory

For A∈L(X), B∈L(Y) and C∈L(Y,X) we denote by MC the operator defined on X⊕Y by . In this article, we study defect set DΣ=(Σ(A)∪Σ(B))?Σ(MC) for different spectra including the spectrum, the essential spectrum, Weyl spectrum and the approximate point spectrum. We then apply the obtained results to the stability of such spectra (DΣ=∅) and the classes of operators C for which stability holds of MC using local spectral theory.     

Distributed time-varying formation tracking of multi-quadrotor systems with partial aperiodic sampled data

In this article, a distributed formation tracking controller is proposed for Multi-agent systems (MAS) consisting of quadrotors. It is considered that each quadrotor in the MAS only shares its translation position information with its neighbors. Moreover, position information is transmitted at nonuniform and asynchronous time instants. The control system is divided into an outer-loop for the position control and an inner-loop for the attitude control. A continuous-discrete time observer is used in the outer-loop to estimate both position and velocity of the quadrotor and its neighbors using discrete position information it receives. Then, these estimated states are used to design the position controller in order to enable quadrotors to generate the required geometric shape. A finite-time attitude controller is designed to track the desired attitude as dictated by the position controller. Finally, a closed-loop stability analysis of the overall system including nonlinear coupling is performed.

     

Antioxidant properties of phenolic Schiff bases: structure–activity relationship and mechanism of action

Phenolic Schiff bases are known for their diverse biological activities and ability to scavenge free radicals. To elucidate (1) the structure–antioxidant activity relationship of a series of thirty synthetic derivatives of 2-methoxybezohydrazide phenolic Schiff bases and (2) to determine the major mechanism involved in free radical scavenging, we used density functional theory calculations (B3P86/6-31+(d,p)) within polarizable continuum model. The results showed the importance of the bond dissociation enthalpies (BDEs) related to the first and second (BDE_d) hydrogen atom transfer (intrinsic parameters) for rationalizing the antioxidant activity. In addition to the number of OH groups, the presence of a bromine substituent plays an interesting role in modulating the antioxidant activity. Theoretical thermodynamic and kinetic studies demonstrated that the free radical scavenging by these Schiff bases mainly proceeds through proton-coupled electron transfer rather than sequential proton loss electron transfer, the latter mechanism being only feasible at relatively high pH.     

Slow magnetic relaxation and electron delocalization in an S = 9/2 iron(II∕III) complex with two crystallographically inequivalent iron sites

The magnetic, electronic, and Mo?ssbauer spectral properties of [Fe(2)L(μ-OAc)(2)]ClO(4), 1, where L is the dianion of the tetraimino-diphenolate macrocyclic ligand, H(2)L, indicate that 1 is a class III mixed valence iron(II∕III) complex with an electron that is fully delocalized between two crystallographically inequivalent iron sites to yield a [Fe(2)](V) cationic configuration with a S(t) = 9∕2 ground state. Fits of the dc magnetic susceptibility between 2 and 300 K and of the isofield variable-temperature magnetization of 1 yield an isotropic magnetic exchange parameter, J, of -32(2) cm(-1) for an electron transfer parameter, B, of 950 cm(-1), a zero-field uniaxial D(9∕2) parameter of -0.9(1) cm(-1), and g = 1.95(5). In agreement with the presence of uniaxial magnetic anisotropy, ac susceptibility measurements reveal that 1 is a single-molecule magnet at low temperature with a single molecule magnetic effective relaxation barrier, U(eff), of 9.8 cm(-1). At 5.25 K the Mo?ssbauer spectra of 1 exhibit two spectral components, assigned to the two crystallographically inequivalent iron sites with a static effective hyperfine field; as the temperature increases from 7 to 310 K, the spectra exhibit increasingly rapid relaxation of the hyperfine field on the iron-57 Larmor precession time of 5 × 10(-8) s. A fit of the temperature dependence of the average effective hyperfine field yields |D(9∕2)| = 0.9 cm(-1). An Arrhenius plot of the logarithm of the relaxation frequency between 5 and 85 K yields a relaxation barrier of 17 cm(-1).     

A Goal-Oriented Adaptive Moreau-Yosida Algorithm for Control- and State-Constrained Elliptic Control Problems

In this work, we develop an adaptive algorithm for solving elliptic optimal control problems with simultaneously appearing state and control constraints. The algorithm combines a Moreau-Yosida technique for handling state constraints with a semi-smooth Newton method for solving the optimality systems of the regularized sub-problems. The state and adjoint variables are discretized using continuous piecewise linear finite elements while a variational discretization concept is applied for the control. To perform the adaptive mesh refinements cycle we derive local error estimators which extend the goal-oriented error approach to our setting. The performance of the overall adaptive solver is assessed by numerical examples.     

Exotic Hadrons and Underlying Z2,3 Symmetries

The recent observation of higher quark combinations, tetraquarks and pentaquarks, is a strong indication of more exotic hadrons. Using Z₂ and Z₃ symmetries and standard model data, a general quark combination producing new hadronic states is proposed in terms of polygon geometries according to the Dynkin diagrams of  _n affine Lie algebras. It has been shown that Z_2,3 invariance is crucial in the determination of the mesonic or the baryonic nature of these states. The hexagonal geometry is considered in some details producing both mesonic and baryonic states. A general class of this family is also presented.