Converging algorithm for a class of BMI applied on state-dependent stabilization of switched systems

In this paper, a design of a stabilizing state-dependent switching law is presented. First, it is based on a new reformulation of this control problem into a class of BMI (Bilinear Matrix Inequality) problem. The originality of this reformulation is that it will be used, in a second part, by an algorithm dedicated to solve this class of BMI without loss of generality. The construction of this algorithm is then specified, and the proof of its convergence is given for the two-subsystem case. The last part of the work consists in presenting the problem for a polytopic switching system, and how the previous algorithm can be extended. The proposed scheme is illustrated by an academical example.     

A Dirichlet form approach to MCMC optimal scaling

This paper shows how the theory of Dirichlet forms can be used to deliver proofs of optimal scaling results for Markov chain Monte Carlo algorithms (specifically, Metropolis–Hastings random walk samplers) under regularity conditions which are substantially weaker than those required by the original approach (based on the use of infinitesimal generators). The Dirichlet form methods have the added advantage of providing an explicit construction of the underlying infinite-dimensional context. In particular, this enables us directly to establish weak convergence to the relevant infinite-dimensional distributions.     

The relationship between coefficients of expansion and heat capacities of simple metals

The authors of this paper, being intrigued by statements in the literature that the coefficients of expansion of metals are proportional to the heat capacities, have put these statements to the test. This paper shows that the experimental ratios of coefficients of expansion and heat capacities at constant pressure are indeed a constant for each metal over wide temperature ranges and the constants are in fair agreement with the values computed from theory.     

On the generation and characterization of the spiro[2,5]octadienyl anion in the gas phase

Three routes have been explored in both a high-pressure chemical ionization (CI) source and a low-pressure Fourier transform ion cyclotron resonance (FT-ICR) cell to generate the spiro[2,5]octadienyl anion in the gas phase: (i) proton abstraction from spiro[2,5]octa-4,6-diene; (ii) expulsion of trimethysilyl fluoride by phenyl ring participation following fluoride anion attack upon the silicon centre of 2-phenylethyl trimethylsilane; and (iii) collisionally induced dissociation (CID) of the carboxylate anion of 3-phenylpropanoic acid via carbon dioxide loss. From comparison of the CID spectra of various reference [C₈H₉]^? ions with those of the [C₈H₉]^? ions which could be generated via the routes (i) and (iii) in the CI source it can be concluded that only the third route yields a [C₈H₉]^?ion whose CID spectrum is not inconsistent with the one expected for the spiro[2,5]octadienyl anion. In the FT-ICR cell [C₈H₉]^? ions are generated along all three routes; their structures have been identified by specific ion-molecule reactions and appear to be different. Route (i) yields an α-methyl benzyl anion, probably due to isomerization within the ion-molecule complex formed. An ortho-ethylphenyl anion is formed along route (ii), presumably due to an intramolecular ortho proton abstraction in the generated trimethylsilyl fluoride solvated 2-phenylethyl primary carbanion. The [C₈H₉]^? ion formed along route (iii) shows reactions similar to those of the 1,1-dimethylcyclohexadienyl anion which is structurally related to the spiro[2,5]octadienyl anion. Furthermore, the [C₈H₉]^? ion generated via route (iii) reacts with hexafluorobenzene under expulsion of only one hydrogen fluoride molecule which contains exclusively one of the original phenyl ring hydrogen atoms. On the basis of all these observations it is therefore quite likely that the spiro[2,5]octadienyl anion is formed by collisionally induced decarboxylation of the 3-phenylpropanoic acid carboxylate anion and can be a long-lived and stable species in the gas phase.     

Temperature driven reactant solubilization synthesis of BiCuOSe

Phase-pure BiCuOSe, which is isostructural to the layered p-type transparent conductor LaCuOS, has been synthesized in high yield by a single-step hydrothermal reaction at low temperature (250 degrees C) and pressure (<20 atm). A moderate reaction temperature of 250 degrees C was sufficiently high to solubilize both Bi2O3 and Cu2O and stabilize monovalent copper and low enough to impede the oxidation of dianionic selenium. BiCuOSe exhibits a relatively high electrical conductivity (sigma approximately 3.3 S cm(-1)) and a reduced band gap (E(g) = 0.75 eV), which compare favorably with the optoelectronic properties of BiCuOS and the cerium-based oxysulfides, CeAgOS and CeCuOS.     

Solutions of the congruence

To supplement existing data, solutions of are tabulated for primes with and . For , five new solutions 2^{32}$"> are presented. One of these, for , also satisfies the ``reverse' congruence . An effective procedure for searching for such ``double solutions' is described and applied to the range , . Previous to this, congruences are generally considered for any and fixed prime to see where the smallest prime solution occurs.

     

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.     

Thermal study of PN thermoelectric couple by laser induced Seebeck EMF measurement

We propose in this paper an in-depth study of a method, both experimental and theoretical, for the determination of thermoelectric properties, in single, or multi-layered thermoelectric devices. We use a modulated laser beam as a heater in order to generate a thermally induced Seebeck EMF. The laser beam, line shaped, can be focused at any location along the sample surface, allowing spatially resolved measurements. Seebeck EMF measurements, associated with a versatile modeling method based on the thermal quadrupoles, allow determining sample Seebeck EMF profile. We contemplate to apply this technique to thermal and thermoelectric properties identification.