Completely positive mappings and mean matrices

Some functions f:R⁺→R⁺ induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices. Moreover, such a function f can define a linear mapping on matrices (which is basic in the constructions of monotone metrics). The present subject is to check the complete positivity of in the case of a few concrete functions f. This problem has been motivated by applications in quantum information.     

Regularity of flat free boundaries in two-phase problems for the p-Laplace operator

In this paper we continue the study in Lewis and Nyström (2010) [19], concerning the regularity of the free boundary in a general two-phase free boundary problem for the p-Laplace operator, by proving regularity of the free boundary assuming that the free boundary is close to a Lipschitz graph.     

Structure of premixed flames of propylene oxide: Molecular beam mass spectrometric study and numerical simulation

The knowledge of the combustion chemistry of oxygenated fuels is essential for the development of detailed kinetic mechanisms suitable for the combustion processes involving biofuels. Moreover, epoxidized olefins, are increasingly used as chemical intermediates or as bulk chemicals. Nevertheless, a dearth of data for their reactivity in the oxidative environment can be observed in the current literature. This study reports the experimental and the model characterization of the flame structure of propylene oxide at stoichiometric and fuel-rich conditions at atmospheric pressure. To this aim, the species mole fractions in three premixed flames stabilized on a flat-flame burner have been quantitatively measured by using the flame sampling molecular beam mass spectrometry. Three chemical kinetic mechanisms retrieved from the current literature involving propylene oxide chemistry have been validated against the novel experimental data. In general, the predictions appeared to be in satisfactory agreement with measurements except for acetaldehyde and ketene. The rate of production analysis in the flame has shown that the discrepancies observed for these species are related basically to the incorrect ratio between the rates of primary reaction pathways of propylene oxide destruction.     

Efficient computation of the Gauss-Newton direction when fitting NURBS using ODR

We consider a subproblem in parameter estimation using the Gauss-Newton algorithm with regularization for NURBS curve fitting. The NURBS curve is fitted to a set of data points in least-squares sense, where the sum of squared orthogonal distances is minimized. Control-points and weights are estimated. The knot-vector and the degree of the NURBS curve are kept constant. In the Gauss-Newton algorithm, a search direction is obtained from a linear overdetermined system with a Jacobian and a residual vector. Because of the properties of our problem, the Jacobian has a particular sparse structure which is suitable for performing a splitting of variables. We are handling the computational problems and report the obtained accuracy using different methods, and the elapsed real computational time. The splitting of variables is a two times faster method than using plain normal equations.     

Jensen measures and boundary values of plurisubharmonic functions

We study different classes of Jensen measures for plurisubharmonic functions, in particular the relation between Jensen measures for continuous functions and Jensen measures for upper bounded functions. We prove an approximation theorem for plurisubharmonic functions inB-regular domain. This theorem implies that the two classes of Jensen measures coincide inB-regular domains. Conversely we show that if Jensen measures for continuous functions are the same as Jensen measures for upper bounded functions and the domain is hyperconvex, the domain satisfies the same approximation theorem as above. The paper also contains a characterisation in terms of Jensen measures of those continuous functions that are boundary values of a continuous plurisubharmonic function.     

Convergence analysis of the local defect correction method for diffusion equations

Summary. This paper is concerned with the convergence analysis of the local defect correction (LDC) method for diffusion equations. We derive a general expression for the iteration matrix of the method. We consider the model problem of Poisson's equation on the unit square and use standard five-point finite difference discretizations on uniform grids. It is shown via both an upper bound for the norm of the iteration matrix and numerical experiments, that the rate of convergence of the LDC method is proportional to H ² with H the grid size of the global coarse grid. Mathematics Subject Classification (2000):65N22, 65N50     

Precision measurements with LPCTrap at GANIL

The experimental achievements and the results obtained so far with the LPCTrap device installed at GANIL are presented. The apparatus is dedicated to the study of the weak interaction at low energy by means of precise measurements of the β ? ν angular correlation parameter in nuclear β decays. So far, the data collected with three isotopes have enabled to determine, for the first time, the charge state distributions of the recoiling ions, induced by shakeoff process. The analysis is presently refined to deduce the correlation parameters, with the potential of improving both the constraint deduced at low energy on exotic tensor currents (⁶He¹⁺) and the precision on the V _{u d} element of the quark-mixing matrix (³⁵Ar¹⁺ and ¹⁹Ne¹⁺) deduced from the mirror transitions dataset.     

Influence of Ga/(Ga + In) grading on deep‐defect states of Cu(In,Ga)Se2 solar cells

The benefits of gallium (Ga) grading on Cu(In,Ga)Se₂ (CIGS) solar cell performance are demonstrated by comparing with ungraded CIGS cells. Using drive‐level capacitance profiling (DLCP) and admittance spectroscopy (AS) analyses, we show the influence of Ga grading on the spatial variation of deep defects, free‐carrier densities in the CIGS absorber, and their impact on the cell's open‐circuit voltage V_oc. The parameter most constraining the cell's V_oc is found to be the deep‐defect density close to the space charge region (SCR). In ungraded devices, high deep‐defect concentrations (4.2 × 10¹⁶cm^–3) were observed near the SCR, offering a source for Shockley–Read–Hall recombination, reducing the cell's V_oc. In graded devices, the deep‐defect densities near the SCR decreased by one order of magnitude (2.5 × 10¹⁵ cm^–3) for back surface graded devices, and almost two orders of magnitude (8.6 × 10¹⁴ cm^–3) for double surface graded devices, enhancing the cell's V_oc. In compositionally graded devices, the free‐carrier density in the absorber's bulk decreased in tandem with the ratio of gallium to gallium plus indium ratio GGI = Ga/(Ga + In), increasing the activation energy, hindering the ionization of the defect states at room temperature and enhancing their role as recombination centers within the energy band. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

A piston-and-cylinder device for compressibility studies on polymers and other “soft” materials

Abstract

We describe an all-steel piston-and-cylinder device for pVT studies on “soft” materials, including liquids, in the range 100–450 K and 0–1.5 GPa. The internal diameter is 15 mm with sample lengths between 10 and 50 mm. Piston displacements are measured to within 0.1 μm using differential transformer transducers. Pressure is calculated from force per unit area and the deformation of pistons and cylinder under pressure are taken into account. The inaccuracy in ΔV/V is less than 0.5%. Experimental data are shown for indium and urea.     

Two Questions of Erdős on Hypergraphs above the Turán Threshold

For ordinary graphs it is known that any graph G with more edges than the Turán number of must contain several copies of , and a copy of , the complete graph on vertices with one missing edge. Erd?s asked if the same result is true for , the complete 3‐uniform hypergraph on s vertices. In this note, we show that for small values of n, the number of vertices in G, the answer is negative for . For the second property, that of containing a , we show that for the answer is negative for all large n as well, by proving that the Turán density of is greater than that of .