A comparison theorem for a piecewise Lipschitz continuous Hamiltonian and application to Shape-from-Shading problems

Summary The reconstruction from a shaded image of a Lambertian and not self-shadowing surface illuminated by a single distant pointwise light source may be written as a first-order Hamilton-Jacobi equation.In this paper, we continue the investigation begun in E. Rouy and A. Tourin into the uniqueness of the solution of this equation; the approach is based on the viscosity solutions theory and the dynamic programming principle.More precisely, we concentrate here on the uniqueness of the viscosity solution of this equation in case the measured luminous intensity reflected by the surface is discontinuous along a smooth curve. We prove a general comparison result for a piecewise Lipschitz continuous Hamiltonian and illustrate it by numerical experiments.     

Comparative Study of Alkali-Cation-Based (Li+, Na+, K+) Electrolytes in Acetonitrile and Alkylcarbonates

The development of a suitable functional electrolyte is urgently required for fast-charging and high-voltage alkali-ion (Li, Na, K) batteries as well as next-generation hybrids supercapacitors. Many recent works focused on an optimal selection of electrolytes for alkali-ion based systems and their electrochemical performance but the understanding of the fundamental aspect that explains their different behaviour is rare. Herein, we report a comparative study of transport properties for LiPF₆, NaPF₆, KPF₆ in acetonitrile (AN) and a binary mixture of ethylene carbonate (EC), dimethyl carbonate (DMC): (EC/DMC : 1/1, weigh) through conductivities, densities and viscosities measurements in wide temperature domain. By application of the Stokes-Einstein, Nernst-Einstein, and Jones Dole equations, the effective ionic solvated radius of cation (r_eff), the ionic dissociation coefficient (α_D) and structuring Jones Dole's parameters (A, B) for salt are calculated and discussed according to solvent or cation nature as a function of temperature. From the results, we demonstrate that better mobility of potassium can be explained by the nature of the ion-ion and ion-solvent interactions due to its polarizability. In the same time, the predominance of triple ions in the case of K⁺, is a disadvantage at high concentration.     

Discrete limit theorems for general Dirichlet series. III

Here we prove a limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for a general Dirichlet series. The explicit form of the limit measure in this theorem is given. Partially supported by Lithuanian Foundation of Studies and Science     

Discrete Universality in the Selberg Class

The Selberg class S consists of functions L(s) that are defined by Dirichlet series and satisfy four axioms (Ramanujan conjecture, analytic continuation, functional equation, and Euler product). It has been known that functions in S that satisfy the mean value condition on primes are universal in the sense of Voronin, i.e., every function in a sufficiently wide class of analytic functions can be approximated by the shifts L(s + iτ ), τ ∈ R. In this paper we show that every function in the same class of analytic functions can be approximated by the discrete shifts L(s + ikh), k = 0, 1,..., where h > 0 is an arbitrary fixed number.     

Enzyme association with lipidic Langmuir-Blodgett films: interests and applications in nanobioscience

This review presents the recent advances in the achievement of organized proteo-lipidic nanostructures based on Langmuir-Blodgett technology and their potential applications in the nanobioscience area. By using the self-assembled properties of amphiphilic biomolecules at the air-water interface, the Langmuir-Blodgett (LB) technique offers the possibility to prepare ultrathin layers suitable for biomolecule immobilization at the molecular level. This review will provide a general overview of the enzyme association with preformed Langmuir-Blodgett films in connection with their potential applications in biosensing device developments, and then introduce the design of a new functionalised biomimetic nanostructure with oriented recognition site. The potential applications of such an organized proteo-lipidic nanostructure for biocatalysis investigations of an immobilised enzyme in a biomimetic situation and for the development of bioelectronic devices are finally discussed.     

Synthesis of Functionalized Mono‐, Bis‐, and Trisethynyltriptycenes for One‐Dimensional Self‐Assembly on Surfaces

This paper describes the synthesis of triptycene‐based building blocks that are able to interact through hydrogen bonds to form one‐dimensional self‐assembled motifs on surfaces. We designed 9,10‐diethynyltriptycene derivatives functionalized at the ethynyl end groups by a variety of hydrogen‐bonding groups for homomolecular recognition and complementary building blocks for heteromolecular recognition. We also present the synthesis of bis‐ and trisethynyltriptycenes with terminal alkyne functional groups available for on‐surface azide–alkyne cycloaddition reaction to expand the potential of the triptycene building block.     

Application of cosmogenic radionuclides in ozone tracer studies

Downward flux of stratospheric ozone contributes to the near ground level ozone concentrations. The intensity, amount of vertical ozone flow can be evaluated by the ratio of two cosmogenic radionuclides (³³P/³²P, ⁷Be/³²P). Some examples presented in this paper are demonstrating the possibilities of this method. The application of tracer method makes evident the seasonal variations (with maxima during the spring — summer months and minima during winter) of the amount of stratospheric ozone in the ground air. Average monthly contribution from stratospheric ozone in the lower level of the atmosphere ranged from 0 to 18% in 1998–99. During short term intervals (2–3 days) the amount of the stratospheric ozone can increase up to ∼90%.     

Micellar Electrokinetic Chromatography of X-Ray Film Developing Baths

A simple and fast micellar electrokinetic chromatographic (MEKC) method for the determination of five main compounds (hydroquinone, metol, phenidone, 2-hydroxy-5-methylaminobenzenesulphonate and 2,5-dihydroxybenzenesulphonate) in X-ray film developing solutions was developed. The optimal conditions for the separation were established by varying the concentration of sodium dodecyl sulfate (SDS), the electrolyte pH and the temperature. Successful results were obtained with a 25mmolL^–1 Tris-phosphate buffer at pH 9.0 in the presence of 50mmolL^–1 SDS using direct UV detection at 214nm. Under these conditions, baseline separation of the five compounds was achieved in less than 8min. The method was validated in terms of precision, linearity, accuracy, and successfully applied to the analysis of X-ray film developing baths.