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.     

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.     

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     

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.     

Monte Carlo study of impact ionization in n-type InAs induced by intense ultrashort terahertz pulses

Electron impact ionization induced in n-type InAs by single-cycle pulses of picosecond and subpicosecond duration has been investigated by Monte Carlo method. It is established that the rate of generation of electron–hole pairs decreases with the decrease of the pulse duration. The impact ionization threshold field is found to depend linearly on frequency for the fields oscillating at frequencies much higher than reciprocal momentum relaxation time. Good agreement between calculations and available experimental data has been obtained.     

Aerosol source (biomass,traffic and coal emission) apportionment in Lithuania using stable carbon and radiocarbon analysis*

In the present study, a combination of the stable carbon isotope ratio (¹³C/¹²C) with radiocarbon data (¹⁴C) allowed us to perform the aerosol source apportionment. Filter samples of PM₁ were collected during the warm and cold periods in rural and urban sites in Lithuania. The ¹⁴C/¹²C ratio of total carbon (TC) was measured using the single stage accelerator mass spectrometer quantifying of fossil and non-fossil derived aerosol emissions. The δ¹³C value was measured using an elemental analyser interfaced with an isotope ratio mass spectrometer. We have found that the highest fraction of contemporary carbon (f_c?=?0.82) was measured during a warm period in a rural location. A higher fraction of fossil fuel-derived carbon was observed for air masses transported from highly industrialized Western European regions during both seasons. Isotope mass balance calculations revealed that the traffic emissions composed 15 and 25?% in rural and urban sites, respectively, and did not change during either season. Input from coal-derived aerosol particles was estimated to be 15?% at an urban site during the cold period. The combination of the stable carbon isotope ratio with the radiocarbon data allowed us to distinguish coal, liquid fossil fuel combustion, and non-fossil derived aerosol particle emissions.     

Decidability of Some Classes of Modal Logic

We describe a modal sequential calculus some modal rules of which do not contain duplications of the main formula. We also prove its equivalence to the modal calculus S4 and the decidability of some classes of formulas containing only oneplace predicate variables.