The correlations in a star molecule fluid. Integral equation theory and Monte Carlo study

The structure of a starlike molecule (SLM) fluid with four arms of different length is studied by applying the associative Percus–Yevick integral equation (IE) theory and canonical Monte Carlo (MC) simulations. In the IE study the SLM fluid is modelled by a fluid of hard spheres with four associative sites on each sphere while the MC has been performed for a freely-joined tangent hard sphere fluid. The total radial distribution functions have been calculated in both approaches for different volume fraction regimes and different arm lengths. It is shown that the associative IE theory predicts the structure of SLM fluid best for relatively long arms and at high densities. Additionally, the dependence of the SLM centre–centre correlations on the functionality and fluid particle density has been analysed using the MC results.     

Recovery of differential equations with nonlinear dependence on the spectral parameter

The inverse spectral problem of recovering pencils of second-order differential operators on the half-line is studied. We give a formulation of the inverse problem, prove the uniqueness theorem and provided a procedure for constructing the solution of the inverse problem. We also establishe connections with inverse problems for partial differential equations.     

Inverse problem for differential pencils on a hedgehog graph

We study boundary value problems on a hedgehog graph for second-order ordinary differential equations with a nonlinear dependence on the spectral parameter. We establish properties of spectral characteristics and consider the inverse spectral problem of reconstructing the coefficients of a differential pencil on the basis of spectral data. For this inverse problem, we prove a uniqueness theorem and obtain a procedure for constructing its solution.     

A Lightweight Flexible Solar Cell Based on a Heteroepitaxial InGaP/GaAs Structure

Technical Physics - Problems arising in fabrication of lightweight flexible solar cells based on heteroepitaxial AIIIBV structures with substrate etching are discussed. Possible solutions are...     

Electrochemical oxidative phosphorylation of azoles in the presence of silver catalysts

A new method for the phosphorylation of benzo-1,3-azoles (benzoxazole, benzothiazole, and 3-methylindole) with diethyl phosphite by electrocatalytic oxidation was proposed. The process occurs under electrochemical mild conditions (room temperature, normal pressure) in the presence of silver salts or silver oxide. This method allows one to obtain 2-phosphorylated products of benzo-1,3-azoles in good yield (up to 75%).     

On Ambarzumyan-type theorems

Generalizations of the classical Ambarzumyan theorem are provided for wide classes of self-adjoint differential operators with arbitrary self-adjoint boundary conditions: scalar Sturm–Liouville operators, higher-order differential operators, matrix Sturm–Liouville operators and operators on spatial networks.     

A Remark on Inverse Problems for Sturm�CLiouville Operators on Graphs

We compare some formulations of the inverse spectral problems for differential operators on graphs with the classical inverse problems on an interval.