Study of E/Z isomerization of (arylamino)methylidenefuran‐2(3H)‐ones by 1H, 13C, 15N spectroscopy and DFT calculations in different solvents

The structure and configuration of the series of previously unknown arylaminomethylidenefuran‐2(3H)‐ones have been determined in solution by ¹H, ¹³C, ¹⁵N nuclear magnetic resonance spectroscopy including two‐dimensional experiments such as ¹H─¹H COSY, dqCOSY, ¹H─¹³C HSQC, ¹H─¹³C HMBC. It was found that synthesized substances exist as an equilibrium mixture of E‐ and Z‐enamines in solution. It was established on the basis of density functional theory calculations that the exchange between the two push–pull enamines is a simple rotation around an exocyclic partial double bond that depends on the effect of the solvents. Copyright © 2017 John Wiley & Sons, Ltd.     

From molecule to materials: crystalline superlattices of nanoscopic CdS clusters

Make way for a superlattice! A crystalline 3D superlattice of 2.3?nm molecular CdS nanoclusters was prepared from a convenient mononuclear cadmium thiophenolate precursor. HRTEM and STEM tomography show highly crystalline repetition of monodisperse frameworks. This combined with elemental and thermogravimetric analyses suggests an approximate formula [Cd(130)S(103)(SPh)(54)].     

Hydrated zirconia nanoparticles as media for electrical charge accumulation

Journal of Nanoparticle Research - The series of LaF3 nanoparticles with closed pores filled with water H2O and heavy water D2O are synthesized by the hydrothermal treatment in autoclave at...     

Solitary wave and other solutions for nonlinear heat equations

A number of explicit solutions for the heat equation with a polynomial non-linearity and for the Fisher equation is presented. An extended class of non-linear heat equations admitting solitary wave solutions is described. The generalization of the Fisher equation is proposed whose solutions propagate with arbitrary ad hoc fixed velocity.     

Exit problems for the difference of a compound Poisson process and a compound renewal process

In this paper we solve a two-sided exit problem for a difference of a compound Poisson process and a compound renewal process. More specifically, we determine the Laplace transforms of the joint distribution of the first exit time, the value of the overshoot and the value of a linear component at this time instant. The results obtained are applied to solve the two-sided exit problem for a particular class of stochastic processes, i.e. the difference of the compound Poisson process and the renewal process whose jumps are exponentially distributed. The advantage is that these results are in a closed form, in terms of resolvent sequences of the process. We determine the Laplace transforms of the busy period of the systems M ^? |G ^δ |1|B, G ^δ |M ^? |1|B in case when δ～exp?(λ). Additionally, we prove the weak convergence of the two-boundary characteristics of the process to the corresponding functionals of the standard Wiener process.     

Busy period,virtual waiting time and number of customers in G<Superscript><Emphasis Type="Italic">δ</Emphasis></Superscript>|M<Superscript><Emphasis Type="Italic">ϰ</Emphasis></Superscript>|1|B system

In this article, we determine the integral transforms of several two-boundary functionals for a difference of a compound Poisson process and a compound renewal process. Another part of the article is devoted to studying the above-mentioned process reflected at its infimum. We use the results obtained to study a G ^δ |M ^ϰ |1|B system with batch arrivals and finite buffer in the case when δ∼ge(λ). We derive the distributions of the main characteristics of the queuing system, such as the busy period, the time of the first loss of a customer, the number of customers in the system, the virtual waiting time in transient and stationary regimes. The advantage is that these results are given in a closed form, namely, in terms of the resolvent sequences of the process.