The triple pyrophosphate Cs3CaFe(P2O7)2

The complex phosphate tricaesium calcium iron bis(diphosphate), Cs₃CaFe(P₂O₇)₂, has been prepared by the flux method. Isolated [FeO₅] and [CaO₆] polyhedra are linked by two types of P₂O₇ groups into a three‐dimensional framework. The latter is penetrated by hexagonal channels along the a axis where three Cs atoms are located. Calculations of caesium Voronoi–Dirichlet polyhedra give coordination schemes for the three Cs atoms as [8 + 3], [9 + 1] and [9 + 4]. The structure includes features of both two‐ and three‐dimensional frameworks of caesium double pyrophosphates.     

Optical and microstructural properties of self-assembled InAs quantum structures in silicon

The InAs quantum structures were formed in silicon by sequential ion implantation and subsequent thermal annealing. Two kinds of crystalline InAs nanostructures were successfully synthesized: nanodots (NDs) and nanopyramids (NPs). The peaks at 215 and 235 cm^?1, corresponding to the transverse optical (TO) and longitudinal optical (LO) InAs single-phonon modes, respectively, are clearly visible in the Raman spectra. Moreover, the PL band at around 1.3 µm, due to light emission from InAs NDs with an average diameter 7±2 nm, was observed. The InAs NPs were found only in samples annealed for 20 ms at temperatures ranging from 1000 up to 1200°C. The crystallinity and pyramidal shape of InAs quantum structures were confirmed by HRTEM and XRD techniques. The average size of the NPs is 50 nm base and 50 nm height, and they are oriented parallel to the Si (001) planes. The lattice parameter of the NPs increases from 6.051 to 6.055 Å with the annealing temperature increasing from 1100 to 1200°C, due to lattice relaxation. Energy dispersive spectroscopy (EDS) shows almost stoichiometric composition of the InAs NPs.     

On Toughness and Hamiltonicity of 2K2‐Free Graphs

The toughness of a (noncomplete) graph G is the minimum value of t for which there is a vertex cut A whose removal yields components. Determining toughness is an NP‐hard problem for general input graphs. The toughness conjecture of Chvátal, which states that there exists a constant t such that every graph on at least three vertices with toughness at least t is hamiltonian, is still open for general graphs. We extend some known toughness results for split graphs to the more general class of 2K₂‐free graphs, that is, graphs that do not contain two vertex‐disjoint edges as an induced subgraph. We prove that the problem of determining toughness is polynomially solvable and that Chvátal's toughness conjecture is true for 2K₂‐free graphs.     

Regular 4‐critical graphs of even degree

In 1960, Dirac posed the conjecture that r‐connected 4‐critical graphs exist for every r ≥ 3. In 1989, Erd?s conjectured that for every r ≥ 3 there exist r‐regular 4‐critical graphs. In this paper, a technique of constructing r‐regular r‐connected vertex‐transitive 4‐critical graphs for even r ≥ 4 is presented. Such graphs are found for r = 6, 8, 10. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 103–130, 2004     

Parametric analysis of the oscillatory solutions to stochastic differential equations with the Wiener and Poisson components by the Monte Carlo method

Using the Monte Carlo method, we address the influence of the Wiener and Poisson random noises on the behavior of oscillatory solutions to systems of stochastic differential equations (SDEs). For the linear and Van der Pol oscillators, we study the accuracy of estimates of the functionals of numerical solutions to SDEs obtained by the generalized explicit Euler method. For a linear oscillator, we obtain the exact analytical expressions for the mathematical expectation and the variance of the SDE solution. These expressions allow us to investigate the dependence of the accuracy of estimates of the solution moments on the values of SDE parameters, the size of meshsize, and the ensemble of simulated trajectories of the solution. For the Van der Pol oscillator, we study the dependence of the frequency and the damping rate of the oscillations of the mathematical expectation of SDE solution on the values of parameters of the Poisson component. The results of the numerical experiments are presented.     

On disjunctions of algebraic sets in completely simple semigroups

A semigroup S is called an equational domain if any finite union of algebraic sets over S is algebraic. We give some necessary and su?cient conditions for a completely simple semigroup to be an equational domain.     

Reactions of fluorinated silanes with 2-nitrocinnamates

The interaction of 2-nitrocinnamates with silicon reagents Me₃SiR_f (R_f = CF₃, C₂F₅, and C₆F₅) promoted either by sodium acetate in DMF or by tetrabutylammonium acetate in dichloromethane has been described. The reactions proceed as conjugate addition of fluorinated carbanion at the CC bond and afford 3-aryl-2-nitrobutanoates bearing a fluorinated substituent in good yields as diastereomeric mixtures in ratio from 1:1 to 1.6:1.     

Electrochemical scanning tunnelling spectroscopy of a ferrocene-modified n-Si(111)-surface: electrolyte gating and ambipolar FET behaviour

As revealed for the first time by in situ scanning tunnelling spectroscopy (STS), ferrocene-modified Si(111) substrates show ambipolar field effect transistor (FET) behaviour upon electrolyte gating.