The Reaction of Cs2[Tc(NO)F5] with BF3 in Acetonitrile: Formation and Structure of [{Tc(NO)(CH3CN)4}2(μ‐F)](BF4)3

The deep blue, paramagnetic Cs₂[Tc^II(NO)F₅] is formed during reactions of pertechnetate, acetohydroxamic acid, and CsF in aqueous HF. A reaction of Cs₂[Tc(NO)F₅] with BF₃ · MeOH in acetonitrile gives yellow blocks of the fluorido‐bridged dimer [{Tc^I(NO)(CH₃CN)₄}₂F](BF₄)₃. The compound is stable as solid and in acetonitrile solutions. The complex cation contains a bent μ‐F^– ligand and two linear nitrosyl groups.     

Benz[c]octalen

An expedient new synthesis of benzo[c]octalene starting from the Diels-Alder adduct of benzocyclobutadiene to 7,8-dimethylenecycloocta-1,3,5-triene is described. This octalene derivative, in solution, exists as an equilibrating mixture of the double bond isomers (2) and (3) whereas in its crystalline state only the isomer (2) is present.     

Selective mono,bis, and trisiminoformylation of 2,4,6-trialkyl-1,3,5-triazines - unusual enol acylenamine tautomerism of hydroxyalkenyl-1,3,5-triazines

2,4,6-Trialkyl-1,3,5-triazines 1 can selectively be mono, bis or trisiminoformylated by reaction with trismorpholinomethane 2 or chloromethylene iminium salts 3 (Vilsmeier reagents), with each alkyl substituent reacting with only one molecule of the electrophile. The resulting aminoalkenyltriazines 4, 5 and 6 are partially or fully hydrolysed to corresponding formylation products. The latter exist either in enol or in unusual acylenamine tautomeric structures 10, 12 , and 13 , depending on the number of enamine or enol units found in the molecule. Reaction of triazines 1 with chlorobenzylidene iminium salts 16 gives monoiminobenzoylation to enaminotriazines 17 .     

Planetenbewegungen des Flaggenraumes

In [8] the author gave a report on some properties of flag space motions, especially of the composition of screw motions or rotations in flag space. Planet motions more generally are motions which can be composed by two one-parameter-groups. These motions are investigated with respect to their orbits, their multiple ways of construction and the tubular surfaces they can determine. Some of them yield tubular screw surfaces, some others move every sphere the way that it again envellopes a sphere. These motions, which have no Euclidean counterpart, determine non-trivial, kinematically generated LIE-transformations in flag space.     

On the Dynamics of the Classical Transverse Field Ising Chain

We investigate stationary and travelling wave solutions of a special lattice differential equation in one space dimension. Depending on a parameter λ, results are given on the existence, shape and stability for these kind of solutions. The analysis of travelling wave solutions leads us to a functional differential equation with both forward and backward shifts. The existence of solutions of this equation will be proved by use of the implicit function theorem. In particular, we consider kink solutions and periodic solutions.     

Simulations of full multivariate Tweedie with flexible dependence structure

We employ a variables-in-common method for constructing multivariate Tweedie distributions, based on linear combinations of independent univariate Tweedie variables. The method lies on the convolution and scaling properties of the Tweedie laws, using the cumulant generating function for characterization of the distributions and correlation structure. The routine allows the equivalence between independence and zero correlation and gives a parametrization through given values of the mean vector and dispersion matrix, similarly to the Gaussian vector. Our approach leads to a matrix representation of multivariate Tweedie models, which permits the simulations of many known distributions, including Gaussian, Poisson, non-central gamma, gamma, and inverse Gaussian, both positively or negatively correlated.     

Functional Limit Theorems for the Fractional Ornstein–Uhlenbeck Process

Journal of Theoretical Probability - We prove a functional limit theorem for vector-valued functionals of the fractional Ornstein–Uhlenbeck process, providing the foundation for the...