Jacobi-type identities in algebras and superalgebras

We introduce two remarkable identities written in terms of single commutators and anticommutators for any three elements of an arbitrary associative algebra. One is a consequence of the other (fundamental identity). From the fundamental identity, we derive a set of four identities (one of which is the Jacobi identity) represented in terms of double commutators and anticommutators. We establish that two of the four identities are independent and show that if the fundamental identity holds for an algebra, then the multiplication operation in that algebra is associative. We find a generalization of the obtained results to the super case and give a generalization of the fundamental identity in the case of arbitrary elements. For nondegenerate even symplectic (super)manifolds, we discuss analogues of the fundamental identity.     

Steady-state analysis of M/M/c/c-type retrial queueing systems with constant retrial rate

The paper deals with a research of bivariate Markov process \(\{X(t), t\ge 0\}\) whose state space is a lattice semistrip \(S(X)=\{0,1,{\ldots },c\} \times Z_{+}\). The process \(\{X(t), t\ge 0\}\) describes the service policy of a multi-server retrial queue in which the rate of repeated flow does not depend on the number of sources of retrial calls. In this class of queues, a vector–matrix representation of steady-state distribution was obtained. This representation allows to write down the stationary probabilities through the model parameters in closed form and to propose the closed formulas of its main performance measures. The investigative techniques use an approximation of the initial model by means of the truncated one and the direct passage to the limit.     

Polysilazane-induced aggregation of hydrophobic silver colloids

Adsorbing polymers such as polysilazanes induce irreversible coagulation of hydrophobic silver colloids in nonpolar solvents. This is accompanied by broadening of the surface plasmon resonance (SPR) peak. A method to analyze the coagulation kinetics based on von Smoluchowski's theory utilizing the SPR change is described. The approach allows evaluating extinction spectra of aggregates of small sizes. A model for polymer adsorption kinetics in combination with a modified bridging efficiency model explains the observed coagulation inhibition over time in terms of macromolecules adsorption, spreading, and mutual repulsion.     

Positive Results and Counterexamples in Comonotone Approximation

We estimate the degree of comonotone polynomial approximation of continuous functions f, on [?1,1], that change monotonicity s??1 times in the interval, when the degree of unconstrained polynomial approximation E _n (f)??n ^??? , n??1. We ask whether the degree of comonotone approximation is necessarily ??c(??,s)n ^??? , n??1, and if not, what can be said. It turns out that for each s??1, there is an exceptional set A _s of ????s for which the above estimate cannot be achieved.     

A Facile Approach to Bis(isoxazoles), Promising Ligands of the AMPA Receptor

A convenient synthetic approach to novel functionalized bis(isoxazoles), the promising bivalent ligands of the AMPA receptor, was elaborated. It was based on the heterocyclization reactions of readily available electrophilic alkenes with the tetranitromethane-triethylamine complex. The structural diversity of the synthesized compounds was demonstrated. In the electrophysiological experiments using the patch clamp technique on Purkinje neurons, the compound 1,4-phenylenedi(methylene)bis(5-aminoisoxazole-3-carboxylate) was shown to be highly potent positive modulator of the AMPA receptor, potentiating kainate-induced currents up to 70% at 10⁻¹¹ M.