Special Lie superalgebras with maximality condition for subalgebras

We consider finitely generated Lie superalgebras over a field of characteristic zero satisfying Capelli identities. We prove that any such an algebra with the maximality condition for abelian subalgebras is finite dimensional. In particular, any special Lie superalgebra with the maximality condition for its subalgebras has a finite dimension. We also prove that the universal enveloping algebra U(L) of special Lie superalgebra L is Noetherian if and only if $\dim L<\infty$ .     

Peculiarities of the synthesis and thermolysis of heterometallic coordination compounds used as precursors for nickelates of rare-earth elements

The influence of the solvent on the composition of solid products is investigated using the example of the interaction of rare-earth element (REE) nitrates, Ln(NO₃)₃, with square-planar complexes of nickel and Schiff bases, Ni(SB). The composition of solid products is determined by X-ray fluorescence analysis and elemental analysis. It is shown that from the labile Ln(NO₃)₃-Ni(SB) systems, individual heterometallic compounds can be obtained, moreover, if in systems there are complexes with more dentate Ni(mosalen) ligands, only binuclear heterocomplexes can be produced. In case of Ni(salen) ligand, the formation of trinuclear complexes is achieved by selecting the optimal solvent. Among the considered compounds, binuclear complexes are of special interest due to the possibility of their use as precursors of REE nickelates.     

Identification of a source of size polydispersity and its solution in Brust-Schiffrin metal nanoparticle synthesis

The co-presence of thiol vs. disulfide in the well-known Brust-Schiffrin two-phase synthesis has been identified as a source of size polydispersity in nanoparticles synthesized and a procedure has been proposed to address this long outstanding issue.     

Controlled electrochemically-assisted deposition of sol-gel biocomposite on electrospun platinum nanofibers

The modification of platinum nanofibers by silica using the electrochemically-assisted deposition is reported here. Pt nanofibers are obtained by electrospinning and deposited on a glass substrate. The electrochemically-assisted deposition of the sol-gel material then gives the unique possibility to finely tune the silica film thickness around these nanofibers. It also allows the successful encapsulation of a biomolecule (glucose oxidase was chosen here as a model) while retaining its biological activity, as pointed out via the electrochemical monitoring of H(2)O(2) produced upon addition of glucose in the medium. This silica-glucose oxidase composite offers the possibility of comparing systematically the influence of the deposition time on the bioelectrode response and to compare it with the particular features of the deposits. It was found that the film first grew uniformly around the nanofibers and then started to deposit between them, covering the whole sample (fibers and glass substrate), and tended to fully embed the nanofibers for prolonged deposition. The thickness of the silica film is critical for the electroactivity of the biocomposite, the best response being obtained for a silica layer thickness in the range of the fiber diameter (～50 nm).     

Spontaneous electric fields in films of cis-methyl formate

A recent publication described a new group of spontaneously polarized materials in which electric fields in excess of 10(8) V m(-1) may be present. This phenomenon arises through dipole alignment in solid films formed by straightforward deposition from vapour and characterises a novel class of materials. Here we present further results for the properties of these materials, focusing on films of cis-methyl formate. These films are shown to display some notable new chemical physics. We find the novel result that the degree of dipole alignment and the corresponding electric field in films of cis-methyl formate can have a counter-intuitive temperature dependence, increasing six-fold between 80 K and 89 K, in sharp contrast to the pronounced and expected fall with deposition temperature seen both here between 50 K and 75 K and in numerous other species. A theoretical model demonstrates that the switch of gradient with rising temperature should be a general phenomenon and is associated with crossing of a singularity in the gradient occurring at a set of critical values of temperature and alignment.     

Correlation of Electronic and Magnetic Properties of Thin Polymer Layers with Cobalt Nanoparticles

Nanoparticles (NPs) of cobalt are synthesized in shallow layers of polyimide using 40 keV implantation of Co⁺ ions with a few different fluences at various ion current densities. Nucleation of individual NPs at low fluencies and their percolation at high fluencies are crucial processes governing the electrical and magnetic properties of the metal/polymer nanocomposites that can be controlled by the implantation regimes. In particular, one can tune the magnetoresistance between negative and positive through appropriate choice of ion fluence and current density. The found non‐monotonous dependence of the magnetoresistance on the applied magnetic field allows suggestion of spin‐dependent domain wall scattering affecting the electron transport. The samples implanted with low fluencies demonstrate superparamagnetic behavior down to very low blocking temperatures. For high fluence (1.25 × 10¹⁷ cm⁻²) the transition to ferromagnetic ordering is observed that is related to the increased magnetic interaction of NPs.     

Estimates of a sum of Dirichlet series

We study the Dirichlet series with an arbitrary abscissa of absolute convergence. The lower and upper estimates for sums of these series are found. The above results allow us to establish some relations between the maximum modulus and the maximal term of Dirichlet series, especially to find conditions that ensure that the maximum modulus and the maximal term have the same many-term asymptotics.     

Parabolic contractions of semisimple Lie algebras and their invariants

Let $G$ be a connected semisimple algebraic group with Lie algebra $\mathfrak{g }$ and $P$ a parabolic subgroup of $G$ with $\mathrm{Lie\, }P=\mathfrak{p }$ . The parabolic contraction $\mathfrak{q }$ of $\mathfrak{g }$ is the semi-direct product of $\mathfrak{p }$ and a $\mathfrak{p }$ -module $\mathfrak{g }/\mathfrak{p }$ regarded as an abelian ideal. We are interested in the polynomial invariants of the adjoint and coadjoint representations of $\mathfrak{q }$ . In the adjoint case, the algebra of invariants is easily described and it turns out to be a graded polynomial algebra. The coadjoint case is more complicated. Here we found a connection between symmetric invariants of $\mathfrak{q }$ and symmetric invariants of centralisers $\mathfrak{g }_e\subset \mathfrak{g }$ , where $e\in \mathfrak{g }$ is a Richardson element with polarisation $\mathfrak{p }$ . Using this connection and results of Panyushev et al. (J Algebra 313:343–391, 2007), we prove that the algebra of symmetric invariants of $\mathfrak{q }$ is free for all parabolic subalgebras in types $\mathbf A$ and $\mathbf C$ and some parabolics in type $\mathbf B$ . This technique also applies to the minimal parabolic subalgebras in all types. For $\mathfrak{p }=\mathfrak{b }$ , a Borel subalgebra of $\mathfrak{g }$ , one gets a contraction of $\mathfrak{g }$ recently introduced by Feigin (Selecta Math 18:513–537, 2012) and studied from invariant-theoretic point of view in our previous paper (Panyushev and Yakimova in Ann Inst Fourier 62(6):2053–2068, 2012).     

Different mechanisms govern the two-phase Brust-Schiffrin dialkylditelluride syntheses of Ag and Au nanoparticles

Here we report the first unambiguous identification of the chemical structures of the precursor species involving metal (Au and Ag) ions and Te-containing ligands in the Brust-Schiffrin syntheses of the respective metal nanoparticles, through which the different reaction pathways involved are delineated.