Geometry and electronic structure of a heterometallic cluster Mo<Subscript>2</Subscript>Mg<Subscript>2</Subscript> in different oxidation states of Mo: a DFT study

Reduction of tetranuclear heterometallic complex Mo₂Mg₂ was simulated using the B3LYP and PBE density functional methods. The results of geometry calculations of the initial complex [Mo^VIO₂Mg(MeOH)₂(OMe)₄]₂ and a partially reduced Mo^V complex are in good agreement with experimental data. The reduced Mo^III complex is characterized by a decrease in the binding energy of aqua ligands. Structural rearrangement of the complex with release of a coordination position at the Mo atoms requires small energy expenditure. One can assume that the reduction of the polynuclear complex causes overcrowding of its coordination sphere, which favors formation of dinitrogen complexes. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 441–457, March, 2008.     

A local characterization of the johnson scheme

Within the Johnson schemeI(m, d) we find the graphK(m, d) ofd-subsets of anm-set, two such adjacent when disjoint. Among all connected graphs,K(m, d) is characterized by the isomorphism type of its vertex neighborhoods providedm is sufficiently large compared tod. Partial support provided by NSF (USA), SERC (UK), ZWO (NL).     

Low-energy ion-assisted control of interfacial structures in metallic multilayers

A molecular dynamics method has been used to simulate the argon ion-assisted deposition of Cu/Co/Cu multilayers and to explore ion beam assistance strategies that can be used during or after the growth of each layer to control interfacial structures. A low-argon ion energy of 5–10 eV was found to minimize a combination of interfacial roughness and interlayer mixing (alloying) during the ion-assisted deposition of multilayers. However, complete flattening with simultaneous ion assistance could not be achieved without some mixing between the layers when a constant ion energy approach was used. It was found that multilayers with lower interfacial roughness and intermixing could be grown either by modulating the ion energy during the growth of each metal layer or by utilizing ion assistance only after the completion of each layers deposition. In these latter approaches, relatively high-energy ions could be used since the interface is buried and less susceptible to intermixing. The interlayer mixing dependence upon the thickness of the over layer has been determined as a function of ion energy.     

Observation of p(1×1)-type rows on TiO2(110)-p(1×2) surface by scanning tunneling microscope (STM)

The TiO₂(110) surfaces were observed by a Scanning Tunneling Microscope (STM). We found two types of bright p(1×1)-type rows on the p(1×2) surface. One p(1×1)-type formed independently and corresponds to the bridging oxygen rows. The second p(1×1)-type appeared in a bright grouping, forming narrow rows, and corresponds to the five-fold titanium rows. The above results suggest the following two conclusions. First, the density of state (DOS) on the bridging oxygen rows becomes higher than that on the five-fold titanium atom rows when a bridging oxygen row exists independently on the p(1×2) surface. Second, the bright rows on a TiO₂(110)-p(1×1) surface correspond to the five-fold titanium atom rows. The results further show the validity of DOS calculations on the TiO₂(110)-p(1×1) surface by Diebold et al. [Phys. Rev. Lett. 77 (1996) 1322]. The difference of width for Ti₂O₃ unit rows on the p(1×2) and p(1×3) surfaces in STM images are also discussed.     

Bounds on the inverses of nonnegative triangular matrices with monotonicity properties

Some bounds on the entries and on the norm of the inverse of triangular matrices with nonnegative and monotone entries are found. All the results are obtained by exploiting the properties of the fundamental matrix of the recurrence relation which generates the sequence of the entries of the inverse matrix. One of the results generalizes a theorem contained in a recent article of one of the authors about Toeplitz matrices.     

Extendible elements of the alternating groups

An element σ of A_n, the Alternating group of degree n, is extendible in S_n, the Symmetric group of degree n, if there exists a subgroup H of S_n but not A_n whose intersection with A_n is the cyclic group generated by σ. A simple number-theoretic criterion, in terms of the cycle-decomposition, for an element of A_n to be extendible in S_n is given here.     

Congruences,equational theories and lattice representations

We survey results concerning the representations of lattices as lattices of congruences and as lattices of equational theories. Recent results and open problems will be mentioned.To László Fuchs on the occasion of his 70th birthday     

On the geometries of the rational unfoldings of X k

With a view to applications to self-regulating dynamical processes in biology, we determine the geometric structure of what we call isotangent curves, i.e. curves parametrized by the slopes of their points. They come up naturally as bifurcation curves of rational unfoldings of X ^k, and we classify them according to degree and number of cusps. They, as well as their isotangent involute curves, turn up in simulations of these processes.     

Disordered charge distributions and dielectric loss in extra dense flint glasses

The complex permittivities of some extra dense flint glasses (EDF glasses) have been studied. The dielectric features of the samples are dominated by their PbO content. Both refractive indices and dielectric losses exhibit a close relation to the concentration of Pb ions. The latter are located either at sites of the network atoms or filling the potential minima interstitially. They can be identified by their different relaxation mechanisms. The dispersion in the submillimeter wave and FIR area is characterized by a very broad distribution of comparably sharp resonant states. Thermal lens — or hysteresis effects can be excluded.     

A remark on partial linear spaces of girth 5 with an application to strongly regular graphs

We derive a lower bound on the number of points of a partial linear space of girth 5. As an application, certain strongly regular graphs with=2 are ruled out by observing that the first subconstituents are partial linear spaces.