Dimeric ruthenium complexes of dicyanopyrazines: complexes with an unstable mixed-valence state

Pentaammineruthenium complexes bridged by 2,3-dicyanopyrazine and 2,3-dicyano-5, 6-dimethylpyrazine have been prepared and characterized. The bridging ligand binds to the metal atoms through the cyano nitrogen. Complexes can be prepared in the +4 and +6 oxidation states but the mixed-valence, +5, state is not observed experimentally, unlike the previously prepared 1,2-dicyanobenzene dimer which does have a stable +5 state. A simple electronic model is constructed from the spectroscopic data and is used to show that the electronic perturbations caused by the uncomplexed nitrogen atoms in the pyrazine ring are sufficient to drive the disproportionation reaction of the +5 state.     

Spectrum (super-) symmetries of particles in a Coulomb potential

The Schrödinger equation for a spin-0 particle in the field of a dyon is obtained by dimensional reduction of the four-dimensional harmonic oscillator; the reduction is effected by imposing an equivariance condition on the wave functions of the latter system. This geometrical construction allows for a simple derivation of the SO(4, 2) spectrum symmetry of the dyon system. A supermultiplet of one $\text{spin}\text{-}\text{1}\text{2}$ and two spin-0 particles in a Coulomb potential is demonstrated to possess an N = 2 conformal supersymmetry through a generalization of the same method. The states and wave functions for these systems can be obtained from the representation theory of the corresponding symmetry algebras. A particular case for which this approach provides a complete group theoretical analysis is that of the Pauli equation for a $\text{spin}\text{-}\text{1}\text{2}$ particle in the field of a dyon.     

Shifting From Ziegler–Natta to Philips‐Type Catalyst? A Simple and Safe Access to Reduced Titanium Systems for Ethylene Polymerization

Silica‐supported titanium(IV) chloride is readily reduced by Mashima and co‐workers' reagent (1‐methyl‐3,6‐bis(trimethylsilyl)‐1,4‐cyclohexadiene) to afford materials active in ethylene polymerisation without need of aluminum alkyl cocatalyst.     

On the Intersection Problem for Steiner Triple Systems of Different Orders

A Steiner triple system of order v, or STS(v), is a pair (V, ) with V a set of v points and a set of 3-subsets of V called blocks or triples, such that every pair of distinct elements of V occurs in exactly one triple. The intersection problem for STS is to determine the possible numbers of blocks common to two Steiner triple systems STS(u), (U, ), and STS(v), (V, ), with U⊆V. The case where U=V was solved by Lindner and Rosa in 1975. Here, we let U⊂V and completely solve this question for v−u=2,4 and for v≥2u−3. supported by NSERC research grant #OGP0170220. supported by NSERC postdoctoral fellowship. supported by NSERC research grant #OGP007621.     

Reverse lexicographic and lexicographic shifting

A short new proof of the fact that all shifted complexes are fixed by reverse lexicographic shifting is given. A notion of lexicographic shifting, Δ_lex—an operation that transforms a monomial ideal of S = K[x_i: i ∈ ℕ] that is finitely generated in each degree into a squarefree strongly stable ideal—is defined and studied. It is proved that (in contrast to the reverse lexicographic case) a squarefree strongly stable ideal I ⊂ S is fixed by lexicographic shifting if and only if I is a universal squarefree lexsegment ideal (abbreviated USLI) of S. Moreover, in the case when I is finitely generated and is not a USLI, it is verified that all the ideals in the sequence } are distinct. The limit ideal is well defined and is a USLI that depends only on a certain analog of the Hilbert function of I. Research partially supported by NSF grants DMS 0070571 and DMS 0100141.     

Modularity of a certain Calabi-Yau threefold and combinatorial congruences

We prove a certain Calabi-Yau threefold is modular in the sense that the number of points on its reduction modulo p is expressed in terms of the pth coefficient of a weight 4 newform in S₄(Γ₀(6)). We also give a mod p² combinatorial expression for these coefficients. 2000 Mathematics Subject Classification: 11G25, 11G40     

On the R-Matrix Realization of Yangians and their Representations

We study the Yangians associated with the simple Lie algebras of type B, C or D. The algebra can be regarded as a quotient of the extended Yangian whose defining relations are written in an R-matrix form. In this paper we are concerned with the algebraic structure and representations of the algebra . We prove an analog of the Poincaré–Birkhoff–Witt theorem for and show that the Yangian can be realized as a subalgebra of . Furthermore, we give an independent proof of the classification theorem for the finite-dimensional irreducible representations of which implies the corresponding theorem of Drinfeld for the Yangians . We also give explicit constructions for all fundamental representation of the Yangians. Communicated by Petr Kulish Dedicated to Daniel Arnaudon Submitted: November 22, 2005; Accepted: February 1, 2006     

Sugawara and Vertex Operator Constructions for Deformed Virasoro Algebras

From the defining exchange relations of the elliptic quantum algebra, we construct subalgebras which can be characterized as q-deformed W_N algebras. The consistency conditions relating the parameters p, q, N and the central charge c are shown to be related to the singularity structure of the functional coefficients defining the exchange relations of specific vertex operators representations of available when N = 2. Communicated by Petr Kulish Submitted: January 13, 2006; Accepted: March 6, 2006 Dedicated to our friend Daniel Arnaudon     

Gold(I) and platinum(II) complexes with a new diphosphine ligand based on the cyclotriphosphazene platform

A new diphosphine ligand assembled on the cyclotriphosphazene platform forms linear chelate and dimetallic bridged complexes with Au(I) and a cis-chelate complex with Pt(II).