Reaction of SbPO4 with lithium in non-aqueous electrochemical cells: preliminary study and evaluation of its electrochemical performance in anodes for lithium ion batteries

SbPO₄, a phosphate with a layered structure, was tested as an electrode material for lithium cells spanning the 3.0-0.0 V range. Two main electrochemical processes were detected as extensive plateaus at ca. 1.6 and 0.7 V in galvanostatic measurements. The first process was found to be irreversible, thus excluding a potential intercalation-like mechanism for the reaction and being better interpreted as a decomposition reaction leading to the formation of elemental Sb. This precludes the use of this compound as a cathodic material for lithium cells. By contrast, the process at 0.7 V is reversible and can be ascribed to the formation of lithium-antimony alloys. The best electrochemical response was obtained by cycling the cell at a C/20 discharge rate over the voltage range 1.25-0.25 V. Under these conditions, the cell delivers an average capacity of 165 Ah/kg—a value greater than those reported for other phosphates—upon successive cycling.     

On divisibility properties of certain multinomial coefficients—II

A recent conjecture of Myerson and Sander concerns divisibility properties of certain multinomial coefficients. We obtain results in this direction by further pursuing a line of attack developed earlier by the first author.     

Small zeros of quadratic forms with linear conditions

Given a quadratic form and M linear forms in N+1 variables with coefficients in a number field K, suppose that there exists a point in K^N+1 at which the quadratic form vanishes and all the linear forms do not. Then we show that there exists a point like this of relatively small height. This generalizes a result of D.W. Masser.     

Separable free quadratic algebras over quadratic integers

The aim of the paper is to determine all free separable quadratic algebras over the rings of integers of quadratic fields in terms of the properties of the fundamental unit in the real case. The paper corrects some earlier published results on the subject.     

The Hochschild class of the Chern character for semifinite spectral triples

We provide a proof of Connes’ formula for a representative of the Hochschild class of the Chern character for (p,∞)-summable spectral triples. Our proof is valid for all semifinite von Neumann algebras, and all integral p?1. We employ the minimum possible hypotheses on the spectral triples.     

Tangent circle bundles admit positive open book decompositions along arbitrary links

In the present paper we generalize the divide lying in the unit disk, introduced by A'Campo, to compact, oriented, smooth surfaces, and prove a fibration theorem for generalized divides. As a consequence, we will show that, for any link L in the tangent circle bundle Y to the compact surface, there exists an additional knot K such that the link L∪K is the binding of a “positive” open book decomposition of Y.     

Zero-divisor graphs, von Neumann regular rings, and Boolean algebras

For a commutative ring R with set of zero-divisors Z(R), the zero-divisor graph of R is Γ(R)=Z(R)−{0}, with distinct vertices x and y adjacent if and only if xy=0. In this paper, we show that Γ(T(R)) and Γ(R) are isomorphic as graphs, where T(R) is the total quotient ring of R, and that Γ(R) is uniquely complemented if and only if either T(R) is von Neumann regular or Γ(R) is a star graph. We also investigate which cardinal numbers can arise as orders of equivalence classes (related to annihilator conditions) in a von Neumann regular ring.     

The convergence rate of continued fractions representing solutions of a Riccati equation

The aim of this note is to generalize and apply results on matrix continued fractions representing the solution of discrete matrix Riccati equations. Assuming uniform bounds for the norm of the matrix coefficients of the continued fraction, the minimal and maximal solutions of the corresponding algebraic Riccati equation can be accurately enclosed.     

First countability, tightness, and other cardinal invariants in remainders of topological groups

We consider the following natural questions: when a topological group G has a first countable remainder, when G has a remainder of countable tightness? This leads to some further questions on the properties of remainders of topological groups. Let G be a topological group. The following facts are established. 1. If Gω has a first countable remainder, then either G is metrizable, or G is locally compact. 2. If G has a countable network and a first countable remainder, then either G is separable and metrizable, or G is σ-compact. 3. Under (MA+¬CH) every topological group with a countable network and a first countable remainder is separable and metrizable. Some new open problems are formulated.