A discrete function f defined on Zn is said to be logconcave if f(λx+(1− λ)y) ≥ [f(x)]λ[f(y)]1−λ for x, y, λx + (1− λ)y ∈ Zn. A more restrictive notion is strong unimodality. Following Barndorff-Nielsen (1973) a discrete function p(z), z ∈ Zn is called strongly unimodal if there exists a convex function f(x), x ∈ Rn such that f(x) = − log p(x), if x ∈ Zn. In this paper sufficient conditions are...

We give first a simple proof of a generalized Jacobi identity for n-dimensional odd diagonal lattices which specializes to the classical Jacobi identity for the lattice Z2. For Z +√ Z, it recovers a one-parameter family of Jacobi identities discovered recently by Chan, Chua and Solé, used to deduce two quadratically converging algorithms for computing π corresponding to elliptic functions for t...

The present study seeks to investigate the role of cathepsin L in glutamate receptor-induced transcription factor nuclear factor-kappa B (NF-κB) activation and excitotoxicity in rats striatal neurons. Stereotaxic administration of the N-methyl-d-aspartate (NMDA) receptor agonist Quinolinic acid (QA) into the unilateral striatum was used to produce the in vivo excitotoxic model. Co-administratio...

We have implemented a simple model to identify the likely sites of the first stars and galaxies in the high-resolution simulations of the formation of galactic dark matter halos of the Aquarius Project. The first star in a galaxy like the Milky Way formed around redshift z = 35; by z = 10, the young galaxy contained up to ∼ 3 × 10 dark matter haloes capable of forming stars by molecular hydroge...

We construct and study a new near octagon of order (2, 10) which has its full automorphism group isomorphic to the group G2(4) : 2 and which contains 416 copies of the Hall-Janko near octagon as full subgeometries. Using this near octagon and its substructures we give geometric constructions of the G2(4)-graph and the Suzuki graph, both of which are strongly regular graphs contained in the Suzu...

We consider a generalized version of the proximal point algorithm for solving the perturbed inclusion y ∈ T (x), where y is a perturbation element near 0 and T is a set-valued mapping acting from a Banach space X to a Banach space Y which is metrically regular around some point point (x̄, 0) in its graph. We study the behavior of the convergent iterates generated by the algorithm and we prove th...

We investigate if every quasi-minimal group is abelian, and give a positive answer for a quasi-minimal pure group having a ∅-definable partial order with uncountable chains. We also relate two properties of a complete theory in a countable language: the existence of a quasi-minimal model and the existence of a strongly regular type. As a consequence we derive the equivalence of conjectures on c...

We develop a theory of representations in Rm for directed strongly regular graphs, which gives a new proof of a nonexistence condition of Jørgensen [8]. We also describe some new constructions.