We construct differential forms of all orders and a covariant derivative together with its adjoint on the probability space of a standard Poisson process, using derivation operators. In this framewok we derive a de Rham-HodgeKodaira decomposition as well as Weitzenböck and Clark-Ocone formulae for random differential forms. As in the Wiener space setting, this construction provides two distinct...

It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the power spectrum behavior of the excitation energy fluctuations, which is different for chaotic and integrable systems. Using random matrix theory, we derive theoretical expressions that explain without free parameters the universal behavi...

Let gl(n, R) be the Lie algebra consisting of all n × n matrices over a commutative ring R with identity 1. In this paper, we prove that every generalized Lie triple derivation of gl(n, R)(n ≥ 2) is the sum of a Lie triple derivation and a homothety.

We consider large-N multi-matrix models whose action closely mimics that of Yang–Mills theory, including gauge-fixing and ghost terms. We show that the factorized Schwinger–Dyson loop equations, expressed in terms of the generating series of gluon and ghost correlations G(ξ), are quadratic equations S G = GξG in concatenation of correlations. The Schwinger–Dyson operator S i is built from the l...

let a be a banach algebra. a is called ideally amenable if for every closed ideal i of a, the first cohomology group of a with coefficients in i* is trivial. we investigate the closed ideals i for which h1 (a,i* )={0}, whenever a is weakly amenable or a biflat banach algebra. also we give some hereditary properties of ideal amenability.

let r and s be reduced rings with identities whose idempotents are central, and let m be an(r, s)-bimodule such that annr (m)=0. in this paper, we determine first the structure of automorphisms ofthe triangular ring, =sr mt0, and then, for all automorphisms α ,β of t we determine the structureof (α,β)-derivations of t.

This is a case report of a 51 year old male who was found to have an incidental left sided non-functioning adrenal mass on routine medical examination and which was confirmed by CT and MRI scans. A laparoscopic left adrenalectomy was done. On gross examination the tumour was a solitary well circumscribed solid-cystic mass with a homogenous pinkish white cut surface. On microscopic examination, ...

A fundamental physics-based derivation of intraspecific scaling laws of vascular trees has not been previously realized. Here, we provide such a theoretical derivation for the volume-diameter and flow-length scaling laws of intraspecific vascular trees. In conjunction with the minimum energy hypothesis, this formulation also results in diameter-length, flow-diameter and flow-volume scaling laws...