Let X be a complex elliptic curve. In this paper we define a natural Poisson structure on the moduli spaces of stable triples (E1, E2,Φ) where E1, E2 are algebraic vector bundles on X of fixed ranks (r1, r2) and degrees (d1, d2), Φ : E2 → E1 is a homomorphism. Such triples are considered up to an isomorphism and the stability condition depends on a real parameter τ . These moduli spaces were in...

The common structure of the space of pure states P of a classical or a quantum mechanical system is that of a Poisson space with a transition probability. This is a topological space equipped with a Poisson structure, as well as with a function p : P×P → [0, 1], with certain properties. The Poisson structure is connected with the transition probabilities through unitarity (in a specific formula...

The common structure of the space of pure states P of a classical or a quantum mechanical system is that of a Poisson space with a transition probability. This is a topological space equipped with a Poisson structure, as well as with a function p : P × P → [0, 1], with certain properties. The Poisson structure is connected with the transition probabilities through unitarity (in a specific formu...

The common structure of the space of pure states P of a classical and a quantum mechanical system is that of a Poisson space with a transition probability. This is a uniform space equipped with a Poisson structure, as well as with a function p : P × P → [0, 1], with certain properties. The Poisson structure is connected with the transition probabilities through unitarity: each point ρ ∈ P defin...

In the remainder, we call such a variety a convex symplectic variety. A convex symplectic variety has been studied in [K-V], [Ka 1] and [G-K]. One of main difficulties we meet is the fact that tangent objects TX and T 1 Y are not finite dimensional, since Y may possibly have non-isolated singularities; hence the usual deformation theory does not work well. Instead, in [K-V], [G-K], they introdu...

in the analysis of spatial point patterns, complete spatial randomness (csr) hypothesis,which is a restriction of a homogenous poisson process to study region a, operates as a dividinghypothesis between “regular” and “aggregated” patterns. meanwhile, many alternatives to csr inaggregated patterns are extensions of homogenous poisson processes themselves. therefore, when thecsr hypothesis is rej...

Change point estimation in the area of statistical process control has received considerable attentions in the recent decades because it helps process engineer to identify and remove assignable causes as quickly as possible. On the other hand, improving in measurement systems and data storage, lead to taking observations very close to each other in time and as a result increasing autocorrelatio...

Although the random sum distribution has been well-studied in probability theory, inference for the mean of such distribution is very limited in the literature. In this paper, two approaches are proposed to obtain inference for the mean of the Poisson-Exponential distribution. Both proposed approaches require the log-likelihood function of the Poisson-Exponential distribution, but the exact for...

The elliptic algebra Aq,p(ŝl(N)c) at the critical level c = −N has an extended center containing trace-like operators t(z). Families of Poisson structures, defining q-deformations of the WN algebra, are constructed. The operators t(z) also close an exchange algebra when (−p1/2)NM = q−c−N for M ∈ Z. It becomes Abelian when in addition p = qNh where h is a non-zero integer. The Poisson structures...