Z_2-graded Gelfand-Kirillov dimension of the Grassmann algebra

We consider the infinite dimensional Grassmann algebra E over a field F of characteristic 0 or p, where p>2, and we compute its Z_2-graded Gelfand-Kirillov dimension as a Z_2-graded PI-algebra

A model for the relatively free graded algebra of block triangular matrices with entries from a graded algebra

Let G be a group and A be a G-graded algebra satisfying a polynomial identity. We buid up a model for the relative free G-graded algebra and we obtain, as an application, the "factoring" property for the T_G-ideals of block triangular matrices with entries from the finite dimensional Grassmann algebra E for some particular Z_2-grading

Value allocations in economies with coalition structure

We embody a notion of stability for coalition structures by Hart and Kurz (1983) into the framework of general equilibrium, by generalizing the classical value allocation notion (Shapley, 1969) to situations where: (a) agents organize themselves voluntarily into coalition structures (b) the process of coalition formation is treated as endogenous. To this end we introduce the definition of stable coalition structure value allocation and provide, under standard hypotheses, a preliminary existence result for the three player case in an exchange economy.

On some recent results about the graded Gelfand-Kirillov dimension of graded PI-algebras

2010 Mathematics Subject Classification: 16R10, 16W55, 15A75.We survey some recent results on graded Gelfand-Kirillov dimension of PI-algebras over a field F of characteristic 0. In particular, we focus on verbally prime algebras with the grading inherited by that of Vasilovsky and upper triangular matrices, i.e., UTn(F), UTn(E) and UTa,b(E), where E is the infinite dimensional Grassmann algebra

Speckle statistics in adaptive optics images at visible wavelengths

Residual speckles in adaptive optics (AO) images represent a well-known limitation on the achievement of the contrast needed for faint source detection. Speckles in AO imagery can be the result of either residual atmospheric aberrations, not corrected by the AO, or slowly evolving aberrations induced by the optical system. We take advantage of the high temporal cadence (1 ms) of the data acquired by the System for Coronagraphy with High-order Adaptive Optics from R to K bands-VIS forerunner experiment at the Large Binocular Telescope to characterize the AO residual speckles at visible wavelengths. An accurate knowledge of the speckle pattern and its dynamics is of paramount importance for the application of methods aimed at their mitigation. By means of both an automatic identification software and information theory, we study the main statistical properties of AO residuals and their dynamics. We therefore provide a speckle characterization that can be incorporated into numerical simulations to increase their realism and to optimize the performances of both real-time and postprocessing techniques aimed at the reduction of the speckle noise