Some genus 3 curves with many points

Using an explicit family of plane quartic curves, we prove the existence of a genus 3 curve over any finite field of characteristic 3 whose number of rational points stays within a fixed distance from the Hasse-Weil-Serre upper bound. We also provide an intrinsic characterization of so-called Legendre elliptic curves

Representations and KK-theory of Discrete Groups

Let $\Gamma$ be a discrete group of finite virtual cohomological dimension with certain finiteness conditions of the type satisfied by arithmetic groups. We define a representation ring for $\Gamma$, determined on its elements of finite order, which is of finite type. Then we determine the contribution of this ring to the topological $K$-theory $K^*(B\Gamma)$, obtaining an exact formula for the difference in terms of the cohomology of the centralizers of elements of finite order in $\Gamma$.Comment: 4 page

Strongly bounded groups and infinite powers of finite groups

We define a group as strongly bounded if every isometric action on a metric space has bounded orbits. This latter property is equivalent to the so-called uncountable strong cofinality, recently introduced by G. Bergman. Our main result is that G^I is strongly bounded when G is a finite, perfect group and I is any set. This strengthens a result of Koppelberg and Tits. We also prove that omega_1-existentially closed groups are strongly bounded.Comment: 10 pages, no figure. Versions 1-3 were entitled "Uncountable groups with Property (FH)". To appear in Comm. Algebr

Group entropies, correlation laws and zeta functions

The notion of group entropy is proposed. It enables to unify and generalize many different definitions of entropy known in the literature, as those of Boltzmann-Gibbs, Tsallis, Abe and Kaniadakis. Other new entropic functionals are presented, related to nontrivial correlation laws characterizing universality classes of systems out of equilibrium, when the dynamics is weakly chaotic. The associated thermostatistics are discussed. The mathematical structure underlying our construction is that of formal group theory, which provides the general structure of the correlations among particles and dictates the associated entropic functionals. As an example of application, the role of group entropies in information theory is illustrated and generalizations of the Kullback-Leibler divergence are proposed. A new connection between statistical mechanics and zeta functions is established. In particular, Tsallis entropy is related to the classical Riemann zeta function.Comment: to appear in Physical Review

Defect mediated melting and the breaking of quantum double symmetries

In this paper, we apply the method of breaking quantum double symmetries to some cases of defect mediated melting. The formalism allows for a systematic classification of possible defect condensates and the subsequent confinement and/or liberation of other degrees of freedom. We also show that the breaking of a double symmetry may well involve a (partial) restoration of an original symmetry. A detailed analysis of a number of simple but representative examples is given, where we focus on systems with global internal and external (space) symmetries. We start by rephrasing some of the well known cases involving an Abelian defect condensate, such as the Kosterlitz-Thouless transition and one-dimensional melting, in our language. Then we proceed to the non-Abelian case of a hexagonal crystal, where the hexatic phase is realized if translational defects condense in a particular rotationally invariant state. Other conceivable phases are also described in our framework.Comment: 10 pages, 4 figures, updated reference

Fabrication of ultrathin MIL-96(Al) films and study of CO2 adsorption/desorption processes using quartz crystal microbalance

This contribution reports the fabrication and characterization of ultrathin films of nanoparticles of the water stable microporous Al tricarboxylate metal organic framework MIL-96(Al). The preparation of MOF dispersions in chloroform has been optimized to obtain dense monolayer films of good quality, without nanoparticle agglomeration, at the air-water interface that can be deposited onto solid substrates of different nature without any previous substrate functionalization. The MOF studied shows great interest for CO2 capture because it presents Al3+ Lewis centers and hydroxyl groups that strongly interact with CO2 molecules. A comparative CO2 adsorption study on drop-cast, Langmuir-Blodgett (LB) and Langmuir-Schaefer (LS) films using a Quartz Crystal Microbalance-based setup (QCM) has revealed that the CO2 uptake depends strongly on the film fabrication procedure and the storage conditions. Noteworthy the CO2 adsorption capacity of LB films is increased by 30% using a simple and green treatment (immersion of the film into water during 12 h just after film preparation). Finally, the stability of LB MOF monolayers upon several CO2 adsorption/desorption cycles has been demonstrated, showing that CO2 can be easily desorbed from the films at 303 K by flowing an inert gas (He). These results show that MOF LB monolayers can be of great interest for the development of MOF-based devices that require the use of very small MOF quantities, especially gas sensors

A Theory of Object Recognition: Computations and Circuits in the Feedforward Path of the Ventral Stream in Primate Visual Cortex

We describe a quantitative theory to account for the computations performed by the feedforward path of the ventral stream of visual cortex and the local circuits implementing them. We show that a model instantiating the theory is capable of performing recognition on datasets of complex images at the level of human observers in rapid categorization tasks. We also show that the theory is consistent with (and in some case has predicted) several properties of neurons in V1, V4, IT and PFC. The theory seems sufficiently comprehensive, detailed and satisfactory to represent an interesting challenge for physiologists and modelers: either disprove its basic features or propose alternative theories of equivalent scope. The theory suggests a number of open questions for visual physiology and psychophysics

Optimization of MIL-178(Fe) and Pebax® 3533 loading in mixed matrix membranes for CO2 capture

Global warming is considered as a consequence of extensive use of fossil fuels. Post combustion CO2 capture is an interesting and alternative solution where mixed matrix membranes (MMMs) can be an exciting candidate. This research focuses on the optimization of MMM composition consisting of Pebax® 3533 as the polymer matrix and porous coordination polymer (PCP) MIL-178(Fe) as a filler for gas separation application. MIL-178(Fe) characterized with SEM, TEM and TGA were applied to compare bare polymer and MMM. Optimum composition of the MMM obtained was 5 wt.% MIL-178(Fe) in Pebax® 3533. Average thickness of the optimized dense MMM was 116 ± 8 µm. Such MMM showed CO2 permeability and CO2/N2 selectivity of 312 ± 5 Barrer and 25.0 ± 0.5, respectively, 12% and 25% improved regarding the bare membrane. Additionally, optimum MMM was applied for CO2/CH4 separation and successfully compared in terms of improved CO2 permeability and CO2/CH4 selectivity

Asymptotic description of solutions of the exterior Navier Stokes problem in a half space

We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall, in an otherwise unbounded domain. This situation is modeled by the incompressible Navier-Stokes equations in an exterior domain in a half space, with appropriate boundary conditions on the wall, the body, and at infinity. We focus on the case where the size of the body is small. We prove in a very general setup that the solution of this problem is unique and we compute a sharp decay rate of the solution far from the moving body and the wall