Decidability of quantified propositional intuitionistic logic and S4 on trees

Quantified propositional intuitionistic logic is obtained from propositional intuitionistic logic by adding quantifiers \forall p, \exists p over propositions. In the context of Kripke semantics, a proposition is a subset of the worlds in a model structure which is upward closed. Kremer (1997) has shown that the quantified propositional intuitionistic logic H\pi+ based on the class of all partial orders is recursively isomorphic to full second-order logic. He raised the question of whether the logic resulting from restriction to trees is axiomatizable. It is shown that it is, in fact, decidable. The methods used can also be used to establish the decidability of modal S4 with propositional quantification on similar types of Kripke structures.Comment: v2, 9 pages, corrections and additions; v1 8 page

Irreversible Processes in a Universe modelled as a mixture of a Chaplygin gas and radiation

The evolution of a Universe modelled as a mixture of a Chaplygin gas and radiation is determined by taking into account irreversible processes. This mixture could interpolate periods of a radiation dominated, a matter dominated and a cosmological constant dominated Universe. The results of a Universe modelled by this mixture are compared with the results of a mixture whose constituents are radiation and quintessence. Among other results it is shown that: (a) for both models there exists a period of a past deceleration with a present acceleration; (b) the slope of the acceleration of the Universe modelled as a mixture of a Chaplygin gas with radiation is more pronounced than that modelled as a mixture of quintessence and radiation; (c) the energy density of the Chaplygin gas tends to a constant value at earlier times than the energy density of quintessence does; (d) the energy density of radiation for both mixtures coincide and decay more rapidly than the energy densities of the Chaplygin gas and of quintessence.Comment: 8 pages, 1 figure, to be published in GR

Evidence of a bond-nematic phase in LiCuVO4

Polarized and unpolarized neutron scattering experiments on the frustrated ferromagnetic spin-1/2 chain LiCuVO4 show that the phase transition at HQ of 8 Tesla is driven by quadrupolar fluctuations and that dipolar correlations are short-range with moments parallel to the applied magnetic field in the high-field phase. Heat-capacity measurements evidence a phase transition into this high-field phase, with an anomaly clearly different from that at low magnetic fields. Our experimental data are consistent with a picture where the ground state above HQ has a next-nearest neighbour bond-nematic order along the chains with a fluid-like coherence between weakly coupled chains.Comment: 5 pages, 4 figures. To appear in Phys. Rev. Let

Revealing the pure confinement effect in glass-forming liquids by dynamic mechanical analysis

Many molecular glass forming liquids show a shift of the glass transition Tg to lower temperatures when the liquid is confined into mesoporous host matrices. Two contrary explanations for this effect are given in literature: First, confinement induced acceleration of the dynamics of the molecules leads to an effective downshift of Tg increasing with decreasing pore size. Secondly, due to thermal mismatch between the liquid and the surrounding host matrix, negative pressure develops inside the pores with decreasing temperature, which also shifts Tg to lower temperatures. Here we present novel dynamic mechanical analysis measurements of the glass forming liquid salol in Vycor and Gelsil with pore sizes of d = 2.6, 5.0 and 7.5 nm. The dynamic complex elastic susceptibility data can be consistently described with the assumption of two relaxation processes inside the pores: A surface induced slowed down relaxation due to interaction with rough pore interfaces and a second relaxation within the core of the pores. This core relaxation time is reduced with decreasing pore size d, leading to a downshift of Tg in perfect agreement with recent DSC measurements

Normal origamis of Mumford curves

An origami (also known as square-tiled surface) is a Riemann surface covering a torus with at most one branch point. Lifting two generators of the fundamental group of the punctured torus decomposes the surface into finitely many unit squares. By varying the complex structure of the torus one obtains easily accessible examples of Teichm\"uller curves in the moduli space of Riemann surfaces. The p-adic analogues of Riemann surfaces are Mumford curves. A p-adic origami is defined as a covering of Mumford curves with at most one branch point, where the bottom curve has genus one. A classification of all normal non-trivial p-adic origamis is presented and used to calculate some invariants. These can be used to describe p-adic origamis in terms of glueing squares.Comment: 21 pages, to appear in manuscripta mathematica (Springer

Transport properties of a kinetic model for chemical reactions without barriers

A kinetic model of the Boltzmann equation for chemical reactions without energy barrier is considered here with the aim of evaluating the reaction rate and characterizing the transport coefficient of shear viscosity for the reactive system. The Chapman-Enskog solution of the Boltzmann equation is used to compute the chemical reaction effects, in a flow regime for which the reaction process is close to the final equilibrium state. Some numerical results are provided illustrating that the considered chemical reaction without energy barrier can induce an appreciable influence on the reaction rate and on the transport coefficient of shear viscosity.Minho University Mathematics Centre (CMAT-FCT)Project FCT-PTDC/MAT/68615/2006Brazilian Research Council (CNPq

Adenoviral delivery of angiotensin-(1-7) or angiotensin-(1-9) inhibits cardiomyocyte hypertrophy via the mas or angiotensin Type 2 receptor

The counter-regulatory axis of the renin angiotensin system peptide angiotensin-(1-7) [Ang-(1-7)] has been identified as a potential therapeutic target in cardiac remodelling, acting via the mas receptor. Furthermore, we recently reported that an alternative peptide, Ang-(1-9) also counteracts cardiac remodelling via the angiotensin type 2 receptor (AT(2)R). Here, we have engineered adenoviral vectors expressing fusion proteins which release Ang-(1-7) [RAdAng-(1-7)] or Ang-(1-9) [RAdAng-(1-9)] and compared their effects on cardiomyocyte hypertrophy in rat H9c2 cardiomyocytes or primary adult rabbit cardiomyocytes, stimulated with angiotensin II, isoproterenol or arg-vasopressin. RAdAng-(1-7) and RAdAng-(1-9) efficiently transduced cardiomyocytes, expressed fusion proteins and secreted peptides, as demonstrated by western immunoblotting and conditioned media assays. Furthermore, secreted Ang-(1-7) and Ang-(1-9) inhibited cardiomyocyte hypertrophy (Control = 168.7±8.4 µm; AngII = 232.1±10.7 µm; AngII+RAdAng-(1-7) = 186±9.1 µm, RAdAng-(1-9) = 180.5±9 µm; P<0.05) and these effects were selectively reversed by inhibitors of their cognate receptors, the mas antagonist A779 for RAdAng-(1-7) and the AT(2)R antagonist PD123,319 for RAdAng-(1-9). Thus gene transfer of Ang-(1-7) and Ang-(1-9) produces receptor-specific effects equivalent to those observed with addition of exogenous peptides. These data highlight that Ang-(1-7) and Ang-(1-9) can be expressed via gene transfer and inhibit cardiomyocyte hypertrophy via their respective receptors. This supports applications for this approach for sustained peptide delivery to study molecular effects and potential gene therapeutic actions

H-theorem and trend to equilibrium of chemically reacting mixture of gases

The trend to equilibrium of a quaternary mixture of monatomic gases undergoing a reversible reaction of bimolecular type is studied in a quite rigorous mathematical picture within the framework of Boltzmann equation extended to chemically reacting mixture of gases. The H-theorem and entropy inequality allow to prove two main results under the assumption of uniformly boundedness and equicontinuity of the distribution functions. One of the results establishes the tendency of a reacting mixture to evolve to an equilibrium state as time becomes large. The other states that the solution of the Boltzmann equation for chemically reacting mixture of gases converges in strong L1-sense to its equilibrium solution.Universidade Nova de Lisboa. Centro de Matemática(CMA-UNL)Brazilian Research Council (CNPq)Universidade do Minho. Centro de Matemática(CMat)Fundação para a Ciência e a Tecnologia (FCT) - PTDC/MAT/68615/200