Sagnac Effect of Gödel's Universe

We present exact expressions for the Sagnac effect of Gödel's Universe. For this purpose we first derive a formula for the Sagnac time delay along a circular path in the presence of an arbitrary stationary metric in cylindrical coordinates. We then apply this result to Gödel's metric for two different experimental situations: First, the light source and the detector are at rest relative to the matter generating the gravitational field. In this case we find an expression that is formally equivalent to the familiar nonrelativistic Sagnac time delay. Second, the light source and the detector are rotating relative to the matter. Here we show that for a special rotation rate of the detector the Sagnac time delay vanishes. Finally we propose a formulation of the Sagnac time delay in terms of invariant physical quantities. We show that this result is very close to the analogous formula of the Sagnac time delay of a rotating coordinate system in Minkowski spacetime.     

Decision methods for linearly ordered Heyting algebras

The decision problem for positively quantified formulae in the theory of linearly ordered Heyting algebras is known, as a special case of work of Kreisel, to be solvable; a simple solution is here presented, inspired by related ideas in Gödel-Dummett logic.     

Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces

Let D be a simply laced Dynkin diagram of rank r whose affinization has the shape of a star (i.e., D₄,E₆,E₇,E₈). To such a diagram one can attach a group G whose generators correspond to the legs of the affinization, have orders equal to the leg lengths plus 1, and the product of the generators is 1. The group G is then a 2-dimensional crystallographic group: G=Z??Z², where ? is 2, 3, 4, and 6, respectively. In this paper, we define a flat deformation H(t,q) of the group algebra C[G] of this group, by replacing the relations saying that the generators have prescribed orders by their deformations, saying that the generators satisfy monic polynomial equations of these orders with arbitrary roots (which are deformation parameters). The algebra H(t,q) for D₄ is the Cherednik algebra of type C^∨C₁, which was studied by Noumi, Sahi, and Stokman, and controls Askey-Wilson polynomials. We prove that H(t,q) is the universal deformation of the twisted group algebra of G, and that this deformation is compatible with certain filtrations on C[G]. We also show that if q is a root of unity, then for generic t the algebra H(t,q) is an Azumaya algebra, and its center is the function algebra on an affine del Pezzo surface. For generic q, the spherical subalgebra eH(t,q)e provides a quantization of such surfaces. We also discuss connections of H(t,q) with preprojective algebras and Painlevé VI.     

On the Arithmetic of Del Pezzo Surfaces of Degree 2

We study the arithmetic of certain del Pezzo surfaces of degree2. We produce examples of Brauer-Manin obstruction to the Hasseprinciple, coming from 2- and 4-torsion elements in the Brauergroup. 2000 Mathematics Subject Classification 14G05 (primary),12G05 (secondary).     

Categories of models of R-mingle

We give a new Esakia-style duality for the category of Sugihara monoids based on the Davey-Werner natural duality for lattices with involution, and use this duality to greatly simplify a construction due to Galatos-Raftery of Sugihara monoids from certain enrichments of their negative cones. Our method of obtaining this simplification is to transport the functors of the Galatos-Raftery construction across our duality, obtaining a vastly more transparent presentation on duals. Because our duality extends Dunn's relational semantics for the logic R-mingle to a categorical equivalence, this also explains the Dunn semantics and its relationship with the more usual Routley-Meyer semantics for relevant logics.     

The Decay of Massive Scalar Field in Non-Static Gödel Type Universe with Viscous Fluid and Heat Flow

In this study, we have investigated the dynamics of non-static Gödel type rotating universe with massive scalar field, viscous fluid and heat flow in the presence of cosmological constant. For various cosmic matter forms, the behavior of the cosmological constant (Λ), shear (η) and bulk (ξ) viscosity coefficients and other kinematic quantities have studied in the early universe. We have showed the decay of massive scalar field in the non-static rotating Gödel type universe and we have obtained constant scalar field with and without source density. Also, we have investigated the effects of massive scalar field on the matter density and pressure. From solutions of the field equations, we have a cosmological model with non-zero expansion, shear, heat flux and rotation. Also some physical and geometrical aspects of the model discussed.     

Nanocomposites based on cationic polyelectrolytes and silver nanoparticles: Synthesis,characterization, molybdate retention and antimicrobial activity

The objective of this work was to synthesize nanocomposites based on cationic polyelectrolytes and silver nanoparticles using poly(N-vinylbenzyl-N-triethylammonium chloride) as polymer phase. For that, a nanostructured crosslinker was synthesized from silver nanoparticles (AgNPs) and acrylic acid. Molybdate retention properties of nanocomposites were studied in function of pH and ionic strength. In addition, their antimicrobial properties were evaluated against E. coli and S. aureus. It was evidenced that AgNPs can be stabilized using acrylic acid and that this material can be incorporated to the polymer phase during polymerization by free radical of cationic monomers. The effect of pH on retention of molybdate, by the nanostructured polymer, was significant only to low ionic strength (the order seen was pH 5.0 > pH 7.0 > pH 9.0 for 0.0% NaCl). Results suggest that the main interaction influencing the molybdate retention is electrostatic in nature. Finally, antimicrobial activity was enhanced by incorporation of polymerizable nanostructured crosslinker based on AgNPs.     

Gödel Kink Spacetime

A 2+1 version of a rotating perfect fluid spacetime of Gödel type is examined to see whether it has a Finkelstein-Misner kink. It is shown, by three different methods, that the kink number is one.     

Degeneration of torsors over families of del Pezzo surfaces

Let S be a split family of del Pezzo surfaces over a discrete valuation ring such that the general fiber is smooth and the special fiber has $\mathbf{ADE}$-singularities. Let G be the reductive group given by the root system of these singularities. We construct a G-torsor over S whose restriction to the generic fiber is the extension of structure group of the universal torsor. This extends a construction of Friedman and Morgan for individual singular del Pezzo surfaces. In case of very good residue characteristic, this torsor is unique and infinitesimally rigid.