Finite element approximations of a nonlinear diffusion model with memory

The convergence of a finite element scheme approximating a nonlinear system of integro-differential equations is proven. This system arises in mathematical modeling of the process of a magnetic field penetrating into a substance. Properties of existence, uniqueness and asymptotic behavior of the solutions are briefly described. The decay of the numerical solution is compared with both the theoretical and finite difference results.     

Spontaneous lorentz breaking and massive gravity

Theories with an extra spin-two field coupled to gravity admit a massive phase with broken Lorentz symmetry. While the equivalence principle is respected, the Newtonian potentials are in general modified, but they may be protected by a scale symmetry of the coupling term. The gravitational waves phenomenology is quite rich: two gravitons, one massive and one massless, oscillate and propagate with distinct velocities, different from the speed of light. A time of flight difference between gravitons and photons from a common source would provide a clear signal of this theory.     

Star-regularity and regular completions

In this paper we establish a new characterisation of star-regular categories, using a property of internal reflexive graphs, which is suggested by a recent result due to O. Ngaha Ngaha and the first author. We show that this property is, in a suitable sense, invariant under regular completion of a category in the sense of A. Carboni and E.M. Vitale. Restricting to pointed categories, where star-regularity becomes normality in the sense of the second author, this reveals an unusual behaviour of the exactness property of normality (i.e. the property that regular epimorphisms are normal epimorphisms) compared to other closely related exactness properties studied in categorical algebra.     

Categorical (binary) difference terms and protomodularity

In this paper we obtain an intrinsic syntactical characterization of protomodularity, via so-called categorical difference terms, similar to the one known in the case of varieties involving binary terms d satisfying d(x, x) = d(y, y). We also show that purely categorical modifications of the condition in the characterization give characterizations of Mal’tsev and additive categories, thus revealing a new conceptual link between these three classes of categories, and hence, also between the corresponding classes of varieties.     

On the deconstruction of time

In this note we discuss the possibility of getting a time rather than space in the scenario of (de)construction of a new dimension.     

Subtractive Categories

We introduce a notion of a subtractive category. It generalizes the notion of a pointed subtractive variety of universal algebras in the sense of A. Ursini. Subtractive categories are closely related to Mal’tsev and additive categories: (i) a category C with finite limits is a Mal’tsev category if and only if for every object X in C the category Pt(X)=((X,1_X)↓(C↓X)) of “points over X” is subtractive; (ii) a pointed category C with finite limits is additive if and only if C is subtractive and half-additive.Mathematics Subject Classifications (2000) 18C99, 18E05, 08B05.     

The low temperature magnetic phase diagram of EuxSr1−xTiO3

Specific heat and magnetization measurements demonstrate that the antiferromagnetic (AFM) phase transition at T _N  = 5.7 K of EuTiO₃ is rapidly suppressed with Sr doping in Eu _x Sr_1?x TiO₃. Close to x = 0.25, T _N  = 0 K and AFM order vanishes. Above this critical concentration a finite transition temperature to an AFM phase is observed. The exchange couplings are derived as a function of x and the corresponding low temperature phase diagram is presented.