Scalar-tensor cosmologies with dust matter in the general relativity limit

We consider flat Friedmann-Lema\^{\i}tre-Robertson-Walker cosmological models in the framework of general scalar-tensor theories of gravity with arbitrary coupling functions, set in the Jordan frame, in the cosmological epoch when the energy density of the ordinary dust matter dominates over the energy density of the scalar potential. Motivated by cosmological observations, we apply an approximation scheme in the regime close to the so-called limit of general relativity. The ensuing nonlinear approximate equations for the scalar field and the Hubble parameter can be solved analytically in cosmological time. This allows us to distinguish the theories with solutions that asymptotically converge to general relativity and draw some implications about the cosmological dynamics near this limit.Comment: 15 page

Katse mõista keraamikut

Ceramics has never had particular significance in Estonian folk art. Traditionally, the Estonians expressed their creativity by cutting wood or forging iron. Thus, we cannot speak about popular tradition of folk ceramics, as it is a relatively recent field of art or consumer art. Throughout times, Maanus Mikkel's creation has possessed the underlying quality that enables to call it ethnic art, regardless of the stylistic changes it has undergone. His works create the sense of a certain paradigm. A major part of Mikkel's creation, regardless of the technique, appears expressive, robust. Virility of his art is emphasised by the use of rough clay and often also irregular form. Although being primordially Ugric, the theme has not a single speck of grotesque in it. Figures are blown bigger, and have nothing in them indicative of the usual reticence of the Estonians. Most of the works are serious; others express a small hint of tongue-in-cheek irony. It is not very common to ceramic pottery to have animate creatures depicted on them. Mikkel's creation almost always has clearly animate representations, though sometimes of unknown origin, including, for example, flying dragons as well as the tentative category of prehistoric animals. The figures, which sometimes disappear from the pottery only to re-emerge later, represent creatures of the times before the Ice Age. Of known species the most popular representations are that of bat and fish, even though some fish seem to favour flying, too. Some earlier works are reminiscent of prehistoric cave art, but this style has become considerably rarer. The new figures that have appeared in his work are humans - men and women. Love in the inane. Mikkel's earlier darker tone has become considerably brighter, his lines more round and fluent. Fortunately, the primordial fossils have not altogether disappeared in Mikkel's work; thus his already versatile world has acquired a new dimension. And who knows what course his art will take in the future

Permutations preserving divisibility

We give a proof of a theorem on the common divisibility of polynomials and permuted polynomials (over GF(2)) by a polynomial g(x)

A least-squares implicit RBF-FD closest point method and applications to PDEs on moving surfaces

The closest point method (Ruuth and Merriman, J. Comput. Phys. 227(3):1943-1961, [2008]) is an embedding method developed to solve a variety of partial differential equations (PDEs) on smooth surfaces, using a closest point representation of the surface and standard Cartesian grid methods in the embedding space. Recently, a closest point method with explicit time-stepping was proposed that uses finite differences derived from radial basis functions (RBF-FD). Here, we propose a least-squares implicit formulation of the closest point method to impose the constant-along-normal extension of the solution on the surface into the embedding space. Our proposed method is particularly flexible with respect to the choice of the computational grid in the embedding space. In particular, we may compute over a computational tube that contains problematic nodes. This fact enables us to combine the proposed method with the grid based particle method (Leung and Zhao, J. Comput. Phys. 228(8):2993-3024, [2009]) to obtain a numerical method for approximating PDEs on moving surfaces. We present a number of examples to illustrate the numerical convergence properties of our proposed method. Experiments for advection-diffusion equations and Cahn-Hilliard equations that are strongly coupled to the velocity of the surface are also presented