What if Dark matter is Bosonic and self-interacting

Recently the problem of singular galactic cores and over-abundant formation of dwarf galaxies, inherent to the standard cold dark matter model, had attracted a great deal of attention. One scenario which may be free of these problems invokes a self-interacting Bose-field. We find the limiting core density in this model due to the self-annihilation of the scalar field into its own relativistic quanta. The limiting density may correspond to the observable one if there is only one dark matter component. Alternatively, there may be more than one dark matter species and the annihilation of one species may be very efficient with subsequent expansion of the other, thus avoiding the problem of singular cores.Comment: Discussion of red-shif is correcetd, refferences adde

Positive definite collections of disks

Let $Q(z,w)=-\prod_{k=1}^n [(z-a_k)(\bar{w}-\bar{a}_k)-R_k^2]$. M. Putinar and B. Gustafsson proved recently that the matrix $Q(a_i,a_j)$, $1\leq i,j\leq n$, is positive definite if disks $|z-a_i|<R_i$ form a disjoint collection. We extend this result on symmetric collections of discs with overlapping. More precisely, we show that in the case when the nodes $a_j$ are situated at the vertices of a regular $n$-gon inscribed in the unit circle and $\forall i: R_i\equiv R$, the matrix $Q(a_i,a_j)$ is positive definite if and only if $R<\rho_n$, where $z=2\rho_n^2-1$ is the smallest $\ne-1$ zero of the Jacobi polynomial $\mathcal{P}^{n-2\nu,-1}_\nu(z)$, $\nu=[n/2]$.Comment: 24 page

V.M. Miklyukov: from dimension 8 to nonassociative algebras

In this short survey we give a background and explain some recent developments in algebraic minimal cones and nonassociative algebras. A good deal of this paper is recollections of my collaboration with my teacher, PhD supervisor and a colleague, Vladimir Miklyukov on minimal surface theory that motivated the present research. This paper is dedicated to his memory.Comment: 19 page

Inflation

Inflationary cosmology is reviewed. Particular attention is given to processes of creation.Comment: Invited Review Lecture at Taup200

Cuts and penalties: comment on "The clustering of ultra-high energy cosmic rays and their sources"

In a series of papers we have found statistically significant correlations between arrival directions of ultra-high energy cosmic rays and BL Lacertae objects. Recently, our calculations were partly repeated by Evans, Ferrer and Sarkar with different conclusions. We demonstrate that the criticism of Evans, Ferrer and Sarkar is incorrect. We also present the details of our method.Comment: Replaced with version accepted for publication in Phys. Rev.

Correlations and Charge Composition of UHECR without Knowledge of Galactic Magnetic Field

We develop a formalism which allows to study correlations of charged UHECR with potential sources without using any Galactic Magnetic Field (GMF) model. The method is free of subjective chose of parameters on which the significance of correlations depends strongly. We show that correlations of the AGASA dataset with BL Lacs (found previously after reconstruction of particle trajectories in a specific GMF) are present intrinsically and can be detected without reference to a particular model of magnetic field.Comment: To be published in the Proceedings of the 28th International Cosmic Ray Conferenc