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A large number of observations have shown that the dark matter halo surface density, given by the product of halo core radius and core density is nearly constant for a diverse suite of galaxies. Although this invariance of the halo surface…

Bulk-surface systems on evolving domains are studied. Such problems appear typically from modelling receptor-ligand dynamics in biological cells. Our first main result is the global existence and boundedness of solutions in all dimensions.…

By means of a combined use of the type Ia supernovae and H(z) data tests, together with the study of the asymptotic properties in the equivalent phase space - through the use of the dynamical systems tools - we demonstrate that the bulk…

Recently, Park and Gott reported an interesting observation: image separation of lensed QSOs declines with QSO redshift more precipitously than expected in any realistic world model, if the lenses are taken to be either singular isothermal…

An argument is made to show that the singularity in the General Theory of Relativity (GTR) is the expression of a non-Machian feature. It can be avoided with a scale-invariant dynamical theory, a property lacking in GTR. It is further…

In a Comment [arXiv:0910.1256], Behnia contends that the surface theory put forward in our recent Letter [Phys. Rev. Lett. 103, 136803 (2009); arXiv:0905.0689] as an alternative explanation of the anomalous peaks observed in Nernst…

We present a detailed study of the structural properties of four gravitationally lensed disk galaxies at z=1. Modelling the rotation curves on sub-kpc scales we derive the values for the disk mass, the reference dark matter density and core…

An analytical model is presented for calculating the surface density as a function of radius $\Sigma(r)$ in protoplanetary disks in which a planet has opened a gap. This model is also applicable to circumbinary disks with extreme binary…

A simple model for the dust media describing evolution of the system like spiral galaxy is considered. In contrast to previous considerations we show that the initial density fold should be quasi-one-dimensional (bar-like) instead of…

We use the marginal stability condition for galactic disks and the stellar velocity dispersion data published by different authors to place upper limits on the disk local surface density at two radial scalelengths $R=2h$. Extrapolating…

Recently a new no-global-recollapse argument was given for some inhomogeneous and anisotropic cosmologies that utilizes surface deformation by the mean curvature flow. In this paper we discuss important properties of the mean curvature flow…

In this lecture we deal with the construction of surface densities for the angular momentum of the sources of asymptotically flat vacuum stationary axisymmetric spacetimes. These sources arise from the discontinuities of the twist…

The DiskMass survey recently provided measurements of the vertical velocity dispersions of disk stars in a sample of nearly face-on galaxies. By setting the disk scale-heights to be equal to those of edge-on galaxies with similar…

Dynamos in astrophysical disks are usually explained in terms of the standard alpha-omega mean field dynamo model where the local helicity generates a radial field component from an azimuthal field. The subsequent shearing of the radial…

In an attempt to place an explicit constraint on dark matter models, we define and estimate a mean surface density of a dark halo within a radius of maximum circular velocity, which is derivable for various galaxies with any dark-matter…

I discuss measurements of disk mass from non-circular streaming motions of gas in the barred galaxies NGC 3095 and NGC 4123. In these galaxies with strong shocks and non-circular motions, the inner regions must be disk-dominated to…

The goal of the article is to provide different explicit quantifications of the non density of simple closed geodesics on hyperbolic surfaces. In particular, we show that within any embedded metric disk on a surface, lies a disk of radius…

The kinematic dispersions of disc stars can be used to measure the dynamic contributions of baryons to the rotation curves of spiral galaxies and hence to trace the amount and distribution of the remaining dark matter. However, the simple…

We discuss generalizations of the recent theorem by Dafermos (hep-th/0403033) forbidding a certain class of naked singularities in the spherical collapse of a scalar field. Employing techniques similar to the ones Dafermos used, we consider…

A fuzzy version of the ordinary round 2-sphere has been constructed with an invariant curvature. We here consider linear connections on arbitrary fuzzy surfaces of genus zero. We shall find as before that they are more or less rigidly…