Related papers: Nonnegative Grassman Chambers are Balls
For a general radially symmetric, non-increasing, non-negative kernel $h\in L ^ 1 _{loc} ( R ^ d)$, we study the rigidity of measurable sets in $R ^ d$ with constant nonlocal $h$-mean curvature. Under a suitable "improved integrability"…
Motivated by the nonlinear star formation efficiency found in recent numerical simulations by a number of workers, we perform high-resolution adaptive mesh refinement simulations of star formation in self-gravitating turbulently driven gas.…
We show that lattice regularization of noncommutative field theories can be used to study non-perturbative vacuum phases. Specifically we provide evidence for the existence of a striped phase in two-dimensional noncommutative scalar field…
We consider the singular configurations of gravitating gas [1] which could be used as a model for disk galaxies. The simplest steady configuration, which corresponds to rotation of stars around center gives flat rotational curve, provided…
A finite family ${\mathcal B}$ of balls with respect to an arbitrary norm in ${\mathbb R}^d$ ($d\geq 2$) is called a non-separable family if there is no hyperplane disjoint from $\bigcup {\mathcal B}$ that strictly separates some elements…
We provide a novel analytical proof of an improved version of [10, Theorem 3.1], showing that the complement of a closed set satisfying the extended exterior sphere condition is nothing but the union of closed balls with lower…
Let $G_n=\mathbb{Z}_n\times \mathbb{Z}_n$ for $n\geq 4$ and $S=\{(i,0),(0,i),(i,i): 1\leq i \leq n-1\}\subset G_n$. Define $\Gamma(n)$ to be the Cayley graph of $G_n$ with respect to the connecting set $S$. It is known that $\Gamma(n)$ is a…
Using 2D nonlinear simulations, we study the generation and nonlinear evolution of spiral structure in a star-forming multi-component gravitating disk. We confirm in agreement with previous studies the destabilizing role of a cold gaseous…
We study transient spiral structures in an isothermal, thin, galactic disc. We find no instability that can grow everywhere from infinitesimal disturbances, but spiral structure does grow in the disc due to an arbitrarily strong,…
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 investigate photometric properties of spiral arms and stellar complexes/associations inside these arms in the grand design NGC 628 (M74) galaxy.We analyze GALEX ultraviolet, optical UBVRI, and H-alpha? surface photometry data, including…
Observations of line emission from water masers near the center of the galaxy NGC 4258 have recently provided compelling evidence for rotating disk of gas, viewed nearly edge-on, surrounding a massive black hole (Miyoshi etal. 1995). We…
We draw attention to the bright galaxies that do not show a bar in their structure but have a flocculent spiral structure. Using the THINGS' and HERACLES' kinematic data for four barless galaxies (NGC~2841, NGC~3512, NGC~5055, NGC~7331) we…
In this paper we adapt work of Z.-D. Liu to prove a ball covering property for non-branching $\mathsf{CD}$ spaces with nonnegative curvature outside a compact set. As a consequence we obtain uniform bounds on the number of ends of such…
The shape of a cusped galactic nucleus is constrained by the range of shapes of orbits in its gravitational potential. It is shown for scale-free non-axisymmetric discs that while a plausible elongated density model requires at least some…
The causes of spiral structure in galaxies remain uncertain. Leaving aside the grand bisymmetric spirals with their own well-known complications, here we consider the possibility that multi-armed spiral features originate from density…
In this paper we study the space $\mathcal{M}$ of all nonempty compact metric spaces considered up to isometry, equipped with the Gromov--Hausdorff distance. We show that each ball in $\mathcal{M}$ with center at the one-point space is…
We show that expander graphs must have Gromov-hyperbolicity at least proportional to their diameter, with a constant of proportionality depending only on the expansion constant and maximal degree. In other words, expanders contain geodesic…
The inner disc of the local group galaxy M33 appears to be in settled rotational balance, and near IR images reveal a mild, large-scale, two-arm spiral pattern with no strong bar. We have constructed N-body models that match all the…
(abridged) Photometry and long-slit spectroscopy are presented for a sample of 6 galaxies with a low surface brightness stellar disc and a bulge. The stellar and ionised-gas kinematics were measured along the major and minor axis in half of…