Related papers: Star-covering properties: generalized $\Psi$-space…
This paper concerns the self-similarity of topological spaces, in the sense defined in math.DS/0411344. I show how to recognize self-similar spaces, or more precisely, universal solutions of self-similarity systems. Examples include the…
We address various notions of shadowing and expansivity for continuous maps restricted to a proper subset of their domain. We prove new equivalences of shadowing and expansive properties, we demonstrate under what conditions certain…
Physical properties of stars such as luminosity, surface temperature, distance, or mass are measured from observations. These physical properties are of paramount importance to understand how stars are born, live, and die in the universe…
The polarization state of starlight reflected by a planetary atmosphere uniquely reveals coverage, particle size, and composition of aerosols as well as changing cloud patterns. It is not possible to obtain a comparable level of detailed…
We obtain several new characterizations of ultrametric spaces in terms of roundness, generalized roundness, strict p-negative type, and p-polygonal equalities (p > 0). This allows new insight into the isometric embedding of ultrametric…
We are now in an era where we can image details on the surfaces of stars. When resolving stellar surfaces, we see that every surface is uniquely complicated. Each imaged star provides insight into not only the stellar surface structures,…
We define a new spectrum for compact length spaces and Riemannian manifolds called the "covering spectrum" which roughly measures the size of the one dimensional holes in the space. More specifically, the covering spectrum is a set of real…
We present results of numerical simulations of the flux (irradiance), F, and the degree of polarization (i.e. the ratio of polarized to total flux), P, of light that is reflected by Earth-like extrasolar planets orbiting solar-type stars,…
We introduce the notion of star-symmetry for relations in a multi-pointed category and use it to obtain a characterization of the projective covers of 2-star-permutable categories. This generalizes the results of Rosick\'y-Vitale for…
Photometric pipelines struggle to estimate both the flux and flux uncertainty for stars in the presence of structured backgrounds such as filaments or clouds. However, it is exactly stars in these complex regions that are critical to…
We study scaling properties of self avoiding polymer stars and networks of arbitrary given but fixed topology. We use massive field theoretical renormalization group framework to calculate critical exponents governing their universal…
We hypothesise that properties of space could underly some patterns observed in nature. We explore the possibility that the observed variety of matter particles and the pattern of their properties arise due to the non-orientability of the…
We introduce a covering notion depending on two cardinals, which we call $\mathcal O $-$ [ \mu, \lambda ]$-compactness, and which encompasses both pseudocompactness and many other generalizations of pseudocompactness. For Tychonoff spaces,…
We find the radius of starlikeness of order $\alpha$, $0\leq \alpha<1$, of normalized analytic functions $f$ on the unit disk satisfying either $\operatorname{Re}(f(z)/g(z))>0$ or $\left| (f(z)/g(z))-1\right|<1$ for some close-to-star…
A space $X$ is said to have the set star Hurewicz property if for each nonempty subset $A$ of $X$ and each sequence $(\mathcal{U}_n: n \in \mathbb{N})$ of sets open in $X$ such that for each $n\in \mathbb N$, $\overline{A} \subset \cup…
Elliptically contoured distributions can be considered to be the distributions for which the contours of the density functions are proportional ellipsoids. We generalize elliptically contoured densities to ``star-shaped distributions'' with…
Assume hat a functionally Hausdorff space $X$ is a continuous image of a \v{C}ech complete space $P$ with Lindel\"of number $l(P)<\mathfrak c$. Then the following conditions are equivalent: (i) every compact subset of $X$ is scattered, (ii)…
In the setting of a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we prove the fine Kellogg property, the quasi-Lindel\"of principle, and the Choquet property for the fine topology in…
P-stars are compact stars made of up and down quarks in $\beta$-equilibrium with electrons in a chromomagnetic condensate. P-stars are able to account for compact stars as well as stars with radius comparable with canonical neutron stars.…
We introduce a rigorous and general framework to study systematically self-gravitating elastic materials within general relativity, and apply it to investigate the existence and viability, including radial stability, of spherically…