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Supersymmetric (SUSY) optical structures display a number of intriguing properties that can lead to a variety of potential applications, ranging from perfect global phase matching to highly efficient mode conversion and novel multiplexing…
A generalized theory of spatial coherence for superposition of two speckle patterns with polarization diversity is presented. The presented theory deals with superposition in different scenarios i.e. superposition of two fully correlated,…
A new model of charged compact star is reported by solving the Einstein-Maxwell field equations by choosing a suitable form of radial pressure. The model parameters $\rho$, $p_r$, $p_{\perp}$ and $E^{2}$ are in closed form and all are well…
A topological space is totally paracompact if any base of this space contains a locally finite subcover. We focus on a problem of Curtis whether in the class of regular Lindel\"of spaces total paracompactness is equivalent to the Menger…
Many classically used function space structures (including the topology of pointwise convergence, the compact-open topology, the Isbell topology and the continuous convergence) are induced by a hyperspace structure counterpart. This scheme…
Very little is known about the polarimetric properties of CH stars and carbon-enhanced metal-poor (CEMP) stars, although many of these objects have been studied in detail both photometrically and spectroscopically. We aim to derive…
Cardinal functions provide valuable insight into the topological properties of spaces, helping to analyze and compare spaces in terms of their covering, convergence and separation properties. This paper focuses on investigating cardinal…
We introduce notions of nearly good relations and N-sticky modulo a relation as tools for proving that spaces are D-spaces. As a corollary to general results about such relations, we show that C_p(X) is hereditarily a D-space whenever X is…
In this paper, we prove an optimal isoperimetric inequality for spacelike, compact, star-shaped, and $2$-convex hypersurfaces in de Sitter space.
A static, spherically symmetric spacetime with negative pressures is conjectured inside a star. The gravitational field is repulsive and so a central singularity is avoided. The positive energy density and the pressures of the imperfect…
Light echoes of debris disks around active stars can reveal disk structure and composition even when disks are not spatially resolved. Unfortunately, distinguishing reflected light from quiescent starlight and unexpected post-peak flare…
We study the general properties of a spherically symmetric body described through the generalized Chaplygin equation of state. We conclude that such object, dubbed generalized Chaplygin dark star, should exist within the context of the…
We obtain the geodesics for the simplest possible stealth defect which has a flat spacetime. We, then, discuss the lensing properties of such a defect, and the corresponding image formation. Similar lensing properties can be expected to…
We analyze empirical relationships between the optical, near infrared, and HI characteristics of isolated galaxies from the 2MIG Catalog covering the entire sky. Data on morphological types, K_S-, and B-magnitudes, linear diameters, HI…
By a combination of analytical and numerical methods, the density profile of a momentarily at rest spherical star is varied, and the corresponding response in the area of the spherical shells is monitored. It is shown that the inner…
In this paper a generalisation of the notion of polarity is exhibited which allows to completely describe, in an incidence-geometric way, the linear complexes of $h$-subspaces. A generalised polarity is defined to be a partial map which…
We study families of submanifolds in symmetric spaces of compact type arising as exponential images of s-orbits of variable radii. Special attention is given to the cases where the s-orbits are symmetric.
A stationary subset S of a regular uncountable cardinal kappa reflects fully at regular cardinals if for every stationary set T subseteq kappa of higher order consisting of regular cardinals there exists an alpha in T such that S cap alpha…
We study properties of representing and absolutely representing systems of subspaces in Banach spaces. We also present sufficient conditions for the system of subspaces to be a representing system of subspaces.
The local space density of galaxies as a function of their basic structural parameters --like luminosity, surface brightness and scalesize-- is still poorly known. Our poor knowledge is mainly the result of strong selection biases against…