Related papers: Planar Projections and Second Intrinsic Volume
Femtosecond pump-probe measurements find pronounced dimensionality dependence of the optical nonlinearity in cuprates. Although the coherent two-photon absorption (TPA) and linear absorption bands nearly overlap in both quasi-one and…
For an accretion disk around a black hole, the strong relativistic effects affect every aspect of the radiation from the disk, including its spectrum, light-curve, and image. This work investigates in detail how the images of a thin disk…
Medium effects as a function of the mass number $A$ are studied in the total photonuclear cross section from the $\Delta$-resonance region up to the region where shadowing effects are known to exist. A consistent picture is obtained by…
This work investigates observational properties, namely the shadow and photon ring structure, of emission profiles originating near compact objects. In particular, we consider a distorted and deformed compact object characterised by two…
In cosmic shear likelihood analyses the covariance is most commonly assumed to be constant in parameter space. Therefore, when calculating the covariance matrix (analytically or from simulations), its underlying cosmology should not…
On a closed manifold, consider the space of all Riemannian metrics for which -Delta + kR is positive (nonnegative) definite, where k > 0 and R is the scalar curvature. This spectral generalization of positive (nonnegative) scalar curvature…
The currently released datasets of the observational surveys reveal the redshift dependence of the physical features of cosmic voids. We study the void induced hyperbolicity, that is the deviation of the photon beams propagating the voids,…
The universe is not isotropic or spatially homogeneous on local scales. The averaging of local inhomogeneities in general relativity can lead to significant dynamical effects on the evolution of the universe and on the interpretation of…
We prove several results concerning the representation of projections on arbitrary Banach spaces. We also give illustrative examples including an example of a generalized bi-circular projection which can not be written as the average of the…
Discrete forms of the mean and directed curvature are constructed on piecewise flat manifolds, providing local curvature approximations for smooth manifolds embedded in both Euclidean and non-Euclidean spaces. The resulting expressions take…
The groundbreaking image of the black hole at the center of the M87 galaxy has raised questions at the intersection of observational astronomy and black hole physics. How well can the radius of a black hole shadow can be measured, and can…
Reflectance, transmittance and absorbance of a symmetric light pulse, the carrying frequency of which is close to the frequency of interband transitions in a quantum well, are calculated. Energy levels of the quantum well are assumed…
We give a unified description of tetrahedra with lightlike faces in 3d anti-de Sitter, de Sitter and Minkowski spaces and of their duals in 3d anti-de Sitter, hyperbolic and half-pipe spaces. We show that both types of tetrahedra are…
In this paper, we determine the partial positivity(resp., negativity) of the curvature of all irreducible Riemannian symmetric spaces. From the classifications of abstract root systems and maximal subsystems, we can give the calculations…
We show that many well-known transforms in convex geometry (in particular, centroid body, convex floating body, and Ulam floating body) are special instances of a general construction, relying on applying sublinear expectations to random…
For dark compact objects such as black holes or wormholes, the shadow size has long been thought to be determined by the unstable photon sphere (region). However, by considering the asymmetric thin-shell wormhole (ATSW) model, we find that…
We develop a notion of projections between sets of probability measures using the geometric properties of the 2-Wasserstein space. It is designed for general multivariate probability measures, is computationally efficient to implement, and…
Concepts like peculiar velocity, gravitational force, and power spectrum and their interrelationships are of utmost importance in the theories of structure formation. The observational implementation of these concepts is usually based on…
Coherent backscattering is a multiple scattering interference effect which enhances the diffuse reflection off a disordered sample in the backward direction. Classically, the enhanced intensity is twice the average background under well…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…