Related papers: Lens space matter determinants in the vector model
Based on various types of semi-tensor products of matrices, the corresponding equivalences of matrices are proposed. Then the corresponding vector space structures are obtained as the quotient spaces under equivalences, which are called the…
We design a new absolute optical instrument by composing Luneburg lens and Lissajous lens, and analyze its imaging mechanism from the perspective of simple harmonic oscillations. The imaging positions are determined by the periods of…
Lenses may be characterised as objects in the category of algebras over a monad, however they are often understood instead as morphisms, which propagate updates between systems. Working internally to a category with pullbacks, we define…
Matter collineations of locally rotationally symmetric spacetimes are considered. These are investigated when the energy-momentum tensor is degenerate. We know that the degenerate case provides infinite dimensional matter collineations in…
We consider the Lie algebra of all vector fields on a contact manifold as a module over the Lie subalgebra of contact vector fields. This module is split into a direct sum of two submodules: the contact algebra itself and the space of…
We obtain effective results for the global generation of pluritheta line bundles on moduli spaces of vector bundles on curves. The main ingredient is an independent result giving an upper bound on the dimension of the Hilbert scheme of…
One of the simplest viable models for dark matter is an additional neutral scalar, stabilised by a $\mathbb{Z}_2$ symmetry. Using the GAMBIT package and combining results from four independent samplers, we present Bayesian and frequentist…
Dark matter caustics have specific density profiles and, therefore, precisely calculable gravitational lensing properties. We present a formalism which simplifies the relevant calculations, and apply it to four specific cases. In the first…
A representation theory of finite electromagnetic beams in free space is formulated by factorizing the field vector of the plane-wave component into a $3 \times 2$ mapping matrix and a 2-component Jones-like vector. The mapping matrix has…
Vector solitons (VSs), being observed across various fields from optics to Bose-Einstein condensates, are localized structures composed of orthogonal modes bound by nonlinear couplings. Nevertheless, the influence of intermodal linear…
Gravitational potential energy of the homogeneous bispherical concavo-convex lens, with the equal absolute values of radii of curvature of both surfaces is studied.
Lie Yamaguti algebras appear naturally on the smooth sections of the tangent bundle of a reductive homogeneous space when we interpret the torsion and curvature as algebraic operators. In this article we present a description of the free…
By using a model independent Monte Carlo approach, we study the possible structure of charged and neutral lepton mass matrices, under the assumption of an U(2) horizontal symmetry (additional to the usual Standard Model ones) involving the…
The existence and nature of singularities in locally spatially homogeneous solutions of the Einstein equations coupled to various phenomenological matter models is investigated. It is shown that, under certain reasonable assumptions on the…
For any object A in a simplicial model category M, we construct a topological space \^A which classifies homogeneous functors whose value on k open balls is equivalent to A. This extends a classification result of Weiss for homogeneous…
A recent suggestion that vector potentials in electrodynamics (ED) are nontensorial objects under 4D frame rotations is found to be both unnecessary and confusing. As traditionally used in ED, a vector potential $A$ always transforms…
Quadrature formulas for spheres, the rotation group, and other compact, homogeneous manifolds are important in a number of applications and have been the subject of recent research. The main purpose of this paper is to study coordinate…
While gravitational lens inversion holds great promise to reveal the structure of the light-deflecting mass distribution, both light and dark, the existence of various kinds of degeneracies implies that care must be taken when interpreting…
The state space of a homogeneous body is derived under two different assumptions: infinitesimal reducibility and irreducibility. The first assumption leads to a real vector space, used in classical mechanics, while the second one leads to a…
Using the fact that the null geodesics in NUT space lie on spatial cones, we consider the gravomagnetic lens effect on light rays passing a NUT deflector. We show that this effect changes the observed shape, size and orientation of a…