Related papers: Crystallizations of generalized lens spaces
In general relativity (GR), gravitational waves (GWs) propagate the well-known plus and cross polarization modes which are the signature of a massless spin-2 field. However, diffraction of GWs caused by intervening objects along the line of…
This paper means to correct an error by the authors for the composite $q$ case in the paper "Lens Spaces, Isospectral on Forms but not on Functions", published in LMS J. Comput. Math.} 9 (2006), 270-286. All calculations and examples…
In the present paper we generalize the Eulerian numbers (also of the second and third orders). The generalization is connected with an autonomous first-order differential equation, solutions of which are used to obtain integral…
Recently, Park and Gott reported an interesting observation: image separation of lensed QSOs declines with QSO redshift more precipitously than expected in any realistic world model, if the lenses are taken to be either singular isothermal…
According to a well-known result in geometric topology, we have \linebreak $\left (\mathbb{S}^2 \right)^{n}\!\!/\operatorname{Sym}(n) = \mathbb{CP}^{n}$, where $\operatorname{Sym}(n)$ acts on $\left (\mathbb{S}^2 \right)^{n}$ by coordinate…
We consider the grading of $sl(n,\mathbb{C})$ by the group $\Pi_n$ of generalized Pauli matrices. The grading decomposes the Lie algebra into $n^2-1$ one--dimensional subspaces. In the article we demonstrate that the normalizer of grading…
Massive structures, such as galaxies, act as strong gravitational lenses on background sources. When the background source is a quasar, several lensed images are seen, as magnified or de-magnified versions of the same object. The detailed…
Many famous integer sequences including the Catalan numbers and the Motzkin numbers can be expressed in the form $ConstantTermOf\left[P(x)^nQ(x)\right]$ for Laurent polynomials $Q$, and symmetric Laurent trinomials $P$. In this paper we…
We consider spaces of multivariate splines defined on a particular type of simplicial partitions that we call (generalized) oranges. Such partitions are composed of a finite number of maximal faces with exactly one shared medial face. We…
We present a transformation, based on the B\'ezout's identity, which maps the set of pairs of relatively prime numbers $(p,q)$ with fixed $p$ and $0<q<p$, to pairs of relatively prime numbers in the $p\times p$ square in $\mathbb R^2$, in…
Congruences modulo prime powers involving generalized Harmonic numbers are known. While looking for similar congruences, we have encountered a curious triangular array of numbers indexed with positive integers $n,k$, involving the Bernoulli…
This paper gives infinitely many examples of non L-space irreducible integer homology 3-spheres whose fundamental groups do not have nontrivial $\widetilde{PSL_2(\mathbb{R})}$ representations.
We give the lens equation for light deflections caused by point mass condensations in an otherwise spatially homogeneous and flat universe. We assume the signal from a distant source is deflected by a single condensation before it reaches…
This article is a continuation of work on construction and calculation various of modifications of invariant based on the use Euclidean metric values attributed to elements of manifold triangulation. We again address the well investigated…
We have investigated the formation of helium droplets in two physical situations. In the first one, droplets are atomised from superfluid or normal liquid by a fast helium vapour flow. In the second, droplets of normal liquid are formed…
As is well known, crystals have discrete space translational symmetry. It was recently noticed that one-dimensional crystals possibly have discrete Poincar\'{e} symmetry, which contains discrete Lorentz and discrete time translational…
Let $R$ be a Noetherian ring and $x_1,\ldots,x_t$ a permutable regular sequence of elements in $R$. Then there exists a finite set of primes $\Lambda$ and natural number $C$ so that for all $n_1,\ldots,n_t$ there exists a primary…
We introduce a new quantity to probe the glass transition. This quantity is a linear generalized compressibility which depends solely on the positions of the particles. We have performed a molecular dynamics simulation on a glass forming…
Multiple images, giant arcs, Einstein cross, fold, cusp, lip, caustics, critical lines, sources, mapping, time delay, arclets, weak shear, magnification bias, depletion, ellipticities, polarization, smearing, convergence, kernel, mass…
We study complex interpolation of variable Triebel-Lizorkin spaces, especially we present the complex interpolation of $F_{p(\cdot),q}^{\alpha }$ and $F_{p(\cdot ),p(\cdot )}^{\alpha (\cdot )}$ spaces. Also, some limiting cases are given.