Related papers: Crystallizations of generalized lens spaces

Various concepts associated with quadratic algebras admit natural generalizations when the quadratic algebras are replaced by graded algebras which are finitely generated in degree 1 with homogeneous relations of degree N. Such algebras are…

In this article, we extend our previously presented analytical formulas (Phys.Rev.D 109 (2024) 12, 124055) for describing light rays passing near or emitted in the vicinity of compact objects to a broader class of spherically symmetric,…

In this paper we give examples of applications of general methods of quantization by symmetrization of classical integrable systems, which have been illustrated in two previous works by the same authors. We consider two classes of systems…

In a general-relativistic spacetime (Lorentzian manifold), gravitational lensing can be characterized by a lens map, in analogy to the lens map of the quasi-Newtonian approximation formalism. The lens map is defined on the celestial sphere…

Scattering of starlight by dust, molecules and electrons in spiral galaxies will produce a modification of the direct intensity and a polarization in the observed light. We treat the case where the distribution of scatterers can be…

While gravitationally lensed quasars are expected to display an odd number of images, invariably systems are observed with an even number of quasars. For this, lensing galaxies must have very small core radii; this provides strong…

Lensing in a spherically symmetric and static spacetime is considered, based on the lightlike geodesic equation without approximations. After fixing two radius values r_O and r_S, lensing for an observation event somewhere at r_O and static…

While dealing with a class of generalized Bargmann spaces, we rederive their reproducing kernels from the knowledge of an orthonormal basis by using an addition formula for Laguerre polynomials involving the disk polynomials. We construct…

Let K be a non-trivial knot in the 3-sphere with a lens space surgery and L(p,q) a lens space obtained by a Dehn surgery on K. We study a relationship between the order of the fundamental group of L(p,q) and the Seifert genus of K.

We consider the nonlinear Schr\"odinger equation$$-\Delta u + V(x)\,u = a\,u^p + \mu u \quad \text{in }\mathbb{R}^n,\qquad \int_{\mathbb{R}^n} u^2 = 1,$$modeling attractive Bose--Einstein condensates. For all dimensions $n\ge 2$ and all…

The spectrum of $L^2$ on a pseudo-unitary group $U(p,q)$ (we assume $p\ge q$ naturally splits into $q+1$ types. We write explicitly orthogonal projectors in $L^2$ to subspaces with uniform spectra (this is an old question formulated by…

Let $p$ be a prime number. Motivated by the local lifting problem for $(\mathbb{Z}/p\mathbb{Z})^n$ with $n>1$, we prove several new results on certain $\mathbb{F}_p$-vector spaces of logarithmic differential forms on the projective line in…

We study first-passage percolation on random simple triangulations and their dual maps with independent identically distributed link weights. Our main result shows that the first-passage percolation distance concentrates in an…

In [1] the author gives a description of Poisson brackets on some algebras of quantum polynomials $\mathcal{O}_q$, which is called\textit{ general algebra of quantum polynomials}. The main of this paper is to present a generalization of [1]…

Quantum analogues of the homogeneous spaces $\GL(n)/\SO(n)$ and $\GL(2n)/\Sp(2n)$ are introduced. The zonal spherical functions on these quantum homogeneous spaces are represented by Macdonald's symmetric polynomials…

Generalized sine and cosine functions, $\sin_{n}$ and $\cos_{n}$, that parametrize the generalized unit circle $x^n+y^n=1$ are, much like their classical circular counterparts, extendable as complex analytic functions. In this article, we…

Based on transformation optics, we introduce another set of generalized laws of reflection and refraction (differs from that of [Science 334, 333 (2011)]), through which a transformation media slab is derived as a meta-surface, producing…

We classify the orbits of solids in the projective space $\text{PG}(5,q)$, $q$ even, under the setwise stabiliser $K \cong \text{PGL}(3,q)$ of the Veronese surface. For each orbit, we provide an explicit representative $S$ and determine two…

In this work the generalized Collatz problem $qn+1$ ($q$ odd) is studied. As a natural generalization of the original $3n+1$ problem, it consists of a discrete dynamical system of an arithmetical kind. Using standard methods of number…

We study weightings (a.k.a. quasi-homogeneous structures) arising from manifolds with singular Lie filtrations. This generalizes constructions of Choi-Ponge, Van Erp-Yuncken, and Haj-Higson for (regular) Lie filtrations.