Related papers: Non-almost regular quaternary $m$-gonal forms
A weakly distance-regular digraph is quasi-thin if the maximum value of its intersection numbers is 2. In this paper, we show that the valency of any commutative quasi-thin weakly distance-regular digraph is at most 6.
We study the generating function of the excess number of Rogers-Ramanujan partitions with odd rank over those with even rank, and, using combinatorial and analytical techniques, show that this generating function is closely connected with…
This work investigates the rank properties of $A^+(B_n)$, the additive semigroup reduct of affine near-semiring over Brandt semigroup $B_n$. In this connection, this work reports the ranks $r_1$, $r_2$, $r_3$ and $r_5$ of $A^+(B_n)$ and…
The purpose of this paper is to introduce a geometric structure called pseudo-conformal quaternionic CR structure on a (4n+3)-dimensional mamnifold and then exhibit a quaternionic analogue of Chern-Moser's CR structure and uniformization.
We give an upper bound for the norm of the determinant of additively indecomposable, totally positive definite quadratic forms defined over the ring of integers of totally real number fields. We apply these results to find lower and upper…
We find three-dimensional subspaces of four-dimensional connected Lie algebras, generating these algebras, and abnormal extremals on connected Lie groups with these Lie algebras and with left-invariant sub-Finsler quasimetrics defined by…
We provide a general criteria for the integrability of the almost para-quaternionic structure of an almost para-quaternionic manifold (M,P) of dimension bigger or equal to eight, in terms of the integrability of two or three sections of the…
I discuss a special class of singularities obtained as a natural 4-dimensional generalization of the conical singularity. Such singularities (called quasiregular) are ruinous for the predictive force of general relativity, so one often…
In this work, we investigate the quasinormal modes of the Poincar\'e thick brane with a finite extra dimension. Unlike the case with an infinite extra dimension, the gravitational effective potential exhibits three distinct shapes within…
We classify the parabolic unitals in regular nearfield planes of odd order $q^2$ whose linear collineation group has the maximal size of $q^3-q$. We also establish a number of more general results concerning parabolic unitals in regular…
We construct examples of non-formal simply connected and compact oriented manifolds of any dimension bigger or equal to 7.
A myriad of irreducible symplectic 4-manifolds with abelian non-cyclic fundamental group is constructed. The botany of manifolds with finite non-cyclic fundamental groups is also studied.
In this paper, firstly, for some $4n$-dimensional almost complex manifolds $M_{i}, ~1\le i \le \alpha$, we prove that $\left(\sharp_{i=1}^{\alpha} M_{i}\right) \sharp (\alpha{-}1) \mathbb{C} P^{2n}$ must admits an almost complex structure,…
We construct a family of $(2,n)$-almost Grassmannian structures of regularity $C^1$, each admitting a one-parameter group of strongly essential automorphisms, and each not flat on any neighborhood of the higher-order fixed point. This shows…
A matchstick graph is a graph drawn with straight edges in the plane such that the edges have unit length, and non-adjacent edges do not intersect. We call a matchstick graph $(m;n)$-regular if every vertex has only degree $m$ or $n$. In…
We study Artin-Schelter regular algebras of global dimension 4 with three generators of degree one. We classify those which are domains and which have an additional Z x Z-grading, and prove that all of these examples are also strongly…
The expressions for the quasinormal modes (QNMs) of black holes with nonlinear electrodynamics, calculated in the eikonal approximation, are presented. In the eikonal limit QNMs of black holes are determined by the parameters of the…
For $d\geq 2$, the regular genus of a closed connected PL $d$-manifold $M$ is the least genus (resp., half of the genus) of an orientable (resp., a non-orientable) surface into which a crystallization of $M$ imbeds regularly. The regular…
We apply the quaternionic Jordan form to classify the hypercomplex nilpotent almost abelian Lie algebras in all dimensions and to carry out the complete classification of 12-dimensional hypercomplex almost abelian Lie algebras. Moreover, we…
We provide a nontrivial upper bound for the nonnegative rank of rank-three matrices, which allows us to prove that [6(n+1)/7] linear inequalities suffice to describe a convex n-gon up to a linear projection.