scholarly journals The complete classification of five-dimensional Dirichlet–Voronoi polyhedra of translational lattices

2016 ◽  
Vol 72 (6) ◽  
pp. 673-683 ◽  
Author(s):  
Mathieu Dutour Sikirić ◽  
Alexey Garber ◽  
Achill Schürmann ◽  
Clara Waldmann
Keyword(s):  
Mass Formula ◽  
Complete Classification ◽  
Complete List ◽  
Computer Assisted ◽  
Voronoi Polyhedra ◽  
Full Classification ◽  
Topological Mass

This paper reports on the full classification of Dirichlet–Voronoi polyhedra and Delaunay subdivisions of five-dimensional translational lattices. A complete list is obtained of 110 244 affine types (L-types) of Delaunay subdivisions and it turns out that they are all combinatorially inequivalent, giving the same number of combinatorial types of Dirichlet–Voronoi polyhedra. Using a refinement of corresponding secondary cones, 181 394 contraction types are obtained. The paper gives details of the computer-assisted enumeration, which was verified by three independent implementations and a topological mass formula check.

scholarly journals A Complete Classification of 3-dimensional Quadratic AS-regular Algebras of Type EC

2020 ◽  
pp. 1-19
Author(s):  
Masaki Matsuno
Keyword(s):  
Algebraic Geometry ◽  
Complete Classification ◽  
Complete List ◽  
Graded Algebra ◽  
Regular Algebra ◽  
3 Dimensional ◽  
Noncommutative Algebraic Geometry ◽  
Regular Algebras ◽  
Point Scheme

Abstract Classification of AS-regular algebras is one of the main interests in noncommutative algebraic geometry. We say that a $3$ -dimensional quadratic AS-regular algebra is of Type EC if its point scheme is an elliptic curve in $\mathbb {P}^{2}$ . In this paper, we give a complete list of geometric pairs and a complete list of twisted superpotentials corresponding to such algebras. As an application, we show that there are only two exceptions up to isomorphism among all $3$ -dimensional quadratic AS-regular algebras that cannot be written as a twist of a Calabi–Yau AS-regular algebra by a graded algebra automorphism.

scholarly journals Quantum D = 3 Euclidean and Poincaré symmetries from contraction limits

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Jerzy Kowalski-Glikman ◽  
Jerzy Lukierski ◽  
Tomasz Trześniewski
Keyword(s):  
Quantum Gravity ◽  
Cosmological Constant ◽  
Complete Classification ◽  
Complete List ◽  
Drinfeld Double ◽  
Lorentzian Signature ◽  
Quantum Deformations ◽  
Chern Simons

Abstract Following the recently obtained complete classification of quantum-deformed $$ \mathfrak{o} $$ o (4), $$ \mathfrak{o} $$ o (1, 3) and $$ \mathfrak{o} $$ o (2) algebras, characterized by classical r-matrices, we study their inhomogeneous D = 3 quantum IW contractions (i.e. the limit of vanishing cosmological constant), with Euclidean or Lorentzian signature. Subsequently, we compare our results with the complete list of D = 3 inhomogeneous Euclidean and D = 3 Poincaré quantum deformations obtained by P. Stachura. It turns out that the IW contractions allow us to recover all Stachura deformations. We further discuss the applicability of our results in the models of 3D quantum gravity in the Chern-Simons formulation (both with and with- out the cosmological constant), where it is known that the relevant quantum deformations should satisfy the Fock-Rosly conditions. The latter deformations in part of the cases are associated with the Drinfeld double structures, which also have been recently investigated in detail.

Pentapods With Mobility 2

2015 ◽  
Vol 7 (3) ◽  
Author(s):  
Georg Nawratil ◽  
Josef Schicho
Keyword(s):  
Complete List ◽  
Two Dimensional ◽  
Anchor Points ◽  
Special Case ◽  
Full Classification ◽  
Side Result

In this paper, we give a full classification of all pentapods with mobility 2, where neither all platform anchor points nor all base anchor points are located on a line. Therefore, this paper solves the famous Borel–Bricard problem for two-dimensional motions beside the excluded case of five collinear points with spherical trajectories. But even for this special case, we present three new types as a side-result. Based on our study of pentapods, we also give a complete list of all nonarchitecturally singular hexapods with two-dimensional self-motions.

COMPLETE CLASSIFICATION OF EQUILIBRIA AND THEIR STABILITY IN A DELAYED NEURON NETWORK

2008 ◽  
Vol 18 (07) ◽  
pp. 2017-2027 ◽  
Author(s):  
YUMING CHEN ◽  
JIANHONG WU
Keyword(s):  
Complete Classification ◽  
Memory Storage ◽  
Neuron Network ◽  
Dynamic Memory ◽  
Storage And Retrieval ◽  
Tangent Function ◽  
Spatio Temporal ◽  
Delay Differential ◽  
Full Classification

We consider the following system of delay differential equations [Formula: see text] where i (mod 3), and S(x) is the hyperbolic tangent function. The system models the evolution of a network of three identical neurons with delayed feedback. We provide a full classification of all equilibria and their stability in the (α,τ)-parameter space. Such a classification is essential for the description of spatio-temporal patterns of the model system and for the applications to dynamic memory storage and retrieval.

scholarly journals PROJECTIVE THREEFOLDS WITH HOLOMORPHIC CONFORMAL STRUCTURE

2005 ◽  
Vol 16 (06) ◽  
pp. 595-607 ◽  
Author(s):  
PRISKA JAHNKE ◽  
IVO RADLOFF
Keyword(s):  
Tangent Bundle ◽  
Complete Classification ◽  
Conformal Structure ◽  
Complete List ◽  
Projective Threefolds ◽  
Symmetric Square

The authors give a complete classification of projective threefolds admitting a holomorphic conformal structure. A corollary is the complete list of projective threefolds, whose tangent bundle is a symmetric square.

scholarly journals Polarized Rigid Del Pezzo Surfaces in Low Codimension

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1567
Author(s):  
Muhammad Imran Qureshi
Keyword(s):  
Computer Algebra System ◽  
Symmetric Matrix ◽  
Single Equation ◽  
Complete Classification ◽  
Computer Assisted ◽  
Del Pezzo Surfaces ◽  
Linearly Independent ◽  
Del Pezzo ◽  
Detailed Computer

We provide explicit graded constructions of orbifold del Pezzo surfaces with rigid orbifold points of type ki×1ri(1,ai):3≤ri≤10,ki∈Z≥0 as well-formed and quasismooth varieties embedded in some weighted projective space. In particular, we present a collection of 147 such surfaces such that their image under their anti-canonical embeddings can be described by using one of the following sets of equations: a single equation, two linearly independent equations, five maximal Pfaffians of 5×5 skew symmetric matrix, and nine 2×2 minors of size 3 square matrix. This is a complete classification of such surfaces under certain carefully chosen bounds on the weights of ambient weighted projective spaces and it is largely based on detailed computer-assisted searches by using the computer algebra system MAGMA.

scholarly journals Triharmonic Curves in 3-Dimensional Homogeneous Spaces

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
S. Montaldo ◽  
A. Pámpano
Keyword(s):  
Riemannian Manifold ◽  
Homogeneous Spaces ◽  
Arbitrary Dimension ◽  
Complete Classification ◽  
Constant Gaussian Curvature ◽  
Space Forms ◽  
3 Dimensional ◽  
The Family ◽  
Full Classification

AbstractWe first prove that, unlike the biharmonic case, there exist triharmonic curves with nonconstant curvature in a suitable Riemannian manifold of arbitrary dimension. We then give the complete classification of triharmonic curves in surfaces with constant Gaussian curvature. Next, restricting to curves in a 3-dimensional Riemannian manifold, we study the family of triharmonic curves with constant curvature, showing that they are Frenet helices. In the last part, we give the full classification of triharmonic Frenet helices in space forms and in Bianchi–Cartan–Vranceanu spaces.

Powerfully nilpotent groups of rank 2 or small order

2020 ◽  
Vol 23 (4) ◽  
pp. 641-658
Author(s):  
Gunnar Traustason ◽  
James Williams
Keyword(s):  
Detailed Analysis ◽  
Special Kind ◽  
Nilpotent Groups ◽  
Nilpotency Class ◽  
Central Series ◽  
Rank 2 ◽  
Full Classification

AbstractIn this paper, we continue the study of powerfully nilpotent groups. These are powerful p-groups possessing a central series of a special kind. To each such group, one can attach a powerful nilpotency class that leads naturally to the notion of a powerful coclass and classification in terms of an ancestry tree. In this paper, we will give a full classification of powerfully nilpotent groups of rank 2. The classification will then be used to arrive at a precise formula for the number of powerfully nilpotent groups of rank 2 and order {p^{n}}. We will also give a detailed analysis of the ancestry tree for these groups. The second part of the paper is then devoted to a full classification of powerfully nilpotent groups of order up to {p^{6}}.

scholarly journals Multiplicative automatic sequences

2021 ◽  
Author(s):  
Jakub Konieczny ◽  
Mariusz Lemańczyk ◽  
Clemens Müllner
Keyword(s):  
Complete Classification ◽  
Automatic Sequences ◽  
Complex Valued

AbstractWe obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

scholarly journals Characteristic cohomology and observables in higher spin gravity

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Alexey Sharapov ◽  
Evgeny Skvortsov
Keyword(s):  
Higher Spin Gravity ◽  
Complete Classification ◽  
Gravity Models ◽  
Simons Theory ◽  
Surface Charges ◽  
Higher Spin ◽  
Dynamical Invariants ◽  
Chern Simons ◽  
Conserved Currents

Abstract We give a complete classification of dynamical invariants in 3d and 4d Higher Spin Gravity models, with some comments on arbitrary d. These include holographic correlation functions, interaction vertices, on-shell actions, conserved currents, surface charges, and some others. Surprisingly, there are a good many conserved p-form currents with various p. The last fact, being in tension with ‘no nontrivial conserved currents in quantum gravity’ and similar statements, gives an indication of hidden integrability of the models. Our results rely on a systematic computation of Hochschild, cyclic, and Chevalley-Eilenberg cohomology for the corresponding higher spin algebras. A new invariant in Chern-Simons theory with the Weyl algebra as gauge algebra is also presented.

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