scholarly journals On KM-Arcs in Small Desarguesian Planes

10.37236/6057 ◽  
2017 ◽  
Vol 24 (1) ◽  
Author(s):  
Peter Vandendriessche
Keyword(s):  
Existence Problem ◽  
Desarguesian Planes ◽  
Projective Equivalence ◽  
Full Classification

In this paper we study the existence problem for KM-arcs in small Desarguesian planes. We establish a full classification of KM$_{q,t}$-arcs for $q\le 32$, up to projective equivalence. We also construct a KM$_{64,4}$-arc; as $t=4$ was the only value for which the existence of a KM$_{64,t}$-arc was unknown, this fully settles the existence problem for $q\le 64$.

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 On the maximal Sobolev regularity of distributions supported by subsets of Euclidean space

2016 ◽  
Vol 15 (05) ◽  
pp. 731-770 ◽  
Author(s):  
D. P. Hewett ◽  
A. Moiola
Keyword(s):  
Maximal Regularity ◽  
Cantor Sets ◽  
Characteristic Functions ◽  
Bessel Potential ◽  
Empty Interior ◽  
Cartesian Products ◽  
Sobolev Regularity ◽  
Full Classification ◽  
Differential And Integral Equations

This paper concerns the following question: given a subset [Formula: see text] of [Formula: see text] with empty interior and an integrability parameter [Formula: see text], what is the maximal regularity [Formula: see text] for which there exists a non-zero distribution in the Bessel potential Sobolev space [Formula: see text] that is supported in [Formula: see text]? For sets of zero Lebesgue measure, we apply well-known results on set capacities from potential theory to characterize the maximal regularity in terms of the Hausdorff dimension of [Formula: see text], sharpening previous results. Furthermore, we provide a full classification of all possible maximal regularities, as functions of [Formula: see text], together with the sets of values of [Formula: see text] for which the maximal regularity is attained, and construct concrete examples for each case. Regarding sets with positive measure, for which the maximal regularity is non-negative, we present new lower bounds on the maximal Sobolev regularity supported by certain fat Cantor sets, which we obtain both by capacity-theoretic arguments, and by direct estimation of the Sobolev norms of characteristic functions. We collect several results characterizing the regularity that can be achieved on certain special classes of sets, such as [Formula: see text]-sets, boundaries of open sets, and Cartesian products, of relevance for applications in differential and integral equations.

scholarly journals Natural Paracontact Magnetic Trajectories on Unit Tangent Bundles

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 72
Author(s):  
Mohamed Tahar Kadaoui Abbassi ◽  
Noura Amri
Keyword(s):  
Gaussian Curvature ◽  
Tangent Bundle ◽  
Two Dimensional ◽  
Constant Gaussian Curvature ◽  
Metric Structures ◽  
Unit Tangent Bundle ◽  
Tangent Bundles ◽  
Full Classification ◽  
Kaluza Klein

In this paper, we study natural paracontact magnetic trajectories in the unit tangent bundle, i.e., those that are associated to g-natural paracontact metric structures. We characterize slant natural paracontact magnetic trajectories as those satisfying a certain conservation law. Restricting to two-dimensional base manifolds of constant Gaussian curvature and to Kaluza–Klein type metrics on their unit tangent bundles, we give a full classification of natural paracontact slant magnetic trajectories (and geodesics).

scholarly journals On the symmetries of three-dimensional generalized symmetric spaces

2021 ◽  
Vol 13(62) (2) ◽  
pp. 451-462
Author(s):  
Lakehal Belarbi
Keyword(s):  
Symmetric Spaces ◽  
Vector Fields ◽  
Killing Vector ◽  
Three Dimensional ◽  
Riemannian Metric ◽  
Killing Vector Fields ◽  
Generalized Symmetric Space ◽  
Generalized Symmetric Spaces ◽  
Full Classification

In this work we consider the three-dimensional generalized symmetric space, equipped with the left-invariant pseudo-Riemannian metric. We determine Killing vector fields and affine vectors fields. Also we obtain a full classification of Ricci, curvature and matter collineations

scholarly journals Classification of Elliptic Cubic Curves Over The Finite Field of Order Nineteen

2016 ◽  
Vol 13 (4) ◽  
pp. 846-852
Author(s):  
Baghdad Science Journal
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Maximum Size ◽  
Cubic Curves ◽  
Projective Equivalence

Plane cubics curves may be classified up to isomorphism or projective equivalence. In this paper, the inequivalent elliptic cubic curves which are non-singular plane cubic curves have been classified projectively over the finite field of order nineteen, and determined if they are complete or incomplete as arcs of degree three. Also, the maximum size of a complete elliptic curve that can be constructed from each incomplete elliptic curve are given.

Super-Penrose process

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040058
Author(s):  
O. B. Zaslavskii
Keyword(s):  
Black Hole ◽  
Flat Space ◽  
Space Time ◽  
Centre Of Mass ◽  
Rotating Black Hole ◽  
Mass Frame ◽  
Penrose Process ◽  
Energy Formula ◽  
Full Classification

If two particles collide near a rotating black hole, their energy in the centre of mass frame can become unbounded under certain conditions. In doing so, the Killing energy [Formula: see text] of debris at infinity is, in general, remain restricted. If [Formula: see text] is also unbounded, this is called the super-Penrose process. We elucidate when such a process is possible and give full classification of corresponding relativistic objects for rotating space-times. We also discuss the case of a pure electric super-Penrose process that is valid even in the flat space-time. The key role in consideration is played by the Wald inequalities.

scholarly journals Mixed threefolds isogenous to a product

2019 ◽  
Vol 18 (12) ◽  
pp. 1950239 ◽  
Author(s):  
Christian Gleissner
Keyword(s):  
Finite Group ◽  
Riemann Surfaces ◽  
Mixed Type ◽  
General Type ◽  
Canonical Class ◽  
Trivial Element ◽  
Compact Riemann Surfaces ◽  
A Finite Group ◽  
Full Classification

In this paper, we study threefolds isogenous to a product of mixed type i.e. quotients of a product of three compact Riemann surfaces [Formula: see text] of genus at least two by the action of a finite group [Formula: see text], which is free, but not diagonal. In particular, we are interested in the systematic construction and classification of these varieties. Our main result is the full classification of threefolds isogenous to a product of mixed type with [Formula: see text] in the absolutely faithful case, i.e. any automorphism in [Formula: see text], which restricts to the trivial element in [Formula: see text] for some [Formula: see text], is the identity on the product. Since the holomorphic Euler–Poincaré-characteristic of a smooth threefold of general type with ample canonical class is always negative, these examples lie on the boundary, in the sense of threefold geography. To achieve our result we use techniques from computational group theory. Indeed, we develop a MAGMA algorithm to classify these threefolds for any given value of [Formula: see text] in the absolutely faithful case.

scholarly journals Self-motions of pentapods with linear platform

Robotica ◽  
2015 ◽  
Vol 35 (4) ◽  
pp. 832-860 ◽  
Author(s):  
Georg Nawratil ◽  
Josef Schicho
Keyword(s):  
Real Solutions ◽  
Kinematic Mapping ◽  
Bond Theory ◽  
Anchor Points ◽  
Self Motion ◽  
Full Classification ◽  
Direct Kinematics

SUMMARYWe give a full classification of all pentapods with linear platform possessing a self-motion beside the trivial rotation about the platform. Recent research necessitates a contemporary and accurate re-examination of old results on this topic given by Darboux, Mannheim, Duporcq and Bricard, which also takes the coincidence of platform anchor points into account. For our study we use bond theory with respect to a novel kinematic mapping for pentapods with linear platform, beside the method of singular-invariant leg-rearrangements. Based on our results we design pentapods with linear platform, which have a simplified direct kinematics concerning their number of (real) solutions.

scholarly journals Cuspidal and noncuspidal robot manipulators

Robotica ◽  
2007 ◽  
Vol 25 (6) ◽  
pp. 677-689 ◽  
Author(s):  
Philippe Wenger
Keyword(s):  
Robot Manipulators ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Geometric Conditions ◽  
Necessary And Sufficient ◽  
Full Classification

SUMMARYThis article synthezises the most important results on the kinematics of cuspidal manipulators i.e. nonredundant manipulators that can change posture without meeting a singularity. The characteristic surfaces, the uniqueness domains and the regions of feasible paths in the workspace are defined. Then, several sufficient geometric conditions for a manipulator to be noncuspidal are enumerated and a general necessary and sufficient condition for a manipulator to be cuspidal is provided. An explicit DH-parameter-based condition for an orthogonal manipulator to be cuspidal is derived. The full classification of 3R orthogonal manipulators is provided and all types of cuspidal and noncuspidal orthogonal manipulators are enumerated. Finally, some facts about cuspidal and noncuspidal 6R manipulators are reported.

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