On exceptional Lie geometries

Forum of Mathematics Sigma ◽

10.1017/fms.2020.57 ◽

2021 ◽

Vol 9 ◽

Author(s):

Anneleen De Schepper ◽

Jeroen Schillewaert ◽

Hendrik Van Maldeghem ◽

Magali Victoor

Keyword(s):

Wide Class ◽

Algebraic Groups ◽

Geometric Approach ◽

Intersection Property ◽

Incidence Geometries ◽

Parapolar Spaces ◽

Point Line

Abstract Parapolar spaces are point-line geometries introduced as a geometric approach to (exceptional) algebraic groups. We characterize a wide class of Lie geometries as parapolar spaces satisfying a simple intersection property. In particular, many of the exceptional Lie incidence geometries occur. In an appendix, we extend our result to the locally disconnected case and discuss the locally disconnected case of some other well-known characterizations.

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A Geometric Approach to Dynamically Feasible, Real-Time Formation Control

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.4003209 ◽

2011 ◽

Vol 133 (2) ◽

Cited By ~ 7

Author(s):

D. H. A. Maithripala ◽

D. H. S. Maithripala ◽

S. Jayasuriya

Keyword(s):

Real Time ◽

Wide Class ◽

Formation Control ◽

Geometric Approach ◽

Control Problems ◽

Multi Agent Systems ◽

Individual Agent ◽

Planning Algorithm ◽

Explicit Consideration ◽

Multi Agent

We propose a framework for synthesizing real-time trajectories for a wide class of coordinating multi-agent systems. The class of problems considered is characterized by the ability to decompose a given formation objective into an equivalent set of lower dimensional problems. These include the so called radar deception problem and the formation control problems that fall under formation keeping and/or formation reconfiguration tasks. The decomposition makes the approach scalable, computationally economical, and decentralized. Most importantly, the designed trajectories are dynamically feasible, meaning that they maintain the formation while satisfying the nonholonomic and saturation type velocity and acceleration constraints of each individual agent. The main contributions of this paper are (i) explicit consideration of second order dynamics for agents, (ii) explicit consideration of nonholonomic and saturation type velocity and acceleration constraints, (iii) unification of a wide class of formation control problems, and (iv) development of a real-time, distributed, scalable, computationally economical motion planning algorithm.

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A Geometric Approach to Homology Theory

10.1017/cbo9780511662669 ◽

1976 ◽

Cited By ~ 26

Author(s):

S. Buonchristiano ◽

C. P. Rourke ◽

B. J. Sanderson

Keyword(s):

Geometric Approach ◽

Homology Theory

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Linear Algebraic Groups and Finite Groups of Lie Type

10.1017/cbo9780511994777 ◽

2009 ◽

Cited By ~ 57

Author(s):

Gunter Malle ◽

Donna Testerman

Keyword(s):

Finite Groups ◽

Algebraic Groups ◽

Linear Algebraic Groups ◽

Groups Of Lie Type

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Introduction to Algebraic Geometry and Algebraic Groups

10.1016/s0304-0208(08)x7077-x ◽

1980 ◽

Keyword(s):

Algebraic Geometry ◽

Algebraic Groups

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A GEOMETRIC APPROACH TO DISSIPATION AND ITS APPLICATION TO DISSIPATIVE NUCLEAR DYNAMICS

Le Journal de Physique Colloques ◽

10.1051/jphyscol:1984610 ◽

1984 ◽

Vol 45 (C6) ◽

pp. C6-87-C6-94

Author(s):

H. Reinhardt ◽

R. Balian ◽

Y. Alhassid

Keyword(s):

Geometric Approach ◽

Nuclear Dynamics

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Computer Modeling of a Tire under Cornering Loads

Tire Science and Technology ◽

10.2346/1.2141681 ◽

1989 ◽

Vol 17 (2) ◽

pp. 86-99 ◽

Cited By ~ 4

Author(s):

I. Gardner ◽

M. Theves

Keyword(s):

Finite Element Analysis ◽

Geometric Approach ◽

Lateral Force ◽

Slip Angle ◽

Element Analysis ◽

Pressure Distributions ◽

Slip Effects ◽

Improved Accuracy ◽

Nonlinear Geometric ◽

Good Agreement

Abstract During a cornering maneuver by a vehicle, high forces are exerted on the tire's footprint and in the contact zone between the tire and the rim. To optimize the design of these components, a method is presented whereby the forces at the tire-rim interface and between the tire and roadway may be predicted using finite element analysis. The cornering tire is modeled quasi-statically using a nonlinear geometric approach, with a lateral force and a slip angle applied to the spindle of the wheel to simulate the cornering loads. These values were obtained experimentally from a force and moment machine. This procedure avoids the need for a costly dynamic analysis. Good agreement was obtained with experimental results for self-aligning torque, giving confidence in the results obtained in the tire footprint and at the rim. The model allows prediction of the geometry and of the pressure distributions in the footprint, since friction and slip effects in this area were considered. The model lends itself to further refinement for improved accuracy and additional applications.

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Geometric approach to nondestructive identification of faults in stochastic structural systems

AIAA Journal ◽

10.2514/3.13568 ◽

1997 ◽

Vol 35 ◽

pp. 700-705

Author(s):

M. H. Sadeghi ◽

S. D. Fassois

Keyword(s):

Geometric Approach ◽

Structural Systems ◽

Nondestructive Identification

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PERSPECTIVES OF ELLIPTICAL CRYPTOGRAPHY TO ENSURE THE INTEGRITY AND CONFIDENTIALITY OF INFORMATION

Visnyk Universytetu “Ukraina” ◽

10.36994/2707-4110-2019-2-23-26 ◽

2019 ◽

Author(s):

Anna ILYENKO ◽

Sergii ILYENKO ◽

Yana MASUR

Keyword(s):

Information Systems ◽

Elliptic Curve ◽

Elliptic Curves ◽

Finite Fields ◽

Computational Efficiency ◽

Digital Signature ◽

Discrete Logarithm ◽

Algebraic Groups ◽

Schnorr Signature ◽

Stability Of Algorithms

In this article, the main problems underlying the current asymmetric crypto algorithms for the formation and verification of electronic-digital signature are considered: problems of factorization of large integers and problems of discrete logarithm. It is noted that for the second problem, it is possible to use algebraic groups of points other than finite fields. The group of points of the elliptical curve, which satisfies all set requirements, looked attractive on this side. Aspects of the application of elliptic curves in cryptography and the possibilities offered by these algebraic groups in terms of computational efficiency and crypto-stability of algorithms were also considered. Information systems using elliptic curves, the keys have a shorter length than the algorithms above the finite fields. Theoretical directions of improvement of procedure of formation and verification of electronic-digital signature with the possibility of ensuring the integrity and confidentiality of information were considered. The proposed method is based on the Schnorr signature algorithm, which allows data to be recovered directly from the signature itself, similarly to RSA-like signature systems, and the amount of recoverable information is variable depending on the information message. As a result, the length of the signature itself, which is equal to the sum of the length of the end field over which the elliptic curve is determined, and the artificial excess redundancy provided to the hidden message was achieved.

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