scholarly journals Robot Kinematics – The Algebraic Point of View

2021 ◽  
Vol 352 ◽  
pp. 1-3
Author(s):  
Manfred L. Husty
Keyword(s):  
Point Of View ◽  
Robot Kinematics ◽  
Algebraic Point

scholarly journals CONFLICTS AND FAIR TESTING

2006 ◽  
Vol 17 (04) ◽  
pp. 797-813 ◽  
Author(s):  
ROBI MALIK ◽  
DAVID STREADER ◽  
STEVE REEVES
Keyword(s):  
Discrete Event Systems ◽  
Process Algebra ◽  
Discrete Event ◽  
Denotational Semantics ◽  
Point Of View ◽  
Algebraic Point ◽  
Event Systems ◽  
Common Task ◽  
Testing Theory ◽  
Process Algebraic

This paper studies conflicts from a process-algebraic point of view and shows how they are related to the testing theory of fair testing. Conflicts have been introduced in the context of discrete event systems, where two concurrent systems are said to be in conflict if they can get trapped in a situation where they are waiting or running endlessly, forever unable to complete their common task. In order to analyse complex discrete event systems, conflict-preserving notions of refinement and equivalence are needed. This paper characterises an appropriate refinement, called the conflict preorder, and provides a denotational semantics for it. Its relationship to other known process preorders is explored, and it is shown to generalise the fair testing preorder in process-algebra for reasoning about conflicts in discrete event systems.

scholarly journals Localizability of unicycle mobiles robots: An algebraic point of view

2012 ◽  
Author(s):  
Hugues Sert ◽  
Wilfrid Perruquetti ◽  
Annemarie Kokosy ◽  
Xin Jin ◽  
Jorge Palos
Keyword(s):  
Point Of View ◽  
Algebraic Point

MAGNETIC GROUP ON THE PSEUDOSPHERE

1992 ◽  
Vol 06 (21) ◽  
pp. 3525-3537 ◽  
Author(s):  
V. BARONE ◽  
V. PENNA ◽  
P. SODANO
Keyword(s):  
Magnetic Field ◽  
Hilbert Space ◽  
Quantum Mechanics ◽  
Constant Magnetic Field ◽  
Coherent States ◽  
Compact Operators ◽  
Point Of View ◽  
Algebraic Point ◽  
Planar Limit ◽  
Discrete Part

The quantum mechanics of a particle moving on a pseudosphere under the action of a constant magnetic field is studied from an algebraic point of view. The magnetic group on the pseudosphere is SU(1, 1). The Hilbert space for the discrete part of the spectrum is investigated. The eigenstates of the non-compact operators (the hyperbolic magnetic translators) are constructed and shown to be expressible as continuous superpositions of coherent states. The planar limit of both the algebra and the eigenstates is analyzed. Some possible applications are briefly outlined.

scholarly journals Connectivity of pseudomanifold graphs from an algebraic point of view

2015 ◽  
Vol 353 (12) ◽  
pp. 1061-1065 ◽  
Author(s):  
Karim A. Adiprasito ◽  
Afshin Goodarzi ◽  
Matteo Varbaro
Keyword(s):  
Point Of View ◽  
Algebraic Point

A lattice of extension rings for a commutative ring

1978 ◽  
Vol 84 (2) ◽  
pp. 225-234 ◽  
Author(s):  
D. Kirby ◽  
M. R. Adranghi
Keyword(s):  
Point Of View ◽  
Local Rings ◽  
Algebraic Point ◽  
Multiple Points ◽  
One Dimensional ◽  
Maximal Ideals ◽  
Blowing Up ◽  
Abstract Case ◽  
Algebroid Curve

The work of this note was motivated in the first place by North-cott's theory of dilatations for one-dimensional local rings (see, for example (4) and (5)). This produces a tree of local rings as in (4) which corresponds, in the abstract case, to the branching sequence of infinitely-near multiple points on an algebroid curve. From the algebraic point of view it seems more natural to characterize such one-dimensional local rings R by means of the set of rings which arise by blowing up all ideals Q which are primary for the maximal ideals M of R. This set of rings forms a lattice (R), ordered by inclusion, each ring S of which is a finite R-module. Moreover the length of the R-module S/R is just the reduction number of the corresponding ideal Q (cf. theorem 1 of Northcott (6)). Thus the lattice (R) provides a finer classification of the rings R than does the set of reduction numbers (cf. Kirby (1)).

Freeness in classes without equality

1999 ◽  
Vol 64 (3) ◽  
pp. 1159-1194 ◽  
Author(s):  
Raimon Elgueta
Keyword(s):  
Structural Properties ◽  
Universal Algebra ◽  
Reduction Process ◽  
Point Of View ◽  
Basic Notion ◽  
Algebraic Point ◽  
Generic Problem

AbstractThis paper is a continuation of [27], where we provide the background and the basic tools for studying the structural properties of classes of models over languages without equality. In the context of such languages, it is natural to make distinction between two kinds of classes, the so-called abstruct classes, which correspond to those closed under isomorphic copies in the presence of equality, and the reduced classes, i.e., those obtained by factoring structures by their largest congruences. The generic problem described in [27] is to investigate under what conditions this reduction process does not alter the metatheory of a class.Here we focus our attention on a concrete aspect of this generic problem that we import from universal algebra, namely the existence and description of free models. As in [27], we can find here again the basic notion of protoalgebraicity, which was originally introduced in [7] as the weakest condition to guarantee that the reduction process behaves reasonably well from an algebraic point of view. Our concern, however, takes us to handle a further notion, that of semialgebraicity, which corresponds to the notion of equivalential logic of [18]; semialgebraicity turns out to be the property which ensures that freeness is fully preserved by the reduction process.

Assur’s Groups, AKCs, Basic Trusses, SOCs, etc.: Modular Kinematics of Planar Linkages

1996 ◽  
Author(s):  
E. Ceresole ◽  
P. Fanghella ◽  
C. Galletti
Keyword(s):  
Kinematic Chain ◽  
Point Of View ◽  
Robot Kinematics ◽  
Systems Of Equations ◽  
Topological Properties ◽  
Cad Systems ◽  
Solution Algorithms ◽  
Modular Method ◽  
The Common ◽  
Planar Linkages

Abstract The paper presents a unified point of view on modular methods of kinematic analysis of planar linkages. It is shown that various approaches adopted in different fields, such as linkage analysis, robot kinematics, variational CAD systems, are based on the common idea of decoupling complex systems of equations by solving sequences of simpler subsystems. These subsystems correspond to modules with particular topological properties. Then, the three main issues of a modular method, namely, systematic topology of the modules, solution algorithms for each module, and module recognition in a given mechanism, are discussed and solutions are provided by means of the general unifying concept of Assur Kinematic Chain (AKC).

scholarly journals PARAGRASSMANN ANALYSIS AND QUANTUM GROUPS

1992 ◽  
Vol 07 (23) ◽  
pp. 2129-2141 ◽  
Author(s):  
A. T. FILIPPOV ◽  
A. P. ISAEV ◽  
A. B. KURDIKOV
Keyword(s):  
Differential Operator ◽  
Quantum Groups ◽  
Natural Generalization ◽  
Point Of View ◽  
Algebraic Point ◽  
Root Of Unity ◽  
Deformation Parameters ◽  
One And Many

Paragrassmann algebras with one and many paragrassmann variables are considered from the algebraic point of view without using the Green ansatz. A differential operator with respect to paragrassmann variable and a covariant para-super-derivative are introduced giving a natural generalization of the Grassmann calculus to a paragrassmann one. Deep relations between paragrassmann algebras and quantum groups with deformation parameters being root of unity are established.

Fourth-rank tensors of the thirty-two crystal classes: multiplication tables

1984 ◽  
Vol 391 (1800) ◽  
pp. 149-179 ◽  
Keyword(s):  
Associative Algebra ◽  
Point Of View ◽  
Complex Numbers ◽  
Hypercomplex Numbers ◽  
Algebraic Point ◽  
Multiplication Tables

The fourth-rank tensors that embody the elastic or other properties of crystalline anisotropic substances can be partitioned into a number of sets in order that each shall acknowledge the symmetry of one or more of the crystal classes and moreover shall make up a closed linear associative algebra of hypercomplex numbers for the purpose of calculating the sums, products and inverses of its constituent tensors, to which end coordinate invariant expressions of the tensors are adopted. The calculations are simplified immensely, and ensuing physical analyses are well prepared for, once the structure of every algebra is unravelled completely in terms of a number of separate subalgebras isomorphic to familiar algebras such as the binary one of the complex numbers, the quaternary one of the 2x2 matrices and the octonary one of the complex quaternions. The fourth-rank tensors do not seem to have been submitted previously to the present algebraic point of view, and nor do those of any other rank: a parallel, but less intricate, development can be provided for the second-rank ones.

scholarly journals Commutative and non-commutative bialgebras of quasi-posets and applications to Ehrhart polynomials

2019 ◽  
Vol 10 (1) ◽  
pp. 27-63 ◽  
Author(s):  
Loïc Foissy
Keyword(s):  
Hopf Algebra ◽  
Point Of View ◽  
Duality Principle ◽  
Algebraic Proof ◽  
Ehrhart Polynomial ◽  
Algebraic Point ◽  
Ehrhart Polynomials ◽  
Lattice Polytope ◽  
Algebra Morphism

Abstract To any poset or quasi-poset is attached a lattice polytope, whose Ehrhart polynomial we study from a Hopf-algebraic point of view. We use for this two interacting bialgebras on quasi-posets. The Ehrhart polynomial defines a Hopf algebra morphism with values in \mathbb{Q}[X] . We deduce from the interacting bialgebras an algebraic proof of the duality principle, a generalization and a new proof of a result on B-series due to Whright and Zhao, using a monoid of characters on quasi-posets, and a generalization of Faulhaber’s formula. We also give non-commutative versions of these results, where polynomials are replaced by packed words. We obtain, in particular, a non-commutative duality principle.

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