scholarly journals Dual Numbers and Invariant Theory of the Euclidean Group with Applications to Robotics

2021 ◽  
Author(s):  
◽  
Mohammed Daher
Keyword(s):  
Rational Function ◽  
Invariant Theory ◽  
Adjoint Action ◽  
Point Of View ◽  
Dual Numbers ◽  
Euclidean Group ◽  
Link Length ◽  
Algebraic Point ◽  
Geometric Point ◽  
Points Of View

<p>In this thesis we study the special Euclidean group SE(3) from two points of view, algebraic and geometric. From the algebraic point of view we introduce a dualisation procedure for SO(3;ℝ) invariants and obtain vector invariants of the adjoint action of SE(3) acting on multiple screws. In the case of three screws there are 14 basic vector invariants related by two basic syzygies. Moreover, we prove that any invariant of the same group under the same action can be expressed as a rational function evaluated on those 14 vector invariants.  From the geometric point of view, we study the Denavit-Hartenberg parameters used in robotics, and calculate formulae for link lengths and offsets in terms of vector invariants of the adjoint action of SE(3). Moreover, we obtain a geometrical duality between the offsets and the link lengths, where the geometrical dual of an offset is a link length and vice versa.</p>

scholarly journals Dual Numbers and Invariant Theory of the Euclidean Group with Applications to Robotics

2021 ◽  
Author(s):  
◽  
Mohammed Daher
Keyword(s):  
Rational Function ◽  
Invariant Theory ◽  
Adjoint Action ◽  
Point Of View ◽  
Dual Numbers ◽  
Euclidean Group ◽  
Link Length ◽  
Algebraic Point ◽  
Geometric Point ◽  
Points Of View

<p>In this thesis we study the special Euclidean group SE(3) from two points of view, algebraic and geometric. From the algebraic point of view we introduce a dualisation procedure for SO(3;ℝ) invariants and obtain vector invariants of the adjoint action of SE(3) acting on multiple screws. In the case of three screws there are 14 basic vector invariants related by two basic syzygies. Moreover, we prove that any invariant of the same group under the same action can be expressed as a rational function evaluated on those 14 vector invariants.  From the geometric point of view, we study the Denavit-Hartenberg parameters used in robotics, and calculate formulae for link lengths and offsets in terms of vector invariants of the adjoint action of SE(3). Moreover, we obtain a geometrical duality between the offsets and the link lengths, where the geometrical dual of an offset is a link length and vice versa.</p>

NONSENSE, ABSURDITY AND PARADOX AS LINGUISTIC AND CULTURAL CATEGORIES

2019 ◽  
Keyword(s):  
Cognitive Function ◽  
Common Sense ◽  
Point Of View ◽  
Ontological Category ◽  
Ordinary Meaning ◽  
New Meanings ◽  
Points Of View ◽  
Human Thinking

In the article the analysis of nonsense, absurdity and paradox from the standpoint of linguistics is giv-en. Different points of view on these categories in relation to the meaning are considered. An attempt is made to reveal the commonality and specificity of nonsense, absurdity and paradox. Some researchers consider nonsense and paradox as a kind of absurdity. There is a dichotomous point of view on nonsense as one of the components of absurdity. However, there are works where these categories are differentiat-ed, for example, absurdity is understood as an ontological category, and nonsense as an epistemological category. There is a view of these categories through the allocation of "non-sense", "out-sense" and 136 "counter-sense" there is also a view that in the case of nonsense we are talking about the incompatibility of representations, and in the case of absurdity-the incompatibility of objects. If there are criteria that allow us to consider the presence of this phenomenon as natural, absurdity ceases to exist. Consequently, the view is expressed that nonsense, absurdity and paradox are different categories of thinking. Paradox is a contradiction arising from the presence of two or more common sense. The absurdity can be seen as a" counter-sense» opposing common sense and putting forward the concept of active impossibility of the latter's existence. As for nonsense, it is the meaning of metaphysical level – a meaning that goes beyond the ordinary meaning and creates new meanings. It is concluded that nonsense, absurdity and paradox are independent categories of human thinking, which is a manifestation of the cognitive function of hu-man consciousness.

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 Laws of the iterated logarithm on covering graphs with groups of polynomial volume growth

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ryuya Namba
Keyword(s):  
Random Walks ◽  
Quadratic Forms ◽  
Volume Growth ◽  
Moderate Deviation ◽  
Point Of View ◽  
Iterated Logarithm ◽  
Large Numbers ◽  
Geometric Point ◽  
Rate Functions ◽  
The Given

AbstractModerate deviation principles (MDPs) for random walks on covering graphs with groups of polynomial volume growth are discussed in a geometric point of view. They deal with any intermediate spatial scalings between those of laws of large numbers and those of central limit theorems. The corresponding rate functions are given by quadratic forms determined by the Albanese metric associated with the given random walks. We apply MDPs to establish laws of the iterated logarithm on the covering graphs by characterizing the set of all limit points of the normalized random walks.

THE CONCEPT AS THE OBJECT OF STUDY OF LINGUISTICS

2020 ◽  
Vol 72 (2) ◽  
pp. 236-242
Author(s):  
K. Galiyeva ◽  
◽  
S. Isakova ◽  
Keyword(s):  
Cognitive Linguistics ◽  
Point Of View ◽  
Subject Areas ◽  
The Subject ◽  
Basic Concepts ◽  
Points Of View ◽  
Definition Of ◽  
Object Of Study ◽  
Linguistic Phenomenon ◽  
Scientific Fields

The article is devoted to the definition of concept in modern linguistics. Various points of view and definitions of the basic concepts are considered: "concept", "conceptual sphere", "content". The aim of the article is to describe and explain such a complex unit as a concept from the point of view of linguistics. The object of research is studied in its various manifestations, the combination of verbal and nonverbal means of information expression in the conceptual sphere is revealed. the relevance of this topic is due to the need for a detailed consideration of the concept of concept based on the works of prominent scientists and linguists. Researchers treat the concept as a cognitive, psycholinguistic, linguocultural, cultural and linguistic phenomenon. The concept is an umbrella term because it "covers" the subject areas of several scientific fields: primarily cognitive psychology and cognitive linguistics.

Jules Verne’s ‘Around the World in 80 Days’: Multilingualism, Multiculturalism and Symbols

2021 ◽  
Vol 2021 ii (15) ◽  
pp. 146-182
Author(s):  
Haroula Hatzimihail ◽  
Ioannis Pantelidis
Keyword(s):  
Key Words ◽  
Age Groups ◽  
Literary Work ◽  
Point Of View ◽  
Social Classes ◽  
Jules Verne ◽  
The World ◽  
Semiotic Systems ◽  
Points Of View ◽  
Different Cultures

In this announcement, the various –linguistic and non-linguistic- symbols used in the literary work 'Around the world in 80 days', written by Jules Verne, are examined from an intertemporal and contemporary point of view. The references through these points of view, in matters of multiculturalism and multilingualism, are becoming classical in nature: they concern the necessity of the applied ability to communicate between individuals who belong to different social classes and age groups, speak the same or different languages, come from different cultures, with rights and obligations in their various areas of life, etc. Key-words: linguistics, multilingualism, multiculturalism, semiotics, semiotic systems, symbols

LEGAL STATUS OF THE SOLE EXECUTIVE BODY OF A LIMITED LIABILITY COMPANY

2021 ◽  
Author(s):  
Yulia Fanilevna Aitova ◽  
Keyword(s):  
General Theory ◽  
Legal Status ◽  
Limited Liability ◽  
Point Of View ◽  
Limited Liability Company ◽  
Points Of View ◽  
Theory Of Law ◽  
The Individual ◽  
Executive Body

The article analyzes the issue of determining the legal status of the individual management body of a limited liability company. The author begins his research with the concept of legal status existing in the general theory of law, and then proceeds to consider the issue from the point of view of philosophical categories. In addition, the work explores the diversity of points of view existing in the doctrine regarding the legal status of the individual management body of economic societies.

UNEXPECTED BEHAVIOR IN THE CROSSING OF MICROWAVE AND OPTICAL BEAMS

2005 ◽  
Vol 19 (27) ◽  
pp. 1403-1410 ◽  
Author(s):  
E. ALLARIA ◽  
R. MEUCCI ◽  
D. MUGNAI ◽  
A. RANFAGNI ◽  
C. RANFAGNI
Keyword(s):  
Lorentz Invariance ◽  
Point Of View ◽  
Experimental Results ◽  
Light Velocity ◽  
Broken Lorentz Invariance ◽  
Points Of View ◽  
Optical Beams ◽  
Definite Solution ◽  
Unexpected Behavior

The question of the superluminal speed of information was stopped at crossroads in the last few years. According to one point of view, this speed must be limited to the light velocity in vacuum, whereas a different point of view is more open in this respect and, under specific conditions, this limit is considered surmountable. Very recently, a third approach (based on the hypothesis of a local broken Lorentz-invariance) was proposed and, if confirmed, would go beyond the controversy of the two points of view mentioned above. It is therefore worthwhile to recall attention to this problem, which is far from having a definite solution. The present paper reports some experimental results (similar to those of Ref. 1) which can contribute to these discussions, and also considers the fact that they seem to give some support to the aforesaid third approach, although revised in terms of decaying waves.

Dynamics of Multibody Systems: Generalized Mass Metric in Riemannian Velocity Space and Recursive Momentum Formulation

2007 ◽  
Author(s):  
Qiang Zhao ◽  
Hong Tao Wu
Keyword(s):  
Point Of View ◽  
Velocity Space ◽  
Motion Equations ◽  
Closed Loop Systems ◽  
Dynamics Of Multibody Systems ◽  
Operator Factorization ◽  
Geometric Point ◽  
Mass Tensor ◽  
Generalized Momentum ◽  
Serial Chains

This paper describes two aspects of multibody system (MBS) dynamics on a generalized mass metric in Riemannian velocity space and recursive momentum formulation. Firstly, we present a detailed expression of the Riemannian metric and operator factorization of a generalized mass tensor for the dynamics of general-topology rigid MBS. The derived expression allows a clearly understanding the components of the generalized mass tensor, which also constitute a metric of the Riemannian velocity space. It is being the fact that there does exist a common metric in Lagrange and recursive Newton-Euler dynamic equation, we can determine, from the Riemannian geometric point of view, that there is the equivalent relationship between the two approaches to a given MBS. Next, from the generalized momentum definition in the derivation of the Riemannian velocity metrics, recursive momentum equations of MBS dynamics are developed for progressively more complex systems: serial chains, topological trees, and closed-loop systems. Through the principle of impulse and momentum, a new method is proposed for reorienting and locating the MBS form a given initial orientation and location to desired final ones without needing to solve the motion equations.

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