scholarly journals Slow Invariant Manifolds of Slow–Fast Dynamical Systems

2021 ◽  
Vol 31 (07) ◽  
pp. 2150112
Author(s):  
Jean-Marc Ginoux
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Singular Perturbation ◽  
Invariant Manifolds ◽  
The Other ◽  
Singularly Perturbed ◽  
Van Der Pol ◽  
Flow Curvature ◽  
The One

Slow–fast dynamical systems, i.e. singularly or nonsingularly perturbed dynamical systems possess slow invariant manifolds on which trajectories evolve slowly. Since the last century various methods have been developed for approximating their equations. This paper aims, on the one hand, to propose a classification of the most important of them into two great categories: singular perturbation-based methods and curvature-based methods, and on the other hand, to prove the equivalence between any methods belonging to the same category and between the two categories. Then, a deep analysis and comparison between each of these methods enable to state the efficiency of the Flow Curvature Method which is exemplified with paradigmatic Van der Pol singularly perturbed dynamical system and Lorenz slow–fast dynamical system.

Somatoform disorders: diseases of the civilization

2020 ◽  
pp. 25-30
Author(s):  
I. Kukhtevich
Keyword(s):  
Health Professionals ◽  
Somatoform Disorders ◽  
Neuropsychiatric Disorders ◽  
The Other ◽  
Significant Part ◽  
Organic Basis ◽  
Autonomic Disorders ◽  
The One ◽  
Somatic Diseases

Functional autonomic disorders occupy a significant part in the practice of neurologists and professionals of other specialties as well. However, there is no generally accepted classification of such disorders. In this paper the authors tried to show that functional autonomic pathology corresponds to the concept of somatoform disorders combining syndromes manifested by visceral, borderline psychopathological, neurological symptoms that do not have an organic basis. The relevance of the problem of somatoform disorders is that on the one hand many health professionals are not familiar enough with manifestations of borderline neuropsychiatric disorders, often forming functional autonomic disorders, and on the other hand they overestimate somatoform symptoms that are similar to somatic diseases.

N. Belknap's Four-Valued Logic, Belknap Computer and New Proximity Functions for Comparing Discrete Objects

2021 ◽  
Vol 1 (2 (6)) ◽  
Author(s):  
Valerii Dmitrienko ◽  
Sergey Leonov ◽  
Mykola Mezentsev
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
The Other ◽  
Proximity Function ◽  
Input Information ◽  
Proximity Measures ◽  
The One ◽  
True Values

The idea of ​​Belknap's four-valued logic is that modern computers should function normally not only with the true values ​​of the input information, but also under the conditions of inconsistency and incompleteness of true failures. Belknap's logic introduces four true values: T (true - true), F (false - false), N (none - nobody, nothing, none), B (both - the two, not only the one but also the other).  For ease of work with these true values, the following designations are introduced: (1, 0, n, b). Belknap's logic can be used to obtain estimates of proximity measures for discrete objects, for which the functions Jaccard and Needhem, Russel and Rao, Sokal and Michener, Hamming, etc. are used. In this case, it becomes possible to assess the proximity, recognition and classification of objects in conditions of uncertainty when the true values ​​are taken from the set (1, 0, n, b). Based on the architecture of the Hamming neural network, neural networks have been developed that allow calculating the distances between objects described using true values ​​(1, 0, n, b). Keywords: four-valued Belknap logic, Belknap computer, proximity assessment, recognition and classification, proximity function, neural network.

scholarly journals Verbal Monomials in English for Audit and Accounting

2021 ◽  
Vol 04 (03) ◽  
Author(s):  
Oksana Chaika ◽  
Keyword(s):  
Functional Properties ◽  
Functional Property ◽  
The Other ◽  
Discussion Section ◽  
Work In Progress ◽  
The One

The paper research is work in progress and makes part of a publication set devoted the study of the English monomials and polynomials in the professional domain of audit and accounting, on the one hand. On the other, the research can be treated as a standalone piece for the study into the nature of verbal monomials as set term clusters in English for Audit and Accounting. The scope of research arrives at the following objectives. One objective is to give an overview of the term ‘monomial’ in English for Audit and Accounting, or English for A&A, which leads to understanding of the verbal monomial in English for A&A, correspondingly. The other objective refers to the classification introduced earlier as attributable to the analysis of the structure of the mentioned monomials and polynomials in English for A&A from a morphological perspective of the head term in a monomial, i.e. nounal, verbal, adjectival and adverbial. The said classification in this work associates with verbal monomials in English for A&A only, and provides a relevant sub-classification of the relevant verbal monomials through the lens of their functional properties and roles in a sentence, under the professional language framework. The results and discussion section presents five distinct groups of verbal monomials in English for Audit and Accounting, each corresponding to a specific syntactical role and functional property in a sentence. A variety of the examples helps see and identify the type of the English verbal monomial in the area of audit and accounting.

The Two Kinds of Depression According to St. Paul

1967 ◽  
Vol 113 (500) ◽  
pp. 779-780 ◽  
Author(s):  
Mark D. Altschule
Keyword(s):  
The Other ◽  
The Bible ◽  
The World ◽  
Current Classification ◽  
English Translations ◽  
The One ◽  
Similar Classification

One current classification of depression divides the syndrome into psychotic and non-psychotic varieties. It is interesting that a similar classification developed over a thousand years ago out of some words of St. Paul. In his Second Epistle to the Corinthians, Ch. 7, v. 10, Paul wrote: “For godly sorrow worketh repentance to salvation not to be repented of, but the sorrow of the world worketh death.” The word sorrow used in English translations of the Bible stood for the tristitia of Latin versions (Greek λνπη); connoting sadness, sorrow, despondency, depression. Paul's distinction between the two kinds of tristitia, the one “from God” and the other “of the world”, led mediaeval theologians to enlarge on differences between the two kinds of depression.

scholarly journals Steroids and/or Cytotoxic Agents Should Be Used Early in the Management of Patients with IPF -- The Con Argument

2004 ◽  
Vol 11 (3) ◽  
pp. 212-213 ◽  
Author(s):  
Stephen K Field
Keyword(s):  
Systemic Corticosteroid ◽  
Usual Interstitial Pneumonia ◽  
The Other ◽  
Cytotoxic Agents ◽  
European Respiratory Society ◽  
Progressive Decline ◽  
Current Classification ◽  
The 1960S ◽  
The One

The recently published American Thoracic Society/European Respiratory Society statement distinguishes idiopathic pulmonary fibrosis (IPF), also known as usual interstitial pneumonia (UIP), from the other idiopathic interstitial pneumonias (IIPs) (1). Although the current classification of IIPs is different from the one developed by Liebow and Carrington (2) in the 1960s, the description of UIP has not changed, and it is still recognized as having distinctive clinical and pathological features that distinguish it from the other IIPs. IPF responds differently to systemic corticosteroid (steroid) therapy and has a different prognosis than the other IIPs, such as nonspecific interstitial pneumonitis, which previously were felt to be variants of the same condition (1,3,4). Despite therapy, most patients with IPF experience a progressive decline in pulmonary function, leading to respiratory failure and death, unless they undergo lung transplantation.

scholarly journals DIFFERENTIAL GEOMETRY AND MECHANICS: APPLICATIONS TO CHAOTIC DYNAMICAL SYSTEMS

2006 ◽  
Vol 16 (04) ◽  
pp. 887-910 ◽  
Author(s):  
JEAN-MARC GINOUX ◽  
BRUNO ROSSETTO
Keyword(s):  
Differential Geometry ◽  
Dynamical Systems ◽  
Slow Manifold ◽  
Van Der Pol ◽  
New Approach ◽  
Metric Properties ◽  
Chaotic Dynamical Systems ◽  
Mechanics Concepts ◽  
The One ◽  
Curvature And Torsion

The aim of this article is to highlight the interest to apply Differential Geometry and Mechanics concepts to chaotic dynamical systems study. Thus, the local metric properties of curvature and torsion will directly provide the analytical expression of the slow manifold equation of slow-fast autonomous dynamical systems starting from kinematics variables (velocity, acceleration and over-acceleration or jerk). The attractivity of the slow manifold will be characterized thanks to a criterion proposed by Henri Poincaré. Moreover, the specific use of acceleration will make it possible on the one hand to define slow and fast domains of the phase space and on the other hand, to provide an analytical equation of the slow manifold towards which all the trajectories converge. The attractive slow manifold constitutes a part of these dynamical systems attractor. So, in order to propose a description of the geometrical structure of attractor, a new manifold called singular manifold will be introduced. Various applications of this new approach to the models of Van der Pol, cubic-Chua, Lorenz, and Volterra–Gause are proposed.

scholarly journals CANARDS FROM CHUA'S CIRCUIT

2013 ◽  
Vol 23 (04) ◽  
pp. 1330010 ◽  
Author(s):  
JEAN-MARC GINOUX ◽  
JAUME LLIBRE ◽  
LEON O. CHUA
Keyword(s):  
Dynamical Systems ◽  
Singularly Perturbed ◽  
Fast Variable ◽  
Chua’S Circuit ◽  
Chua's Circuit ◽  
Flow Curvature ◽  
Cubic Model ◽  
Generic Existence

The aim of this work is to extend Benoît's theorem for the generic existence of "canards" solutions in singularly perturbed dynamical systems of dimension three with one fast variable to those of dimension four. Then, it is established that this result can be found according to the Flow Curvature Method. Applications to Chua's cubic model of dimension three and four enable to state the existence of "canards" solutions in such systems.

Taxonomy and its Pleasures

2017 ◽  
Vol 47 (3) ◽  
pp. 429-448
Author(s):  
Anne O’Byrne
Keyword(s):  
Natural World ◽  
The Other ◽  
The World ◽  
The One ◽  
Natural Purpose

Abstract Taxonomy is our response to the proliferating variety of the natural world on the one hand, and the principle of unrelieved universality on the other. From Aristotle, through Porphyry to Linneaus, Kant and others, thinkers have struggled to develop taxonomies that could order what we know and also what we do not yet know, and this essay is a reflection on the existential desire that propels this effort. Porphyry’s tree of logic is an exhaustive account of the things we can say about the sort of beings we are; Linneaus’s system of nature reaches completion in the classification of humans; Kant discovers a way to have natural and logical forms coincide in the thought of natural purpose and purposiveness. The stakes are high. When we order the world, we order ourselves: when we enter the taxonomy, it enters us and confronts us with our judgments of kind, race and kin.

New Asian Races, New Mixtures, and the “Mexican” Race

2017 ◽  
Author(s):  
Paul Schor
Keyword(s):  
Twentieth Century ◽  
The Other ◽  
Racial Classification ◽  
Racial Categorization ◽  
Early Twentieth Century ◽  
The Us ◽  
European Immigrants ◽  
The One ◽  
Us Census

This chapter discusses changes in racial categorization in the early twentieth century with respect to the US census. Whenever there was a question of the racial classification of new populations, whether in the continental United States or in the territories acquired since 1867, the census always relied on the principles and techniques developed since 1850 to distinguish blacks from whites. Chief among these was the principle of hypodescent, in more or less rigid forms. However, the early twentieth century saw change occurring in two directions: on the one hand, the racialization of a growing number of non-European immigrants and their descendants; on the other, the weakening of the distinctions between the descendants of European immigrants. The remainder of the chapter details the disappearance of the “mulatto” category and the introduction and forcible elimination of the “Mexican” category.

scholarly journals SKEW CATEGORY ALGEBRAS ASSOCIATED WITH PARTIALLY DEFINED DYNAMICAL SYSTEMS

2012 ◽  
Vol 23 (04) ◽  
pp. 1250040 ◽  
Author(s):  
PATRIK LUNDSTRÖM ◽  
JOHAN ÖINERT
Keyword(s):  
Dynamical Systems ◽  
Topological Space ◽  
Large Class ◽  
Additive Group ◽  
Nonzero Ideal ◽  
Intersection Property ◽  
The Other ◽  
The One ◽  
Category Algebras ◽  
The Ideal

We introduce partially defined dynamical systems defined on a topological space. To each such system we associate a functor s from a category G to Topop and show that it defines what we call a skew category algebra A ⋊σ G. We study the connection between topological freeness of s and, on the one hand, ideal properties of A ⋊σ G and, on the other hand, maximal commutativity of A in A ⋊σ G. In particular, we show that if G is a groupoid and for each e ∈ ob (G) the group of all morphisms e → e is countable and the topological space s(e) is Tychonoff and Baire. Then the following assertions are equivalent: (i) s is topologically free; (ii) A has the ideal intersection property, i.e. if I is a nonzero ideal of A ⋊σ G, then I ∩ A ≠ {0}; (iii) the ring A is a maximal abelian complex subalgebra of A ⋊σ G. Thereby, we generalize a result by Svensson, Silvestrov and de Jeu from the additive group of integers to a large class of groupoids.

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