scholarly journals On the Numerical Classification of the Singularities of Robot Manipulators

2012 ◽  
Author(s):  
Oriol Bohigas ◽  
Dimiter Zlatanov ◽  
Montserrat Manubens ◽  
Lluís Ros
Keyword(s):  
Numerical Method ◽  
Recent Work ◽  
Robot Manipulators ◽  
Linear Equations ◽  
Numerical Classification ◽  
Redundant Manipulator ◽  
Linear Relaxations ◽  
Lower Dimensional

This paper is concerned with the task to obtain a complete description of the singularity set of any given non-redundant manipulator, including the identification and the precise computation of each constituent singularity class. Configurations belonging to the same class are equivalent in terms of the various types of kinematic and static degeneracy that characterize mechanism singularity. The proposed approach is an extension of recent work on computing singularities using a numerical method based on linear relaxations. Classification is sought by means of a hierarchy of singularity tests, each formulated as a system of quadratic or linear equations, which yields sets of classes to which an identified singularity cannot belong. A planar manipulator exemplifies the process of classification, and illustrates how, while most singularities get completely classified, for some lower-dimensional subsets one can only identify a restricted list of possible singularity classes.

scholarly journals The local structure of the free boundary in the fractional obstacle problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Matteo Focardi ◽  
Emanuele Spadaro
Keyword(s):  
Hausdorff Dimension ◽  
Free Boundary ◽  
Hausdorff Measure ◽  
Local Structure ◽  
Obstacle Problem ◽  
List Type ◽  
Minkowski Content ◽  
Local Finiteness ◽  
Lower Dimensional

AbstractBuilding upon the recent results in [M. Focardi and E. Spadaro, On the measure and the structure of the free boundary of the lower-dimensional obstacle problem, Arch. Ration. Mech. Anal. 230 2018, 1, 125–184] we provide a thorough description of the free boundary for the solutions to the fractional obstacle problem in {\mathbb{R}^{n+1}} with obstacle function φ (suitably smooth and decaying fast at infinity) up to sets of null {{\mathcal{H}}^{n-1}} measure. In particular, if φ is analytic, the problem reduces to the zero obstacle case dealt with in [M. Focardi and E. Spadaro, On the measure and the structure of the free boundary of the lower-dimensional obstacle problem, Arch. Ration. Mech. Anal. 230 2018, 1, 125–184] and therefore we retrieve the same results:(i)local finiteness of the {(n-1)}-dimensional Minkowski content of the free boundary (and thus of its Hausdorff measure),(ii){{\mathcal{H}}^{n-1}}-rectifiability of the free boundary,(iii)classification of the frequencies and of the blowups up to a set of Hausdorff dimension at most {(n-2)} in the free boundary.Instead, if {\varphi\in C^{k+1}(\mathbb{R}^{n})}, {k\geq 2}, similar results hold only for distinguished subsets of points in the free boundary where the order of contact of the solution with the obstacle function φ is less than {k+1}.

scholarly journals Definiteness Systems and Dialect Classification

Languages ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 128
Author(s):  
Mike Turner
Keyword(s):  
Binary System ◽  
Recent Work ◽  
Classification Schemes ◽  
Modeling Process ◽  
Arabic Dialects ◽  
Dialect Classification ◽  
Semantic Typology

In this article I explore how typological approaches can be used to construct novel classification schemes for Arabic dialects, taking the example of definiteness as a case study. Definiteness in Arabic has traditionally been envisioned as an essentially binary system, wherein definite substantives are marked with a reflex of the article al- and indefinite ones are not. Recent work has complicated this model, framing definiteness instead as a continuum along which speakers can locate referents using a broader range of morphological and syntactic strategies, including not only the article al-, but also reflexes of the demonstrative series and a diverse set of ‘indefinite-specific’ articles found throughout the spoken dialects. I argue that it is possible to describe these strategies with even more precision by modeling them within cross-linguistic frameworks for semantic typology, among them a model known as the ‘Reference Hierarchy,’ which I adopt here. This modeling process allows for classification of dialects not by the presence of shared forms, but rather by parallel typological configurations, even if the forms within them are disparate.

Numerical classification of French vegetation of Carici caryophylleae – Genistetea lobelii J.-C. Klein 1972

2021 ◽  
Vol 42 ◽  
pp. e68062
Author(s):  
Pauline Delbosc ◽  
Mathieu Le Dez ◽  
Jean-Bernard Bouzillé ◽  
Kevin Cianfaglione ◽  
Frédéric Bioret
Keyword(s):  
Expert System ◽  
Dominant Species ◽  
Numerical Classification ◽  
Distribution Map ◽  
Diagnostic Species ◽  
Plant Associations ◽  
Formal Definitions ◽  
Twinspan Classification ◽  
New Association

Carici-Genistetea lobelii Klein 1972 corresponds to cyrno-sardinian oromediterranean cushion scrub and related grasslands. In France, this class is only present in Corsica and the syntaxonomic scheme is debated among phytosociologists. The aim of this paper is to highlight the main plant associations of Carici-Genistetea lobelii Klein 1972 and to define the diagnostic species for each phytosociological unit. We compiled 519 vegetation plots and we applied EuropeanVegetationChecklist expert system for the classes of European vegetation to retain only vegetation plots belonging to Carici-Genistetea lobelii. We obtained a dataset with 189 vegetation plots and we classified them with Modified TWINSPAN classification. Our analyses recognized 6 plant associations and 3 sub-associations already described in the literature; and to describe a new alliance corresponding to the supra-mediterranean vegetations (Genistion salzmannii), a new association (Brimeuro fastigiatae-Juniperetum nanae) and its sub-association (alnetosum suaveolentis). For each of them, we identified diagnostic, constant and dominant species and produced their distribution map. Formal definitions were then written for each phytosociological unit (from subassociation to class) and grouped in an expert system to automatically classify the vegetations of Carici-Genistetea lobelii.

Optimal Configurations for Flexible Redundant Robot Manipulators

1998 ◽  
Author(s):  
Yue Shigang
Keyword(s):  
Real Time ◽  
Robot Manipulators ◽  
Computer Time ◽  
Planning Method ◽  
Initial Configuration ◽  
Redundant Manipulator ◽  
Real Time Control ◽  
Redundant Robot ◽  
Time Control ◽  
Optimal Configurations

Abstract The significant effect of initial configurations of flexible redundant robot manipulators is analyzed in the paper. It is found that the endpoint vibrations of a flexible redundant manipulator are quite different while performing the same endpoint trajectory starting from different initial configurations. Thus an optimal initial configuration with lower vibrations is found based on analysis before the manipulator starts to move. Only small and acceptable vibrations can be stimulated if the flexible redundant manipulator starts to move from the optimal configuration. Lots of computer time can be saved compared with optimal joint planning method. The method can be used in real-time control.

Numerical Classification of Thermus Isolates from Globally Distributed Hot Springs

1989 ◽  
Vol 11 (3) ◽  
pp. 250-256 ◽  
Author(s):  
J. Andrew Hudson ◽  
Hugh W. Morgan ◽  
Roy M. Daniel
Keyword(s):  
Hot Springs ◽  
Numerical Classification ◽  
Globally Distributed

scholarly journals THE REAL ANATOMY OF COMPLEX LINEAR SUPERFIELDS

2012 ◽  
Vol 27 (24) ◽  
pp. 1250143 ◽  
Author(s):  
S. JAMES GATES ◽  
JARED HALLETT ◽  
TRISTAN HÜBSCH ◽  
KORY STIFFLER
Keyword(s):  
Recent Work ◽  
Vast Number ◽  
The Real ◽  
Explicit Analysis ◽  
Complex Linear

Recent work on classification of off-shell representations of N-extended worldline supersymmetry without central charges has uncovered an unexpectedly vast number — trillions of even just (chromo)topology types — of so-called adinkraic supermultiplets. Herein, we show by explicit analysis that a long-known but rarely used representation, the complex linear supermultiplet, is not adinkraic, cannot be decomposed locally, but may be reduced by means of a Wess–Zumino type gauge. This then indicates that the already unexpectedly vast number of adinkraic off-shell supersymmetry representations is but the proverbial tip of the iceberg.

Oscillation Criteria for Semilinear Equations in General Domains

1976 ◽  
Vol 19 (2) ◽  
pp. 137-144 ◽  
Author(s):  
W. Allegretto
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Recent Work ◽  
Linear Equations ◽  
Oscillation Theory ◽  
General Nature ◽  
Nonlinear Ordinary Differential Equations ◽  
Exterior Domains ◽  
Semilinear Equations

Oscillation theory for nonlinear ordinary differential equations has been extensively developed in recent years by several authors. We refer the reader to the recent paper by Noussair and Swanson, [2], where an extensive bibliography may be found. The situation is somewhat different for the case of second order partial differential equations, an area which has recently been virtually untouched, except for the establishment of criteria which depend on a comparison with suitable linear equations and therefore are essentially linear in nature. A bibliography of such results may also be found in [2]. Of a more general nature have been the paper by the author [1], and the more recent work of Noussair and Swanson, [2]. Although the methods employed and the equations considered in [1] and [2] are different, both papers obtained results only for a class of exterior domains of Rn, of which the typical example is the complement of a bounded sphere.

Numerical classification of the Pacific forms of Chlorodesmis (Chlorophyta)

1965 ◽  
Vol 13 (3) ◽  
pp. 489 ◽  
Author(s):  
SC Ducker ◽  
WT Williams ◽  
GN Lance
Keyword(s):  
Mixed Data ◽  
Critical Examination ◽  
Numerical Classification ◽  
Control Data ◽  
Green Algal ◽  
The Pacific ◽  
Algal Genus ◽  
Single Genus

The boundaries of the green algal genus Chlorodesmis are ill defined, and the reported species appear to overlap widely. Fourreen specimens of the large-celled (Pacific) forms have been subjected to critical examination; the specimens had previously been ascribed to three genera and eight species. Six characters (one qualitative, three 3-state, and two numerical) have been used; the numerical characters, for which measures of variation are available, have been subjected to a conventional statistical examination, and all six characters have been used in an analysis of the data by means of the mixed-data classificatory programme MULTIST on the Control Data 3600 at Canberra. The results strongly suggest that the specimens are referable to a single genus with only four species: C. caespitosa J. Agardh, C. comosa Harvey & Bailey, C. major Zanardini, and C. bulbosa (Womersley) Ducker.

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