A pencil of four-nodal plane sextics

1981 ◽  
Vol 89 (3) ◽  
pp. 413-421 ◽  
Author(s):  
W. L. Edge
Keyword(s):  
Symmetric Group ◽  
The Other ◽  
Nodal Plane ◽  
Geometrical Properties ◽  
Index 2

Wiman, in 1895, found ((5), p. 208) an equation for a 4-nodal plane sextic W that admits a group S of 120 Cremona self-transformations; of these, 24 are projectivities, the other 96 quadratic transformations. S is isomorphic to the symmetric group of degree 5 and Wiman emphasizes that S does permute among themselves 5 pencils (4 pencils of lines and 1 of conics) and 5 nets (4 nets of conics and 1 of lines). But he gives no geometrical properties of W. The omission should be repaired because, as will be explained below, W can be uniquely determined by elementary geometrical conditions. Furthermore: W is only one, though admittedly the most interesting, of a whole pencil P of 4-nodal sextics; every member of P is invariant under S+, the icosahedral subgroup of index 2 in S, while the transformations in the coset S/S+ transpose the members of P in pairs save for two that they leave fixed, W being one of these. When the triangle of reference is the diagonal point triangle of the quadrangle of its nodes the form of W is (7.2) below. Wiman referred his curve to a different triangle.

Induced Representations and Invariants

1950 ◽  
Vol 2 ◽  
pp. 334-343 ◽  
Author(s):  
G. DE B. Robinson
Keyword(s):  
Representation Theory ◽  
Symmetric Group ◽  
Explicit Formula ◽  
Linear Group ◽  
Schur Functions ◽  
The Other ◽  
Induced Representations ◽  
Direct Sum ◽  
Invariant Matrices ◽  
The One

1. Introduction. The problem of the expression of an invariant matrix of an invariant matrix as a direct sum of invariant matrices is intimately associated with the representation theory of the full linear group on the one hand and with the representation theory of the symmetric group on the other. In a previous paper the author gave an explicit formula for this reduction in terms of characters of the symmetric group. Later J. A. Todd derived the same formula using Schur functions, i.e. characters of representations of the full linear group.

Backstroke Organization in Physical Education Students as a Function of Skill and Sex

2005 ◽  
Vol 100 (3) ◽  
pp. 779-790 ◽  
Author(s):  
Robert Lerda ◽  
Chantal Cardelli ◽  
Jean-Pierre Coudereau
Keyword(s):  
Physical Education ◽  
Performance Status ◽  
The Other ◽  
Stroke Rate ◽  
Education Students ◽  
Physical Education Students ◽  
Index 2

This study assessed how stroking in backstroke varies with performance status and sex. A total of 36 subjects were separated into two groups of 18 by sex and further divided into two subgroups of nine, faster and slower, based on velocity in the 100-m event. Stroking parameters and coordination indexes were measured at this 100-m pace. Index 1 characterizes the continuity between propulsive phases of each arm and Index 2, the simultaneity between the beginning of the pull of one arm and of the recovery of the other arm. It is shown that the entry-catch and clearing vary ( p< .05) between men (4.5% ± 3.7 and 27.1% ± 9.0) and women (8.3% ± 8.5 and 20.0% ± 4.6). Index 1 indicates that women have a better continuity than men (7.4% ± 6.3 vs −10.7% ± 3.6; p<.05). Performance is mainly explained ( p<.05) by the increase in the entry and catch ( r = .58 for men and .75 for women) at the expense of clearing (respectively, r = −.70 and –.53, p<.05). For men, Index 2 indicates that the simultaneity is higher in faster than in slower swimmers (10.6 ± 7.0% vs 15.5 ± 7.4%; p<.05) and is correlated with performance ( r = −.47, p<.05). Index 2 is related to the clearing ( r = .71), the number of kicks per cycle (K · C−1, r = −.61), and the pull ( r = .60). For women, the performance is explained by Index 1 ( r = .48, p< .05). Index 1 is related ( p<.05) to stroke rate ( r = .84), the clearing ( r = −.70), and K · C−1 ( r = −.61). K · C−1 increases from 6.4 ± .70 for the faster to 7.8 ± 2.0 for the slower group ( p< .05).

scholarly journals Comparison of Different Technologies for Soft Robotics Grippers

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 3253
Author(s):  
Silvia Terrile ◽  
Miguel Argüelles ◽  
Antonio Barrientos
Keyword(s):  
Comparative Study ◽  
Environmental Conditions ◽  
The Other ◽  
Soft Robotics ◽  
Geometrical Properties ◽  
Pneumatic Actuation ◽  
Specific Item ◽  
Wide Range ◽  
Soft Objects ◽  
Electromechanical Actuation

Soft grippers have experienced a growing interest due to their considerable flexibility that allows them to grasp a variety of objects, in contrast to hard grippers, which are designed for a specific item. One of their most remarkable characteristics is the ability to manipulate soft objects without damaging them. This, together with their wide range of applications and the use of novels materials and technologies, renders them a very robust device. In this paper, we present a comparison of different technologies for soft robotics grippers. We fabricated and tested four grippers. Two use pneumatic actuation (the gripper with chambered fingers and the jamming gripper), while the other two employ electromechanical actuation (the tendon driver gripper and the gripper with passive structure). For the experiments, a group of twelve objects with different mechanical and geometrical properties have been selected. Furthermore, we analyzed the effect of the environmental conditions on the grippers, by testing each object in three different environments: normal, humid, and dusty. The aim of this comparative study is to show the different performances of different grippers tested under the same conditions. Our findings indicate that we can highlight that the mechanical gripper with a passive structure shows greater robustness.

The Poset of Conjugacy Classes and Decomposition of Products in the Symmetric Group

1992 ◽  
Vol 35 (2) ◽  
pp. 152-160 ◽  
Author(s):  
François Bédard ◽  
Alain Goupil
Keyword(s):  
Symmetric Group ◽  
Group Algebra ◽  
Conjugacy Classes ◽  
The Other ◽  
Linear Combinations ◽  
Graded Poset

AbstractThe action by multiplication of the class of transpositions of the symmetric group on the other conjugacy classes defines a graded poset as described by Birkhoff ([2]). In this paper, the edges of this poset are given a weight and the structure obtained is called the poset of conjugacy classes of the symmetric group. We use weights of chains in the posets to obtain new formulas for the decomposition of products of conjugacy classes of the symmetric group in its group algebra as linear combinations of conjugacy classes and we derive a new identity involving partitions of n.

Form Discrimination: Features or Invariants?

1988 ◽  
Vol 67 (1) ◽  
pp. 311-317
Author(s):  
G. J. F. Smets ◽  
P. J. Stappers ◽  
B. J. A. Kröse
Keyword(s):  
The Other ◽  
Direct Approach ◽  
Feature Analysis ◽  
Form Discrimination ◽  
Geometrical Properties ◽  
Large Screen ◽  
Direct Theory ◽  
Large Screen Projection

Does form discrimination rely on feature analysis, as the indirect theory of perception supposes, or on affordances (behavioural meanings specified by invariant patterns), as direct theory states. Subjects were to indicate the position of a target in a perspective rendering of a plane, displayed for 100 msec. in a large screen projection. In one of the conditions the target disrupted the plane, in the other it did not. Although targets of the two conditions shared the same features, the disruptive targets were discriminated more often than the nondisruptive targets. This result supports the direct approach to perception which states that a perceiver discriminates behaviourally relevant patterns rather than geometrical properties.

Galois groups of Taylor polynomials of some elementary functions

2019 ◽  
Vol 15 (06) ◽  
pp. 1127-1141
Author(s):  
Khosro Monsef Shokri ◽  
Jafar Shaffaf ◽  
Reza Taleb
Keyword(s):  
Symmetric Group ◽  
Galois Groups ◽  
Alternating Group ◽  
Integer Number ◽  
Elementary Functions ◽  
Type Formula ◽  
Number Formula ◽  
Taylor Polynomials ◽  
Index 2

Motivated by Schur’s result on computing the Galois groups of the exponential Taylor polynomials, this paper aims to compute the Galois groups of the Taylor polynomials of the elementary functions [Formula: see text] and [Formula: see text]. We first show that the Galois groups of the [Formula: see text]th Taylor polynomials of [Formula: see text] are as large as possible, namely, [Formula: see text] (full symmetric group) or [Formula: see text] (alternating group), depending on the residue of the integer number [Formula: see text] modulo [Formula: see text]. We then compute the Galois groups of the [Formula: see text]th Taylor polynomials of [Formula: see text] and show that these Galois groups essentially coincide with the Coexter groups of type [Formula: see text] (or an index 2 subgroup of the corresponding Coexter group).

scholarly journals Fricke's octavic curve

1984 ◽  
Vol 27 (1) ◽  
pp. 91-101
Author(s):  
W. L. Edge
Keyword(s):  
Symmetric Group ◽  
Complete Intersection ◽  
The Other ◽  
Quartic Surface

The paper is concerned with a curve F, the complete intersection of a quadric with a quartic surface, that admits a group of self-projectivities isomorphic to the symmetric group of degree 5. Every generator of the quadric is, as shown at the end of the paper, cut by F equianharmonically. F has 80 stalls, points where its osculating plane is stationary; they are of two kinds, 60 to be labelled ∑, the other 20 Ω. F also has inflections at 24 points which compose a figure encountered on earlier occasions. A search is made for tritangent planes of F of which, when reckoned according to proper multiplicity, there must be 2048. Among them are 60 all of whose three contacts are ∑ while a further 120 each involve a single ∑ among their contacts and 420 each involve a single Ω.

scholarly journals Signed Words and Permutations II; The Euler-Mahonian Polynomials

10.37236/1879 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
Dominique Foata ◽  
Guo-Niu Han
Keyword(s):  
Symmetric Group ◽  
Generating Functions ◽  
Statistical Study ◽  
Record Values ◽  
The Other ◽  
Length Function ◽  
Major Index ◽  
Signed Permutations ◽  
Inversion Number ◽  
The One

As for the symmetric group of ordinary permutations there is also a statistical study of the group of signed permutations, that consists of calculating multivariable generating functions for this group by statistics involving record values and the length function. Two approaches are here systematically explored, using the flag-major index on the one hand, and the flag-inversion number on the other hand. The MacMahon Verfahren appears as a powerful tool throughout.

scholarly journals Modelling of Flexible Elements

2019 ◽  
Author(s):  
Елена Афонина ◽  
Elena Afonina ◽  
Марина Николаевна Левая ◽  
Marina Nikolaevna Levaya ◽  
Игорь Сергеевич Левый ◽  
...  
Keyword(s):  
Standard Method ◽  
Computer Games ◽  
Design Method ◽  
The Other ◽  
Programming Environment ◽  
Geometrical Properties ◽  
New Methods ◽  
Standard Design ◽  
Current Task ◽  
A Current

Flexible elements are used for modeling of various hawsers, chains, ropes, tail-ropes and other elements in the programmes of simulation. Depending on a current task a set of requirements necessary for a flexible element modeling is formulated. The article presents two methods of rope, wire, cable designing in computer games programming environment Unity3D based on the use of primitive objects. The standard design method grounded in hinge joints employment is considered. The disadvantages of a standard method are noted and two new methods of modeling are offered. The developed methods consider the requirements necessary for the solution of the task at hand, they include the reality of a scene, the interaction with surrounding objects, the possibility to specify the function of a natural sag. Two methods of modeling are compared taking into account the implementation area of programs, the reflection of physical and geometrical properties of modelled entity and the reality of a scene. Both methods meet specified requirements, however it is expedient to use one of the methods for mobile scenes, such as games, exercise machines, simulators of processes, while the other fits better for static programmes.

A seismological study of two Attica, New York earthquakes

1978 ◽  
Vol 68 (3) ◽  
pp. 641-651 ◽  
Author(s):  
Robert B. Herrmann
Keyword(s):  
New York ◽  
Source Parameters ◽  
Focal Depth ◽  
Strike Slip ◽  
Focal Mechanisms ◽  
The Other ◽  
Nodal Plane ◽  
Reverse Faulting ◽  
Epicentral Intensity ◽  
East West

abstract The Attica, New York earthquakes of January 1, 1966 and June 12, 1967 are studied in detail to obtain their focal mechanisms, depths and seismic moments. Both events have similar source parameters with one nodal plane striking about 120° and dipping 60°S and the other nodal plane striking about 20° and dipping 70°E. The fault motion on the NNE nodal plane has a component of right lateral strike slip and one of reverse faulting. Though this nodal plane parallels the Clarendon-Linden structure, the possibility of associating the other nodal plane with a diffuse east-west seismicity trend cannot be excluded. The shallow focal depth of 2 to 3 km for these two events can be used as an explanation of the relatively high epicentral intensity VIII of the Attica event of 1929.

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