The characters of the cubic surface group

1956 ◽  
Vol 237 (1208) ◽  
pp. 132-147 ◽  
Keyword(s):  
Orthogonal Group ◽  
Dimensional Space ◽  
Surface Group ◽  
Cubic Surface ◽  
Permutation Character

The characters of the cubic surface group G are got by using its representation as a group of orthogonal projectivities in a four-dimensional space a over GF (3). In α , G permutes 27 pentagons transitively and 6 other characters, in addition to the permutation character of degree 27, are obtained by noting how the 5 vertices of each invariant pentagon are permuted. Other geometrical objects that afford transitive permutation representations are available, and provide material for similar investigations. The papers that have preceded this, wherein not only is the geometry described in detail but also many 5-rowed matrices of the orthogonal group are explicitly given, are laid under contribution. In particular, the table at the end of the most recent paper provides at sight not only permutation characters but monomial characters as well.

The conjugate classes of the cubic surface group in an orthogonal representation

1955 ◽  
Vol 233 (1192) ◽  
pp. 126-146 ◽  
Keyword(s):  
Orthogonal Group ◽  
Surface Group ◽  
The Other ◽  
Identity Matrix ◽  
Orthogonal Matrices ◽  
Linear Spaces ◽  
Cubic Surface ◽  
Orthogonal Representation ◽  
Conjugate Class ◽  
Group A

The cubic surface group, of order 51840, has a representation by orthogonal matrices, of 5 rows and determinant + 1, over GF (3). It can be partitioned into conjugate classes on geometrical grounds because each matrix has two skew linear spaces, S + of even and S - of odd dimension, of latent points; the matrices fall into categories A, B, C according as the join of S + and S - has dimension 4, 2, 0. Subdivisions of A, B, C rest on the relation of S + and S - to the invariant quadric of the orthogonal group. A accounts for the identity matrix and the 4 types of involutions. B falls into two parts; one of 4 classes, discussed in §§5 to 8, the other of 9 classes, discussed in §§9 to 14. §§ 15 and 16 mention criteria for checking the number of operations in a conjugate class. Those classes in category C fall into 3 subcategories of 3, 2, 2 classes and are described in §§ 18 to 25.

Polytopes Over GF(2) and their Relevance for the Cubic Surface Group

1959 ◽  
Vol 11 ◽  
pp. 646-650
Author(s):  
H. S. M. Coxeter
Keyword(s):  
Quadratic Form ◽  
Preceding Paper ◽  
Surface Group ◽  
Real Space ◽  
Regular Polytope ◽  
Group Of Automorphisms ◽  
Cubic Surface ◽  
Residue Classes ◽  
Finite Space

In the preceding paper, Edge represented the celebrated “cubic surface group” of order 72.6! = 51840 as the group of automorphisms of a senary quadratic form over the field of residue-classes mod 2. The object of this sequel is to compare Edge's finite space with a real space, thus identifying his non-ruled quadric in PG(5, 2) with a modular counterpart of the semi-regular polytope 221 which was discovered by Gosset in 1897.

Quadrics Over GF(2) and their Relevance for the Cubic Surface Group

1959 ◽  
Vol 11 ◽  
pp. 625-645 ◽  
Author(s):  
W. L. Edge
Keyword(s):  
Surface Group ◽  
Cubic Surface

About half the following pages are concerned with the “cubic surface group” G, of order 51840, and the geometry cognate to a certain representation thereof. The literature of this group, with its subgroup of order 25920, is already voluminous; the addition of these few pages to it will not, it is hoped, be regarded askance as a perverse and misdirected indulgence in archaism.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Three Dimensional structure and organization of diploid chromosomes by optical section microscopy

1987 ◽  
Vol 45 ◽  
pp. 633-635
Author(s):  
David A. Agard ◽  
Yasushi Hiraoka ◽  
John W. Sedat
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Developmental State ◽  
Mitotic Cell ◽  
Biological Properties ◽  
Dimensional Structure ◽  
Specific Gene ◽  
Three Dimensional Structure ◽  
Complementary Techniques ◽  
Dynamic Structures

In an effort to understand the complex relationship between structure and biological function within the nucleus, we have embarked on a program to examine the three-dimensional structure and organization of Drosophila melanogaster embryonic chromosomes. Our overall goal is to determine how DNA and proteins are organized into complex and highly dynamic structures (chromosomes) and how these chromosomes are arranged in three dimensional space within the cell nucleus. Futher, we hope to be able to correlate structual data with such fundamental biological properties as stage in the mitotic cell cycle, developmental state and transcription at specific gene loci.Towards this end, we have been developing methodologies for the three-dimensional analysis of non-crystalline biological specimens using optical and electron microscopy. We feel that the combination of these two complementary techniques allows an unprecedented look at the structural organization of cellular components ranging in size from 100A to 100 microns.

Diffraction contrast of dislocations in icosahedral quasicrystals

1990 ◽  
Vol 48 (4) ◽  
pp. 454-455
Author(s):  
K. Urban ◽  
Z. Zhang ◽  
M. Wollgarten ◽  
D. Gratias
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Complete Characterization ◽  
Extinction Condition ◽  
Burgers Vector ◽  
Diffraction Contrast ◽  
Lattice Geometry ◽  
Reference Space ◽  
Icosahedral Quasicrystals ◽  
The One

Recently dislocations have been observed by electron microscopy in the icosahedral quasicrystalline (IQ) phase of Al65Cu20Fe15. These dislocations exhibit diffraction contrast similar to that known for dislocations in conventional crystals. The contrast becomes extinct for certain diffraction vectors g. In the following the basis of electron diffraction contrast of dislocations in the IQ phase is described. Taking account of the six-dimensional nature of the Burgers vector a “strong” and a “weak” extinction condition are found.Dislocations in quasicrystals canot be described on the basis of simple shear or insertion of a lattice plane only. In order to achieve a complete characterization of these dislocations it is advantageous to make use of the one to one correspondence of the lattice geometry in our three-dimensional space (R3) and that in the six-dimensional reference space (R6) where full periodicity is recovered . Therefore the contrast extinction condition has to be written as gpbp + gobo = 0 (1). The diffraction vector g and the Burgers vector b decompose into two vectors gp, bp and go, bo in, respectively, the physical and the orthogonal three-dimensional sub-spaces of R6.

Flavin radicals, conformational sampling and robust design principles in interprotein electron transfer: the trimethylamine dehydrogenase-electron-transferring flavoprotein complex

2004 ◽  
Vol 71 ◽  
pp. 1-14
Author(s):  
David Leys ◽  
Jaswir Basran ◽  
François Talfournier ◽  
Kamaldeep K. Chohan ◽  
Andrew W. Munro ◽  
...  
Keyword(s):  
Electron Transfer ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Kinetic Studies ◽  
Molecular Assembly ◽  
Conformational Sampling ◽  
Trimethylamine Dehydrogenase ◽  
Key Residues ◽  
Electron Transferring Flavoprotein ◽  
Electron Transfer Complex

TMADH (trimethylamine dehydrogenase) is a complex iron-sulphur flavoprotein that forms a soluble electron-transfer complex with ETF (electron-transferring flavoprotein). The mechanism of electron transfer between TMADH and ETF has been studied using stopped-flow kinetic and mutagenesis methods, and more recently by X-ray crystallography. Potentiometric methods have also been used to identify key residues involved in the stabilization of the flavin radical semiquinone species in ETF. These studies have demonstrated a key role for 'conformational sampling' in the electron-transfer complex, facilitated by two-site contact of ETF with TMADH. Exploration of three-dimensional space in the complex allows the FAD of ETF to find conformations compatible with enhanced electronic coupling with the 4Fe-4S centre of TMADH. This mechanism of electron transfer provides for a more robust and accessible design principle for interprotein electron transfer compared with simpler models that invoke the collision of redox partners followed by electron transfer. The structure of the TMADH-ETF complex confirms the role of key residues in electron transfer and molecular assembly, originally suggested from detailed kinetic studies in wild-type and mutant complexes, and from molecular modelling.

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

Analysis method ofrecruitment needs for the regional economy: Occupational section

2017 ◽  
pp. 142-149 ◽  
Author(s):  
E. Pitukhin ◽  
S. Shabaeva ◽  
I. Stepus ◽  
D. Moroz
Keyword(s):  
Cluster Analysis ◽  
Labor Market ◽  
Comparative Analysis ◽  
Regional Economy ◽  
Dimensional Space ◽  
Analysis Method ◽  
Scalar Form ◽  
Regional Labor Market ◽  
Regional Labor ◽  
Regional Specificity

The paper deals with comparative analysis of occupations in the regional labor market. Occupation is treated as a multi-dimensional space of characte- ristics, whereas a scalar form of a characteristic makes it possible to carry out a comparative analysis of occupations. Using cluster analysis of a pilot region indicators five meaningfully interpretable clusters of occupations were identified, reflecting their regional specificity.

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