scholarly journals On the Group of Alternating Colored Permutations

10.37236/3974 ◽  
2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Eli Bagno ◽  
David Garber ◽  
Toufik Mansour
Keyword(s):  
Wreath Product ◽  
Point Of View ◽  
Length Function ◽  
Alternating Group ◽  
Natural Analogue ◽  
Colored Permutations

The group of alternating colored permutations is the natural analogue of the classical alternating group, inside the wreath product $\mathbb{Z}_r \wr S_n$. We present a 'Coxeter-like' presentation for this group and compute the length function with respect to that presentation. Then, we present this group as a covering of $\mathbb{Z}_{\frac{r}{2}} \wr S_n$ and use this point of view to give another expression for the length function. We also use this covering to lift several known parameters of $\mathbb{Z}_{\frac{r}{2}} \wr S_n$ to the group of alternating colored permutations.

scholarly journals The Derived Subgroups of Sylow 2-Subgroups of the Alternating Group, Commutator Width of Wreath Product of Groups

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 472 ◽  
Author(s):  
Ruslan V. Skuratovskii
Keyword(s):  
Wreath Product ◽  
Commutator Subgroup ◽  
Direct Limit ◽  
Alternating Group ◽  
Generating Set ◽  
Cyclic Groups ◽  
Group A ◽  
Commutator Width ◽  
Minimal Generating Set ◽  
Product Of Groups

The structure of the commutator subgroup of Sylow 2-subgroups of an alternating group A 2 k is determined. This work continues the previous investigations of me, where minimal generating sets for Sylow 2-subgroups of alternating groups were constructed. Here we study the commutator subgroup of these groups. The minimal generating set of the commutator subgroup of A 2 k is constructed. It is shown that ( S y l 2 A 2 k ) 2 = S y l 2 ′ A 2 k , k > 2 . It serves to solve quadratic equations in this group, as were solved by Lysenok I. in the Grigorchuk group. It is proved that the commutator length of an arbitrary element of the iterated wreath product of cyclic groups C p i , p i ∈ N equals to 1. The commutator width of direct limit of wreath product of cyclic groups is found. Upper bounds for the commutator width ( c w ( G ) ) of a wreath product of groups are presented in this paper. A presentation in form of wreath recursion of Sylow 2-subgroups S y l 2 ( A 2 k ) of A 2 k is introduced. As a result, a short proof that the commutator width is equal to 1 for Sylow 2-subgroups of alternating group A 2 k , where k > 2 , the permutation group S 2 k , as well as Sylow p-subgroups of S y l 2 A p k as well as S y l 2 S p k ) are equal to 1 was obtained. A commutator width of permutational wreath product B ≀ C n is investigated. An upper bound of the commutator width of permutational wreath product B ≀ C n for an arbitrary group B is found. The size of a minimal generating set for the commutator subgroup of Sylow 2-subgroup of the alternating group is found. The proofs were assisted by the computer algebra system GAP.

The Geosciences Applied to Lunar Exploration

1962 ◽  
Vol 14 ◽  
pp. 169-257 ◽  
Author(s):  
J. Green
Keyword(s):  
Lunar Surface ◽  
Probable Mechanism ◽  
Point Of View ◽  
Lunar Exploration ◽  
Geological Model ◽  
Apply Geophysics ◽  
Surface Features ◽  
The Impact

The term geo-sciences has been used here to include the disciplines geology, geophysics and geochemistry. However, in order to apply geophysics and geochemistry effectively one must begin with a geological model. Therefore, the science of geology should be used as the basis for lunar exploration. From an astronomical point of view, a lunar terrain heavily impacted with meteors appears the more reasonable; although from a geological standpoint, volcanism seems the more probable mechanism. A surface liberally marked with volcanic features has been advocated by such geologists as Bülow, Dana, Suess, von Wolff, Shaler, Spurr, and Kuno. In this paper, both the impact and volcanic hypotheses are considered in the application of the geo-sciences to manned lunar exploration. However, more emphasis is placed on the volcanic, or more correctly the defluidization, hypothesis to account for lunar surface features.

How a sheperd guides a sheep herd?

1984 ◽  
Vol 75 ◽  
pp. 331-337
Author(s):  
Richard Greenberg
Keyword(s):  
Point Of View ◽  
Single Ring ◽  
Damping Effects ◽  
Ring Particle

ABSTRACTThe mechanism by which a shepherd satellite exerts a confining torque on a ring is considered from the point of view of a single ring particle. It is still not clear how one might most meaningfully include damping effects and other collisional processes into this type of approach to the problem.

The growth of mica polytypes as studied by conventional and high-resolution TEM

1983 ◽  
Vol 41 ◽  
pp. 174-177
Author(s):  
A. Baronnet ◽  
M. Amouric
Keyword(s):  
Water Pressure ◽  
Point Of View ◽  
Temperature Fields ◽  
Natural Occurrence ◽  
Growth Mechanisms ◽  
Long Period ◽  
High Resolution Tem ◽  
Layer Stacking ◽  
Experimental Works ◽  
Potential Use

The origin of mica polytypes has long been a challenging problem for crystal- lographers, mineralogists and petrologists. From the petrological point of view, interest in this field arose from the potential use of layer stacking data to furnish further informations about equilibrium and/or kinetic conditions prevailing during the crystallization of the widespread mica-bearing rocks. From the compilation of previous experimental works dealing with the occurrence domains of the various mica "polymorphs" (1Mr, 1M, 2M1, 2M2 and 3T) within water-pressure vs temperature fields, it became clear that most of these modifications should be considered as metastable for a fixed mica species. Furthermore, the natural occurrence of long-period (or complex) polytypes could not be accounted for by phase considerations. This highlighted the need of a more detailed kinetic approach of the problem and, in particular, of the role growth mechanisms of basal faces could play in this crystallographic phenomenon.

Radiation Damage in Ceramics

1982 ◽  
Vol 40 ◽  
pp. 600-603
Author(s):  
T. E. Mitchell ◽  
M. R. Pascucci ◽  
R. A. Youngman
Keyword(s):  
Radiation Damage ◽  
Outer Space ◽  
Point Of View ◽  
Nuclear Waste Storage ◽  
Waste Storage ◽  
Storage Media ◽  
Transmission Electron ◽  
Fundamental Point ◽  
Small Defect ◽  
Present Understanding

1. Introduction. Studies of radiation damage in ceramics are of interest not only from a fundamental point of view but also because it is important to understand the behavior of ceramics in various practical radiation enyironments- fission and fusion reactors, nuclear waste storage media, ion-implantation devices, outer space, etc. A great deal of work has been done on the spectroscopy of point defects and small defect clusters in ceramics, but relatively little has been performed on defect agglomeration using transmission electron microscopy (TEM) in the same kind of detail that has been so successful in metals. This article will assess our present understanding of radiation damage in ceramics with illustrations using results obtained from the authors' work.

Structural aspects of osmoregulation in porphyra

1978 ◽  
Vol 36 (2) ◽  
pp. 412-413
Author(s):  
C. Wiencke ◽  
A. Lauchli
Keyword(s):  
Culture Medium ◽  
Point Of View ◽  
Chemical Fixation ◽  
Cellular Organization ◽  
Osmotic Adaptation ◽  
Osmotic Balance ◽  
Activity Of Enzymes ◽  
Osmotic Agents ◽  
Vacuolar System ◽  
Structural Aspects

Osmoregulatory mechanisms in algae were investigated mainly from a physiological point of view (KAUSS 1977, HELLEBUST 1976). In Porphyra two osmotic agents, i. e. floridoside/isofloridoside (KAUSS 1968) and certain ions, such as K+ and Na+(EPPLEY et al. 1960) are considered for osmotic balance. Accumulations of ions (particularly Na+) in the cytoplasm during osmotic adaptation is improbable, because the activity of enzymes is generally inhibited by high ionic concentrations (FLOWERS et al. 1977).The cellular organization of Porphyra was studied with special emphasis on the development of the vacuolar system under different hyperosmotic conditions. Porphyra was cultivated at various strengths of the culture medium ASP 12 (PROVASOLI 1961) ranging from normal to 6 times concentrated (6x) culture medium. Por electron microscopy freeze fracturing was used (specimens fixed in 2% glutaraldehyde and incubated in 30% glycerol, preparation in a BALZERS BA 360 M apparatus), because chemical fixation gave poor results.

Elucidation of block boundaries as the dissolution channels in hydrated cement

1978 ◽  
Vol 36 (1) ◽  
pp. 484-485
Author(s):  
N.V. Belov ◽  
U.I. Papiashwili ◽  
B.E. Yudovich
Keyword(s):  
Liquid Phase ◽  
Grain Boundaries ◽  
Benzoyl Peroxide ◽  
Phase Contrast ◽  
Active Role ◽  
Point Of View ◽  
Hardened Cement ◽  
Hydrated Cement ◽  
Hardened Cement Paste

It has been almost universally adopted that dissolution of solids proceeds with development of uniform, continuous frontiers of reaction.However this point of view is doubtful / 1 /. E.g. we have proved the active role of the block (grain) boundaries in the main phases of cement, these boundaries being the areas of hydrate phases' nucleation / 2 /. It has brought to the supposition that the dissolution frontier of cement particles in water is discrete. It seems also probable that the dissolution proceeds through the channels, which serve both for the liquid phase movement and for the drainage of the incongruant solution products. These channels can be appeared along the block boundaries.In order to demonsrate it, we have offered the method of phase-contrast impregnation of the hardened cement paste with the solution of methyl metacrylahe and benzoyl peroxide. The viscosity of this solution is equal to that of water.

Electron microscopy in diagnostic virology

1984 ◽  
Vol 42 ◽  
pp. 70-73
Author(s):  
S. E. Miller
Keyword(s):  
Electron Microscopy ◽  
Tissue Culture ◽  
Molecular Identification ◽  
Point Of View ◽  
Negative Stain ◽  
Viral Diagnosis ◽  
Electron Microscopist ◽  
Diagnostic Virology

The techniques for detecting viruses are many and varied including FAT, ELISA, SPIRA, RPHA, SRH, TIA, ID, IEOP, GC (1); CF, CIE (2); Tzanck (3); EM, IEM (4); and molecular identification (5). This paper will deal with viral diagnosis by electron microscopy and will be organized from the point of view of the electron microscopist who is asked to look for an unknown agent--a consideration of the specimen and possible agents rather than from a virologist's view of comparing all the different viruses. The first step is to ascertain the specimen source and select the method of preparation, e. g. negative stain or embedment, and whether the sample should be precleared by centrifugation, concentrated, or inoculated into tissue culture. Also, knowing the type of specimen and patient symptoms will lend suggestions of possible agents and eliminate some viruses, e. g. Rotavirus will not be seen in brain, nor Rabies in stool, but preconceived notions should not prejudice the observer into missing an unlikely pathogen.

An Ultrastructural Study of the Proliferation Patterns of the Reserve Cells of the Human Cervix Uteri

1972 ◽  
Vol 30 ◽  
pp. 80-81
Author(s):  
Takanori Sohda ◽  
Hiroshi Saito ◽  
Goro Asano ◽  
Katsunari Fukushi ◽  
Katsuya Suzuki ◽  
...  
Keyword(s):  
Ultrastructural Study ◽  
Age Groups ◽  
Point Of View ◽  
University Hospital ◽  
Cervix Uteri ◽  
Morphological Aspect ◽  
Functional Aspect ◽  
Pathological Conditions ◽  
Human Cervix ◽  
Morphological Patterns

Recently, the functional aspect as well as morphological aspect of the reserve cells in the cervix uteri drew much attention in view of the carcinogenesis in squamocolumunar junction. In this communication, the authors elucidate the ultrastructural features of the reserve cells in patients of various age groups visiting our university hospital and affiliated hospital.From conventional light microscopic point of view, the reserve cells tend to be pronounced in various pathological conditions, such as the persisting inflammation, proliferative disorders and irritation of hormones. The morphological patterns of the reserve cells from various stage and degree of irritation were observed.

In situ TEM studies of irradiation effects for materials improvement

1991 ◽  
Vol 49 ◽  
pp. 452-453
Author(s):  
Charles W. Allen
Keyword(s):  
Nuclear Reactor ◽  
Austenitic Stainless Steels ◽  
High Energy ◽  
Point Of View ◽  
In Situ Tem ◽  
Irradiation Effects ◽  
Tem Analysis ◽  
Radiation Induced ◽  
Analytical Tools

Irradiation effects studies employing TEMs as analytical tools have been conducted for almost as many years as materials people have done TEM, motivated largely by materials needs for nuclear reactor development. Such studies have focussed on the behavior both of nuclear fuels and of materials for other reactor components which are subjected to radiation-induced degradation. Especially in the 1950s and 60s, post-irradiation TEM analysis may have been coupled to in situ (in reactor or in pile) experiments (e.g., irradiation-induced creep experiments of austenitic stainless steels). Although necessary from a technological point of view, such experiments are difficult to instrument (measure strain dynamically, e.g.) and control (temperature, e.g.) and require months or even years to perform in a nuclear reactor or in a spallation neutron source. Consequently, methods were sought for simulation of neutroninduced radiation damage of materials, the simulations employing other forms of radiation; in the case of metals and alloys, high energy electrons and high energy ions.

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