A chain of normalizers in the sylow $$\mathbf{2}$$-subgroups of the symmetric group on $${\mathbf{2}}^{\varvec{n}}$$ letters

2021 ◽  
Author(s):  
Riccardo Aragona ◽  
Roberto Civino ◽  
Norberto Gavioli ◽  
Carlo Maria Scoppola
Keyword(s):  
Symmetric Group ◽  
A Chain

scholarly journals The Combinatorics of Orbital Varieties Closures of Nilpotent Order 2 in sl${}_n$

10.37236/1918 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Anna Melnikov
Keyword(s):  
Symmetric Group ◽  
Linear Algebra ◽  
Young Tableau ◽  
Dominance Order ◽  
Young Tableaux ◽  
Young Diagrams ◽  
Special Linear ◽  
A Chain ◽  
Standard Young Tableaux ◽  
Right Order

We consider two partial orders on the set of standard Young tableaux. The first one is induced to this set from the weak right order on symmetric group by Robinson-Schensted algorithm. The second one is induced to it from the dominance order on Young diagrams by considering a Young tableau as a chain of Young diagrams. We prove that these two orders of completely different nature coincide on the subset of Young tableaux with 2 columns or with 2 rows. This fact has very interesting geometric implications for orbital varieties of nilpotent order 2 in special linear algebra $sl_n.$

scholarly journals Symmetric Chain Decompositions of Quotients by Wreath Products

10.37236/5073 ◽  
2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Dwight Duffus ◽  
Kyle Thayer
Keyword(s):  
Symmetric Group ◽  
Elementary Proof ◽  
Boolean Lattice ◽  
Wreath Products ◽  
Cyclic Groups ◽  
Chain Order ◽  
A Chain ◽  
Symmetric Chain ◽  
Symmetric Chain Order

Subgroups of the symmetric group $S_n$ act on $C^n$ (the $n$-fold product $C \times \cdots \times C$ of a chain $C$) by permuting coordinates, and induce automorphisms of the power $C^n$. For certain families of subgroups of $S_n$, the quotients defined by these groups can be shown to have symmetric chain decompositions (SCDs). These SCDs allow us to enlarge the collection of subgroups $G$ of $S_n$ for which the quotient $\mathbf{2}^n/G$ on the Boolean lattice $\mathbf{2}^n$ is a symmetric chain order (SCO). The methods are also used to provide an elementary proof that quotients of powers of SCOs by cyclic groups are SCOs.

scholarly journals The cofinality spectrum of the infinite symmetric group

1997 ◽  
Vol 62 (3) ◽  
pp. 902-916 ◽  
Author(s):  
Saharon Shelah ◽  
Simon Thomas
Keyword(s):  
Symmetric Group ◽  
Inaccessible Cardinal ◽  
Singular Cardinal ◽  
Natural Numbers ◽  
Maximum Element ◽  
Infinite Symmetric Group ◽  
Regular Cardinals ◽  
Uncountable Cardinals ◽  
A Chain

AbstractLet S be the group of all permutations of the set of natural numbers. The cofinality spectrum CF(S) of S is the set of all regular cardinals λ such that S can be expressed as the union of a chain of λ proper subgroups. This paper investigates which sets C of regular uncountable cardinals can be the cofinality spectrum of S. The following theorem.is the main result of this paper.Theorem. Suppose that V ⊨ GCH. Let C be a set of regular uncountable cardinals which satisfies the following conditions.(a) C contains a maximum element.(b) If μ is an inaccessible cardinal such thatμ = sup(C ∩ μ), thenμ ∈ C.(c) if μ is a singular cardinal such thatμ = sup(C ∩ μ), thenμ+ ∈ C.Then there exists a c.c.c. notion of forcing ℙ such that Vℙ ⊨ CF(S) = C.We shall also investigate the connections between the cofinality spectrum and pcf theory; and show that CF(S) cannot be an arbitrarily prescribed set of regular uncountable cardinals.

Observation of Atom Rows in Thorium Pyromellitate Using a Field Emission STEM

1977 ◽  
Vol 35 ◽  
pp. 80-81
Author(s):  
H. Todokoro ◽  
S. Nomura ◽  
T. Komoda
Keyword(s):  
Field Emission ◽  
Amorphous Carbon ◽  
Carbon Film ◽  
Dark Field Image ◽  
Dark Field ◽  
Amorphous Carbon Film ◽  
Atomic Size ◽  
Wide Range ◽  
A Chain

It is interesting to observe polymers at atomic size resolution. Some works have been reported for thorium pyromellitate by using a STEM (1), or a CTEM (2,3). The results showed that this polymer forms a chain in which thorium atoms are arranged. However, the distance between adjacent thorium atoms varies over a wide range (0.4-1.3nm) according to the different authors.The present authors have also observed thorium pyromellitate specimens by means of a field emission STEM, described in reference 4. The specimen was prepared by placing a drop of thorium pyromellitate in 10-3 CH3OH solution onto an amorphous carbon film about 2nm thick. The dark field image is shown in Fig. 1A. Thorium atoms are clearly observed as regular atom rows having a spacing of 0.85nm. This lattice gradually deteriorated by successive observations. The image changed to granular structures, as shown in Fig. 1B, which was taken after four scanning frames.

Time-Resolved Cryo-Electron Microscopy of Oscillating Microtubules

1990 ◽  
Vol 48 (1) ◽  
pp. 502-503
Author(s):  
Eva-Maria Mandelkow ◽  
Ron Milligan
Keyword(s):  
Electron Microscopy ◽  
Dynamic Instability ◽  
Entire Solution ◽  
Reaction Scheme ◽  
Time Resolved ◽  
X Ray ◽  
X Ray Scattering ◽  
A Chain ◽  
Ray Scattering

Microtubules form part of the cytoskeleton of eukaryotic cells. They are hollow libers of about 25 nm diameter made up of 13 protofilaments, each of which consists of a chain of heterodimers of α-and β-tubulin. Microtubules can be assembled in vitro at 37°C in the presence of GTP which is hydrolyzed during the reaction, and they are disassembled at 4°C. In contrast to most other polymers microtubules show the behavior of “dynamic instability”, i.e. they can switch between phases of growth and phases of shrinkage, even at an overall steady state [1]. In certain conditions an entire solution can be synchronized, leading to autonomous oscillations in the degree of assembly which can be observed by X-ray scattering (Fig. 1), light scattering, or electron microscopy [2-5]. In addition such solutions are capable of generating spontaneous spatial patterns [6].In an earlier study we have analyzed the structure of microtubules and their cold-induced disassembly by cryo-EM [7]. One result was that disassembly takes place by loss of protofilament fragments (tubulin oligomers) which fray apart at the microtubule ends. We also looked at microtubule oscillations by time-resolved X-ray scattering and proposed a reaction scheme [4] which involves a cyclic interconversion of tubulin, microtubules, and oligomers (Fig. 2). The present study was undertaken to answer two questions: (a) What is the nature of the oscillations as seen by time-resolved cryo-EM? (b) Do microtubules disassemble by fraying protofilament fragments during oscillations at 37°C?

Do Event-Related Brain Potentials Reflect Mental (Cognitive) Operations?

2002 ◽  
Vol 16 (3) ◽  
pp. 129-149 ◽  
Author(s):  
Boris Kotchoubey
Keyword(s):  
Cognitive Processes ◽  
Point Of View ◽  
Internal Variables ◽  
Brain Potentials ◽  
Cognitive Operations ◽  
External Variables ◽  
Series Of Experiments ◽  
Mental Operations ◽  
A Chain ◽  
Processing Mechanisms

Abstract Most cognitive psychophysiological studies assume (1) that there is a chain of (partially overlapping) cognitive processes (processing stages, mechanisms, operators) leading from stimulus to response, and (2) that components of event-related brain potentials (ERPs) may be regarded as manifestations of these processing stages. What is usually discussed is which particular processing mechanisms are related to some particular component, but not whether such a relationship exists at all. Alternatively, from the point of view of noncognitive (e. g., “naturalistic”) theories of perception ERP components might be conceived of as correlates of extraction of the information from the experimental environment. In a series of experiments, the author attempted to separate these two accounts, i. e., internal variables like mental operations or cognitive parameters versus external variables like information content of stimulation. Whenever this separation could be performed, the latter factor proved to significantly affect ERP amplitudes, whereas the former did not. These data indicate that ERPs cannot be unequivocally linked to processing mechanisms postulated by cognitive models of perception. Therefore, they cannot be regarded as support for these models.

Right-Hemisphere Specialization for Contour Grouping

2014 ◽  
Vol 61 (5) ◽  
pp. 331-339 ◽  
Author(s):  
Gregor Volberg
Keyword(s):  
Right Hemisphere ◽  
Contour Detection ◽  
Global Processing ◽  
Detection Accuracy ◽  
Frequency Spectra ◽  
Visual Hemifield ◽  
Spatial Frequencies ◽  
A Chain ◽  
The Right ◽  
Hemisphere Specialization

Previous studies often revealed a right-hemisphere specialization for processing the global level of compound visual stimuli. Here we explore whether a similar specialization exists for the detection of intersected contours defined by a chain of local elements. Subjects were presented with arrays of randomly oriented Gabor patches that could contain a global path of collinearly arranged elements in the left or in the right visual hemifield. As expected, the detection accuracy was higher for contours presented to the left visual field/right hemisphere. This difference was absent in two control conditions where the smoothness of the contour was decreased. The results demonstrate that the contour detection, often considered to be driven by lateral coactivation in primary visual cortex, relies on higher-level visual representations that differ between the hemispheres. Furthermore, because contour and non-contour stimuli had the same spatial frequency spectra, the results challenge the view that the right-hemisphere advantage in global processing depends on a specialization for processing low spatial frequencies.

A chain model for chromosomes

1961 ◽  
Vol 58 ◽  
pp. 1072-1077 ◽  
Author(s):  
Frank Stahl
Keyword(s):  
Chain Model ◽  
A Chain

Fibrinogen Montreal

1973 ◽  
Vol 29 (03) ◽  
pp. 536-546 ◽  
Author(s):  
M Lacombe ◽  
J Soria ◽  
C Soria ◽  
G d’Angelo ◽  
R Lavallee ◽  
...  
Keyword(s):  
Optical Density ◽  
Polyacrylamide Gel ◽  
Clotting Time ◽  
Functional Defect ◽  
A Chain ◽  
Fibrin Monomers

SummaryA new case of congenital dysfibrinogenemia characterized by a prolonged thrombin clotting time and a low optical density of the polymerization curve has been discovered in Montreal. The functional defect is due to an abnormal aggregation of fibrin monomers.The characteristics of this abnormal fibrinogen are serum gélification (Paracoagulation) at 37°, 22° and 4° C, a normal immuno-electrophoretic and electrofocusing pattern, a slight increase in the mobility in the α (A) chain by electrophoresis of the dissociated chains in polyacrylamide gel. However, no abnormality was found in the α (A) chain of the disulphide knot.

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