Factorizations of Finite Groups and Related Topics

2020 ◽  
Vol 27 (01) ◽  
pp. 149-180
Author(s):  
Lev Kazarin
Keyword(s):  
Finite Groups ◽  
Recent Progress ◽  
Wide Area ◽  
Nilpotent Algebras ◽  
Fundamental Paper

This is a survey on the recent progress in the theory of finite groups with factorizations and around it, done by the author and his co-authors, and this has no pretensions to cover all topics in this wide area of research. In particular, we only touch the great consequences of the fundamental paper of Liebeck, Praeger and Saxl on maximal factorizations of almost simple finite groups for the theory of groups with factorizations. In each case the reader can find additional references at the end of Section 1. Some of the methods of investigation can be used to obtain information about finite groups in general, nilpotent algebras and related nearrings.

Weights for Covering Groups of Symmetric and Alternating Groups, р ≠ 2

1991 ◽  
Vol 43 (4) ◽  
pp. 792-813 ◽  
Author(s):  
G. O. Michler ◽  
J. B. Olsson
Keyword(s):  
Finite Group ◽  
Representation Theory ◽  
Conjugacy Class ◽  
Finite Groups ◽  
Irreducible Character ◽  
Modular Representation ◽  
Modular Representation Theory ◽  
A Finite Group ◽  
Covering Groups ◽  
Fundamental Paper

In his fundamental paper [1] J. L. Alperin introduced the idea of a weight in modular representation theory of finite groups G. Let p be a prime. A p-subgroup R is called a radical subgroup of G if R = Op(NG(R)). An irreducible character φ of NG(R) is called a weight character if φ is trivial on R and belongs to a p-block of defect zero of NG(R)/R. The G-conjugacy class of the pair (R, φ) is a weight of G. Let b be the p-block of NG(R) containing φ, and let B be p-block of G. A weight (R, φ) is a B-weight for the block B of G if B = bG, which means that B and b correspond under the Brauer homomorphism. Alperin's conjecture on weights asserts that the number l*(B) of B-weights of a p-block B of a finite group G equals the number l(B) of modular characters of B.

Recent progress in wide-area surveillance: protecting our pipeline infrastructure

2015 ◽  
Author(s):  
Vijayan K. Asari ◽  
Sidike Paheding ◽  
Chen Cui ◽  
Varun Santhaseelan
Keyword(s):  
Recent Progress ◽  
Wide Area ◽  
Area Surveillance ◽  
Wide Area Surveillance

scholarly journals Physiology of Cerebellar Reserve: Redundancy and Plasticity of a Modular Machine

2021 ◽  
Vol 22 (9) ◽  
pp. 4777
Author(s):  
Hiroshi Mitoma ◽  
Shinji Kakei ◽  
Kazuhiko Yamaguchi ◽  
Mario Manto
Keyword(s):  
Synaptic Plasticity ◽  
Brain Structure ◽  
Recent Progress ◽  
Mossy Fibers ◽  
Neural Substrates ◽  
Therapeutic Strategies ◽  
Wide Area ◽  
Redundant Information ◽  
Pathological Conditions ◽  
Physiological Properties

The cerebellum is endowed with the capacity for compensation and restoration after pathological injury, a property known as cerebellar reserve. Such capacity is attributed to two unique morphological and physiological features of the cerebellum. First, mossy fibers that convey peripheral and central information run mediolaterally over a wide area of the cerebellum, resulting in the innervation of multiple microzones, commonly known as cerebellar functional units. Thus, a single microzone receives redundant information that can be used in pathological conditions. Secondly, the circuitry is characterized by a co-operative interplay among various forms of synaptic plasticity. Recent progress in understanding the mechanisms of redundant information and synaptic plasticity has allowed outlining therapeutic strategies potentiating these neural substrates to enhance the cerebellar reserve, taking advantage of the unique physiological properties of the cerebellum which appears as a modular and potentially reconfiguring brain structure.

scholarly journals Representations of the ℓ1-algebra of an inverse semigroup having the separation property

1977 ◽  
Vol 18 (2) ◽  
pp. 131-143 ◽  
Author(s):  
Bruce A. Barnes
Keyword(s):  
Inverse Semigroup ◽  
Banach Algebra ◽  
Free Semigroup ◽  
Present Author ◽  
Recent Progress ◽  
Semigroup Algebra ◽  
Countably Infinite ◽  
Infinite Set ◽  
Fundamental Paper ◽  
Made In

Let S be a semigroup, and let ℓ1(S) denote the l1-semigroup algebra of S. Beginning with the fundamental paper of E. Hewitt and H. Zuckerman [5], there has been a considerable amount of research done concerning the Banach algebra ℓ1(S) in the case when S is abelian; see the bibliography [7]. However, until recently, there was very little information known concerning ℓ1(S) when S was nonabelian and infinite. Now for certain classes of infinite nonabelian semigroups with involution, recent progress has been made in the study of the Banach *-algebra ℓ1(S) and the *-representations of l1(S). In [2], B. Barnes and J. Duncan prove that ℓ1(S) is Jacobson semisimple, study the spectrum of elements in ℓ1(S), and construct and study *-representations of ℓ1(S) when S is the free semigroup with a finite or countably infinite set of generators (and also in some cases where the generators satisfy certain relations). In [1], the present author considered the representation theory of ℓ1(S) where S is an inverse semigroup. This paper is a sequel to [1].

scholarly journals The Structure of Galaxies at Faint Light Levels: Probing Galaxy Assembly

2006 ◽  
Vol 2 (S235) ◽  
pp. 175-179
Author(s):  
Annette M. N. Ferguson
Keyword(s):  
Quantitative Study ◽  
Fossil Record ◽  
Recent Progress ◽  
Wide Area ◽  
Assembly Process ◽  
The Past ◽  
Light Levels ◽  
The Galaxy ◽  
Galaxy Assembly

AbstractMany clues about the galaxy assembly process lurk in the faint outer regions of galaxies. Although quantitative study of these parts has been severely limited in the past, breakthroughs are now being made thanks to the combination of wide-area star counts, deep HST imagery and 8-m class spectroscopy. I highlight here some recent progress made on deciphering the fossil record encoded in the outskirts of our nearest large neighbours, M31 and M33.

Electron-Mirror Microscopic Aspects of Ferroelectric Domains of BaTiO3 And Ca2Sr (C2H5CO2)6

1970 ◽  
Vol 28 ◽  
pp. 478-479
Author(s):  
Teruo Someya ◽  
Jinzo Kobayashi
Keyword(s):  
Surface Layer ◽  
Electric Fields ◽  
Quantitative Study ◽  
Recent Progress ◽  
Ferroelectric Domain ◽  
Resolving Power ◽  
Surface Pattern ◽  
Crystal Surfaces ◽  
One Dimensional ◽  
Ferroelectric Domains

Recent progress in the electron-mirror microscopy (EMM), e.g., an improvement of its resolving power together with an increase of the magnification makes it useful for investigating the ferroelectric domain physics. English has recently observed the domain texture in the surface layer of BaTiO3. The present authors ) have developed a theory by which one can evaluate small one-dimensional electric fields and/or topographic step heights in the crystal surfaces from their EMM pictures. This theory was applied to a quantitative study of the surface pattern of BaTiO3).

Algorithms for automated montage synthesis of images from laser-scanning confocal microscopes

1995 ◽  
Vol 53 ◽  
pp. 650-651
Author(s):  
D. E. Becker
Keyword(s):  
Image Analysis ◽  
High Resolution ◽  
Laser Scanning ◽  
Cell Counting ◽  
Wide Area ◽  
Data Set ◽  
Computational Synthesis ◽  
Automated Cell Counting ◽  
Partial View ◽  
The Individual

An efficient, robust, and widely-applicable technique is presented for computational synthesis of high-resolution, wide-area images of a specimen from a series of overlapping partial views. This technique can also be used to combine the results of various forms of image analysis, such as segmentation, automated cell counting, deblurring, and neuron tracing, to generate representations that are equivalent to processing the large wide-area image, rather than the individual partial views. This can be a first step towards quantitation of the higher-level tissue architecture. The computational approach overcomes mechanical limitations, such as hysterisis and backlash, of microscope stages. It also automates a procedure that is currently done manually. One application is the high-resolution visualization and/or quantitation of large batches of specimens that are much wider than the field of view of the microscope.The automated montage synthesis begins by computing a concise set of landmark points for each partial view. The type of landmarks used can vary greatly depending on the images of interest. In many cases, image analysis performed on each data set can provide useful landmarks. Even when no such “natural” landmarks are available, image processing can often provide useful landmarks.

On convenient use of nanoprobe and scanning without a stem unit in an EM-420

1987 ◽  
Vol 45 ◽  
pp. 138-139
Author(s):  
K. K. Christenson ◽  
J. A. Eades
Keyword(s):  
Wide Area ◽  
Pole Piece ◽  
Operating Condition ◽  
Objective System

One of the strengths of the Philips EM-400 series of TEMs is their ability to operate under two distinct optical configurations: “microprobe”, the normal TEM operating condition which allows wide area illumination, and “nanoprobe”, which gives very small probes with high angular convergence for STEM imaging, microchemical and microstructural analyses. This change is accomplished by effectively turning off the twin lens located in the upper pole piece which changes the illumination from a telefocus system to a condenser-objective system. The deflection and tilt controls and alignments are designed for microprobe use and do not function properly when in nanoprobe. For instance, in nanoprobe the deflection control gives a mix of deflection and tilt; as does the tilt control.

The Nature of Oxide Surfaces: Topographic and Electronic Structure

1993 ◽  
Vol 51 ◽  
pp. 966-967
Author(s):  
Dawn A. Bonnell ◽  
Yong Liang
Keyword(s):  
Transition Metal Oxides ◽  
Electronic Structures ◽  
Recent Progress ◽  
Spatial Localization ◽  
Level Of Detail ◽  
Scanning Tunneling ◽  
Oxide Surfaces ◽  
Tunneling Microscopy ◽  
Considerable Effort ◽  
Complete Understanding

Recent progress in the application of scanning tunneling microscopy (STM) and tunneling spectroscopy (STS) to oxide surfaces has allowed issues of image formation mechanism and spatial resolution limitations to be addressed. As the STM analyses of oxide surfaces continues, it is becoming clear that the geometric and electronic structures of these surfaces are intrinsically complex. Since STM requires conductivity, the oxides in question are transition metal oxides that accommodate aliovalent dopants or nonstoichiometry to produce mobile carriers. To date, considerable effort has been directed toward probing the structures and reactivities of ZnO polar and nonpolar surfaces, TiO2 (110) and (001) surfaces and the SrTiO3 (001) surface, with a view towards integrating these results with the vast amount of previous surface analysis (LEED and photoemission) to build a more complete understanding of these surfaces. However, the spatial localization of the STM/STS provides a level of detail that leads to conclusions somewhat different from those made earlier.

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