scholarly journals THE WIDTH OF VERBAL SUBGROUPS IN THE GROUP OF UNITRIANGULAR MATRICES OVER A FIELD

2012 ◽  
Vol 22 (03) ◽  
pp. 1250019 ◽  
Author(s):  
AGNIESZKA BIER
Keyword(s):  
Finite Width ◽  
Triangular Matrices ◽  
Verbal Subgroups

Let K be a field and let UTn(K) and Tn(K) denote the groups of all unitriangular and triangular matrices over field K, respectively. In the paper, the lattices of verbal subgroups of the above groups are characterized. Consequently, the equalities between certain verbal subgroups and their verbal width are determined. The considerations bring a series of verbal subgroups with exactly known finite width equal to 2. An analogous characterization and results for the groups of infinitely dimensional triangular and unitriangular matrices are established in the last part of the paper.

On the width of verbal subgroups of the groups of triangular matrices over a field of arbitrary characteristic

2016 ◽  
Vol 26 (02) ◽  
pp. 217-222
Author(s):  
Yury Vasilevich Sosnovskiy
Keyword(s):  
Arbitrary Field ◽  
Triangular Matrices ◽  
Verbal Subgroup ◽  
Arbitrary Characteristic ◽  
Number Formula ◽  
Group Words ◽  
Commutator Word ◽  
Outer Commutator ◽  
Outer Commutator Word ◽  
Verbal Subgroups

The width [Formula: see text] of the verbal subgroup [Formula: see text] of a group [Formula: see text] defined by a collection of group words [Formula: see text] is the smallest number [Formula: see text] in [Formula: see text] such that every element of [Formula: see text] is the product of at most [Formula: see text] words in [Formula: see text] evaluated on [Formula: see text] and their inverses. Well known that every verbal subgroup of the group [Formula: see text] of triangular matrices over an arbitrary field [Formula: see text] can be defined by just one word: an outer commutator word or a power word. We prove that [Formula: see text] for every outer commutator word [Formula: see text] and that [Formula: see text] except for two cases, when it is equal to 2. For finitary triangular groups, the situation is similar.

Dispersion Characteristics of Multi-Step Open Slow-Wave Systems of Finite Width: Analysis

1997 ◽  
Vol 51 (8) ◽  
pp. 77-84
Author(s):  
L. M. Buzik ◽  
O. F. Pishko ◽  
S.A. Churilova ◽  
O. I. Sheremet
Keyword(s):  
Slow Wave ◽  
Finite Width ◽  
Dispersion Characteristics

Quantum Tunneling

2017 ◽  
Author(s):  
Frank S. Levin
Keyword(s):  
Quantum Tunneling ◽  
Alpha Particles ◽  
Attractive Potential ◽  
Scanning Tunneling ◽  
Finite Width ◽  
Potential Well ◽  
Surface Molecules ◽  
Repulsive Coulomb ◽  
The Subject ◽  
The One

Quantum tunneling, wherein a quanject has a non-zero probability of tunneling into and then exiting a barrier of finite width and height, is the subject of Chapter 13. The description for the one-dimensional case is extended to the barrier being inverted, which forms an attractive potential well. The first application of this analysis is to the emission of alpha particles from the decay of radioactive nuclei, where the alpha-nucleus attraction is modeled by a potential well and the barrier is the repulsive Coulomb potential. Excellent results are obtained. Ditto for the similar analysis of proton burning in stars and yet a different analysis that explains tunneling through a Josephson junction, the connector between two superconductors. The final application is to the scanning tunneling microscope, a device that allows the microscopic surfaces of solids to be mapped via electrons from the surface molecules tunneling into the tip of the STM probe.

scholarly journals Some subordination involving polynomials induced by lower triangular matrices

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Saiful R. Mondal ◽  
Kottakkaran Sooppy Nisar ◽  
Thabet Abdeljawad
Keyword(s):  
Unit Disk ◽  
Triangular Matrices ◽  
Cesàro Mean ◽  
Cesaro Mean ◽  
Lower Triangular ◽  
Lower Triangular Matrices

Abstract The article considers several polynomials induced by admissible lower triangular matrices and studies their subordination properties. The concept generalizes the notion of stable functions in the unit disk. Several illustrative examples, including those related to the Cesàro mean, are discussed, and connections are made with earlier works.

Finite-width waveguide and waveguide intersections for self-collimated beams in photonic crystals

2004 ◽  
Vol 85 (21) ◽  
pp. 4834-4836 ◽  
Author(s):  
Zhaofeng Li ◽  
Haibo Chen ◽  
Zhitang Song ◽  
Fuhua Yang ◽  
Songlin Feng
Keyword(s):  
Photonic Crystals ◽  
Finite Width

Automated Deburring with a Filamentary Brush: Prescribed Burr Geometry

1999 ◽  
Vol 121 (3) ◽  
pp. 385-392 ◽  
Author(s):  
Robert J. Stango ◽  
Lienjing Chen ◽  
Vikram Cariapa
Keyword(s):  
Penetration Depth ◽  
Dynamic Model ◽  
Control Strategy ◽  
Feed Rate ◽  
Material Removal ◽  
Vision System ◽  
Closed Form Solution ◽  
Straight Edge ◽  
Finite Width ◽  
Production Environment

In this paper, a dynamic model for removal of edge burrs with a compliant brushing tool is reported. Description of the burr geometry is assumed to be known through on-line measurement methods such as a computer vision system in the flexible manufacturing cell. Dynamic response of the brush/workpiece system is evaluated on the basis of experimentally obtained data. Master Curves are introduced as machining descriptors which characterize the incremental burr removal performance of the brush/workpiece system, leading to the development of an analytical dynamic model for orthogonal burr removal using a finite-width brushing tool. Based upon the dynamic model for material removal, a control strategy for automatic deburring is presented for burr configurations having constant height as well as variable height. A closed-form solution for transverse brush feed rate is obtained which is applicable for removal of burrs having variable height, as described by suitable geometry functions. For illustrative purposes, simulations are carried out for a straight-edge burr profile and sinusoidal burr geometry. Results are reported which identify important relationships among brush feed rate, brush penetration depth, and brush rotational speed. In order to help assess the validity of the proposed analytical model and control strategy, experimental results are reported for a combination ramp/straight-edge burr configuration. The results demonstrate generally good correlation between the predicted and actual profile for the edge burr that has been machined. In addition, some important observations include; (1) burr removal is most rapidly carried out by using the highest brush speed and deepest brush/workpiece penetration depth, subject to the condition that the brush fiber is not damaged, (2) Currently available polymer abrasive brushing tools exhibit very slow machining characteristics and must be improved in order to be used in a production environment where burr size is appreciable, (3) Material removal characteristics of the leading and trailing edge of brushes may be a source of error which merits further investigation.

Sign in / Sign up

Export Citation Format

Share Document