IDENTITIES AND A BOUNDED HEIGHT CONDITION FOR SEMIGROUPS

2003 ◽  
Vol 13 (05) ◽  
pp. 565-583 ◽  
Author(s):  
L. M. SHNEERSON
Keyword(s):  
Polynomial Growth ◽  
Nilpotent Groups ◽  
The Other ◽  
Finitely Generated ◽  
Different Types ◽  
Associative Rings ◽  
Nontrivial Identity

We consider two different types of bounded height condition for semigroups. The first one originates from the classical Shirshov's bounded height theorem for associative rings. The second which is weaker, in fact was introduced by Wolf and also used by Bass for calculating the growth of finitely generated (f.g.) nilpotent groups. Both conditions yield polynomial growth. We give the first two examples of f.g. semigroups which have bounded height and do not satisfy any nontrivial identity. One of these semigroups does not have bounded height in the sense of Shirshov and the other satisfies the classical bounded height condition. This develops further one of the main results of the author's paper (J. Algebra, 1993) where the first examples of f.g. semigroups of polynomial growth and without nontrivial identities were given.

scholarly journals Translation-like actions of nilpotent groups

2019 ◽  
Vol 11 (02) ◽  
pp. 357-370
Author(s):  
David Bruce Cohen ◽  
Mark Pengitore
Keyword(s):  
Lipschitz Function ◽  
Classical Result ◽  
Polynomial Growth ◽  
Nilpotent Groups ◽  
The Other ◽  
Finitely Generated ◽  
Asymptotic Cones ◽  
Homogeneous Dimension ◽  
Lipschitz Embeddings ◽  
Torsion Free

We give a new obstruction to translation-like actions on nilpotent groups. Suppose we are given two finitely generated torsion-free nilpotent groups with the same degree of polynomial growth, but non-isomorphic Carnot completions (asymptotic cones). We show that there exists no injective Lipschitz function from one group to the other. It follows that neither group can act translation-like on the other. As Lipschitz injections need not be bi-Lipschitz embeddings, this is a strengthening of a classical result of Pansu in the context of groups of the same homogeneous dimension.

Decision problems concerning S-arithmetic groups

1985 ◽  
Vol 50 (3) ◽  
pp. 743-772 ◽  
Author(s):  
Fritz Grunewald ◽  
Daniel Segal
Keyword(s):  
Additive Group ◽  
Nilpotent Groups ◽  
Isomorphism Problem ◽  
Algorithmic Problem ◽  
Finitely Generated ◽  
Finitely Presented Groups ◽  
Finite Dimensional ◽  
Associative Rings ◽  
Finitely Presented ◽  
Torsion Free

This paper is a continuation of our previous work in [12]. The results, and some applications, have been described in the announcement [13]; it may be useful to discuss here, a little more fully, the nature and purpose of this work.We are concerned basically with three kinds of algorithmic problem: (1) isomorphism problems, (2) “orbit problems”, and (3) “effective generation”.(1) Isomorphism problems. Here we have a class of algebraic objects of some kind, and ask: is there a uniform algorithm for deciding whether two arbitrary members of are isomorphic? In most cases, the answer is no: no such algorithm exists. Indeed this has been one of the most notable applications of methods of mathematical logic in algebra (see [26, Chapter IV, §4] for the case where is the class of all finitely presented groups). It turns out, however, that when consists of objects which are in a certain sense “finite-dimensional”, then the isomorphism problem is indeed algorithmically soluble. We gave such algorithms in [12] for the following cases: = {finitely generated nilpotent groups}; = {(not necessarily associative) rings whose additive group is finitely generated}; = {finitely Z-generated modules over a fixed finitely generated ring}.Combining the methods of [12] with his own earlier work, Sarkisian has obtained analogous results with the integers replaced by the rationals: in [20] and [21] he solves the isomorphism problem for radicable torsion-free nilpotent groups of finite rank and for finite-dimensional Q-algebras.

scholarly journals Elementary equivalence and genus of finitely generated nilpotent groups

1988 ◽  
Vol 37 (1) ◽  
pp. 61-68 ◽  
Author(s):  
Francis Oger
Keyword(s):  
Finite Index ◽  
Nilpotent Groups ◽  
The Other ◽  
Finitely Generated ◽  
Elementary Equivalence

We show that, if two finitely generated nilpotent groups are elementarily equivalent, and more generally if they satisfy the same sentences with one alternation of quantifiers, then, they are quite similar, though not necessarily isomorphic. For instance, each of them is isomorphic to a subgroup of finite index of the other and they have the same finite images, the same Mislin genus and the same Pickel genus.

Automorphisms of finite order of nilpotent groups II

2014 ◽  
Vol 51 (4) ◽  
pp. 547-555 ◽  
Author(s):  
B. Wehrfritz
Keyword(s):  
Nilpotent Group ◽  
Finite Order ◽  
Finite Index ◽  
Nilpotent Groups ◽  
Finitely Generated

Let G be a nilpotent group with finite abelian ranks (e.g. let G be a finitely generated nilpotent group) and suppose φ is an automorphism of G of finite order m. If γ and ψ denote the associated maps of G given by \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\gamma :g \mapsto g^{ - 1} \cdot g\phi and \psi :g \mapsto g \cdot g\phi \cdot g\phi ^2 \cdots \cdot \cdot g\phi ^{m - 1} for g \in G,$$ \end{document} then Gγ · kerγ and Gψ · ker ψ are both very large in that they contain subgroups of finite index in G.

Comparative Surface Imaging Study of Multifocal Diffractive Intraocular Lenses

2021 ◽  
Author(s):  
Hyeck Soo Son ◽  
Jung Min Lee ◽  
Ramin Khoramnia ◽  
Chul Young Choi
Keyword(s):  
Imaging Study ◽  
The Other ◽  
Intraocular Lenses ◽  
Optical Surface ◽  
Diffractive Optic ◽  
Atomic Force ◽  
Acceptable Range ◽  
Different Types ◽  
Concentric Pattern

Abstract Purpose To analyse and compare the surface topography and roughness of three different types of diffractive multifocal IOLs. Methods Using scanning electron microscope (SEM, Inspect F, 5.0 KV, maximum magnification up to 20,000) and atomic force microscope (AFM, Park Systems, XE-100, non-contact, area profile comparison, 10 × 10 µm, 40 × 40 µm), the surface quality of the following diffractive IOLs was studied: the AcrySof IQ PanOptix (Alcon, USA), the AT LARA 829MP (Carl Zeiss Meditec, Germany), and Tecnis Symfony (Johnson&Johnson Vision, USA). The measurements were made over three representative areas (central non-diffractive optic, central diffractive optic, and diffractive step) of each IOL. Roughness profile in terms of mean arithmetic roughness (Ra) and root-mean-squared roughness (Rq) values were obtained and compared statistically. Results In SEM examination, all IOLs showed a smooth optical surface without any irregularities at low magnification. At higher magnification, Tecnis Symfony showed unique highly regular, concentric, and lineate structures in the diffractive optic area which could not be seen in the other studied diffractive IOLs. The differences in the measured Ra and Rq values of the Tecnis Symfony were statistically significant compared to the other models (p < 0.05). Conclusion Various different topographical traits were observed in three diffractive multifocal IOLs. The Ra values of all studied IOLs were within an acceptable range. Tecnis Symfony showed statistically significant higher surface Ra values at both central diffractive optic and diffractive step areas. Furthermore, compared to its counterparts, Tecnis Symfony demonstrated highly ordered, concentric pattern in its diffractive surfaces.

RADIATION EXPOSURE TO THE BACK WITH DIFFERENT TYPES OF APRONS

2021 ◽  
Author(s):  
Seung Wan Hong ◽  
Tae Won Kim ◽  
Jae Hun Kim
Keyword(s):  
Radiation Exposure ◽  
Effective Dose ◽  
Exposure Time ◽  
The Other ◽  
Lead Apron ◽  
Type Group ◽  
Air Kerma ◽  
Different Types ◽  
The Relationship

Abstract Physicians and nurses stand with their back towards the C-arm fluoroscope when using the computer, taking things out of closets and preparing drugs for injection or instruments for intervention. This study was conducted to investigate the relationship between the type of lead apron and radiation exposure to the backs of physicians and nurses while using C-arm fluoroscopy. We compared radiation exposure to the back in the three groups: no lead apron (group C), front coverage type (group F) and wrap-around type (group W). The other wrap-around type apron was put on the bed instead of on a patient. We ran C-arm fluoroscopy 40 times for each measurement. We collected the air kerma (AK), exposure time (ET) and effective dose (ED) of the bedside table, upper part and lower part of apron. We measured these variables 30 times for each location. In group F, ED of the upper part was the highest (p &lt; 0.001). ED of the lower part in group C and F was higher than that in group W (p = 0.012). The radiation exposure with a front coverage type apron is higher than that of the wrap-around type and even no apron at the neck or thyroid. For reducing radiation exposure to the back of physician or nurse, the wrap-around type apron is recommended. This type of apron can reduce radiation to the back when the physician turns away from the patient or C-arm fluoroscopy.

scholarly journals Residual dimension of nilpotent groups

2020 ◽  
Vol 23 (5) ◽  
pp. 801-829
Author(s):  
Mark Pengitore
Keyword(s):  
New York ◽  
Nilpotent Group ◽  
Nilpotent Groups ◽  
Finitely Generated ◽  
Nontrivial Element ◽  
Maximum Order ◽  
Asymptotic Bounds ◽  
Group Morphism ◽  
A Finite Group

AbstractThe function {\mathrm{F}_{G}(n)} gives the maximum order of a finite group needed to distinguish a nontrivial element of G from the identity with a surjective group morphism as one varies over nontrivial elements of word length at most n. In previous work [M. Pengitore, Effective separability of finitely generated nilpotent groups, New York J. Math. 24 2018, 83–145], the author claimed a characterization for {\mathrm{F}_{N}(n)} when N is a finitely generated nilpotent group. However, a counterexample to the above claim was communicated to the author, and consequently, the statement of the asymptotic characterization of {\mathrm{F}_{N}(n)} is incorrect. In this article, we introduce new tools to provide lower asymptotic bounds for {\mathrm{F}_{N}(n)} when N is a finitely generated nilpotent group. Moreover, we introduce a class of finitely generated nilpotent groups for which the upper bound of the above article can be improved. Finally, we construct a class of finitely generated nilpotent groups N for which the asymptotic behavior of {\mathrm{F}_{N}(n)} can be fully characterized.

scholarly journals MITOTIC CROSSING OVER AND NONDISJUNCTION IN TRANSLOCATION HETEROZYGOTES OF ASPERGILLUS

Genetics ◽  
1976 ◽  
Vol 82 (4) ◽  
pp. 605-627
Author(s):  
Etta Käfer
Keyword(s):  
Selective Advantage ◽  
The Other ◽  
Translocation Chromosome ◽  
Crossing Over ◽  
Selective Marker ◽  
Reciprocal Translocations ◽  
Poor Growth ◽  
Different Types ◽  
Diploid Genotype ◽  
One Step

ABSTRACT To analyze mitotic recombination in translocation heterozygotes of A. nidulans two sets of well-marked diploids were constructed, homo- or heterozygous for the reciprocal translocations T1(IL;VIIR) or T2(IL;VIIIR) and heterozygous for selective markers on IL. It was found that from all translocation heterozygotes some of the expected mitotic crossover types could be selected. Such crossovers are monosomic for one translocated segment and trisomic for the other and recovery depends on the relative viabilities of these unbalanced types. The obtained segregants show characteristically reduced growth rates and conidiation dependent on sizes and types of mono- and trisomic segments, and all spontaneously produce normal diploid sectors. Such secondary diploid types either arose in one step of compensating crossing over in the other involved arm, or—more conspicuously—in two steps of nondisjunction via a trisomic intermediate.—In both of the analyzed translocations the segments translocated to IL were extremely long, while those translocated from IL were relatively short. The break in I for T1(I;VII) was located distal to the main selective marker in IL, while that of T2(I;VIII) had been mapped proximal but closely linked to it. Therefore, as expected, the selected primary crossover from the two diploids with T2(I;VIII) in coupling or in repulsion to the selective marker, showed the same chromosomal imbalance and poor growth. These could however be distinguished visually because they spontaneously produced different trisomic intermediates in the next step, in accordance with the different arrangement of the aneuploid segments. On the other hand, from diploids heterozygous for T1(I;VII) mitotic crossovers could only be selected when the selective markers were in coupling with the translocation; these crossovers were relatively well-growing and produced frequent secondary segregants of the expected trisomic, 2n+VII, type. For both translocations it was impossible to recover the reciprocal crossover types (which would be trisomic for the distal segments of I and monosomic for most of groups VII or VIII) presumably because these were too inviable to form conidia.—In addition to the selected segregants of expected types a variety of unexpected ones were isolated. The conditions of selection used favour visual detection of aneuploid types, even if these produce only a few conidial heads and are not at a selective advantage. For T2(I;VIII) these "non-selected" unbalanced segregants were mainly "reciprocal" crossovers of the same phenotype and imbalance as the selected ones. For T1(I;VII) two quite different types were obtained, both possibly originating with loss of the small VII-Itranslocation chromosome. One was isolated when the selective marker in repulsion to T1(I;VII) was used and, without being homo- or hemizygous for the selective marker, it produced stable sectors homozygous for this marker. The other was obtained from both coupling and repulsion diploids and showed a near-diploid genotype; it produced practically only haploid stable sectors of the type expected from monosomics, 2n-1 for the short translocation chromosome.

scholarly journals Development of Speech Recognition Systems in Emergency Call Centers

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 634
Author(s):  
Alakbar Valizada ◽  
Natavan Akhundova ◽  
Samir Rustamov
Keyword(s):  
Speech Recognition ◽  
Markov Model ◽  
Hidden Markov ◽  
Call Centers ◽  
The Other ◽  
Language Models ◽  
Emergency Call ◽  
Acoustic Model ◽  
Different Types ◽  
Recognition Systems

In this paper, various methodologies of acoustic and language models, as well as labeling methods for automatic speech recognition for spoken dialogues in emergency call centers were investigated and comparatively analyzed. Because of the fact that dialogue speech in call centers has specific context and noisy, emotional environments, available speech recognition systems show poor performance. Therefore, in order to accurately recognize dialogue speeches, the main modules of speech recognition systems—language models and acoustic training methodologies—as well as symmetric data labeling approaches have been investigated and analyzed. To find an effective acoustic model for dialogue data, different types of Gaussian Mixture Model/Hidden Markov Model (GMM/HMM) and Deep Neural Network/Hidden Markov Model (DNN/HMM) methodologies were trained and compared. Additionally, effective language models for dialogue systems were defined based on extrinsic and intrinsic methods. Lastly, our suggested data labeling approaches with spelling correction are compared with common labeling methods resulting in outperforming the other methods with a notable percentage. Based on the results of the experiments, we determined that DNN/HMM for an acoustic model, trigram with Kneser–Ney discounting for a language model and using spelling correction before training data for a labeling method are effective configurations for dialogue speech recognition in emergency call centers. It should be noted that this research was conducted with two different types of datasets collected from emergency calls: the Dialogue dataset (27 h), which encapsulates call agents’ speech, and the Summary dataset (53 h), which contains voiced summaries of those dialogues describing emergency cases. Even though the speech taken from the emergency call center is in the Azerbaijani language, which belongs to the Turkic group of languages, our approaches are not tightly connected to specific language features. Hence, it is anticipated that suggested approaches can be applied to the other languages of the same group.

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