Metric mean dimension for algebraic actions of Sofic groups

Ben Hayes

doi:10.1090/tran/6834

Local and doubly empirical convergence and the entropy of algebraic actions of sofic groups

Ergodic Theory and Dynamical Systems ◽

10.1017/etds.2017.69 ◽

2017 ◽

Vol 39 (4) ◽

pp. 930-953

Author(s):

BEN HAYES

Keyword(s):

Compact Group ◽

Topological Entropy ◽

Haar Measure ◽

Algebraic Actions ◽

Sofic Groups

Let $G$ be a sofic group and $X$ a compact group with $G\curvearrowright X$ by automorphisms. Using (and reformulating) the notion of local and doubly empirical convergence developed by Austin, we show that in many cases the topological and the measure-theoretic entropy with respect to the Haar measure of $G\curvearrowright X$ agree. Our method of proof recovers all known examples. Moreover, the proofs are direct and do not go through explicitly computing the measure-theoretic or topological entropy.

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Mean dimension, mean rank, and von Neumann–Lück rank

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crelle-2015-0046 ◽

2018 ◽

Vol 2018 (739) ◽

pp. 207-240 ◽

Cited By ~ 6

Author(s):

Hanfeng Li ◽

Bingbing Liang

Keyword(s):

Abelian Group ◽

Amenable Group ◽

Inverse Limits ◽

Integral Group ◽

Addition Formula ◽

Von Neumann ◽

Algebraic Actions ◽

Finite Subgroups ◽

Mean Dimension ◽

The Mean

AbstractWe introduce an invariant, called mean rank, for any module{\mathcal{M}}of the integral group ring of a discrete amenable group Γ, as an analogue of the rank of an abelian group. It is shown that the mean dimension of the induced Γ-action on the Pontryagin dual of{\mathcal{M}}, the mean rank of{\mathcal{M}}, and the von Neumann–Lück rank of{\mathcal{M}}all coincide. As applications, we establish an addition formula for mean dimension of algebraic actions, prove the analogue of the Pontryagin–Schnirelmann theorem for algebraic actions, and show that for elementary amenable groups with an upper bound on the orders of finite subgroups, algebraic actions with zero mean dimension are inverse limits of finite entropy actions.

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GAMBARAN BEBAN KERJA MENTAL PADA DOSEN FAKULTAS X UNIVERSITAS X

Journal of Nursing Care ◽

10.24198/jnc.v2i3.19013 ◽

2019 ◽

Vol 2 (3) ◽

Author(s):

Kartiani Dewi ◽

Suryani S ◽

Ahmad Yamin

Keyword(s):

Community Service ◽

Mental Workload ◽

Sampling Technique ◽

Mean Value ◽

Descriptive Statistics ◽

Large Contribution ◽

Mean Dimension ◽

The Mean ◽

Quantitative Descriptive ◽

University Lecturers

Lecturers are responsible for implementing the three main responsibilities in university (Tridharma Perguruan Tinggi) with 12 credits to 16 credits each semester. However, many lecturers feel that the workload is very excessive. The purpose of this study was to describe the mental workload of lecturers at the Faculty of X Padjadjaran University. The method of this research was quantitative descriptive by using a total sampling technique involving 43 lecturers. Data collection used NASA-TLX instruments. Data were analysed using descriptive statistics. The results of the study showed that overall the mental workload of the Faculty of X Padjadjaran University lecturers was included in the high category both in education and teaching assignments (74.4%), research assignments (76.7%), and community service assignments (74.4%). ) Effort dimensions have the highest mean value that is equal to 51.8, while the dimensions that have the lowest mean are Perfomance dimension, namely 9.4, where the greater the mean dimension shows the large contribution in the mental workload felt by the lecturer. The conclusions, this study show that most lecturers have a high mental workload. It is suggested that the lecturers need to have balance numbers of tasks according to their abilities, balance the time working with recreation, and meet the needs of rest. The results of this study need to be followed up by examining methods or efforts that can reduce the lecturers' mental workload.

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Moduli Space of Brody Curves, Energy and Mean Dimension

Nagoya Mathematical Journal ◽

10.1017/s0027763000025964 ◽

2008 ◽

Vol 192 ◽

pp. 27-58 ◽

Cited By ~ 10

Author(s):

Masaki Tsukamoto

Keyword(s):

Complex Plane ◽

Moduli Space ◽

Hermitian Manifold ◽

Value Distribution ◽

Holomorphic Map ◽

Infinite Dimensional ◽

Mean Dimension ◽

The Mean ◽

Moduli Theory ◽

Bounded Derivative

AbstractA Brody curve is a holomorphic map from the complex plane ℂ to a Hermitian manifold with bounded derivative. In this paper we study the value distribution of Brody curves from the viewpoint of moduli theory. The moduli space of Brody curves becomes infinite dimensional in general, and we study its “mean dimension”. We introduce the notion of “mean energy” and show that this can be used to estimate the mean dimension.

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On a Hölder covariant version of mean dimension

Comptes Rendus Mathematique ◽

10.1016/j.crma.2009.10.014 ◽

2009 ◽

Vol 347 (23-24) ◽

pp. 1389-1392 ◽

Cited By ~ 2

Author(s):

Antoine Gournay

Keyword(s):

Mean Dimension ◽

Covariant Version

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Mine surveying technique and steel storage tank base deformation removal

Izvestiya vysshikh uchebnykh zavedenii Gornyi zhurnal ◽

10.21440/0536-1028-2021-7-69-79 ◽

2021 ◽

Vol 1 (7) ◽

pp. 69-79

Author(s):

Aleksandr I. Barulin ◽

Keyword(s):

Low Cost ◽

Operating Time ◽

Construction Period ◽

Steel Tank ◽

Steel Tanks ◽

Algebraic Actions ◽

Minimum Height ◽

Survey Accuracy ◽

Tank Bottom ◽

Mine Surveying

Introduction. Vertical steel tanks are extensively used in oil fields to hold crude oil and other liquids. Their construction requires continuous surveying control. However, measurement procedures, data processing, and deviations and documentation correction are not universal and cannot be applied for tanks with a capacity of less than 3000 m3. Moreover, the process of correcting the detected bottom irregularities is poorly substantiated and intuitive. Research objective is to improve the as-built survey accuracy and reliability of the low-capacity steel tank bottom, substantiate the minimum height of its irregularities, increase the objectivity and productivity of measurement processing, develop an unambiguous method for time-predictable correction of bottom irregularities, and substantiate the optimal contents of its relief’s as-built scheme. Methods of research. Geometric leveling for the bottom profile survey failed to provide adequate accuracy and was therefore replaced by the method of trigonometric leveling. A method has been developed for determining the deviations of the existent tank bottom profile from the design position by means of algebraic actions with surfaces of a topographic order. The accuracy of determining the smallest height of bottom irregularities has been estimated under the tacheometric survey. A method has been proposed for controlling the correction of tank bottom irregularities based on evaluation calculations of bottom deformations by the finite element method. Research results. All the development results are exemplified by a specific production example. It was found that for a full completion of work, two iterations of tank bottom irregularities correction are enough. Methods of optimal design for the facility’s as-built schemes are presented. Conclusions. A simple, accurate, low-cost, productive, and time-predictable method of mine surveying, mathematical processing and correction of deviations in the tank bottom profile has been developed. This technique reduces the construction period and increases the operating time of the facility.

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