scholarly journals Coarse quotients by group actions and the maximal Roe algebra

2019 ◽  
Vol 11 (04) ◽  
pp. 875-907
Author(s):  
Logan Higginbotham ◽  
Thomas Weighill
Keyword(s):  
Automorphism Group ◽  
Metric Space ◽  
Large Scale ◽  
Countable Group ◽  
Crossed Product ◽  
Property A ◽  
Bounded Geometry ◽  
Roe Algebra ◽  
Scale Spaces ◽  
The Ideal

For a finitely generated group [Formula: see text] acting on a metric space [Formula: see text], Roe defined the warped space [Formula: see text], which one can view as a kind of large scale quotient of [Formula: see text] by the action of [Formula: see text]. In this paper, we generalize this notion to the setting of actions of arbitrary groups on large scale spaces. We then restrict our attention to what we call coarsely discontinuous actions by coarse equivalences and show that for such actions the group [Formula: see text] can be recovered as an appropriately defined automorphism group [Formula: see text] when [Formula: see text] satisfies a large scale connectedness condition. We show that for a coarsely discontinuous action of a countable group [Formula: see text] on a discrete bounded geometry metric space [Formula: see text] there is a relation between the maximal Roe algebras of [Formula: see text] and [Formula: see text], namely that there is a ∗-isomorphism [Formula: see text], where [Formula: see text] is the ideal of compact operators. If [Formula: see text] has Property A and [Formula: see text] is amenable, then [Formula: see text] has Property A, and thus the maximal Roe algebra and full crossed product can be replaced by the usual Roe algebra and reduced crossed product respectively in the above equation.

THE FOREST FOR THE TREES: SOCIETY AND THE HOUSEHOLD IN EARLY MODERN EUROPE

1998 ◽  
Vol 41 (4) ◽  
pp. 1161-1172 ◽  
Author(s):  
JOEL F. HARRINGTON
Keyword(s):  
Large Scale ◽  
University Of Pennsylvania ◽  
Italian Renaissance ◽  
German History ◽  
Early Modern Europe ◽  
Cambridge University ◽  
Johns Hopkins University ◽  
Big Picture ◽  
To Come ◽  
The Ideal

Gender relations in German history: power, agency, and experience from the sixteenth to the twentieth century. Edited by Lynn Abrams and Elizabeth Harvey. London: UCL, 1996. Pp. x+262. ISBN 1-85728-485-2. £12.95.Adultery and divorce in Calvin's Geneva. By Robert M. Kingdon. Cambridge, Mass., and London: Harvard UP, 1995. Pp. ix+214. ISBN 0-674-00520-1 (hb). £18.50.Housecraft and statecraft: domestic service in Renaissance Venice, 1400–1600. By Dennis Romano. Baltimore: Johns Hopkins University Press, 1996. Pp. xxvi+333. ISBN 0-8018-5288-9. £37.00.The European nobility, 1400–1800. By Jonathan Dewald. New approaches to European history, ix. Cambridge: Cambridge University Press, 1996. Pp. xvii+209. ISBN 0-521-42528-x (pb). £12.95.Garden and grove: the Italian Renaissance garden in the English imagination, 1600–1750. By John Dixon Hunt. Philadelphia: University of Pennsylvania, 1996. Pp. xix+268. ISBN 0-8122-1604-0 (pb). £23.50.Like an ancient woodsman or a guide through the Amazonian jungle, the ideal historian possesses at least two kinds of expertise: enough familiarity with the general terrain to plan successful expeditions and enough experience in the field to make inevitable adjustments to ‘the big picture’ when underway. Of course in the real world (of both geography and history) the tasks of exploration and cartography are often bifurcated, without necessarily disastrous results. The historian who is equally skilled at both close-up description and large-scale theorizing is consequently celebrated as a rare and valued anomaly. Meanwhile, for most of us stumbling scouts, the world beyond our familiar trails remains largely one of learned lore, with connections to our own limited forays often vague at best. Unless, of course, we are fortunate enough to come across something which provides an almost magical link between the narrow and the wide, the micro and the macro.

scholarly journals Applying Biomimetic Principles to Thermoelectric Cooling Devices for Water Collection

2017 ◽  
Vol 7 (3) ◽  
pp. 27
Author(s):  
Kyle B Davidson ◽  
Bahram Asiabanpour ◽  
Zaid Almusaied
Keyword(s):  
Large Scale ◽  
Cost Effective ◽  
Thermoelectric Cooling ◽  
Device Structure ◽  
Cooling Systems ◽  
Cooling Devices ◽  
Water Collection ◽  
Maximum Water ◽  
The Ideal

The shortage of freshwater resources in the world has developed the need for sustainable, cost-effective technologies that can produce freshwater on a large scale. Current solutions often have extensive manufacturing requirements, or involve the use of large quantities of energy or toxic chemicals. Atmospheric water generating solutions that minimize the depletion of natural resources can be achieved by incorporating biomimetics, a classification of design inspired by nature. This research seeks to optimize thermoelectric cooling systems for use in water harvesting applications by analyzing the different factors that affect surface temperature and water condensation in TEC devices. Further experiments will be directed towards developing a robust, repeatable system, as well as an accurate measurement system. Surface modifications, device structure and orientation, and power generation will also be studied to better understand the ideal conditions for maximum water collection in thermoelectric cooling systems.

scholarly journals THE IDEAL AGGREGATE OF CRIMES STIPULATED BY ARTICLES 168, 264 OF THE CRIMINAL CODE OF THE RUSSIAN FEDERATION

2020 ◽  
Vol 11 ◽  
pp. 37-40
Author(s):  
Evgeniy V. Khromov ◽  
Keyword(s):  
Russian Federation ◽  
Large Scale ◽  
Criminal Liability ◽  
Criminal Code ◽  
Civil Code ◽  
Road Accidents ◽  
Property Damage ◽  
Legal Assessment ◽  
The Russian Federation ◽  
The Ideal

The issue of criminal legal assessment of the consequences of road accidents in the event of property damage is relevant. Disposition of Art. 168 of the Criminal Code provides for criminal liability for the destruction or damage of another’s property on a large scale, including through reckless handling of a source of increased danger. By virtue of h. 1 Article. 1079 of the Civil Code of the Russian Federation, vehicles are considered sources of increased danger.

scholarly journals The ideal of Lipschitz classical p-compact operators and its injective hull

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Toufik Tiaiba ◽  
Dahmane Achour
Keyword(s):  
Banach Space ◽  
Compact Operator ◽  
Metric Space ◽  
Metric Spaces ◽  
Compact Operators ◽  
Operator Ideal ◽  
Linear Case ◽  
Injective Hull ◽  
Nuclear Operators ◽  
The Ideal

Abstract We introduce and investigate the injective hull of the strongly Lipschitz classical p-compact operator ideal defined between a pointed metric space and a Banach space. As an application we extend some characterizations of the injective hull of the strongly Lipschitz classical p-compact from the linear case to the Lipschitz case. Also, we introduce the ideal of Lipschitz unconditionally quasi p-nuclear operators between pointed metric spaces and show that it coincides with the Lipschitz injective hull of the ideal of Lipschitz classical p-compact operators.

Retention of memory for large-scale spaces

Memory ◽  
2013 ◽  
Vol 21 (7) ◽  
pp. 807-817 ◽  
Author(s):  
Toru Ishikawa
Keyword(s):  
Large Scale ◽  
Scale Spaces

scholarly journals On minimal self-joinings in topological dynamics

1987 ◽  
Vol 7 (2) ◽  
pp. 211-227 ◽  
Author(s):  
Andrés del Junco
Keyword(s):  
Automorphism Group ◽  
Ergodic Theory ◽  
Metric Space ◽  
Topological Dynamics ◽  
Orbit Closure ◽  
Compact Metric Space ◽  
Minimal Self ◽  
Finite Set ◽  
Countably Infinite

AbstractIf X is a compact metric space and T a homeomorphism of X we say (X, T) has almost minimal power joinings (AMPJ) if there is a dense GδX* in X such that for each finite set k, x∈(X*)k and l:k → ℤ−{0}, the orbit closure cl {} is a product of off-diagonals (POOD) on Xk. By an offdiagonal on Xk′, k′k we mean a set of the form (⊗,j∈k′Tm(j))Δ, Δ the diagonal in Xk′, m:k′→ℤ any function, and by a POOD on Xk we mean that k is split into subsets k′, on each Xk′ we put an off-diagonal and then we take the product of these.We show that examples of AMPJ exist and that this definition leads to a theory completely analogous to Rudolph's theory of minimal self-joinings in ergodic theory. In particular if (X, T) has AMPJ the automorphism group of T is {Tn}, T has only almost 1-1 factors (other than the trivial one) and the automorphism group and factors of ⊕i ∊ kT, k finite or countably infinite, can be very explicitly described. We also discuss ℝ-actions.

scholarly journals Smoke Control in Large Scale Spaces

1985 ◽  
Vol 5 (1) ◽  
pp. 41-54 ◽  
Author(s):  
Toshio Yamana ◽  
Takeyoshi Tanaka
Keyword(s):  
Large Scale ◽  
Smoke Control ◽  
Scale Spaces

scholarly journals Joint Geosequential Preference and Distance Metric Factorization for Point-of-Interest Recommendation

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Chunyang Liu ◽  
Chao Liu ◽  
Haiqiang Xin ◽  
Jian Wang ◽  
Jiping Liu ◽  
...  
Keyword(s):  
Metric Space ◽  
Matrix Factorization ◽  
Euclidean Distance ◽  
Large Scale ◽  
Inner Product ◽  
Interaction Matrix ◽  
Distance Metric ◽  
Point Of Interest ◽  
Poi Recommendation ◽  
Real World Datasets

Point-of-interest (POI) recommendation is a valuable service to help users discover attractive locations in location-based social networks (LBSNs). It focuses on capturing users’ movement patterns and location preferences by using massive historical check-in data. In the past decade, matrix factorization has become a mature and widely used technology in POI recommendation. However, the inner product of latent vectors adopted in matrix factorization methods does not satisfy the triangle inequality property, which may limit the expressiveness and lead to suboptimal solutions. Besides, the extreme sparsity of check-in data makes it challenging to capture users’ movement preferences accurately. In this paper, we propose a joint geosequential preference and distance metric factorization framework, called GeoSeDMF, for POI recommendation. First, we introduce a distance metric factorization method that is capable of learning users’ personalized preferences from a position and distance perspective in the metric space. Specifically, we convert the user-POI interaction matrix into a distance matrix and factorize it into user and POI dense embeddings. Additionally, we measure users’ personalized preference for the POI by using the Euclidean distance metric instead of the inner product. Then, we model the users’ geospatial preference by applying a geographic weight coefficient and model the users’ sequential preference by using the Euclidean distance of continuous check-in locations. Moreover, a pointwise loss strategy and AdaGrad algorithm are adopted to optimize the positions and relationships of users and POIs in a metric space. Finally, experimental results on three large-scale real-world datasets demonstrate the effectiveness and superiority of the proposed method.

scholarly journals On a Crossed Product of a Division Ring

1969 ◽  
Vol 35 ◽  
pp. 47-51 ◽  
Author(s):  
Nobuo Nobusawa
Keyword(s):  
Automorphism Group ◽  
Division Ring ◽  
Crossed Product ◽  
Regular Elements ◽  
Factor Set

1. Let R and C be a ring and its center, and G an automorphism group of R of order n. By a factor set {cα,τ}, we mean a system of regular elements cα,τ (α,τ ∈ G) in C such that(1)

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