scholarly journals A categorical invariant of flow equivalence of shifts

2014 ◽  
Vol 36 (2) ◽  
pp. 470-513 ◽  
Author(s):  
ALFREDO COSTA ◽  
BENJAMIN STEINBERG
Keyword(s):  
Analogous Result ◽  
Mild Conditions ◽  
Equivalence Of Categories ◽  
Natural Equivalence ◽  
Sofic Shifts ◽  
Flow Equivalence ◽  
Flow Invariance ◽  
Natural Sense

We prove that the Karoubi envelope of a shift—defined as the Karoubi envelope of the syntactic semigroup of the language of blocks of the shift—is, up to natural equivalence of categories, an invariant of flow equivalence. More precisely, we show that the action of the Karoubi envelope on the Krieger cover of the shift is a flow invariant. An analogous result concerning the Fischer cover of a synchronizing shift is also obtained. From these main results, several flow equivalence invariants—some new and some old—are obtained. We also show that the Karoubi envelope is, in a natural sense, the best possible syntactic invariant of flow equivalence of sofic shifts. Another application concerns the classification of Markov–Dyck and Markov–Motzkin shifts: it is shown that, under mild conditions, two graphs define flow equivalent shifts if and only if they are isomorphic. Shifts with property ($\mathscr{A}$) and their associated semigroups, introduced by Wolfgang Krieger, are interpreted in terms of the Karoubi envelope, yielding a proof of the flow invariance of the associated semigroups in the cases usually considered (a result recently announced by Krieger), and also a proof that property ($\mathscr{A}$) is decidable for sofic shifts.

The Classification and Analysis of Ancient Calcareous Materials

1966 ◽  
Vol 31 (6) ◽  
pp. 875-878 ◽  
Author(s):  
Edwin R. Littmann
Keyword(s):  
Carbon Dioxide ◽  
Organic Matter ◽  
Analytical Procedure ◽  
Raw Materials ◽  
Iron Compounds ◽  
Systematic Classification ◽  
Mild Conditions ◽  
Sources Of Error ◽  
Calcium And Magnesium

AbstractIn the present paper a systematic classification of ancient calcareous materials has been proposed which more closely defines limestone in terms of the ratio of calcium to magnesium present. The same classification may be applied to mortars and plasters to characterize the raw materials from which they were made. The classification includes "pure" calcium and magnesium minerals and any combination of the two.A new analytical procedure has been devised which eliminates the major sources of error in a previously used method and consists of first igniting the sample to remove all organic matter and most of the carbon dioxide and to oxidize any iron compounds to the ferric state. This is followed by solution of the sample under mild conditions and volumetrically determining the calcium and magnesium under conditions which eliminate the effect of any dissolved impurities.

scholarly journals -ALGEBRAS ASSOCIATED WITH LAMBDA-SYNCHRONIZING SUBSHIFTS AND FLOW EQUIVALENCE

2013 ◽  
Vol 95 (2) ◽  
pp. 241-265 ◽  
Author(s):  
KENGO MATSUMOTO
Keyword(s):  
Algebraic Structure ◽  
Isomorphism Class ◽  
Cartan Subalgebra ◽  
Sofic Shift ◽  
Sofic Shifts ◽  
Flow Equivalence ◽  
Graph System

AbstractThe class of $\lambda $-synchronizing subshifts generalizes the class of irreducible sofic shifts. A $\lambda $-synchronizing subshift can be presented by a certain $\lambda $-graph system, called the $\lambda $-synchronizing $\lambda $-graph system. The $\lambda $-synchronizing $\lambda $-graph system of a $\lambda $-synchronizing subshift can be regarded as an analogue of the Fischer cover of an irreducible sofic shift. We will study algebraic structure of the ${C}^{\ast } $-algebra associated with a $\lambda $-synchronizing $\lambda $-graph system and prove that the stable isomorphism class of the ${C}^{\ast } $-algebra with its Cartan subalgebra is invariant under flow equivalence of $\lambda $-synchronizing subshifts.

scholarly journals Subcategories of singularity categories via tensor actions

2013 ◽  
Vol 150 (2) ◽  
pp. 229-272 ◽  
Author(s):  
Greg Stevenson
Keyword(s):  
Complete Intersection ◽  
Analogous Result ◽  
Complete Classification ◽  
Derived Category ◽  
Hypersurface Singularities ◽  
Regular Scheme ◽  
Affine Scheme

AbstractWe obtain, via the formalism of tensor actions, a complete classification of the localizing subcategories of the stable derived category of any affine scheme that has hypersurface singularities or is a complete intersection in a regular scheme; in particular, this classifies the thick subcategories of the singularity categories of such rings. The analogous result is also proved for certain locally complete intersection schemes. It is also shown that from each of these classifications one can deduce the (relative) telescope conjecture.

scholarly journals Complex manifolds with maximal torus actions

2019 ◽  
Vol 2019 (751) ◽  
pp. 121-184 ◽  
Author(s):  
Hiroaki Ishida
Keyword(s):  
Complete Classification ◽  
Vector Subspace ◽  
Toric Geometry ◽  
Complex Manifolds ◽  
Combinatorial Objects ◽  
Complex Dimension ◽  
Compact Torus ◽  
Equivalence Of Categories ◽  
Compact Tori

AbstractIn this paper, we introduce the notion of maximal actions of compact tori on smooth manifolds and study compact connected complex manifolds equipped with maximal actions of compact tori. We give a complete classification of such manifolds, in terms of combinatorial objects, which are triples {(\Delta,\mathfrak{h},G)} of nonsingular complete fan Δ in {\mathfrak{g}}, complex vector subspace {\mathfrak{h}} of {\mathfrak{g}^{\mathbb{C}}} and compact torus G satisfying certain conditions. We also give an equivalence of categories with suitable definitions of morphisms in these families, like toric geometry. We obtain several results as applications of our equivalence of categories; complex structures on moment-angle manifolds, classification of holomorphic nondegenerate {\mathbb{C}^{n}}-actions on compact connected complex manifolds of complex dimension n, and construction of concrete examples of non-Kähler manifolds.

scholarly journals Assessment and classification of chronic pruritis and its relation to systemic diseases

2021 ◽  
Author(s):  
Nawal Rajeh Alyamani ◽  
Noura Talal Almutairi ◽  
Riam Saleh Alkhamis ◽  
Rehab Bakr Brnawa ◽  
Samah Omar Badeghaish ◽  
...  
Keyword(s):  
Literature Review ◽  
Psychiatric Disorders ◽  
Skin Condition ◽  
Systemic Diseases ◽  
Etiological Diagnosis ◽  
Mild Conditions ◽  
Unpleasant Sensation ◽  
Proper Diagnosis ◽  
Adequate Management

Although pruritis might not be a serious condition with significant healthcare impacts, it is usually associated with an unpleasant sensation that leads to scratching the skin. It has been demonstrated that the severity of the condition is significantly variable and ranges between disabling and mild conditions. Chronic pruritis has been defined as the presence of daily itching for >6 months. In the present literature review, we have discussed the different approaches that have been previously indicated to assess and evaluate chronic pruritis, and the classification of the condition its relation to the different systemic diseases. The classification of chronic pruritis can be done using a clinical or an etiological diagnosis. The clinical diagnosis is usually based a primary skin condition, while the etiological diagnosis is based on the presence of different diseases that may be systematic, neurological, or psychiatric disorders. Accordingly, conducting a thorough examination is essential to establish a proper diagnosis before adequately managing the affected patients. Furthermore, the treatment of the underlying etiology should also be adequately considered for adequate management and enhanced prognosis.

scholarly journals MANY FINITE-DIMENSIONAL LIFTING BUNDLE GERBES ARE TORSION

2021 ◽  
pp. 1-16
Author(s):  
DAVID MICHAEL ROBERTS
Keyword(s):  
Analogous Result ◽  
Connected Components ◽  
Fibre Bundles ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Crossed Modules ◽  
Higher Gauge Theory ◽  
Bundle Gerbes ◽  
Simply Connected

Abstract Many bundle gerbes are either infinite-dimensional, or finite-dimensional but built using submersions that are far from being fibre bundles. Murray and Stevenson [‘A note on bundle gerbes and infinite-dimensionality’, J. Aust. Math. Soc.90(1) (2011), 81–92] proved that gerbes on simply-connected manifolds, built from finite-dimensional fibre bundles with connected fibres, always have a torsion $DD$ -class. I prove an analogous result for a wide class of gerbes built from principal bundles, relaxing the requirements on the fundamental group of the base and the connected components of the fibre, allowing both to be nontrivial. This has consequences for possible models for basic gerbes, the classification of crossed modules of finite-dimensional Lie groups, the coefficient Lie-2-algebras for higher gauge theory on principal 2-bundles and finite-dimensional twists of topological K-theory.

scholarly journals Flow equivalence of sofic shifts

2018 ◽  
Author(s):  
Mike Boyle ◽  
Toke Meier Carlsen ◽  
Søren Eilers
Keyword(s):  
Sofic Shifts ◽  
Flow Equivalence

Strong consistency of a kernel-based rule for spatially dependent data

2019 ◽  
Vol 26 (1/2) ◽  
pp. 211-225
Author(s):  
Ahmad Younso ◽  
Ziad Kanaya ◽  
Nour Azhari
Keyword(s):  
Strong Consistency ◽  
Dependent Data ◽  
Weak Consistency ◽  
Simulation Studies ◽  
Mild Conditions

We consider the kernel-based classifier proposed by Younso (2017). This nonparametric classifier allows for the classification of missing spatially dependent data. The weak consistency of the classifier has been studied by Younso (2017). The purpose of this paper is to establish strong consistency of this classifier under mild conditions. The classifier is discussed in a multi-class case. The results are illustrated with simulation studies and real applications.

scholarly journals Flow equivalence of sofic beta-shifts

2016 ◽  
Vol 37 (3) ◽  
pp. 786-801 ◽  
Author(s):  
RUNE JOHANSEN
Keyword(s):  
Finite Type ◽  
Classification Problem ◽  
Flow Classification ◽  
Fiber Product ◽  
Sofic Shifts ◽  
Flow Equivalence

The Fischer, Krieger, and fiber product covers of sofic beta-shifts are constructed and used to show that every strictly sofic beta-shift is 2-sofic. Flow invariants based on the covers are computed, and shown to depend only on a single integer that can easily be determined from the $\unicode[STIX]{x1D6FD}$-expansion of 1. It is shown that any beta-shift is flow equivalent to a beta-shift given by some $1<\unicode[STIX]{x1D6FD}<2$, and concrete constructions lead to further reductions of the flow classification problem. For each sofic beta-shift, there is an action of $\mathbb{Z}/2\mathbb{Z}$ on the edge shift given by the fiber product, and it is shown precisely when there exists a flow equivalence respecting these $\mathbb{Z}/2\mathbb{Z}$-actions. This opens a connection to ongoing efforts to classify general irreducible 2-sofic shifts via flow equivalences of reducible shifts of finite type (SFTs) equipped with $\mathbb{Z}/2\mathbb{Z}$-actions.

scholarly journals Flow equivalence of sofic shifts

2018 ◽  
Vol 225 (1) ◽  
pp. 111-146 ◽  
Author(s):  
Mike Boyle ◽  
Toke Meier Carlsen ◽  
Søren Eilers
Keyword(s):  
Sofic Shifts ◽  
Flow Equivalence
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