scholarly journals Higher Regularity, Inverse and Polyadic Semigroups

Universe ◽  
2021 ◽  
Vol 7 (10) ◽  
pp. 379
Author(s):  
Steven Duplij
Keyword(s):  
Invariance Principle ◽  
Inverse Semigroups ◽  
Regularity Conditions ◽  
The One ◽  
Higher Regularity

We generalize the regularity concept for semigroups in two ways simultaneously: to higher regularity and to higher arity. We show that the one-relational and multi-relational formulations of higher regularity do not coincide, and each element has several inverses. The higher idempotents are introduced, and their commutation leads to unique inverses in the multi-relational formulation, and then further to the higher inverse semigroups. For polyadic semigroups we introduce several types of higher regularity which satisfy the arity invariance principle as introduced: the expressions should not depend of the numerical arity values, which allows us to provide natural and correct binary limits. In the first definition no idempotents can be defined, analogously to the binary semigroups, and therefore the uniqueness of inverses can be governed by shifts. In the second definition called sandwich higher regularity, we are able to introduce the higher polyadic idempotents, but their commutation does not provide uniqueness of inverses, because of the middle terms in the higher polyadic regularity conditions. Finally, we introduce the sandwich higher polyadic regularity with generalized idempotents.

scholarly journals Embedding inverse semigroups of homeomorphisms on closed subsets

1977 ◽  
Vol 18 (2) ◽  
pp. 199-207 ◽  
Author(s):  
Bridget Bos Baird
Keyword(s):  
Topological Space ◽  
Inverse Semigroup ◽  
Inverse Semigroups ◽  
Topological Spaces ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Countable Space ◽  
The One ◽  
One Point Compactification ◽  
First Countable Space

All topological spaces here are assumed to be T2. The collection F(Y)of all homeomorphisms whose domains and ranges are closed subsets of a topological space Y is an inverse semigroup under the operation of composition. We are interested in the general problem of getting some information about the subsemigroups of F(Y) whenever Y is a compact metric space. Here, we specifically look at the problem of determining those spaces X with the property that F(X) is isomorphic to a subsemigroup of F(Y). The main result states that if X is any first countable space with an uncountable number of points, then the semigroup F(X) can be embedded into the semigroup F(Y) if and only if either X is compact and Y contains a copy of X, or X is noncompact and locally compact and Y contains a copy of the one-point compactification of X.

REPRESENTATIONS OF LOCALLY INVERSE *-SEMIGROUPS

1996 ◽  
Vol 06 (05) ◽  
pp. 541-551
Author(s):  
TERUO IMAOKA ◽  
ISAMU INATA ◽  
HIROAKI YOKOYAMA
Keyword(s):  
Inverse Semigroup ◽  
Wreath Product ◽  
Representation Theorem ◽  
Generalized Inverse ◽  
Inverse Semigroups ◽  
Locally Inverse Semigroup ◽  
The One ◽  
Locally Inverse Semigroups ◽  
Generalized Inverse Semigroups

The first author obtained a generalization of Preston-Vagner Representation Theorem for generalized inverse *-semigroups. In this paper, we shall generalize their results for locally inverse *-semigroups. Firstly, by introducing a concept of a π-set (which is slightly different from the one in [7]), we shall construct the π-symmetric locally inverse *-semigroup on a π-set, and show that any locally inverse *-semigroup can be embedded up to *-isomorphism in the π-symmetric locally inverse semigroup on a π-set. Moreover, we shall obtain that the wreath product of locally inverse *-semigroups is also a locally inverse *-semigroup.

scholarly journals On Bernstein–Kantorovich invariance principle in Hölder spaces and weighted scan statistics

2020 ◽  
Vol 24 ◽  
pp. 186-206
Author(s):  
Alfredas Račkauskas ◽  
Charles Suquet
Keyword(s):  
Asymptotic Behavior ◽  
Brownian Motion ◽  
Weak Convergence ◽  
Invariance Principle ◽  
Brownian Bridge ◽  
Polygonal Line ◽  
Scan Statistics ◽  
Partial Sums ◽  
Kantorovich Theorem ◽  
The One

Let ξn be the polygonal line partial sums process built on i.i.d. centered random variables Xi, i ≥ 1. The Bernstein-Kantorovich theorem states the equivalence between the finiteness of E|X1|max(2,r) and the joint weak convergence in C[0, 1] of n−1∕2ξn to a Brownian motion W with the moments convergence of E∥n−1/2ξn∥∞r to E∥W∥∞r. For 0 < α < 1∕2 and p (α) = (1 ∕ 2 - α) -1, we prove that the joint convergence in the separable Hölder space Hαo of n−1∕2ξn to W jointly with the one of E∥n−1∕2ξn∥αr to E∥W∥αr holds if and only if P(|X1| > t) = o(t−p(α)) when r < p(α) or E|X1|r < ∞ when r ≥ p(α). As an application we show that for every α < 1∕2, all the α-Hölderian moments of the polygonal uniform quantile process converge to the corresponding ones of a Brownian bridge. We also obtain the asymptotic behavior of the rth moments of some α-Hölderian weighted scan statistics where the natural border for α is 1∕2 − 1∕p when E|X1|p < ∞. In the case where the Xi’s are p regularly varying, we can complete these results for α > 1∕2 − 1∕p with an appropriate normalization.

scholarly journals On the accuracy of bootstrapping sample quantiles of strongly mixing sequences

2007 ◽  
Vol 82 (2) ◽  
pp. 263-282 ◽  
Author(s):  
Shuxia Sun
Keyword(s):  
Rate Of Convergence ◽  
Marginal Distribution ◽  
Regularity Conditions ◽  
One Dimensional ◽  
Strongly Mixing ◽  
Moving Block Bootstrap ◽  
Mixing Sequences ◽  
The One ◽  
Approximations To Distributions ◽  
Sample Quantiles

AbstractIn this paper, we examine the rate of convergence of moving block bootstrap (MBB) approximations to the distributions of normalized sample quantiles based on strongly mixing observations. Under suitable smoothness and regularity conditions on the one-dimensional marginal distribution function, the rate of convergence of the MBB approximations to distributions of centered and scaled sample quantiles is of order O(n−1¼ log logn).

scholarly journals Rates in almost sure invariance principle for slowly mixing dynamical systems

2019 ◽  
Vol 40 (9) ◽  
pp. 2317-2348 ◽  
Author(s):  
C. CUNY ◽  
J. DEDECKER ◽  
A. KOREPANOV ◽  
F. MERLEVÈDE
Keyword(s):  
Markov Chain ◽  
Dynamical Systems ◽  
Invariance Principle ◽  
Slowly Varying Function ◽  
Hölder Continuous ◽  
One Dimensional ◽  
Deterministic Dynamical Systems ◽  
Almost Sure Invariance Principle ◽  
The One ◽  
Dependent Processes

We prove the one-dimensional almost sure invariance principle with essentially optimal rates for slowly (polynomially) mixing deterministic dynamical systems, such as Pomeau–Manneville intermittent maps, with Hölder continuous observables. Our rates have form $o(n^{\unicode[STIX]{x1D6FE}}L(n))$, where $L(n)$ is a slowly varying function and $\unicode[STIX]{x1D6FE}$ is determined by the speed of mixing. We strongly improve previous results where the best available rates did not exceed $O(n^{1/4})$. To break the $O(n^{1/4})$ barrier, we represent the dynamics as a Young-tower-like Markov chain and adapt the methods of Berkes–Liu–Wu and Cuny–Dedecker–Merlevède on the Komlós–Major–Tusnády approximation for dependent processes.

Geometric product form queueing networks with concurrent batch movements

1998 ◽  
Vol 30 (04) ◽  
pp. 1111-1129 ◽  
Author(s):  
Hideaki Yamashita ◽  
Masakiyo Miyazawa
Keyword(s):  
Queueing Networks ◽  
Sufficient Conditions ◽  
Queueing Network ◽  
Product Form ◽  
Regularity Conditions ◽  
Geometric Product ◽  
Batch Sizes ◽  
Network States ◽  
The One ◽  
Necessary And Sufficient

Queueing networks have been rather restricted in order to have product form distributions for network states. Recently, several new models have appeared and enlarged this class of product form networks. In this paper, we consider another new type of queueing network with concurrent batch movements in terms of such product form results. A joint distribution of the requested batch sizes for departures and the batch sizes of the corresponding arrivals may be arbitrary. Under a certain modification of the network and mild regularity conditions, we give necessary and sufficient conditions for the network state to have the product form distribution, which is shown to provide an upper bound for the one in the original network. It is shown that two special settings satisfy these conditions. Algorithms to calculate their stationary distributions are considered, with numerical examples.

ON A GROUPOID CONSTRUCTION FOR ACTIONS OF CERTAIN INVERSE SEMIGROUPS

1994 ◽  
Vol 05 (03) ◽  
pp. 349-372 ◽  
Author(s):  
ALEXANDRU NICA
Keyword(s):  
Inverse Semigroup ◽  
Compact Space ◽  
Transformation Group ◽  
Algebraic Theory ◽  
Inverse Semigroups ◽  
Discrete Groups ◽  
Crossed Products ◽  
Locally Compact ◽  
Locally Compact Space ◽  
The One

We consider a version of the notion of F-inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid construction, very similar to the one of a transformation group. We discuss examples related to Toeplitz algebras on subsemigroups of discrete groups, to Cuntz-Krieger algebras, and to crossed-products by partial automorphisms in the sense of Exel.

Geometric product form queueing networks with concurrent batch movements

1998 ◽  
Vol 30 (4) ◽  
pp. 1111-1129 ◽  
Author(s):  
Hideaki Yamashita ◽  
Masakiyo Miyazawa
Keyword(s):  
Queueing Networks ◽  
Sufficient Conditions ◽  
Queueing Network ◽  
Product Form ◽  
Regularity Conditions ◽  
Geometric Product ◽  
Batch Sizes ◽  
Network States ◽  
The One ◽  
Necessary And Sufficient

Queueing networks have been rather restricted in order to have product form distributions for network states. Recently, several new models have appeared and enlarged this class of product form networks. In this paper, we consider another new type of queueing network with concurrent batch movements in terms of such product form results. A joint distribution of the requested batch sizes for departures and the batch sizes of the corresponding arrivals may be arbitrary. Under a certain modification of the network and mild regularity conditions, we give necessary and sufficient conditions for the network state to have the product form distribution, which is shown to provide an upper bound for the one in the original network. It is shown that two special settings satisfy these conditions. Algorithms to calculate their stationary distributions are considered, with numerical examples.

THE HOMOTOPY THEORY OF INVERSE SEMIGROUPS

2002 ◽  
Vol 12 (06) ◽  
pp. 755-790 ◽  
Author(s):  
MARK V. LAWSON ◽  
JOSEPH MATTHEWS ◽  
TIM PORTER
Keyword(s):  
Continuous Function ◽  
Inverse Semigroup ◽  
Homotopy Theory ◽  
Derived Category ◽  
Inverse Semigroups ◽  
Homotopy Equivalence ◽  
The One ◽  
Suitable Notion ◽  
Abstract Homotopy Theory

We show that abstract homotopy theory can be used to define a suitable notion of homotopy equivalence for inverse semigroups. As an application of our theory, we prove a theorem for inverse semigroup homomorphisms which is the exact counterpart of the well-known result in topology which states that every continuous function can be factorized into a homotopy equivalence followed by a fibration. We show that this factorization is isomorphic to the one constructed by Steinberg in his "Fibration Theorem", originally proved using a generalization of Tilson's derived category.

Note on Selection of Coordinate Systems for Geodynamics

1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen
Keyword(s):  
Sea Level ◽  
The Other ◽  
Coordinate Systems ◽  
Mean Sea Level ◽  
The Earth ◽  
The One ◽  
Static Systems ◽  
Selection Of

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.

Sign in / Sign up

Export Citation Format

Share Document