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Characterizing Positively Invariant Sets: Inductive and Topological Methods
[article]

2021
*
arXiv
*
pre-print

We present two

arXiv:2009.09797v2
fatcat:pm47nhta4fhs5o3yq74z2zcgfi
*characterizations*of*positive**invariance*of*sets*under the flow of systems of ordinary differential equations. ...*set*is*positively**invariant*under the flow of a system of polynomial ordinary differential equations. ... unaware); his formal development of an*invariant*checking procedure in differential dynamic logic appeared in [Platzer*and*Tan, 2018]*and*[Platzer*and*Tan, 2020] . ...##
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The Maximal Positively Invariant Set: Polynomial Setting
[article]

2017
*
arXiv
*
pre-print

This note considers the maximal

arXiv:1712.01150v1
fatcat:xvwiedbx35ffzbwmeehhb3onna
*positively**invariant**set*for polynomial discrete time dynamics subject to constraints specified by a basic semialgebraic*set*. ... The finite time convergence of the corresponding maximal trajectory to the maximal*positively**invariant**set*is verified under reasonably mild conditions. ... Acknowledgements The authors would like to thank the Texas A&M Energy Institute,*and*in particular Prof. Efstratios N. Pistikopoulos for providing financial support. ...##
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Sampling sets and sufficient sets for A−∞

2003
*
Journal of Mathematical Analysis and Applications
*

A

doi:10.1016/s0022-247x(02)00616-9
fatcat:hpva3lbyknb5jgr3xj3ntlqo34
*characterization*of (p, q)-sampling*and*weakly sufficient rotation*invariant**sets*is included. It permits us to obtain new examples*and*to solve an open question of Khôi*and*Thomas. ... We give new*characterizations*of the subsets S of the unit disc D of the complex plane such that the*topology*of the space A −∞ of holomorphic functions of polynomial growth on D coincides with the*topology*... His/her suggestions improved both the presentation*and*the mathematics of the paper. ...##
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Uncountable Graphs and Invariant Measures on the Set of Universal Countable Graphs
[article]

2009
*
arXiv
*
pre-print

We give new examples

arXiv:0804.3386v3
fatcat:tfchefjsh5cozd4ifbv5gkhuby
*and*describe the complete lists of all measures on the*set*of countable homogeneous universal graphs*and*K_s-free homogeneous universal graphs (for s≥ 3) that are*invariant*with respect ... The main idea of our construction is based on the new notions of measurable universal,*and**topologically*universal graphs, which are interesting themselves. ... The construction of the*set*Z is*inductive**and*based on the enumeration of arrays of points from Q. We will use the simplest*method*of enumeration suitable both for ordinary*and*triangle-free graphs. ...##
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Extension sets

1946
*
Transactions of the American Mathematical Society
*

Borsuk [12] containing concepts

doi:10.1090/s0002-9947-1946-0014809-1
fatcat:oujwyr7sevho5cfnq5dqw3fgca
*and*results which are related to ideas*and*theorems formulated here. ... References to their papers will be found in [7]*and*[9]. References should also be made to papers by J. Rozanska [ó]*and*C. ... tension*set*is a*topological**invariant*of H*and*that any point of H is an extension*set*. Many of our results are generalizations of well known results of G. T. Whyburn*and*W. L. Ayres (see [9]). ...##
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Dynamical characterization of C-sets and its application

2012
*
Fundamenta Mathematicae
*

In particular, we obtain a dynamical

doi:10.4064/fm216-3-4
fatcat:v6raag7hljh6jncz75hwlq4xfi
*characterization*of C-*sets*, where C-*sets*are the*sets*satisfying the strong Central*Sets*Theorem. ... In this paper, we*set*up a general correspondence between the algebra properties of*and*the*sets*defined by dynamical properties. ... In [14, 12] Furstenberg*and*Weiss found a new way to prove those theorems by*topological*dynamics*methods*. ...##
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Set Theoretic Real Analysis

1997
*
Journal of Applied Analysis
*

This article is a survey of the recent results that concern real functions (from R n into R)

doi:10.1515/jaa.1997.143
fatcat:7t3su4wjcvhrznv32scn4xekji
*and*whose solutions or statements involve the use of*set*theory. ... The choice of the topics follows the author's personal interest in the subject,*and*there are probably some important results in this area that did not make it to this survey. ... However, they can neither be*topologized*nor be*characterized*by associated*sets*. ...##
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Polish group actions and admissible sets
[article]

2008
*
arXiv
*
pre-print

In particular we obtain counterparts of Nadel's theorems about relationships between Scott sentences

arXiv:math/0701788v2
fatcat:mx5x5cqmvjbtbda4ua44c4lbii
*and*admissible*sets*. ... We define some coding of Borel*sets*in admissible*sets*. ... We also give a generalization of another model theoretical result -we*characterize*in admissible*sets*orbits that are pieces of the canonical partition with respect to some 'finer'*topology*(nice*topology*...##
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Random selection of Borel sets

2013
*
Applied General Topology
*

A theory of random Borel

doi:10.4995/agt.2010.1713
fatcat:jin5kbdovrbajgtlc2uujbyfgi
*sets*is presented, based on dyadic resolutions of compact metric spaces. The conditional expectation of the intersection of two independent random Borel*sets*is investigated. ... An example based on an embedding of Sierpiński's universal curve into the space of Borel*sets*is given. 2000 ... We can now construct the measures ν n*inductively*subject to the conditions above, starting with an arbitrary measure ν 0 on the unit segment. ν n+1 can be chosen G n+1 -*invariant*if ν n is G n -*invariant*...##
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On a Method of Solving Some Functional Equations for Set-Valued Functions

2017
*
Set-Valued and Variational Analysis
*

In the first part of the paper we collect

doi:10.1007/s11228-017-0465-0
fatcat:e4yaamdqr5cnhmjpb2ynrny7v4
*and*prove several properties of the Hausdorff metric*and*the Hukuhara difference. ... They are applied in the next part where a tool for solving several equations for*set*-valued functions is described. ... Acknowledgments The author is grateful to the Editor*and*the reviewers for their valuable comments*and*remarks which helped to improve the final version of the paper. ...##
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Attainable sets and one-parameter semigroups of sets

1991
*
Glasgow Mathematical Journal
*

This is possible since the mapping X>->X(e) is a one-to-one correspondence between the

doi:10.1017/s0017089500008223
fatcat:xo4gquyjt5hffn4g372tk37klu
*set*of right*invariant*vector fields*and*T e (G). Let Q be a subset of q. ... Normally we identify g with the*set*of right*invariant*vectors fields on G. ... The*set*L(S) is a wedge, a closed convex*set*closed under addition*and*multiplication by*positive*scalars. ...##
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Mixing sets for non-mixing transformations
[article]

2016
*
arXiv
*
pre-print

Lightly mixing is a stronger property than

arXiv:1604.01090v1
fatcat:ctetjoilvjbd7hq2vu52a6wq7u
*topological*mixing,*and*requires that a lim inf is*positive*. ... Also, we provide a hierarchy for the properties of lightly mixing, sweeping out*and*uniform sweeping out for dense collections,*and*dense algebras of*sets*. ... In particular,*topological*mixing is not an isomorphism*invariant*. Yet, the properties LMDC, LMDA, SODC*and*SODA are all isomorphic*invariants*. ...##
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On forbidden sets
[article]

2015
*
arXiv
*
pre-print

We review

arXiv:1505.07043v1
fatcat:47wswvhtpfabrel64y5orjnzga
*and*complete different attempts to describe the forbidden*set**and*propose new perspectives for further research*and*a list of open problems in this field. ... In recent literature there are an increasing number of papers where the forbidden*sets*of difference equations are computed. ... We thank the anonymous referees for their suggestions*and*comments. ...##
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Information-Geometric Set Embeddings (IGSE): From Sets to Probability Distributions
[article]

2019
*
arXiv
*
pre-print

We relate

arXiv:1911.12463v2
fatcat:o4e6zdm6gzhovezy5o6twiikgq
*set*union*and*intersection operations with corresponding interpolations of probability distributions. ... This letter introduces an abstract learning problem called the "*set*embedding": The objective is to map*sets*into probability distributions so as to lose less information. ... These interpolating*methods*correspond to two basic*set*operations: the union*and*the intersection. ...##
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Proof-Set Search
[chapter]

2003
*
Lecture Notes in Computer Science
*

Proof-

doi:10.1007/978-3-540-40031-8_7
fatcat:styax22dgzhf3ks32pjbk5me7q
*set*search (PSS) is a new search*method*which uses a similar value propagation scheme as proof-number search, but backs up proof*and*disproof*sets*instead of numbers. ... Both proof-number search*and*proof-*set*search are shown to be special cases of È ËË È . ... Section 2 describes the new*method*of proof-*set*search,*and**characterizes*it by a theorem establishing its dominance over PNS on the same DAG. ...
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