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

Khalil Ghorbal, Andrew Sogokon
2021 arXiv   pre-print
We present two 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] .  ... 
arXiv:2009.09797v2 fatcat:pm47nhta4fhs5o3yq74z2zcgfi

The Maximal Positively Invariant Set: Polynomial Setting [article]

Saša V. Raković, Mario E. Villanueva
2017 arXiv   pre-print
This note considers the maximal 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.  ... 
arXiv:1712.01150v1 fatcat:xvwiedbx35ffzbwmeehhb3onna

Sampling sets and sufficient sets for A−∞

José Bonet, Paweł Domański
2003 Journal of Mathematical Analysis and Applications  
A 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.  ... 
doi:10.1016/s0022-247x(02)00616-9 fatcat:hpva3lbyknb5jgr3xj3ntlqo34

Uncountable Graphs and Invariant Measures on the Set of Universal Countable Graphs [article]

F.V.Petrov, A.M.Vershik
2009 arXiv   pre-print
We give new examples 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.  ... 
arXiv:0804.3386v3 fatcat:tfchefjsh5cozd4ifbv5gkhuby

Extension sets

A. D. Wallace
1946 Transactions of the American Mathematical Society  
Borsuk [12] containing concepts 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]).  ... 
doi:10.1090/s0002-9947-1946-0014809-1 fatcat:oujwyr7sevho5cfnq5dqw3fgca

Dynamical characterization of C-sets and its application

Jian Li
2012 Fundamenta Mathematicae  
In particular, we obtain a dynamical 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.  ... 
doi:10.4064/fm216-3-4 fatcat:v6raag7hljh6jncz75hwlq4xfi

Set Theoretic Real Analysis

K. Ciesielski
1997 Journal of Applied Analysis  
This article is a survey of the recent results that concern real functions (from R n into R) 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.  ... 
doi:10.1515/jaa.1997.143 fatcat:7t3su4wjcvhrznv32scn4xekji

Polish group actions and admissible sets [article]

B. Majcher-Iwanow
2008 arXiv   pre-print
In particular we obtain counterparts of Nadel's theorems about relationships between Scott sentences 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  ... 
arXiv:math/0701788v2 fatcat:mx5x5cqmvjbtbda4ua44c4lbii

Random selection of Borel sets

Bernd Günther
2013 Applied General Topology  
A theory of random Borel 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  ... 
doi:10.4995/agt.2010.1713 fatcat:jin5kbdovrbajgtlc2uujbyfgi

On a Method of Solving Some Functional Equations for Set-Valued Functions

Justyna Sikorska
2017 Set-Valued and Variational Analysis  
In the first part of the paper we collect 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.  ... 
doi:10.1007/s11228-017-0465-0 fatcat:e4yaamdqr5cnhmjpb2ynrny7v4

Attainable sets and one-parameter semigroups of sets

I. Chon, J. D. Lawson
1991 Glasgow Mathematical Journal  
This is possible since the mapping X>->X(e) is a one-to-one correspondence between the 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.  ... 
doi:10.1017/s0017089500008223 fatcat:xo4gquyjt5hffn4g372tk37klu

Mixing sets for non-mixing transformations [article]

Terrence M. Adams
2016 arXiv   pre-print
Lightly mixing is a stronger property than 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.  ... 
arXiv:1604.01090v1 fatcat:ctetjoilvjbd7hq2vu52a6wq7u

On forbidden sets [article]

Francisco Balibrea, Antonio Cascales
2015 arXiv   pre-print
We review 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.  ... 
arXiv:1505.07043v1 fatcat:47wswvhtpfabrel64y5orjnzga

Information-Geometric Set Embeddings (IGSE): From Sets to Probability Distributions [article]

Ke Sun, Frank Nielsen
2019 arXiv   pre-print
We relate 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.  ... 
arXiv:1911.12463v2 fatcat:o4e6zdm6gzhovezy5o6twiikgq

Proof-Set Search [chapter]

Martin Müller
2003 Lecture Notes in Computer Science  
Proof-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.  ... 
doi:10.1007/978-3-540-40031-8_7 fatcat:styax22dgzhf3ks32pjbk5me7q
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