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Relevant bibliographies by topics / Subsets and equivalent sets

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Academic literature on the topic 'Subsets and equivalent sets'

Author: Grafiati

Published: 4 June 2021

Last updated: 9 February 2022

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Journal articles on the topic "Subsets and equivalent sets"

1

BENDIT, THEO. "CHEBYSHEV SUBSETS OF A HILBERT SPACE SPHERE." Journal of the Australian Mathematical Society 107, no. 3 (2019): 289–301. http://dx.doi.org/10.1017/s1446788719000508.

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The Chebyshev conjecture posits that Chebyshev subsets of a real Hilbert space $X$ are convex. Works by Asplund, Ficken and Klee have uncovered an equivalent formulation of the Chebyshev conjecture in terms of uniquely remotal subsets of $X$. In this tradition, we develop another equivalent formulation in terms of Chebyshev subsets of the unit sphere of $X\times \mathbb{R}$. We characterise such sets in terms of the image under stereographic projection. Such sets have superior structure to Chebyshev sets and uniquely remotal sets.

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Bell, John L. "Finite sets and frege structures." Journal of Symbolic Logic 64, no. 4 (1999): 1552–56. http://dx.doi.org/10.2307/2586795.

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Call a family of subsets of a set E inductive if and is closed under unions with disjoint singletons, that is, ifA Frege structure is a pair (E, ν) with ν a map to E whose domain dom(ν) is an inductive family of subsets of E such thatIn [2] it is shown in a constructive setting that each Frege structure determines a subset which is the domain of a model of Peano's axioms. In this note we establish, within the same constructive setting, three facts. First, we show that the least inductive family of subsets of a set E is precisely the family of decidable Kuratowski finite subsets of E. Secondly,

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Kuijpers, Bart, Jan Paredaens, and Jan Van den Bussche. "Topological elementary equivalence of closed semi-algebraic sets in the real plane." Journal of Symbolic Logic 65, no. 4 (2000): 1530–55. http://dx.doi.org/10.2307/2695063.

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AbstractWe investigate topological properties of subsets S of the real plane, expressed by first-order logic sentences in the language of the reals augmented with a binary relation symbol for S. Two sets are called topologically elementary equivalent if they have the same such first-order topological properties. The contribution of this paper is a natural and effective characterization of topological elementary equivalence of closed semi-algebraic sets.

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GARTSIDE, PAUL, and ANA MAMATELASHVILI. "THE TUKEY ORDER ON COMPACT SUBSETS OF SEPARABLE METRIC SPACES." Journal of Symbolic Logic 81, no. 1 (2016): 181–200. http://dx.doi.org/10.1017/jsl.2015.49.

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AbstractOne partially ordered set, Q, is a Tukey quotient of another, P, if there is a map (a Tukey quotient) $\phi :P \to Q$ carrying cofinal sets of P to cofinal sets of Q. Two partial orders which are mutual Tukey quotients of each other are said to be Tukey equivalent. Let ${\cal D}_{\rm{&#xF01C;}} $ be the partially ordered set of Tukey equivalence classes of directed sets of size $ \le {\rm{&#xF01C;}}$. It is shown that ${\cal D}_{\rm{&#xF01C;}} $ contains an antichain of size $2^{\rm{&#xF01C;}} $, and so has size $2^{\rm{&#xF01C;}} $. The elements of the antichain ar

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KRAMER, OLIVER, and HOLGER DANIELSIEK. "A CLUSTERING-BASED NICHING FRAMEWORK FOR THE APPROXIMATION OF EQUIVALENT PARETO-SUBSETS." International Journal of Computational Intelligence and Applications 10, no. 03 (2011): 295–311. http://dx.doi.org/10.1142/s1469026811003112.

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In many optimization problems in practice, multiple objectives have to be optimized at the same time. Some multi-objective problems are characterized by multiple connected Pareto-sets at different parts in decision space — also called equivalent Pareto-subsets. We assume that the practitioner wants to approximate all Pareto-subsets to be able to choose among various solutions with different characteristics. In this work, we propose a clustering-based niching framework for multi-objective population-based approaches that allows to approximate equivalent Pareto-subsets. Iteratively, the clusteri

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Llorente, Marta, and Pertti Mattila. "Lipschitz equivalence of subsets of self-conformal sets." Nonlinearity 23, no. 4 (2010): 875–82. http://dx.doi.org/10.1088/0951-7715/23/4/006.

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Canfield, Rodney, Ron Fertig, Daniel Mauldin, and David Moews. "The motif problem: Geometric representations of sets of equivalence relations." Applicable Analysis and Discrete Mathematics 8, no. 1 (2014): 95–110. http://dx.doi.org/10.2298/aadm140126001c.

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A motif is a sequence of L points in Rp satisfying certain equality conditions between specified coordinates, which are described by a motif specification. In this sense a motif is a geometric representation of p equivalence relations on subsets of f1,...., Lg. The main problem considered here is to count the number of motifs that can be made using points from a given r-element subset of Rp. Our principal results are as follows: The number of motifs is bounded above by r?*(H), where ?*(H) is an invariant called the fractional transversal number of a hypergraph, H, which is determined by the mo

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CARLUCCI, LORENZO, and KONRAD ZDANOWSKI. "THE STRENGTH OF RAMSEY’S THEOREM FOR COLORING RELATIVELY LARGE SETS." Journal of Symbolic Logic 79, no. 01 (2014): 89–102. http://dx.doi.org/10.1017/jsl.2013.27.

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Abstract We characterize the effective content and the proof-theoretic strength of a Ramsey-type theorem for bi-colorings of so-called exactly large sets. An exactly large set is a set $X \subset {\bf{N}}$ such that ${\rm{card}}\left( X \right) = {\rm{min}}\left( X \right) + 1$ . The theorem we analyze is as follows. For every infinite subset M of N, for every coloring C of the exactly large subsets of M in two colors, there exists and infinite subset L of M such that C is constant on all exactly large subsets of L. This theorem is essentially due to Pudlák and Rödl and independently to Farmak

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Huang, Huan, and Congxin Wu. "A New Characterization of Compact Sets in Fuzzy Number Spaces." Abstract and Applied Analysis 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/820141.

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We give a new characterization of compact subsets of the fuzzy number space equipped with the level convergence topology. Based on this, it is shown that compactness is equivalent to sequential compactness on the fuzzy number space endowed with the level convergence topology. Our results imply that some previous compactness criteria are wrong. A counterexample also is given to validate this judgment.

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Beer, Gerald. "More on Convergence of Continuous Functions and Topological Convergence of Sets." Canadian Mathematical Bulletin 28, no. 1 (1985): 52–59. http://dx.doi.org/10.4153/cmb-1985-004-9.

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AbstractLet C(X, Y) denote the set of continuous functions from a metric space X to a metric space Y. Viewing elements of C(X, Y) as closed subsets of X × Y, we say {fn} converges topologically to f if Li fn = Lsfn = f. If X is connected, then topological convergence in C(X,R) does not imply pointwise convergence, but if X is locally connected and Y is locally compact, then topological convergence in C(X, Y) is equivalent to uniform convergence on compact subsets of X. Pathological aspects of topological convergence for seemingly nice spaces are also presented, along with a positive Baire cate

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Dissertations / Theses on the topic "Subsets and equivalent sets"

1

Ngcibi, Sakhile L. "Case studies of equivalent fuzzy subgroups of finite abelian groups." Thesis, Rhodes University, 2002. http://hdl.handle.net/10962/d1005215.

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The broad goal is to classify all fuzzy subgroups of a given type of finite group. P.S. Das introduced the ntion of level subgroups to characterize fuzzy subgroups of finite grouops. The notion of equivalence of fuzzy subgroups which is used in this thesis was first introduced by Murali and Makamba. We use this equivalence to charterise fuzzy subgroups of inite Abelian groups (p-groups in particular) for a specified prime p. We characterize some crisp subgroups of p-groups and investigate some cases on equi valent fuzzy subgroups.

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Bozeman, Alan Kyle. "Weakly Dense Subsets of Homogeneous Complete Boolean Algebras." Thesis, University of North Texas, 1990. https://digital.library.unt.edu/ark:/67531/metadc330803/.

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The primary result from this dissertation is following inequality: d(B) ≤ min(2^< wd(B),sup{λ^c(B): λ < wd(B)}) in ZFC, where B is a homogeneous complete Boolean algebra, d(B) is the density, wd(B) is the weak density, and c(B) is the cellularity of B. Chapter II of this dissertation is a general overview of homogeneous complete Boolean algebras. Assuming the existence of a weakly inaccessible cardinal, we give an example of a homogeneous complete Boolean algebra which does not attain its cellularity. In chapter III, we prove that for any integer n > 1, wd_2(B) = wd_n(B). Also in this chapt

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Carnovale, Marc. "Arithmetic Structures in Small Subsets of Euclidean Space." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1555657038785892.

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Allen, Cristian Gerardo. "A Classification of the Homogeneity of Countable Products of Subsets of Real Numbers." Thesis, University of North Texas, 2017. https://digital.library.unt.edu/ark:/67531/metadc1011753/.

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Spaces such as the closed interval [0, 1] do not have the property of being homogeneous, strongly locally homogeneous (SLH) or countable dense homogeneous (CDH), but the Hilbert cube has all three properties. We investigate subsets X of real numbers to determine when their countable product is homogeneous, SLH, or CDH. We give necessary and sufficient conditions for the product to be homogeneous. We also prove that the product is SLH if and only if X is zero-dimensional or an interval. And finally we show that for a Borel subset X of real numbers the product is CDH iff X is a G-delta zero-d

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Talwanga, Matiki. "Counting of finite fuzzy subsets with applications to fuzzy recognition and selection strategies." Thesis, Rhodes University, 2015. http://hdl.handle.net/10962/d1018186.

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The counting of fuzzy subsets of a finite set is of great interest in both practical and theoretical contexts in Mathematics. We have used some counting techniques such as the principle of Inclusion-Exclusion and the Mõbius Inversion to enumerate the fuzzy subsets of a finite set satisfying different conditions. These two techniques are interdependent with the M¨obius inversion generalizing the principle of Inclusion-Exclusion. The enumeration is carried out each time we redefine new conditions on the set. In this study one of our aims is the recognition and identification of fuzzy subsets wit

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Talwanga, Matiki. "The principle of inclusion-exclusion and möbius function as counting techniques in finite fuzzy subsets." Thesis, Rhodes University, 2009. http://hdl.handle.net/10962/d1005227.

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The broad goal in this thesis is to enumerate elements and fuzzy subsets of a finite set enjoying some useful properties through the well-known counting technique of the principle of inclusion-exclusion. We consider the set of membership values to be finite and uniformly spaced in the real unit interval. Further we define an equivalence relation with regards to the cardinalities of fuzzy subsets providing the Möbius function and Möbius inversion in that context.

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Crampton, Raymond J. "A nonlinear statistical MESFET model using low order statistics of equivalent circuit model parameter sets." Thesis, This resource online, 1995. http://scholar.lib.vt.edu/theses/available/etd-03032009-040420/.

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Anderson, Alastair Andrew 1956. "The representation of personal constructs as fuzzy subsets : developing a model and testing its efficacy." Monash University, Dept. of Management, 1999. http://arrow.monash.edu.au/hdl/1959.1/8592.

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Brian, William R. "Topics in general and set-theoretic topology : slice sets, rigid subsets of the reals, Toronto spaces, cleavability, and 'neight'." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:d80b6234-91e4-4c80-8696-a6de7aabc985.

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I explore five topics in topology using set-theoretic techniques. The first of these is a generalization of 2-point sets called slice sets. I show that, for any small-in-cardinality subset A of the real line, there is a subset of the plane meeting every line in a topological copy of A. Under Martin's Axiom, I show how to improve this result to any totally disconnected A. Secondly, I show that it is consistent with and independent of ZFC to have a topologically rigid subset of the real line that is smaller than the continuum. Thirdly, I define and examine a new cardinal function related to clea

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Ngcibi, Sakhile Leonard. "Studies of equivalent fuzzy subgroups of finite abelian p-Groups of rank two and their subgroup lattices." Thesis, Rhodes University, 2006. http://hdl.handle.net/10962/d1005230.

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We determine the number and nature of distinct equivalence classes of fuzzy subgroups of finite Abelian p-group G of rank two under a natural equivalence relation on fuzzy subgroups. Our discussions embrace the necessary theory from groups with special emphasis on finite p-groups as a step towards the classification of crisp subgroups as well as maximal chains of subgroups. Unique naming of subgroup generators as discussed in this work facilitates counting of subgroups and chains of subgroups from subgroup lattices of the groups. We cover aspects of fuzzy theory including fuzzy (homo-) isomorp

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Books on the topic "Subsets and equivalent sets"

1

On sets not belonging to algebras of subsets. American Mathematical Society, 1992.

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Filters and ultrafilters over definable subsets of admissible ordinals. Centrum voor Wiskunde en Informatica, 1986.

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Hrushovski, Ehud, and François Loeser. An equivalence of categories. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0013.

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This chapter deduces from Theorem 11.1.1 an equivalence of categories between a certain homotopy category of definable subsets of quasi-projective varieties over a given valued field and a suitable homotopy category of definable spaces over the o-minimal Γ‎. The chapter introduces three categories that can be viewed as ind-pro definable and admit natural functors to the category TOP of topological spaces with continuous maps. The discussion is often limited to the subcategory consisting of A-definable objects and morphisms. The morphisms are factored out by (strong) homotopy equivalence. The c

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Hrushovski, Ehud, and François Loeser. Applications to the topology of Berkovich spaces. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0014.

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This chapter presents various applications to the topology of classical Berkovich spaces. It deduces from the main theorem several new results on the topology of V(superscript an) which were not known previously in such a level of generality. In particular, it shows that V(superscript an) admits a strong deformation retraction to a subspace homeomorphic to a finite simplicial complex and that V(superscript an) is locally contractible. The chapter also proves the existence of strong retractions to skeleta for analytifications of definable subsets of quasi-projective varieties and goes on to pro

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Ernest, Rodabaugh Stephen, Klement E. P, Höhle Ulrich, and International Seminar on Fuzzy Set Theory (11th : 1989 : Linz, Austria), eds. Applications of category theory to fuzzy subsets. Kluwer Academic Publishers, 1992.

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Green, Dale E. Existence of smalll zero-sum subsets of large sets of residue classes. 1989.

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Green, Dale E. Existence of smalll zero-sum subsets of large sets of residue classes. 1989.

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(Editor), S. E. Rodabaugh, E. P. Klement (Editor), and Ulrich Höhle (Editor), eds. Applications of Category Theory to Fuzzy Subsets (Theory and Decision Library B). Springer, 1991.

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Hrushovski, Ehud, and François Loeser. Definable compactness. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0004.

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This chapter describes the notion of definable compactness for subsets of unit vector V. One of the main results is Theorem 4.2.20, which establishes the equivalence between being definably compact and being closed and bounded. The chapter gives a general definition of definable compactness that may be useful when the definable topology has enough definable types. The o-minimal formulation regarding limits of curves is replaced by limits of definable types. The chapter relates definable compactness to being closed and bounded and shows that the expected properties hold. In particular, the imag

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Hrushovski, Ehud, and François Loeser. Strongly stably dominated points. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161686.003.0008.

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This chapter focuses on the properties of strongly stably dominated types over valued fields bases. In this setting, strong stability corresponds to a strong form of the Abhyankar property for valuations: the transcendence degrees of the extension coincide with those of the residue field extension. The chapter proves a Bertini type result and shows that the strongly stable points form a strict ind-definable subset Vsuperscript Number Sign of unit vector V. It then proves a rigidity statement for iso-definable Γ‎-internal subsets of maximal o-minimal dimension of unit vector V, namely that they

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Book chapters on the topic "Subsets and equivalent sets"

1

Huggett, Stephen, and David Jordan. "Equivalent Subsets." In A Topological Aperitif. Springer London, 2001. http://dx.doi.org/10.1007/978-1-4471-3694-1_3.

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Huggett, Stephen, and David Jordan. "Equivalent Subsets." In A Topological Aperitif. Springer London, 2008. http://dx.doi.org/10.1007/978-1-84800-913-4_3.

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Daepp, Ulrich, and Pamela Gorkin. "Equivalent Sets." In Reading, Writing, and Proving. Springer New York, 2011. http://dx.doi.org/10.1007/978-1-4419-9479-0_21.

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Żytkow, Jan M., and Robert Zembowicz. "Theories that Combine Many Equivalence and Subset Relations." In Rough Sets and Data Mining. Springer US, 1997. http://dx.doi.org/10.1007/978-1-4613-1461-5_16.

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Jones, A. "Fuzzy Subsets in Didactic Processes." In Fuzzy Sets Theory and Applications. Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4682-8_17.

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Mulvey, C. J., and M. Nawaz. "Quantales: Quantal sets." In Non-Classical Logics and their Applications to Fuzzy Subsets. Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0215-5_8.

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Kaufmann, A. "Fuzzy Subsets Applications in O.R. and Management." In Fuzzy Sets Theory and Applications. Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4682-8_13.

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Liu, Guilong, and James Kuodo Huang. "An Equivalent Definition of Rough Sets." In Rough Sets and Current Trends in Computing. Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-88425-5_6.

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Demyanov, V. F., and A. E. Aban’kin. "Conically Equivalent Pairs Of Convex Sets." In Lecture Notes in Economics and Mathematical Systems. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-59073-3_2.

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Kaufmann, A. "Hybrid Data – Various Associations Between Fuzzy Subsets and Random Variables." In Fuzzy Sets Theory and Applications. Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4682-8_10.

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Conference papers on the topic "Subsets and equivalent sets"

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Bohigas, Oriol, Dimiter Zlatanov, Montserrat Manubens, and Lluís Ros. "On the Numerical Classification of the Singularities of Robot Manipulators." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70921.

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This paper is concerned with the task to obtain a complete description of the singularity set of any given non-redundant manipulator, including the identification and the precise computation of each constituent singularity class. Configurations belonging to the same class are equivalent in terms of the various types of kinematic and static degeneracy that characterize mechanism singularity. The proposed approach is an extension of recent work on computing singularities using a numerical method based on linear relaxations. Classification is sought by means of a hierarchy of singularity tests, e

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Freeman, Dane, Dongwook Lim, Elena Garcia, and Dimitri Mavris. "Identification of Product Family Platforms Using Pattern Recognition." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-47472.

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In product family design the goal is to generate a set of lowest cost products that target specific market niches. Sharing components, called platforms, between different products can minimize duplication of effort, thereby lowering family costs. However, if the products’ requirements are too dissimilar, sharing components may compromise the end product; such variance will lead to lower end products being overdesigned and/or higher end products being underdesigned. It is important to identify which components are similar enough, so that sharing does not compromise the individual products’ perf

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Reingold, Omer, Luca Trevisan, Madhur Tulsiani, and Salil Vadhan. "Dense Subsets of Pseudorandom Sets." In 2008 IEEE 49th Annual IEEE Symposium on Foundations of Computer Science (FOCS). IEEE, 2008. http://dx.doi.org/10.1109/focs.2008.38.

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Mendelzon, Alberto O., and Ken Q. Pu. "Concise descriptions of subsets of structured sets." In the twenty-second ACM SIGMOD-SIGACT-SIGART symposium. ACM Press, 2003. http://dx.doi.org/10.1145/773153.773166.

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Kochdumper, Niklas, Bastian Schürmann, and Matthias Althoff. "Utilizing dependencies to obtain subsets of reachable sets." In HSCC '20: 23rd ACM International Conference on Hybrid Systems: Computation and Control. ACM, 2020. http://dx.doi.org/10.1145/3365365.3382192.

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Fan, Mingyu, Xiaojun Chang, Xiaoqin Zhang, Di Wang, and Liang Du. "Top-k Supervise Feature Selection via ADMM for Integer Programming." In Twenty-Sixth International Joint Conference on Artificial Intelligence. International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/228.

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Recently, structured sparsity inducing based feature selection has become a hot topic in machine learning and pattern recognition. Most of the sparsity inducing feature selection methods are designed to rank all features by certain criterion and then select the k top ranked features, where k is an integer. However, the k top features are usually not the top k features and therefore maybe a suboptimal result. In this paper, we propose a novel supervised feature selection method to directly identify the top k features. The new method is formulated as a classic regularized least squares regressio

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Terra-Neves, Miguel, Inês Lynce, and Vasco Manquinho. "Multi-Objective Optimization Through Pareto Minimal Correction Subsets." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/757.

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A Minimal Correction Subset (MCS) of an unsatisfiable constraint set is a minimal subset of constraints that, if removed, makes the constraint set satisfiable. MCSs enjoy a wide range of applications, such as finding approximate solutions to constrained optimization problems. However, existing work on applying MCS enumeration to optimization problems focuses on the single-objective case. In this work, Pareto Minimal Correction Subsets (Pareto-MCSs) are proposed for approximating the Pareto-optimal solution set of multi-objective constrained optimization problems. We formalize and prove an equi

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Kramer, Oliver, and Holger Danielsiek. "DBSCAN-based multi-objective niching to approximate equivalent pareto-subsets." In the 12th annual conference. ACM Press, 2010. http://dx.doi.org/10.1145/1830483.1830575.

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Tian, Chao. "Inequalities for entropies of sets of subsets of random variables." In 2011 IEEE International Symposium on Information Theory - ISIT. IEEE, 2011. http://dx.doi.org/10.1109/isit.2011.6033893.

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Fan, Nianbai, Gongzhu Hu, and Hui Liu. "Study of definable subsets in covering approximation spaces of rough sets." In Integration (IRI). IEEE, 2011. http://dx.doi.org/10.1109/iri.2011.6009514.

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Reports on the topic "Subsets and equivalent sets"

1

Haubrich, Julia, Sarah Benz, Ullrich Isermann, et al. Leq+X - Lärmexposition, Ereignishäufigkeiten und Belästigung: Re-Analyse von Daten zur Belästigung und Schlafstörung durch Fluglärm an deutschen und Schweizer Flughäfen. Universitätsbibliothek der Ruhr-Universität Bochum, 2020. http://dx.doi.org/10.46586/rub.164.139.

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In this study, part of the data sets from 4 large Swiss and German aircraft noise impact studies are re-analysed using logistic multi-level regression models. The aim is to investigate the assumptions that the prediction of a) the percentage of persons highly annoyed by aircraft noise or b) the percentage of persons highly sleep disturbed by aircraft noise can be improved if (i) instead of the energy-equivalent continuous noise level alone, either additional or alternative, more frequency-based aircraft noise metrics and (ii) also airport-specific characteristics are used as predictors. The re

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