Joseph P. S. Kung, Gian‐Carlo Rota,
Tópico(s): Homotopy and Cohomology
1979 - Elsevier BV | Advances in Mathematics
Mary Ellen Rudin, Lynn Arthur Steen, J. Arthur Seebach,
Tópico(s): Constraint Satisfaction and Optimization
1971 - Taylor & Francis | American Mathematical Monthly
... dim X > 0 . The space X is a counterexample to several conjectures in Topology.
Tópico(s): Nonlinear Differential Equations Analysis
1980 - American Mathematical Society | Proceedings of the American Mathematical Society
We construct a counterexamples in dimensions $n>3$ to Gromov's conjecture \cite{Gr1} that the macroscopic dimension of rationally essential $n$-dimensional manifolds equals $n$.
Tópico(s): Geometry and complex manifolds
2011 - Mathematical Sciences Publishers | Geometry & Topology
Carlos J.S. Alves, Pedro R. S. Antunes,
In this work we address the application of the method of fundamental solution (MFS) as a forward solver in some shape optimization problems in two- and three-dimensional domains. It is well known (Kac's problem) that a set of eigenvalues does not determine uniquely the shape of the domain. Moreover, even the existence problem is not well defined due to the Ashbaugh--Benguria inequality. Although these results constitute counterexamples in the general problem of shape determination from the eigenfrequencies, ...
Tópico(s): Numerical methods
2013 - Society for Industrial and Applied Mathematics | SIAM Journal on Scientific Computing
Counterexamples are given to a conjecture communicated to me by I. Dolgachev and E. Looijenga of M. Gizatullin that every rational surface with an infinite automorphism group should have an antipluricanonical curve.
Tópico(s): Homotopy and Cohomology
1987 - American Mathematical Society | Proceedings of the American Mathematical Society
This note provides counterexamples to the conjecture which is formulated in Fessas' correspondence [2].
Tópico(s): Advanced Topics
1979 - Institute of Electrical and Electronics Engineers | IEEE Transactions on Automatic Control
In [1] R. Thomason claims that a retract of a Dwyer map is a Dwyer map to show the closed model category structure he defined on the category of small categories is proper. This paper gives a counterexample to this claim and shows how to give a proof of the propriety axiom.
Tópico(s): Advanced
1999 - | Cahiers de topologie et géométrie différentielle catégoriques
Quasi-abelian categories are additive categories for which the class of all short exact sequences defines an exact structure. Such categories are ubiquitous and form a natural framework for relative homological algebra and K-theory. Higher Ext-groups also exist in categories with the formally weaker property to be semi-abelian. Raikov's conjecture states that both concepts are equivalent. We use a tilted algebra of type 𝔼6 to construct a counterexample.
Tópico(s): Rings, Modules, and Algebras
2008 - Wiley | Bulletin of the London Mathematical Society
Let K be an algebraically closed field endowed with a complete non-archimedean norm. Let f : Y → X be a map of K-affinoid varieties. In this paper we study the analytic structure of the image f(Y ) ⊂ X; such an image is a typical example of a subanalytic set. We show that the subanalytic sets are precisely the D-semianalytic sets, where D is the truncated division function first introduced by Denef and van den Dries. To prove this we establish a Flattening Theorem for affinoid varieties in the style of ...
Tópico(s): Advanced Topics
1994 - Cambridge University Press | Compositio Mathematica
Tópico(s): Advanced Topics
1973 - Duke University Press | Duke Mathematical Journal
Riccardo Longoni, Paolo Salvatore,
We present a counterexample to the conjecture on the homotopy invariance of configuration spaces. More precisely, we consider the lens spaces L7,1 and L7,2, and prove that their configuration spaces are not homotopy equivalent by showing that their universal coverings have different Massey products.
Tópico(s): Algebraic structures and combinatorial models
2005 - Elsevier BV | Topology
Sujoy Mukherjee, Józef H. Przytycki, Marithania Silvero, Xiao Wang, Seung Yeop Yang,
In the Khovanov homology of links, presence of Z2-torsion is a very common phenomenon. Finite number of examples of knots with Zn-torsion for n > 2 were also known, none for n > 8. In this article, we present several infinite families of links whose Khovanov homology contains Zn-torsion for 2 < n < 9 and Z2s-torsion for s < 24. We introduce 4-braid links with Z3-torsion which are counterexamples to parts of the PS braid conjecture. We also provide an infinite family of knots with Z5-torsion in reduced Khovanov ...
Tópico(s): Connective tissue disorders research
2017 - Taylor & Francis | Experimental Mathematics
José Bonet, Juan Carlos Díaz Alcaide, Jari Taskinen,
Tópico(s): Intracerebral and Subarachnoid Hemorrhage Research
1991 - Springer Science+Business Media | Collectanea mathematica
Tim D. Cochran, Christopher William Davis,
In the late 1960s Jerome Levine classified the odd high-dimensional knot concordance groups in terms of a linking matrix associated to an arbitrary bounding manifold for the knot. His proof fails for classical knots in S 3 . Yet this philosophy has remained the only known strategy for understanding the classical knot concordance group. We show that this strategy is fundamentally flawed. Specifically, in 1982, in support of Levine's philosophy, Louis Kauffman conjectured that if a knot in S 3 is a ...
Tópico(s): Botulinum Toxin and Related Neurological Disorders
2015 - Elsevier BV | Advances in Mathematics
... Ti-topologies is not a complemented lattice; a counterexample will be presented in ?2. Let I be the family of all topologies definable on an arbitrary set E. For riE2 ...
Tópico(s): Advanced
1966 - American Mathematical Society | Proceedings of the American Mathematical Society
Tópico(s): Mathematical Dynamics and Fractals
2016 - Springer Science+Business Media | Geometriae Dedicata
Virtual knots, defined by Kauffman, provide a natural generalization of classical knots. Most invariants of knots extend in a natural way to give invariants of virtual knots. In this paper we study the fundamental groups of virtual knots and observe several new and unexpected phenomena. In the classical setting, if the longitude of a knot is trivial in the knot group then the group is infinite cyclic. We show that for any classical knot group there is a virtual knot with that group and trivial longitude. ...
Tópico(s): Botulinum Toxin and Related Neurological Disorders
2000 - World Scientific | Journal of Knot Theory and Its Ramifications
David A. Jorgensen, Liana M. Şega,
We give counterexamples to the following conjecture of Auslander: given a finitely generated module M over an Artin algebra Λ, there exists a positive integer nM such that for all finitely generated Λ-modules N, if ExtΛi(M,N)=0 for all i≫0, then ExtΛi(M,N)=0 for all i⩾nM. Some of our examples moreover yield homologically defined classes of commutative local rings strictly between the class of local complete intersections and the class of local Gorenstein rings.
Tópico(s): Homotopy and Cohomology
2004 - Elsevier BV | Advances in Mathematics
... whole interval. In this article, we give a counterexample to this result in the C 1 -topology.
Tópico(s): Quantum chaos and dynamical systems
2014 - Wiley | Proceedings of the London Mathematical Society
Produção Nacional
Revisado por pares
We compute the homology groups of transformation groupoids associated with odometers and show that certain $(\mathbb{Z}\rtimes \mathbb{Z}_{2})$ -odometers give rise to counterexamples to the HK conjecture, which relates the homology of an essentially principal, minimal, ample groupoid $G$ with the K-theory of $C_{r}^{\ast }(G)$ . We also show that transformation groupoids of odometers satisfy the AH conjecture.
Tópico(s): Advanced Topics
2019 - Cambridge University Press | Ergodic Theory and Dynamical Systems
Produção Nacional
Revisado por pares
Mikhail Y. R. Gadelha, Hussama Ismail, Lucas C. Cordeiro,
The first attempts to apply the k-induction method to software verification are only recent. In this paper, we present a novel proof by induction algorithm, which is built on the top of a symbolic context-bounded model checker and uses an iterative deepening approach to verify, for each step k up to a given maximum, whether a given safety property $$\phi $$ holds in the program. The proposed k-induction algorithm consists of three different cases, called base case, forward condition, and inductive step. ...
Tópico(s): Software Reliability and Analysis Research
2015 - Springer Science+Business Media | International Journal on Software Tools for Technology Transfer
Daniel Kasprowski, Mark Powell, Arunima Ray,
We illustrate the rich landscape of 4-manifold topology through the lens of counterexamples. We consider several of the most commonly studied equivalence relations on 4-manifolds and how they are related to one another. We explain implications e.g. that $h$-cobordant manifolds are stably homeomorphic, and we provide examples illustrating the failure of other potential implications. The information is conveniently organised in a flowchart and a table.
Tópico(s): Homotopy and Cohomology
2023 - | EMS Surveys in Mathematical Sciences
Dilip Raghavan, Stevo Todorčević,
We study Tukey types of ultrafilters on ω, focusing on the question of when Tukey reducibility is equivalent to Rudin–Keisler reducibility. We give several conditions under which this equivalence holds. We show that there are only c many ultrafilters that are Tukey below any basically generated ultrafilter. The class of basically generated ultrafilters includes all known ultrafilters that are not Tukey above [ω1]<ω. We give a complete characterization of all ultrafilters that are Tukey below a selective. ...
Tópico(s): Mathematical Dynamics and Fractals
2011 - Elsevier BV | Annals of Pure and Applied Logic
Yun Sung Choi, Domingo Garcı́a, Sung Guen Kim, Manuel Maestre,
Given an entire mapping $f\in \mathcal{H}_b(X,X)$ of bounded type from a Banach space $X$ into $X$, we denote by $\overline{f}$ the Aron-Berner extension of $f$ to the bidual $X^{\ast\ast}$ of $X$. We show that $\overline{g\circ f} = \overline{g}\circ \overline{f}$ for all $f, g\in \mathcal{H}_b(X,X)$ if $X$ is symmetrically regular. We also give a counterexample on $l_1$ such that the equality does not hold. We prove that the closure of the numerical range of $f$ is the same as that of $\bar{f}$.
Tópico(s): Advanced Topics
2008 - Aarhus University Library | MATHEMATICA SCANDINAVICA
Abstract Epimorphic images of compact (algebraically compact) abelian groups are called cotorsion groups after Harrison. In a recent paper, Ph. Schultz raised the question whether “cotorsion” is a property which can be recognized by its small cotorsion epimorphic images: If G is a torsion-free group such that every torsion-free reduced homomorphic image of cardinality is cotorsion, is G necessarily cortorsion? In this note we will give some counterexamples to this problem. In fact, there is no cardinal ...
Tópico(s): Rings, Modules, and Algebras
1991 - Cambridge University Press | Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics
A topological space X is called well-filtered if for any filtered family $\mathcal{F}$ of compact saturated sets and an open set U , ∩ $\mathcal{F}$ ⊆ U implies F ⊆ U for some F ∈ $\mathcal{F}$ . Every sober space is well-filtered and the converse is not true. A dcpo (directed complete poset) is called well-filtered if its Scott space is well-filtered. In 1991, Heckmann asked whether every U K -admitting (the same as well-filtered) dcpo is sober. In 2001, Kou constructed a counterexample to give a negative answer. In ...
Tópico(s): Rings, Modules, and Algebras
2015 - Cambridge University Press | Mathematical Structures in Computer Science
Lars Winther Christensen, Henrik Holm,
A 2003 counterexample to a conjecture of Auslander brought attention to a family of rings—colloquially called AC rings—that satisfy a natural condition on vanishing of cohomology. Several results attest to the remarkable homological properties of AC rings, but their definition is barely operational, and it remains unknown if they form a class that is closed under typical constructions in ring theory. In this paper, we study transfer of the AC property along local homomorphisms of Cohen–Macaulay ...
Tópico(s): Homotopy and Cohomology
2012 - Springer Science+Business Media | manuscripta mathematica
Martin Edjvet, Paul Hammond, Nathan Thomas,
We report on a computational group theory experiment involving a search for cyclic presentations of the trivial group. The list of such presentations obtained includes counterexamples to a conjecture of M J Dunwoody.
Tópico(s): Advanced Operator Algebra Research
2001 - Taylor & Francis | Experimental Mathematics