Search results for "Existential quantification"
showing 9 items of 39 documents
Singular quasisymmetric mappings in dimensions two and greater
2018
For all $n \geq 2$, we construct a metric space $(X,d)$ and a quasisymmetric mapping $f\colon [0,1]^n \rightarrow X$ with the property that $f^{-1}$ is not absolutely continuous with respect to the Hausdorff $n$-measure on $X$. That is, there exists a Borel set $E \subset [0,1]^n$ with Lebesgue measure $|E|>0$ such that $f(E)$ has Hausdorff $n$-measure zero. The construction may be carried out so that $X$ has finite Hausdorff $n$-measure and $|E|$ is arbitrarily close to 1, or so that $|E| = 1$. This gives a negative answer to a question of Heinonen and Semmes.
Rolewicz-type chaotic operators
2015
In this article we introduce a new class of Rolewicz-type operators in l_p, $1 \le p < \infty$. We exhibit a collection F of cardinality continuum of operators of this type which are chaotic and remain so under almost all finite linear combinations, provided that the linear combination has sufficiently large norm. As a corollary to our main result we also obtain that there exists a countable collection of such operators whose all finite linear combinations are chaotic provided that they have sufficiently large norm.
Bifurcations of links of periodic orbits in non-singular Morse–Smale systems with a rotational symmetry on S3
2000
Abstract In this paper we consider a rotational symmetry on a non-singular Morse–Smale (NMS) system analyzing the restrictions this symmetry imposes on the links defined by the set of its periodic orbits and to the appearance of local generic codimension one bifurcations in the set of NMS flows on S 3 . The topological characterization is obtained by writing the involved links in terms of Wada operations. It is also obtained that symmetry implies that in general bifurcations have to be multiple. On the other hand, we also see that there exists a set of links that cannot be related to any other by sequences of this kind of bifurcation.
Erratum to “Irregularity” [Topology Appl. 154 (8) (2007) 1565–1580]
2012
[2, Proposition 4.4] states that each regular pretopology is topologically regular. Professor F. Mynard (Georgia Southern University) advised the authors that he was not convinced by the proof of that proposition, which enabled us to realize the proposition is wrong, as the example below shows. Recall that (e.g., [2]) a pretopology ξ on a set X is called regular if Vξ (x)⊂ adh ξ Vξ (x) (respectively, topologically regular if Vξ (x)⊂ cl ξ Vξ (x)) for every x ∈ X . As a consequence, in the sequel of [2], regular should be read topologically regular in a few instances, in particular in [2, Theorem 4.6]. [2, Proposition 4.4] is also quoted in [3], where it is used in some reformulations of clas…
Global and multiple test procedures using ordered p-values—a review
2004
This paper reviews global and multiple tests for the combination ofn hypotheses using the orderedp-values of then individual tests. In 1987, Rohmel and Streitberg presented a general method to construct global level α tests based on orderedp-values when there exists no prior knowledge regarding the joint distribution of the corresponding test statistics. In the case of independent test statistics, construction of global tests is available by means of recursive formulae presented by Bicher (1989), Kornatz (1994) and Finner and Roters (1994). Multiple test procedures can be developed by applying the closed test principle using these global tests as building blocks. Liu (1996) proposed represe…
Panel Summary One Model for Vision Systems?
1994
This panel reports some considerations about the definition of vision-models. The panellists are scientists working on vision problems from different perspectives. The concept of model in vision seems to remain still open. In fact, it is dynamic, and context dependent. There exists the need for a better exchange of information, among biologists, engineers, physicists, and psychologists in order to improve our knowledge.
Talking Blockchains: The Perspective of a Database Researcher
2021
There are few topics out there, that seem to create as much confusion and discussion as blockchains. This has a multitude of reasons: (1) A large number of drastically different concepts and systems are unified under the very broad term "blockchain". (2) The topic touches a variety of different fields, including databases, distributed processing, networks, cryptography, and even economics. (3) There exists a large number of different applications of the technology.The goal of this paper is to simplify and structure the discussion of blockchain technology. We first introduce a simple formalization of the basic components, that appear again and again in a variety of blockchain systems. Second…
On Daugavet indices of thickness
2020
Inspired by R. Whitley's thickness index the last named author recently introduced the Daugavet index of thickness of Banach spaces. We continue the investigation of the behavior of this index and also consider two new versions of the Daugavet index of thickness, which helps us solve an open problem which connect the Daugavet indices with the Daugavet equation. Moreover, we will improve the formerly known estimates of the behavior of Daugavet index on direct sums of Banach spaces by establishing sharp bounds. As a consequence of our results we prove that, for every $0<\delta<2$, there exists a Banach space where the infimum of the diameter of convex combinations of slices of the unit ball i…
The origin, definition and nature of the transconscious in the spirituality of Father Stăniloae
2022
In his important work, Orthodox Spirituality , Father Dumitru Staniloae considers that, besides the real existence of the subconscious, there exists in man another reality as well, comprising the superior divine energies found in the human heart and which he defined by using the modern notion of transconscious or supraconscious. Contribution: The present study emphasises on the origin, definitions and content of this concept in the work of Father Staniloae and its great importance in defining a way to know God and his salvation works, from the perspective of an anchorite and Christian mystic, engaged in the existential tension of communion with God.