Subnormality and cyclicity

Franciszek Hugon Szafraniec

Displaying similar documents to “Subnormality and cyclicity”

Note on cyclic decompositions of complete bipartite graphs into cubes

Dalibor Fronček (1999)

Discussiones Mathematicae Graph Theory

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So far, the smallest complete bipartite graph which was known to have a cyclic decomposition into cubes $Q_{d}$ of a given dimension d was $K_{d 2^{d - 1}, d 2^{d - 2}}$ . We improve this result and show that also $K_{d 2^{d - 2}, d 2^{d - 2}}$ allows a cyclic decomposition into $Q_{d}$ . We also present a cyclic factorization of $K_{8, 8}$ into Q₄.

Kannan-type cyclic contraction results in $2$ -Menger space

Binayak S. Choudhury, Samir Kumar BHANDARI (2016)

Mathematica Bohemica

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In this paper we establish Kannan-type cyclic contraction results in probabilistic 2-metric spaces. We use two different types of $t$ -norm in our theorems. In our first theorem we use a Hadzic-type $t$ -norm. We use the minimum $t$ -norm in our second theorem. We prove our second theorem by different arguments than the first theorem. A control function is used in our second theorem. These results generalize some existing results in probabilistic 2-metric spaces. Our results are illustrated with...

Circles passing through five or more integer points

Shaunna M. Plunkett-Levin (2013)

Acta Arithmetica

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We find an improvement to Huxley and Konyagin’s current lower bound for the number of circles passing through five integer points. We conjecture that the improved lower bound is the asymptotic formula for the number of circles passing through five integer points. We generalise the result to circles passing through more than five integer points, giving the main theorem in terms of cyclic polygons with m integer point vertices. Theorem. Let m ≥ 4 be a fixed integer. Let $W_{m} (R)$ be the number...

Cyclic Type Fixed Point Results in 2-Menger Spaces

Binayak S. Choudhury, Samir Kumar BHANDARI, Parbati SAHA (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we introduce generalized cyclic contractions through $r$ number of subsets of a probabilistic 2-metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type $t$ -norm. In another theorem we use a control function with minimum $t$ -norm. Our results generalizes some existing fixed point theorem in 2-Menger spaces. The results are supported with some examples.

Bounded point evaluations for multicyclic operators

M. EL Guendafi, M. Mbekhta, E. H. Zerouali (2005)

Banach Center Publications

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Let T be a multicyclic operator defined on some Banach space. Bounded point evaluations and analytic bounded point evaluations for T are defined to generalize the cyclic case. We extend some known results on cyclic operators to the more general setting of multicyclic operators on Banach spaces. In particular we show that if T satisfies Bishop’s property (β), then $ℬ_{a} = ℬ ∖ σ_{a p} (T)$ . We introduce the concept of analytic structures and we link it to different spectral quantities. We apply this concept...

On the behaviour of the solutions of a $k$ -order cyclic-type system of max difference equations

Gesthimani Stefanidou, Garyfalos Papaschinopoulos (2025)

Czechoslovak Mathematical Journal

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We investigate the behaviour of the solutions of a $k$ -dimensional cyclic system of difference equations with maximum. More precisely, we study the existence and the number of the equilibria in the case when $k$ is an odd or an even positive integer, but also for the various values of the exponents of the terms of the difference equations of this system. In addition, we find invariant intervals for our system and we invistegate the convergence of the solutions to the unique positive equilibrium....

The max norm in $R^{n}$ -isometries and measure

Regina Cohen, James W. Fickett (1982)

Colloquium Mathematicae

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On the Rockafellar theorem for $Φ^{γ (\cdot, \cdot)}$ -monotone multifunctions

S. Rolewicz (2006)

Studia Mathematica

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Let X be an arbitrary set, and γ: X × X → ℝ any function. Let Φ be a family of real-valued functions defined on X. Let $Γ : X \to 2^{Φ}$ be a cyclic $Φ^{γ (\cdot, \cdot)}$ -monotone multifunction with non-empty values. It is shown that the following generalization of the Rockafellar theorem holds. There is a function f: X → ℝ such that Γ is contained in the $Φ^{γ (\cdot, \cdot)}$ -subdifferential of f, $Γ (x) \subset \partial_{Φ}^{γ (\cdot, \cdot)} {f |}_{x}$ .

On the spectral radius in $L_{1} (G)$

E. Porada (1971)

Colloquium Mathematicae

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Moufang loops of order coprime to three that cyclically extend groups of dihedral type

Aleš Drápal (2016)

Commentationes Mathematicae Universitatis Carolinae

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This paper completely solves the isomorphism problem for Moufang loops $Q = G C$ where $G ⊴ Q$ is a noncommutative group with cyclic subgroup of index two and $| Z (G) | \leq 2$ , $C$ is cyclic, $G \cap C = 1$ , and $Q$ is finite of order coprime to three.

On Peano derivatives in $L^{p} (E_{n})$

S. Lasher (1968)

Studia Mathematica

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A note on another construction of graphs with $4 n + 6$ vertices and cyclic automorphism group of order $4 n$

Peteris Daugulis (2017)

Archivum Mathematicum

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The problem of finding minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic groups. This problem was considered earlier by other authors. We give a construction of an undirected graph having $4 n + 6$ vertices and automorphism group cyclic of order $4 n$ , $n \geq 1$ . As a special case we get graphs with $2^{k} + 6$ vertices and cyclic automorphism groups of order $2^{k}$ . It can revive interest in related problems.

Extensions of generic measure-preserving actions

Julien Melleray (2014)

Annales de l’institut Fourier

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We show that, whenever $Γ$ is a countable abelian group and $Δ$ is a finitely-generated subgroup of $Γ$ , a generic measure-preserving action of $Δ$ on a standard atomless probability space $(X, μ)$ extends to a free measure-preserving action of $Γ$ on $(X, μ)$ . This extends a result of Ageev, corresponding to the case when $Δ$ is infinite cyclic.

On the index of length four minimal zero-sum sequences

Caixia Shen, Li-meng Xia, Yuanlin Li (2014)

Colloquium Mathematicae

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Let G be a finite cyclic group. Every sequence S over G can be written in the form $S = (n ₁ g) \cdot . . . \cdot (n_{l} g)$ where g ∈ G and $n ₁, . . ., n_{l} i \in [1, o r d (g)]$ , and the index ind(S) is defined to be the minimum of $(n ₁ + \dots + n_{l}) / o r d (g)$ over all possible g ∈ G such that ⟨g⟩ = G. A conjecture says that every minimal zero-sum sequence of length 4 over a finite cyclic group G with gcd(|G|,6) = 1 has index 1. This conjecture was confirmed recently for the case when |G| is a product of at most two prime powers. However, the general case is still open. In this paper,...