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72. Edge-colouring of graphs and hereditary graph properties
- Creator:
- Dorfling, Samantha and Vetrík, Tomáš
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- mathematics, grafy, edge-colouring, proper colouring, hereditary graph property, 13, and 51
- Language:
- English
- Description:
- Edge-colourings of graphs have been studied for decades. We study edge-colourings with respect to hereditary graph properties. For a graph G, a hereditary graph property P and l\geqslant 1 we define X{'_{P,l}} to be the minimum number of colours needed to properly colour the edges of G, such that any subgraph of G induced by edges coloured by (at most) l colours is in P. We present a necessary and sufficient condition for the existence of X{'_{P,l}} . We focus on edge-colourings of graphs with respect to the hereditary properties Ok and Sk, where Ok contains all graphs whose components have order at most k+1, and Sk contains all graphs of maximum degree at most k. We determine the value of X{'_{{S_k},l}}(G) for any graph G,k \geqslant 1, l\geqslant 1 and we present a number of results on X{'_{{O_k},l}}(G) ., Samantha Dorfling, Tomáš Vetrík., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
73. Edit distance measure for graphs
- Creator:
- Dzido, Tomasz and Krzywdziński, Krzysztof
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- mathematics, extremal graph problem, similarity of graphs, 13, and 51
- Language:
- English
- Description:
- In this paper, we investigate a measure of similarity of graphs similar to the Ramsey number. We present values and bounds for g(n, l), the biggest number k guaranteeing that there exist l graphs on n vertices, each two having edit distance at least k. By edit distance of two graphs G, F we mean the number of edges needed to be added to or deleted from graph G to obtain graph F. This new extremal number g(n, l) is closely linked to the edit distance of graphs. Using probabilistic methods we show that g(n, l) is close to \frac{1} {2}\left( {\begin{array}{*{20}c} n // 2 // \end{array} } \right) for small values of l > 2. We also present some exact values for small n and lower bounds for very large l close to the number of non-isomorphic graphs of n vertices., Tomasz Dzido, Krzysztof Krzywdziński., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
74. Embeddings between weighted Copson and Cesàro function spaces
- Creator:
- Gogatishvili, Amiran, Mustafayev, Rza, and Ünver, Tuğçe
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, Cesàro and Copson function spaces, embedding, iterated Hardy inequalities, 13, and 51
- Language:
- English
- Description:
- In this paper, characterizations of the embeddings between weighted Copson function spaces ${\rm Cop}_{p_1,q_1}(u_1,v_1)$ and weighted Cesàro function spaces ${\rm Ces}_{p_2,q_2}(u_2,v_2)$ are given. In particular, two-sided estimates of the optimal constant $c$ in the inequality $ \align\biggl( \int_0^{\infty} &\biggl( \int_0^t f(\tau)^{p_2}v_2(\tau)\dd\tau\biggr)^{\!\!\frc{q_2}{p_2}} u_2(t)\dd t\biggr)^{\!\!\frc1{q_2}} $ \ $\le c \biggl( \int_0^{\infty} \biggl( \int_t^{\infty} f(\tau)^{p_1} v_1(\tau)\dd\tau\biggr)^{\!\!\frc{q_1}{p_1}} u_1(t)\dd t\biggr)^{\!\!\frc1{q_1}}, $ where $p_1,p_2,q_1,q_2 \in(0,\infty)$, $p_2 \le q_2$ and $u_1,u_2,v_1,v_2$ are weights on $(0,\infty)$, are obtained. The most innovative part consists of the fact that possibly different parameters $p_1$ and $p_2$ and possibly different inner weights $v_1$ and $v_2$ are allowed. The proof is based on the combination of duality techniques with estimates of optimal constants of the embeddings between weighted Cesàro and Copson spaces and weighted Lebesgue spaces, which reduce the problem to the solutions of iterated Hardy-type inequalities., Amiran Gogatishvili, Rza Mustafayev, Tuğçe Ünver., and Obsahuje bibliografii
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
75. Equivalent quasi-norms and atomic decomposition of weak Triebel-Lizorkin spaces
- Creator:
- Li, Wenchang and Xu, Jingshi
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, atom, maximal function, weak Lebesgue space, Triebel-Lizorkin space, equivalent norm, 13, and 51
- Language:
- English
- Description:
- Recently, the weak Triebel-Lizorkin space was introduced by Grafakos and He, which includes the standard Triebel-Lizorkin space as a subset. The latter has a wide applications in aspects of analysis. In this paper, the authors firstly give equivalent quasi-norms of weak Triebel-Lizorkin spaces in terms of Peetre's maximal functions. As an application of those equivalent quasi-norms, an atomic decomposition of weak Triebel-Lizorkin spaces is given., Wenchang Li, Jingshi Xu., and Seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
76. Ergodicity for a stochastic geodesic equation in the tangent bundle of the 2D sphere
- Creator:
- Baňas, Ľubomír, Brzeźniak, Zdzisłlaw, Neklyudov, Mikhail, Ondreját, Martin, and Prohl, Andreas
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- mathematics, geometric stochastic wave equation, stochastic geodesic equation, ergodicity, attractivity, invariant measure, numerical approximation, 13, and 51
- Language:
- English
- Description:
- We study ergodic properties of stochastic geometric wave equations on a particular model with the target being the 2D sphere while considering only solutions which are independent of the space variable. This simplification leads to a degenerate stochastic equation in the tangent bundle of the 2D sphere. Studying this equation, we prove existence and non-uniqueness of invariant probability measures for the original problem and obtain also results on attractivity towards an invariant measure. We also present a structure-preserving numerical scheme to approximate solutions and provide computational experiments to motivate and illustrate the theoretical results., Ľubomír Baňas, Zdzisłlaw Brzeźniak, Mikhail Neklyudov, Martin Ondreját, Andreas Prohl., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
77. Escape dynamics: a continuos-time approximation
- Creator:
- Kolyuzhnov, Dmitri, Bogomolova, Anna, and Slobodyan, Sergey
- Publisher:
- CERGE-Charles University and Academy of Sciences of the Czech Republic. Economics Institute
- Format:
- electronic and 42 s.
- Type:
- text, volume, studie, model:monograph, and TEXT
- Subject:
- Kombinatorika. Teorie grafů. Matematická statistika. Operační výzkum. Matematické modelování, ekonomické modelování, ekonomické modely, matematické metody, matematické modelování, 519.673, 51-7, (048.8), 13, and 519
- Language:
- English
- Description:
- Dmitri Kolyuzhnov, Anna Bogomolova, Sergey Slobodyan.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
78. Espace de Dixmier des opérateurs de Hankel sur les espaces de Bergman à poids
- Creator:
- Tytgat, Romaric
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- mathematics, Hankel operator, Dixmier trace, Bergman space, 13, and 51
- Language:
- English
- Description:
- In this paper, we give theoretical results on Macaev ideal and Dixmier trace. Then we give a characterization of antiholomorphic symbols \overline f such that the Hankel operator {H_{\overline f }} on a Bergman weighted space is in an ideal of Macaev and we give the Dixmier trace. For this, we look at the behavior of Schatten’s norms \mathcal{S}^p when p tends to 1, using results of Engliš and Rochberg on Bergman space. We also give results on powers of such operators., Nous donnons des résultats théoriques sur l’idéal de Macaev et la trace de Dixmier. Ensuite, nous caractérisons les symboles antiholomorphes \overline f tels que l’opérateur de Hankel {H_{\overline f }} sur l’espace de Bergman à poids soit dans l’idéal de Macaev et nous donnons la trace de Dixmier. Pour cela, nous regardons le comportement des normes de Schatten \mathcal{S}^p quand p tend vers 1 et nous nous appuyons sur le résultat de Engliš et Rochberg sur l’espace de Bergman. Nous parlons aussi des puissances de tels opérateurs., Romaric Tytgat., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
79. Essential norm and a new characterization of weighted composition operators from weighted Bergman spaces and Hardy spaces into the Bloch space
- Creator:
- Li, Songxiao, Qian, Ruishen, and Zhou, Jizhen
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, Bloch space, weighted Bergman space, essential norm, weighted composition operator, 13, and 51
- Language:
- English
- Description:
- In this paper, we give some estimates for the essential norm and a new characterization for the boundedness and compactness of weighted composition operators from weighted Bergman spaces and Hardy spaces to the Bloch space., Songxiao Li, Ruishen Qian, Jizhen Zhou., and Obsahuje bibliografické odkazy
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
80. Evolution equations governed by Lipschitz continuous non-autonomous forms
- Creator:
- Sani, Ahmed and Laasri, Hafida
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, sesquilinear form, non-autonomous evolution equation, maximal regularity, convex set, 13, and 51
- Language:
- English
- Description:
- We prove L2-maximal regularity of the linear non-autonomous evolutionary Cauchy problem \dot u(t) + A(t)u(t) = f(t){\text{ for a}}{\text{.e}}{\text{. }}t \in \left[ {0,T} \right],{\text{ }}u(0) = {u_0}, where the operator A(t) arises from a time depending sesquilinear form a(t, ·, ·) on a Hilbert space H with constant domain V. We prove the maximal regularity in H when these forms are time Lipschitz continuous. We proceed by approximating the problem using the frozen coefficient method developed by El-Mennaoui, Keyantuo, Laasri (2011), El-Mennaoui, Laasri (2013), and Laasri (2012). As a consequence, we obtain an invariance criterion for convex and closed sets of H., Ahmed Sani, Hafida Laasri., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public