Dissertationes Mathematicae最新文献_第4页

Complexities and representations of $mathcal F$-Borel spaces 数学F -Borel空间的复杂性和表示

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2019-01-01 DOI: 10.4064/DM794-2-2019

Vojtěch Kovařík

引用次数: 0

Entropy on normed semigroups (towards a unifying approach to entropy) 赋范半群上的熵（走向熵的统一方法）

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2018-08-11 DOI: 10.4064/dm791-2-2019

D. Dikranjan, A. Bruno

{"title":"Entropy on normed semigroups (towards a unifying approach to entropy)","authors":"D. Dikranjan, A. Bruno","doi":"10.4064/dm791-2-2019","DOIUrl":"https://doi.org/10.4064/dm791-2-2019","url":null,"abstract":"We present a unifying approach to the study of entropies in Mathematics, such as measure entropy, topological entropy, algebraic entropy, set-theoretic entropy. We take into account discrete dynamical systems, that is, pairs $(X,T)$, where $X$ is the underlying space and $T:Xto X$ a transformation. We see entropies as functions $h:mathfrak Xto mathbb R_+$, associating to each flow $(X,T)$ of a category $mathfrak X$ either a non negative real or $infty$. We introduce the notion of semigroup entropy $h_mathfrak S:mathfrak Stomathbb R_+$, which is a numerical invariant attached to endomorphisms of the category $mathfrak S$ of normed semigroups. Then, for a functor $F:mathfrak Xtomathfrak S$ from any specific category $mathfrak X$ to $mathfrak S$, we define the functorial entropy $h_F:mathfrak Xtomathbb R_+$ as the composition $h_{mathfrak S}circ F$. Clearly, $h_F$ inherits many of the properties of $h_mathfrak S$, depending also on the properties of $F$. Such general scheme permits to obtain relevant known entropies as functorial entropies $h_F$, for appropriate categories $mathfrak X$ and functors $F$, and to establish the properties shared by them. In this way we point out their common nature. Finally, we discuss and deeply analyze through the looking glass of our unifying approach the relations between pairs of entropies. To this end we formalize the notion of Bridge Theorem between two entropies $h_i:mathfrak X_ito mathbb R_+$, $i=1,2$, with respect to a functor $varepsilon:mathfrak X_1tomathfrak X_2$. Then, for pairs of functorial entropies we use the above scheme to introduce the notion and the related scheme of Strong Bridge Theorem, which allows us to put under the same umbrella various relations between pairs of entropies.","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2018-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48523837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 15

On the Banach structure of multivariate BV spaces 关于多元BV空间的Banach结构

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2018-06-22 DOI: 10.4064/dm801-7-2019

A. Brudnyi, Y. Brudnyi

引用次数: 12

Paracontrolled quasi-geostrophic equation with space-time white noise 带时空白噪声的顺控准地转方程

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2018-06-02 DOI: 10.4064/dm806-7-2020

Y. Inahama, Y. Sawano

引用次数: 0

Projective geometry of Sasaki–Einstein structures and their compactification Sasaki–Einstein结构的投影几何及其紧致化

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2018-03-26 DOI: 10.4064/dm786-7-2019

A. Gover, Katharina Neusser, T. Willse

{"title":"Projective geometry of Sasaki–Einstein structures and their compactification","authors":"A. Gover, Katharina Neusser, T. Willse","doi":"10.4064/dm786-7-2019","DOIUrl":"https://doi.org/10.4064/dm786-7-2019","url":null,"abstract":"We show that the standard definitions of Sasaki structures have elegant and simplifying interpretations in terms of projective differential geometry. For Sasaki-Einstein structures we use projective geometry to provide a resolution of such structures into geometrically less rigid components; the latter elemental components are separately, complex, orthogonal, and symplectic holonomy reductions of the canonical projective tractor/Cartan connection. This leads to a characterisation of Sasaki-Einstein structures as projective structures with certain unitary holonomy reductions. As an immediate application, this is used to describe the projective compactification of indefinite (suitably) complete non-compact Sasaki-Einstein structures and to prove that the boundary at infinity is a Fefferman conformal manifold that thus fibres over a nondegenerate CR manifold (of hypersurface type). We prove that this CR manifold coincides with the boundary at infinity for the c-projective compactification of the K\"ahler-Einstein manifold that arises, in the usual way, as a leaf space for the defining Killing field of the given Sasaki-Einstein manifold. A procedure for constructing examples is given. The discussion of symplectic holonomy reductions of projective structures leads us moreover to a new and simplifying approach to contact projective geometry. This is of independent interest and is treated in some detail.","PeriodicalId":51016,"journal":{"name":"Dissertationes Mathematicae","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2018-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45015547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

Haar-$mathcal I$ sets: looking at small sets in Polish groups through compact glasses Haar-$mathcal I$集：通过紧凑型眼镜观察波兰群体中的小集

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2018-03-18 DOI: 10.4064/dm812-2-2021

T. Banakh, Szymon Glkab, Eliza Jablo'nska, J. Swaczyna

引用次数: 5

Global free boundary problem for viscous non-homogeneous incompressible magnetohydrodynamics 粘性非均匀不可压缩磁流体力学全局自由边界问题

IF 1.8 3区数学

Dissertationes Mathematicae Pub Date : 2018-01-01 DOI: 10.4064/DM767-1-2018

P. Kacprzyk

引用次数: 0

Sturm-Liouville Operator Functions Sturm-Liouville算子函数