The reflexivity and transitivity of subspaces of Toeplitz operators on the Hardy space on the upper half-plane are investigated. The dichotomic behavior (transitive or reflexive) of these subspaces is shown. It refers to the similar dichotomic behavior for subspaces of Toeplitz operators on the Hardy space on the unit disc. The isomorphism between the Hardy spaces on the unit disc and the upper half-plane is used. To keep weak* homeomorphism between $L^\infty $ spaces on the unit circle and the real line we redefine the classical isomorphism between $L^1$ spaces.
In this paper we study the regularity properties of the one-dimensional one-sided Hardy-Littlewood maximal operators M+ and M−. More precisely, we prove that M+ and M− map W¹,p(R) → W1,p(R) with 1 < p < nekonečno, boundedly and continuously. In addition, we show that the discrete versions M+ and M− map BV(ℤ) → BV(ℤ) boundedly and map l¹(ℤ) → BV(ℤ) continuously. Specially, we obtain the sharp variation inequalities of M+ and M−, that is Var(M+(f))<Var(f) and Var(M−(f))<Var(f) if f ∈ BV(ℤ), where Var(f) is the total variation of f on ℤ and BV(ℤ) is the set of all functions f: ℤ → R satisfying Var(f) < nekonečno., Feng Liu, Suzhen Mao., and Obsahuje bibliografii
Matrix factorization or factor analysis is an important task helpful in the analysis of high dimensional real world data. There are several well known methods and algorithms for factorization of real data but many application areas including information retrieval, pattern recognition and data mining require processing of binary rather than real data. Unfortunately, the methods used for real matrix factorization fail in the latter case. In this paper we introduce background and initial version of Genetic Algorithm for binary matrix factorization.
The global environment is faced with growing threats from anthropogenic disturbance, propelling the Earth into a 6th mass extinction. For the world's mammals, this is reflected in the fact that 25% of species are threatened with some risk of extinction. During this time of species loss and environmental alteration, the world's natural history museums (NHMs) are uniquely poised to provide novel insight into many aspects of conservation. This review seeks to provide evidence of the importance of NHMs to mammal conservation, how arguments against continued collecting of physical voucher specimens is counterproductive to these efforts, and to identify additional threats to collecting with a particular focus on small mammals across Africa. NHMs contribute unique data for assessing mammal species conservation status through the International Union for Conservation of Nature's (IUCN) Red List of Threatened species. However, NHMs' contributions to mammal conservation go well beyond supporting the IUCN Red List, with studies addressing topics such as human impacts, climate change, genetic diversity, disease, physiology, and biodiversity education. Increasing and diverse challenges, both domestic and international, highlight the growing threats facing NHMs, especially in regards to the issue of lethally sampling individuals for the purpose of creating voucher specimens. Such arguments are counterproductive to conservation efforts and tend to reflect the moral opposition of individual researchers than a true threat to conservation. The need for continued collecting of holistic specimens of all taxa across space and time could not be more urgent, especially for underexplored biodiversity hotspots facing extreme threats such as the Afrotropics.
In a communication network, vulnerability measures the resistance of the network to disruption of operation after the failure of certain stations or communication links. If we think of a connected graph as model-ing a network, the rupture degree of a graph is one measure of graph vulnerability and it is defined by
r(G) = max{w(G-S)-|S|-m(G-S): S \subset V(G), w(G-S)>1}
where w(G-S) is the number of components of G-S and m(G-S) is the order of a largest component of G-S. In this paper, general results on the rupture degree of a graph are considered. Firstly, some bounds on the rupture degree are given. Further, rupture degree of a complete k-ary tree is calculated. Also several results are given about complete k-ary tree and graph operations. Finally, we give formulas for the rupture degree of the cartesian product of some special graphs.
In this note we prove that there exists a Carathéodory vector lattice $V$ such that $V\cong V^3$ and $V\ncong V^2$. This yields that $V$ is a solution of the Schröder-Bernstein problem for Carathéodory vector lattices. We also show that no Carathéodory Banach lattice is a solution of the Schröder-Bernstein problem.