990 resultados para Herz-Type Hardy Spaces
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The monograph dissertation deals with kernel integral operators and their mapping properties on Euclidean domains. The associated kernels are weakly singular and examples of such are given by Green functions of certain elliptic partial differential equations. It is well known that mapping properties of the corresponding Green operators can be used to deduce a priori estimates for the solutions of these equations. In the dissertation, natural size- and cancellation conditions are quantified for kernels defined in domains. These kernels induce integral operators which are then composed with any partial differential operator of prescribed order, depending on the size of the kernel. The main object of study in this dissertation being the boundedness properties of such compositions, the main result is the characterization of their Lp-boundedness on suitably regular domains. In case the aforementioned kernels are defined in the whole Euclidean space, their partial derivatives of prescribed order turn out to be so called standard kernels that arise in connection with singular integral operators. The Lp-boundedness of singular integrals is characterized by the T1 theorem, which is originally due to David and Journé and was published in 1984 (Ann. of Math. 120). The main result in the dissertation can be interpreted as a T1 theorem for weakly singular integral operators. The dissertation deals also with special convolution type weakly singular integral operators that are defined on Euclidean spaces.
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The topic of this dissertation is the geometric and isometric theory of Banach spaces. This work is motivated by the known Banach-Mazur rotation problem, which asks whether each transitive separable Banach space is isometrically a Hilbert space. A Banach space X is said to be transitive if the isometry group of X acts transitively on the unit sphere of X. In fact, some weaker symmetry conditions than transitivity are studied in the dissertation. One such condition is an almost isometric version of transitivity. Another investigated condition is convex-transitivity, which requires that the closed convex hull of the orbit of any point of the unit sphere under the rotation group is the whole unit ball. Following the tradition developed around the rotation problem, some contemporary problems are studied. Namely, we attempt to characterize Hilbert spaces by using convex-transitivity together with the existence of a 1-dimensional bicontractive projection on the space, and some mild geometric assumptions. The convex-transitivity of some vector-valued function spaces is studied as well. The thesis also touches convex-transitivity of Banach lattices and resembling geometric cases.
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"Genealogy of a Jewish Family: The descendants of Herz Anschel" by W. Rosenstock [or Siegfried Auerbach] and clipping with review
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The object of this dissertation is to study globally defined bounded p-harmonic functions on Cartan-Hadamard manifolds and Gromov hyperbolic metric measure spaces. Such functions are constructed by solving the so called Dirichlet problem at infinity. This problem is to find a p-harmonic function on the space that extends continuously to the boundary at inifinity and obtains given boundary values there. The dissertation consists of an overview and three published research articles. In the first article the Dirichlet problem at infinity is considered for more general A-harmonic functions on Cartan-Hadamard manifolds. In the special case of two dimensions the Dirichlet problem at infinity is solved by only assuming that the sectional curvature has a certain upper bound. A sharpness result is proved for this upper bound. In the second article the Dirichlet problem at infinity is solved for p-harmonic functions on Cartan-Hadamard manifolds under the assumption that the sectional curvature is bounded outside a compact set from above and from below by functions that depend on the distance to a fixed point. The curvature bounds allow examples of quadratic decay and examples of exponential growth. In the final article a generalization of the Dirichlet problem at infinity for p-harmonic functions is considered on Gromov hyperbolic metric measure spaces. Existence and uniqueness results are proved and Cartan-Hadamard manifolds are considered as an application.
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Three items referring to Prof. Jakob Herz: Memorial by Ilse Sponsel in memory of Herz; excerpt from "Erlanger Tagblatt," (May 5, 1983); invitation to participate at the unveiling of the pillar and Alex Bauer's remarks at the occasion, May 5, 1983.
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Expressed sequence tag (EST) databases provide a primary source of nuclear DNA sequences for genetic marker development in non-model organisms. To date, the process has been relatively inefficient for several reasons: - 1) priming site polymorphism in the template leads to inferior or erratic amplification; - 2) introns in the target amplicon are too large and/or numerous to allow effective amplification under standard screening conditions, and; - 3) at least occasionally, a PCR primer straddles an exon–intron junction and is unable to bind to genomic DNA template. The first is only a minor issue for species or strains with low heterozygosity but becomes a significant problem for species with high genomic variation, such as marine organisms with extremely large effective population sizes. Problems arising from unanticipated introns are unavoidable but are most pronounced in intron-rich species, such as vertebrates and lophotrochozoans. We present an approach to marker development in the Pacific oyster Crassostrea gigas, a highly polymorphic and intron-rich species, which minimizes these problems, and should be applicable to other non-model species for which EST databases are available. Placement of PCR primers in the 3′ end of coding sequence and 3′ UTR improved PCR success rate from 51% to 97%. Almost all (37 of 39) markers developed for the Pacific oyster were polymorphic in a small test panel of wild and domesticated oysters.
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Tools known as maximal functions are frequently used in harmonic analysis when studying local behaviour of functions. Typically they measure the suprema of local averages of non-negative functions. It is essential that the size (more precisely, the L^p-norm) of the maximal function is comparable to the size of the original function. When dealing with families of operators between Banach spaces we are often forced to replace the uniform bound with the larger R-bound. Hence such a replacement is also needed in the maximal function for functions taking values in spaces of operators. More specifically, the suprema of norms of local averages (i.e. their uniform bound in the operator norm) has to be replaced by their R-bound. This procedure gives us the Rademacher maximal function, which was introduced by Hytönen, McIntosh and Portal in order to prove a certain vector-valued Carleson's embedding theorem. They noticed that the sizes of an operator-valued function and its Rademacher maximal function are comparable for many common range spaces, but not for all. Certain requirements on the type and cotype of the spaces involved are necessary for this comparability, henceforth referred to as the “RMF-property”. It was shown, that other objects and parameters appearing in the definition, such as the domain of functions and the exponent p of the norm, make no difference to this. After a short introduction to randomized norms and geometry in Banach spaces we study the Rademacher maximal function on Euclidean spaces. The requirements on the type and cotype are considered, providing examples of spaces without RMF. L^p-spaces are shown to have RMF not only for p greater or equal to 2 (when it is trivial) but also for 1 < p < 2. A dyadic version of Carleson's embedding theorem is proven for scalar- and operator-valued functions. As the analysis with dyadic cubes can be generalized to filtrations on sigma-finite measure spaces, we consider the Rademacher maximal function in this case as well. It turns out that the RMF-property is independent of the filtration and the underlying measure space and that it is enough to consider very simple ones known as Haar filtrations. Scalar- and operator-valued analogues of Carleson's embedding theorem are also provided. With the RMF-property proven independent of the underlying measure space, we can use probabilistic notions and formulate it for martingales. Following a similar result for UMD-spaces, a weak type inequality is shown to be (necessary and) sufficient for the RMF-property. The RMF-property is also studied using concave functions giving yet another proof of its independence from various parameters.
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A simple method for evaluating dielectric relaxation parameters ie given whioh can be used for analyeing the arelaxation times of a liquid into two absorptions.
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We propose a new type of high-order elements that incorporates the mesh-free Galerkin formulations into the framework of finite element method. Traditional polynomial interpolation is replaced by mesh-free interpolations in the present high-order elements, and the strain smoothing technique is used for integration of the governing equations based on smoothing cells. The properties of high-order elements, which are influenced by the basis function of mesh-free interpolations and boundary nodes, are discussed through numerical examples. It can be found that the basis function has significant influence on the computational accuracy and upper-lower bounds of energy norm, when the strain smoothing technique retains the softening phenomenon. This new type of high-order elements shows good performance when quadratic basis functions are used in the mesh-free interpolations and present elements prove advantageous in adaptive mesh and nodes refinement schemes. Furthermore, it shows less sensitive to the quality of element because it uses the mesh-free interpolations and obeys the Weakened Weak (W2) formulation as introduced in [3, 5].
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Background: Increased hospital readmission and longer stays in the hospital for patients with type 2 diabetes and cardiac disease can result in higher healthcare costs and heavier individual burden. Thus, knowledge of the characteristics and predictive factors for Vietnamese patients with type 2 diabetes and cardiac disease, at high risk of hospital readmission and longer stays in the hospital, could provide a better understanding on how to develop an effective care plan aimed at improving patient outcomes. However, information about factors influencing hospital readmission and length of stay of patients with type 2 diabetes and cardiac disease in Vietnam is limited. Aim: This study examined factors influencing hospital readmission and length of stay of Vietnamese patients with both type 2 diabetes and cardiac disease. Methods: An exploratory prospective study design was conducted on 209 patients with type 2 diabetes and cardiac disease in Vietnam. Data were collected from patient charts and patients' responses to self-administered questionnaires. Descriptive statistics, bivariate correlation, logistic and multiple regression were used to analyse the data. Results: The hospital readmission rate was 12.0% among patients with both type 2 diabetes and cardiac disease. The average length of stay in the hospital was 9.37 days. Older age (OR= 1.11, p< .05), increased duration of type 2 diabetes (OR= 1.22, p< .05), less engagement in stretching/strengthening exercise behaviours (OR= .93, p< .001) and in communication with physician (OR= .21, p< .001) were significant predictors of 30-dayhospital readmission. Increased number of additional co-morbidities (β= .33, p< .001) was a significant predictor of longer stays in the hospital. High levels of cognitive symptom management (β= .40, p< .001) significantly predicted longer stays in the hospital, indicating that the more patients practiced cognitive symptom management, the longer the stay in hospital. Conclusions: This study provides some evidence of factors influencing hospital readmission and length of stay and argues that this information may have significant implications for clinical practice in order to improve patients' health outcomes. However, the findings of this study related to the targeted hospital only. Additionally, the investigation of environmental factors is recommended for future research as these factors are important components contributing to the research model.
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In this paper I conduct a Foucauldian discourse analysis of a political speech given by Brendon Nelson in 2006 when the Australian Minister for Defence in the Howard Coalition Government. The speech connects conceptualisations of terror, globalization, education and literacy as part of a whole of government security strategy. The analysis examines this speech as an example of a liberal way of governing the conduct of diverse and unpredictable populations. My analysis suggests that the apparatus of government has been strategically used in order to biopolitically contain the rise of complex social forces and protect a set of homogenous cultural values. The purposes of education and uses of literacy are seen as instruments for the inscription of a coded set of values understood to be synonymous with civil society.
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Electrical transport in Bi doped amorphous semiconductors (GeSe3.5)100-xBix (x=0,4,10) is studied in a Bridgman anvil system up to a pressure of 90 kbar and down to 77 K. A pressure induced continuous transition from an amorphous semiconductor to a metal-like solid is observed in GeSe3.5. The addition of Bi disturbs significantly the behaviour of resistivity with pressure. The results are discussed in the light of molecular cluster model for GeySe1-y proposed by Phillips.