Norm convolution inequalities in Lebesgue spaces

We obtain upper and lower estimates of the (p; q) norm of the con-volution operator. The upper estimate sharpens the Young-type inequalities due to O'Neil and Stepanov.

Bergman-type singular operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball

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Interpolation methods for stochastic processes spaces

In this paper the scales of classes of stochastic processes are introduced. New interpolation theorems and boundedness of some transforms of stochastic processes are proved. Interpolation method for generously-monotonous rocesses is entered. Conditions and statements of interpolation theorems concern he xed stochastic process, which diers from the classical results.

Spaces with Noetherian cohomology

Is the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? This note provides, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens-Venkov Theorem. We consider the cohomology of a space with coefficients in a module, and we compare Noetherianity over the field with p elements, with Noetherianity over the p-adic integers, in the case when the fundamental group is a finite p-group.

Hankel operators on holomorphic Hardy-Orlicz spaces

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Interpolation and sampling in small Bergman spaces

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Beurling-Landau densities of weighted Fekete sets and correlation kernel estimates

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On separation of a degenerate differential operator in Hilbert space

A coercive estimate for a solution of a degenerate second order di fferential equation is installed, and its applications to spectral problems for the corresponding dif ferential operator is demonstrated. The suffi cient conditions for existence of the solutions of one class of the nonlinear second order diff erential equations on the real axis are obtained.

Improving Access to Green Spaces

Evidence Review 8 - Improving access to green spaces Briefing 8 - Improving access to green spaces This pair of documents, commissioned by Public Health England, and written by the UCL Institute of Health Equity, address the role of green space in improving health locally. The first part of the evidence review defines ‘accessible’ green space and provides an overview of the evidence linking access to green spaces with health benefits, setting out the potential for reducing health inequalities. The second part provides an overview of interventions implemented at the local level to increase equitable access and use of good quality green spaces. Local authorities and local organisations have taken action on these issues through the implementation of interventions to: 1. Create new areas of green space and improve the quality of existing green spaces 2. Increase accessibility, engagement and use of green spaces The full evidence review and a shorter summary briefing are available to download above. This document is part of a series. An overview document which provides an introduction to this and other documents in the series, and links to the other topic areas, is available on the ‘Local Action on health inequalities’ project page. A video of Michael Marmot introducing the work is also available on our videos page.

On the presence of hepatic stellate cells in portal spaces

Previous studies in mice with hypervitaminosis A have demonstrated that fat-storing cells (hepatic stellate cells-HSCs) participate in schistosomal granuloma fibrogenesis. The origin of such cells in portal areas, away from the Disse spaces, was herein investigated. HSCs were identified in frozen sections of the liver by means of Sudan III staining. They appeared as red-stained cells disposed along the sinusoids of normal mice, but were never found within portal spaces. However, in the chronically inflamed portal spaces of Capillaria hepatica-infected mice, Sudan III-positive cells were frequently present among leukocytes and fibroblast-like cells. Thus, there are no resident HSCs in portal spaces, but their presence there in chronic inflammatory processes indicates that they are able to migrate from peri-sinusoidal areas in order to reach the portal areas.

Smoke Free Spaces: Progress in reducing exposure to second-hand smoke in Northern Ireland incorporating the five year review of smoke-free legislation

This report provides an overview of progress in reducing Second Hand Smoke (SHS) exposure in Northern Ireland that incorporates the five year review of smoke-free legislation, but also extends to a consideration of SHS exposure in non-work environments.  The report considers aspects of inequalities in SHS exposure in particular according to social disadvantage and with a focus on vulnerable subgroups of the population.

Hilbert space on probability density functions with Aitchison geometry

Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densitiesby generalizing the Aitchison geometry for compositions in the simplex into the set probability densities

Rapid Site-Directed Mutagenesis Using Two-PCR-Generated DNA Fragments Reproducing the Plasmid Template.

We describe a new rapid and efficient polymerase chain reaction (PCR)-based site-directed mutagenesis method. This procedure is effective with any plasmid and it employs four oligonucleotide primers. One primer contains the desired mutation, the second is oriented in the opposite direction (one of these two primers should be phosphorylated), and the third and fourth should be coding in complementary fashion for a unique restriction site to be introduced in a nonessential region. The method consists of two simultaneous PCR reactions; the PCR products are digested with the enzyme that recognizes the newly introduced unique restriction site and then ligased and used to transform competent bacteria. Additionally, the use of Dpn I facilitates the elimination of template DNA. The newly introduced restriction site is essential for ligation in the correct orientation of the two-PCR products and is further used for mutant screening. Resulting plasmids carry both the new restriction site and the desired mutation. Using this method, more than 20 mutants have already been generated (using two different kinds of templates); all these mutants were sequenced for the desired mutation and transfected into AtT-20 cells and the expressed mutant proteins encoded by the vector were assayed.