Decompositions of spaces of measures

Let M be the Banach space of sigma-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of M is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon-Nikodym theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen-Wintner purity theorem for our decompositions.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

A novel shrinkage technique based on the normal inverse Gaussian density model

This paper proposes a novel image denoising technique based on the normal inverse Gaussian (NIG) density model using an extended non-negative sparse coding (NNSC) algorithm proposed by us. This algorithm can converge to feature basis vectors, which behave in the locality and orientation in spatial and frequency domain. Here, we demonstrate that the NIG density provides a very good fitness to the non-negative sparse data. In the denoising process, by exploiting a NIG-based maximum a posteriori estimator (MAP) of an image corrupted by additive Gaussian noise, the noise can be reduced successfully. This shrinkage technique, also referred to as the NNSC shrinkage technique, is self-adaptive to the statistical properties of image data. This denoising method is evaluated by values of the normalized signal to noise rate (SNR). Experimental results show that the NNSC shrinkage approach is indeed efficient and effective in denoising. Otherwise, we also compare the effectiveness of the NNSC shrinkage method with methods of standard sparse coding shrinkage, wavelet-based shrinkage and the Wiener filter. The simulation results show that our method outperforms the three kinds of denoising approaches mentioned above.

Full-Scale Marine Exposure Tests on Treated and Untreated Concretes Initial 7-Year Results

An extensive chloride profiling program was undertaken on concrete pier stems erected in the vicinity of the Dornoch Bridge located at the Dornoch Firth in Northeast Scotland. The pier stems were 2 m (6.562 ft) high and octagonal in plan with 0.66 m (2.165 ft) wide faces. The piers were constructed in sets of three with the lowest of each set in the tidal zone and the highest in the atmospheric zone. The pier stems were placed in such a way that they would represent the exposure conditions of the actual bridge piers of the Dornoch Bridge. In all, six of the pier stems were made using plain ordinary portland cement (OPC) concrete (with three of these having the surface treated with silane); the remaining three pier stems had a concrete containing caltite as an additive. Three exposurezones were studied: the tidal zone, the splash zone, and the atmospheric zone. The tidal zone was further subdivided into two levels defined as low-level and high-level. Chloride profiles were obtained from the different regimes over a period of 7 years for all nine pier stems. This paper describes the nature of chloride ingress and the usefulness of diffusion parameters in classifying each exposure regimes. Furthermore, the effectiveness of silane and caltite in protecting concrete from chloride ingress in different exposure zones was studied.

Effects of antidiabetic drugs on dipeptidyl peptidase IV activity: Nateglinide is an inhibitor of DPP IV and augments the antidiabetic activity of glucagon-like peptide-1

Dipeptidyl peptidase IV (DPP IV) is the primary inactivator of glucoregulatory incretin hormones. This has lead to development of DPP IV inhibitors as a new class of agents for the treatment of type 2 diabetes. Recent reports indicate that other antidiabetic drugs, such as metformin, may also have inhibitory effects on DPP IV activity. In this investigation we show that high concentrations of several antidiabetic drug classes, namely thiazolidinediones, sulphonylureas, meglitinides and morphilinoguanides can inhibit DPP IV The strongest inhibitor nateglinide, the insulin-releasing meglitinide was effective at low therapeutically relevant concentrations as low as 25 mu mol/l. Nateglinide also prevented the degradation of glucagon-like peptide-1 (GLP-1) by DPP IV in a time and concentration-dependent manner. In vitro nateglinide and GLP-1 effects on insulin release were additive. In vivo nateglinide improved the glucose-lowering and insulin-releasing activity of GLP-1 in obese-diabetic ob/ob mice. This was accompanied by significantly enhanced circulating concentrations of active GLP-1(7-36)amide and lower levels of DPP IV activity. Nateglinide similarly benefited the glucose and insulin responses to feeding in ob/ob mice and such actions were abolished by coadministration of exendin(9-39) and (Pro(3))GIP to block incretin hormone action. These data indicate that the use of nateglinide as a prandial insulin-releasing agent may partly rely on inhibition of GLP-1 degradation as well as beta-cell K-ATP channel inhibition. (C) 2007 Elsevier B.V. All rights reserved.

Bio-folio: applying portfolio theory to biodiversity

Genes, species and ecosystems are often considered to be assets. The need to ensure a sufficient diversity of this asset is being increasingly recognised today. Asset managers in banks and insurance companies face a similar challenge. They are asked to manage the assets of their investors by constructing efficient portfolios. They deliberately make use of a phenomenon observed in the formation of portfolios: returns are additive, while risks diversify. This phenomenon and its implications are at the heart of portfolio theory. Portfolio theory, like few other economic theories, has dramatically transformed the practical work of banks and insurance companies. Before portfolio theory was developed about 50 years ago, asset managers were confronted with a situation similar to the situation the research on biodiversity faces today. While the need for diversification was generally accepted, a concept that linked risk and return on a portfolio level and showed the value of diversification was missing. Portfolio theory has closed this gap. This article first explains the fundamentals of portfolio theory and transfers it to biodiversity. A large part of this article is then dedicated to some of the implications portfolio theory has for the valuation and management of biodiversity. The last section introduces three development openings for further research.

Ionic liquids as solvent and solvent additives for the synthesis of sol-gel materials

The ionic liquid (IL) 1-butyl-3-methylimidazolium chloride was used as a drying control chemical additive in the synthesis of silica sol-gel materials with and without methanol as a co-solvent. The resulting gels were characterized by using thermogravimetric analysis, differential scanning calorimetry, infrared spectroscopy and water sorption kinetics. Calcined gels were analyzed using scanning electron microscopy and nitrogen adsorption isotherms for surface area and pore volume determination. Non-calcined gels were monolithic and showed general cloudiness with lesser degrees observed at higher IL volumes. Calcinations resulted in the formation of powders with increased available surface area as the amount of IL volume was increased. This is consistent with an increase in respective pore volume but a general decrease in average pore size. The resulting materials exhibited conventional structural microdomains, in contrast to periodicity reported when other ionic liquids were used as templates.

Two-dimensional Banach spaces with polynomial numerical index zero

We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.

Optimization of Cement Grouts Containing Silica Fume and Viscosity Modifying Admixture

There is an increasing need to identify the effect of mix composition on the rheological properties of cementitious grouts using minislump, Marsh cone, cohesion plate, washout test, and cubes to determine the fluidity, the cohesion, and other mechanical properties of grouting applications. Mixture proportioning involves the tailoring of several parameters to achieve adequate fluidity, cohesion, washout resistance and compressive strength. This paper proposes a statistical design approach using a composite fractional factorial design which was carried out to model the influence of key parameters on the performance of cement grouts. The responses relate to performance included minislump, flow time using Marsh cone, cohesion measured by Lombardi plate meter, washout mass loss and compressive strength at 3, 7, and 28 days. The statistical models are valid for mixtures with water-to-binder ratio of 0.37–0.53, 0.4–1.8% addition of high-range water reducer (HRWR) by mass of binder, 4–12% additive of silica fume as replacement of cement by mass, and 0.02–0.8% addition of viscosity modifying admixture (VMA) by mass of binder. The models enable the identification of underlying factors and interactions that influence the modeled responses of cement grout. The comparison between the predicted and measured responses indicated good accuracy of the established models to describe the effect of the independent variables on the fluidity, cohesion, washout resistance and the compressive strength. This paper demonstrates the usefulness of the models to better understand trade-offs between parameters. The multiparametric optimization is used to establish isoresponses for a desirability function for cement grout. An increase of HRWR led to an increase of fluidity and washout, a reduction in plate cohesion value, and a reduction in the Marsh cone time. An increase of VMA demonstrated a reduction of fluidity and the washout mass loss, and an increase of Marsh cone time and plate cohesion. Results indicate that the use of silica fume increased the cohesion plate and Marsh cone, and reduced the minislump. Additionally, the silica fume improved the compressive strength and the washout resistance.

A bargaining set for monotonic simple games based on external and internal stability

A new bargaining set based on notions of both internal and external stability is developed in the context of endogenous coalition formation. It allows to make an explicit distinction between within-group and outside-group deviation options. This type of distinction is not present in current bargaining sets. For the class of monotonic proper simple games, the outcomes in the bargaining set are characterized. Furthermore, it is shown that the bargaining set of any homogeneous weighted majority game contains an outcome for which the underlying coalition structure consists of a minimal winning coalition and its complement.

Coalitional Games and Contracts Based on Individual Deviations

We study what coalitions form and how the members of each coalition split the coalition value in coalitional games in which only individual deviations are allowed. In this context we employ three stability notions: individual, contractual, and compensational stability. These notions differ in terms of the underlying contractual assumptions. We characterize the coalitional games in which individually stable outcomes exist by means of the top-partition property. Furthermore, we show that any coalition structure of maximum social worth is both contractually and compensationally stable.

Country-wise differences in perception of health-related messages in cereal-based food products

The objective of the present study was to explore the impact of health-related messages on the perceived overall healthiness and consumers' likelihood to buy cereal-based products or non-cereal products containing beneficial compounds from grains, across four European countries. The data were collected from a sample of 2392 members of the public in Finland, Germany, Italy and the UK. The results from a conjoint task with a main effects additive model were reported. In general, the presence of a verbal health claim on foods had positive influence on respondents perception of healthiness and on likelihood to buy the products, whereas the pictorial health claims were found to have a weak influence on the two dependent variables. However, the findings showed that health-related information on food labels differently influenced the healthiness perception and the likelihood to buy the product across the four countries, suggesting that different cultures, traditions, and eating habits have to be taken into account before positioning cereal-based products containing beneficial compounds from grains on the market. (C) 2009 Elsevier Ltd. All rights reserved.