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Elliptic Theory for Sets with Higher Co-dimensional Boundaries
Many geometric and analytic properties of sets hinge on the properties of elliptic measure, notoriously missing for sets of higher
co-dimension. The aim of this manuscript is to develop a version of elliptic theory, associated to a linear PDE, which ultimately yields
a notion analogous to that of the harmonic measure, for sets of codimension higher than 1.
To this end, we turn to degenerate
elliptic equations. Let
In another article to appear, we will prove that when
eBook
Price-based investment strategies : how research discoveries reinvented technical analysis
This compelling book examines the price-based revolution in investing, showing how research over recent decades has reinvented technical analysis. The authors discuss the major groups of price-based strategies, considering their theoretical motivation, individual and combined implementation, and back-tested results when applied to investment across country stock markets. Containing a comprehensive sample of performance data, taken from 24 major developed markets around the world and ranging over the last 25 years, the authors construct practical portfolios and display their performance - ensuring the book is not only academically rigorous, but practically applicable too.
Book
Multi-Parameter Hardy Spaces Theory and Endpoint Estimates for Multi-Parameter Singular Integrals
The main purpose of this paper is to establish the theory of the multi-parameter Hardy spaces
More precisely, Street (2014) studied the
eBook
Singular integrals in quantum Euclidean spaces
We shall establish the core of singular integral theory and pseudodifferential calculus over the archetypal algebras of
noncommutative geometry: quantum forms of Euclidean spaces and tori. Our results go beyond Connes’ pseudodifferential calculus for
rotation algebras, thanks to a new form of Calderón-Zygmund theory over these spaces which crucially incorporates nonconvolution
kernels. We deduce
eBook
Characterization of Micronutrients, Bioaccessibility and Antioxidant Activity of Prickly Pear Cladodes as Functional Ingredient
The Opuntia ficus indica (L.) (OFI) is used as a nutritional and pharmaceutical agent in various dietary and value added products. This study underlines the possible use of native prickly pear cladode powder as a functional ingredient for health-promoting food production. To summarise, chemical characterization of polyphenols, minerals and soluble dietary fibre was performed; furthermore, the antioxidant activity and bioaccessibility of polyphenols and minerals were assessed. Eleven compounds between phenolic acids and flavonoids were identified, with piscidic acid and isorhamnetin derivatives being the most abundant. Opuntia’s dietary fibre was mainly constituted of mucilage and pectin, and was composed of arabinose, galactose, glucose, mannose, rhamnose, and xylose sugars. The polyphenols’ bioaccessibility was very high: piscidic acid at 200%, eucomic and ferulic acids >110% and flavonoids from 89% to 100%. The prickly pear cladode powder is also a source of minerals, as cations (calcium, sodium, potassium and magnesium) and anions (sulphate and chloride), with high magnesium bioaccessibilty (93%). OFI powder showed good capacity of radical scavenging measured by DPPH and ABTS methods, with 740 and 775 μmol Trolox/100 g OFI, respectively. Finally, the presented results allow the consideration of this natural product as a source of several essential nutrients, with a possible use in the food industry as a functional ingredient.
Journal Article
Maximal Functions, Littlewood–Paley Theory, Riesz Transforms and Atomic Decomposition in the Multi-parameter Flag Setting
In this paper, we develop via real variable methods various characterisations of the Hardy spaces in the multi-parameter flag
setting. These characterisations include those via, the non-tangential and radial maximal function, the Littlewood–Paley square function
and area integral, Riesz transforms and the atomic decomposition in the multi-parameter flag setting. The novel ingredients in this
paper include (1) establishing appropriate discrete Calderón reproducing formulae in the flag setting and a version of the
Plancherel–Pólya inequalities for flag quadratic forms; (2) introducing the maximal function and area function via flag Poisson kernels
and flag version of harmonic functions; (3) developing an atomic decomposition via the finite speed propagation and area function in
terms of flag heat semigroups. As a consequence of these real variable methods, we obtain the full characterisations of the
multi-parameter Hardy space with the flag structure.
eBook