Sobolev Type Decomposition of Paley-Wiener-Schwartz Space with Application to Sampling Theory

2000 Mathematics Subject Classification: 94A12, 94A20, 30D20, 41A05.

Fractional Trigonometric Korovkin Theory in Statistical Sense

2000 Mathematics Subject Classification: 41A25, 41A36.

Irreducibility of Random Hilbert Schemes

We prove that a random Hilbert scheme that parametrizes the closed subschemes with a fixed Hilbert polynomial in some projective space is irreducible and nonsingular with probability greater than $0.5$. To consider the set of nonempty Hilbert schemes as a probability space, we transform this set into a disjoint union of infinite binary trees, reinterpreting Macaulay's classification of admissible Hilbert polynomials. Choosing discrete probability distributions with infinite support on the trees establishes our notion of random Hilbert schemes. To bound the probability that random Hilbert schemes are irreducible and nonsingular, we show that at least half of the vertices in the binary trees correspond to Hilbert schemes with unique Borel-fixed points.

Strontium isotopes and sedimentology of a marine Triassic succession (upper Ladinian) of the westernmost Tethys, Spain

Chemical Stratigraphy, or the study of the variation of chemical elements within sedimentary sequences, has gradually become an experienced tool in the research and correlation of global geologic events. In this paper 87Sr/ 86Sr ratios of the Triassic marine carbonates (Muschelkalk facies) of southeast Iberian Ranges, Iberian Peninsula, are presented and the representative Sr-isotopic curve constructed for the upper Ladinian interval. The studied stratigraphic succession is 102 meters thick, continuous, and well preserved. Previous paleontological data from macro and micro, ammonites, bivalves, foraminifera, conodonts and palynological assemblages, suggest a Fassanian-Longobardian age (Late Ladinian). Although diagenetic minerals are present in small amounts, the elemental data content of bulk carbonate samples, especially Sr contents, show a major variation that probably reflects palaeoenvironmental changes. The 87Sr/86Sr ratios curve shows a rise from 0.707649 near the base of the section to 0.707741 and then declines rapidly to 0.707624, with a final values rise up to 0.70787 in the upper part. The data up to meter 80 in the studied succession is broadly concurrent with 87Sr/86Sr ratios of sequences of similar age and complements these data. Moreover, the sequence stratigraphic framework and its key surfaces, which are difficult to be recognised just based in the facies analysis, are characterised by combining variations of the Ca, Mg, Mn, Sr and CaCO3 contents

Deterministic Genericity and the Computation of homological Invariants

The main goal of this thesis is to discuss the determination of homological invariants of polynomial ideals. Thereby we consider different coordinate systems and analyze their meaning for the computation of certain invariants. In particular, we provide an algorithm that transforms any ideal into strongly stable position if char k = 0. With a slight modification, this algorithm can also be used to achieve a stable or quasi-stable position. If our field has positive characteristic, the Borel-fixed position is the maximum we can obtain with our method. Further, we present some applications of Pommaret bases, where we focus on how to directly read off invariants from this basis. In the second half of this dissertation we take a closer look at another homological invariant, namely the (absolute) reduction number. It is a known fact that one immediately receives the reduction number from the basis of the generic initial ideal. However, we show that it is not possible to formulate an algorithm – based on analyzing only the leading ideal – that transforms an ideal into a position, which allows us to directly receive this invariant from the leading ideal. So in general we can not read off the reduction number of a Pommaret basis. This result motivates a deeper investigation of which properties a coordinate system must possess so that we can determine the reduction number easily, i.e. by analyzing the leading ideal. This approach leads to the introduction of some generalized versions of the mentioned stable positions, such as the weakly D-stable or weakly D-minimal stable position. The latter represents a coordinate system that allows to determine the reduction number without any further computations. Finally, we introduce the notion of β-maximal position, which provides lots of interesting algebraic properties. In particular, this position is in combination with weakly D-stable sufficient for the weakly D-minimal stable position and so possesses a connection to the reduction number.

Funzioni BV e disuguaglianze isoperimetriche

All'interno della mia tesi verrà introdotta la teoria delle funzioni in R^{n} a variazione limitata (BV), seguendo le presentazioni di Lawrence C.Evans e Ronald F.Gariepy nel libro Measure Theory and Fine Properties of Functions e di Enrico Giusti nell'opera Minimal Surfaces and Functions of Bounded Variation. Le funzioni BV sono funzioni le cui derivate prime deboli sono misure di Radon, ossia misure di Borel regolari finite sui compatti. In particolare verranno anche analizzati gli insiemi E che hanno perimetro finito, ossia tali che la funzione indicatrice dell’insieme E sia una funzione BV. Nello specifico, nel primo capitolo verranno date le definizioni di funzioni BV e insiemi di perimetro finito, sia in una versione globale che in una locale, verrà enunciato un primo importante teorema per le funzioni BV e verrà analizzata la relazione tra funzioni di Sobolev e funzioni BV. Nel secondo capitolo, invece, verranno analizzate la semicontinuità inferiore, l'approssimazione con funzioni lisce e la compattezza di funzioni BV, mentre nel terzo capitolo verranno elencati alcuni risultati sulle funzioni BV riguardanti la Traccia, l'Estensione e la formula di Coarea. Infine, nel quarto ed ultimo capitolo, verranno studiate le disuguaglianze di Sobolev e Poincaré e le disuguaglianze isoperimetriche per funzioni BV.

Research on Behavioral Integrity: A Promising Construct for Positive Organizational Scholarship

Behavioral integrity (BI) is the perception that another person, group, or entity lives by his word—delivers on promises and enacts the same values he espouses. This construct is more basic than trust or justice, and is typically measured as the perceived pattern of alignment between words and deeds. Empirical studies have shown it to have powerful positive consequences for the attitudes and performance of followers, managers, and organizations, and also that BI moderates the impact of other leader behaviors on these outcomes. Only a few studies have examined antecedents, and fewer still have examined moderated antecedents. Although initial terrain has been sketched out by early studies, there is much yet to learn about the workings of this high-potential construct.

Contact dermatitis from shoes: an update

Contact dermatitis is a common inflammatory skin condition characterized by erythematous and pruritic skin lesions that occur after contact with a foreign substance. There are two forms of contact dermatitis: irritant and allergic. Irritant contact dermatitis is caused by the non–immune-modulated irritation of the skin by a substance, leading to skin changes. Allergic contact dermatitis is a delayed hypersensitivity reaction in which a foreign substance comes into contact with the skin; skin changes occur after reexposure to the substance. A medical condition referred to as “shoe dermatitis” is a form of contact dermatitis caused by the contact of the foot with parts of the shoe due to these materials. Shoe dermatitis is a diagnostic and therapeutic challenge and is a common type of contact dermatitis. It is imperative the foot and ankle physician become familiar with recognizing signs and symptoms of shoe dermatitis so that their patients can be accurately diagnosis and appropriately treated to avoid secondary infections and disability. This review will first present causative factors for the etiology of shoe contact dermatitis supported by clinical-based evidence as found in the medical literature. Secondly, a description of the signs and symptoms of shoe contact dermatitis will be presented in a narrative fashion. Finally, both treatment options and preventative measures to avoid shoe.

Do breech presentations in twins and singletons run different risks?

SCOPUS: no.j

Origin and ecological selection of core and food-specific bacterial communities associated with meat and seafood spoilage

The microbial spoilage of meat and seafood products with short shelf lives is responsible for a significant amount of food waste. Food spoilage is a very heterogeneous process, involving the growth of various, poorly characterized bacterial communities. In this study, we conducted 16S ribosomal RNA gene pyrosequencing on 160 samples of fresh and spoiled foods to comparatively explore the bacterial communities associated with four meat products and four seafood products that are among the most consumed food items in Europe. We show that fresh products are contaminated in part by a microbiota similar to that found on the skin and in the gut of animals. However, this animal-derived microbiota was less prevalent and less abundant than a core microbiota, psychrotrophic in nature, mainly originated from the environment (water reservoirs). We clearly show that this core community found on meat and seafood products is the main reservoir of spoilage bacteria. We also show that storage conditions exert strong selective pressure on the initial microbiota: alpha diversity in fresh samples was 189 +/- 58 operational taxonomic units (OTUs) but dropped to 27 +/- 12 OTUs in spoiled samples. The OTU assemblage associated with spoilage was shaped by low storage temperatures, packaging and the nutritional value of the food matrix itself. These factors presumably act in tandem without any hierarchical pattern. Most notably, we were also able to identify putative new clades of dominant, previously undescribed bacteria occurring on spoiled seafood, a finding that emphasizes the importance of using culture-independent methods when studying food microbiota.