Generalization of the effective Wiener-Ikehara theorem

International audienceWe consider the classical Wiener–Ikehara Tauberian theorem, with a generalized condition of slow decrease and some additional poles on the boundary of convergence of the Laplace transform. In this generality, we prove the otherwise known asymptotic evaluation of the transformed function, when the usual conditions of the Wiener-Ikehara theorem hold. However, our version also provides an effective error term, not known thus far in this generality. The crux of the proof is a proper asymptotic variation of the lemmas of Ganelius and Tenenbaum, also constructed for the sake of an effective version of the Wiener–Ikehara theorem

Structural and hydrogen storage characterization of nanocrystalline magnesium synthesized by ECAP and catalyzed by different nanotube additives

Ball-milled nanocrystalline Mg powders catalyzed by TiO2 powder, titanate nanotubes and carbon nanotubes were subjected to intense plastic deformation by equal-channel angular pressing. Microstructural characteristics of these nanocomposites have been investigated by X-ray diffraction. Microstructural parameters, such as the average crystallite size, the average dislocation density and the average dislocation distance have been determined by the modified Williamson–Hall analysis. Complementary hydrogen desorption and absorption experiments were carried out in a Sieverts’ type apparatus. It was found that the Mg-based composite catalyzed by titanate nanotubes exhibits the best overall H-storage performance, reaching 7.1 wt% capacity. The hydrogenation kinetic curves can be fitted by the contracting volume function for all the investigated materials. From the fitted parameters, it is confirmed that the titanate nanotube additive results in far the best kinetic behavior, including the highest hydride front velocity

Harmonikus analízis és additív kombinatorika = Harmonic analysis and additive combinatorics

A jelen pályázatban több cikkünkben kutatást folytattunk különböző struktúrákban összeg- és különbséghalmazok elemszámára vonatkozóan. Általánosítottuk nem kommutatív struktúrákban Plünnecke-tételét. Eredményeket értünk el kommutatív csoportokban a Freiman tétel általánosítására. Ritka halmazok összeghalmazában található számtani sorozatok hosszára adtunk becslést. Az ismert legerősebb formában igazoljuk a Balog-Szemerédi tételt. Hilbert kockákat vizsgáltunk véletlen halmazokban és extremális szempontból. Eredményeink eléréséhez kombinatorikus, valószínűségszámítási módszereket, valamint exponenciális összegeket használtunk. | We have several new publications in which we study the size of sum and/or difference sets in various structures. For example, the generalization of Plünnecke's Theorem to non-commutative groups is provided. Furthermore we have partial results towards the generalization of Freiman's Theorem in commutative groups. We have found new bounds for the length of the longest arithmetic progressions in the sumset of sparse sets. We have proved the Balog-Szemerédi's Theorem in the strongest form at present. We have studied Hilbert's cubes in random sets, we have done it from extremal point of view as well. To derive the above results we have used combinatorial and probabilistic methods frequently with a combination of the method of trigonometric sums and Fourier-analysis

Sociodemographic, clinical, lifestyle, and psychological correlates of peripheral neuropathy among 2- to 12-year colorectal cancer survivors

Background Peripheral neuropathy (PN) is a debilitating complication among colorectal cancer (CRC) survivors that can become chronic. No large-scale study has yet analyzed correlates in multivariable models. We did multivariable analyses to find correlates of PN. Methods In 1,516 all-stage Dutch CRC survivors, cross-sectional data were collected on sensory, motor, autonomic and total PN, sociodemographic (age, sex, education, employment, partner), clinical (time since diagnosis, tumor location, stage, chemotherapy, radiotherapy, co-morbidities), lifestyle (alcohol, smoking, physical activity, body mass index), psychological factors (anxiety, depression, personality) and health-related quality of life (HRQoL). After multiple imputation, correlates were analyzed with linear regressions and eliminated with backwards selection. Results CRC survivors (69 years; 42% female) were on average five years post-diagnosis, and 28-65% reported PN. PN was associated with older age, being male (sensory) or female (motor), shorter time since diagnosis, chemotherapy, co-morbidities, anxiety, depression, and worse scores on HRQoL domains, and pain, nausea, vomiting, insomnia, constipation and financial problems. Conclusions In multivariable analyses, PN is affected by receiving chemotherapy, aging, sex, co-morbidities, stress-related factors and HRQoL in CRC survivors. Future PN-related studies can include these factors, and they can be examined in longitudinal studies to gain more knowledge about chronicity and severity of PN

Anxiety and depression mediate the association between chemotherapy-induced peripheral neuropathy and fatigue:Results from the population-based PROFILES registry

Objective Chemotherapy‐induced sensory peripheral neuropathy (CIPN) is common among colorectal cancer (CRC) survivors. The aim of this study was to examine whether CIPN is associated with both psychological distress (ie, anxiety and depression) and fatigue and whether the relationship between CIPN and fatigue can (partly) be explained by psychological distress. Methods All CRC survivors diagnosed between 2000 and 2009 as registered by the population‐based Netherlands Cancer Registry (Eindhoven region) were eligible for participation. Chemotherapy‐treated survivors completed questions on CIPN (EORTC QLQ‐CIPN20), psychological distress (HADS), and fatigue (FAS) on average 5.6 years after diagnosis. Simple and multiple mediation analyses were performed to examine anxiety and depression as possible mediators in the association between CIPN and fatigue. Results Survivors with high (ie, upper 30% of scores) CIPN (n = 172) reported more anxiety and depressive symptoms and more fatigue compared with those with low CIPN (n = 299). Furthermore, among survivors with high CIPN, those who were anxious, depressed, or both reported more fatigue compared with those without psychological distress. These differences were clinically relevant. Finally, mediation analyses showed that while CIPN was directly associated with fatigue, the relationship between CIPN and fatigue was also significantly mediated by both anxiety and depression. Conclusions CRC survivors with high CIPN report more fatigue, especially those who are also anxious and/or depressed. More research is needed on the direction of the relationship between CIPN, psychological distress, and fatigue. For now, the treatment of fatigue should also focus on addressing psychological distress, as treating fatigue alone might not be sufficient

The maximum modulus of a trigonometric trinomial

Let Lambda be a set of three integers and let C_Lambda be the space of 2pi-periodic functions with spectrum in Lambda endowed with the maximum modulus norm. We isolate the maximum modulus points x of trigonometric trinomials T in C_Lambda and prove that x is unique unless |T| has an axis of symmetry. This permits to compute the exposed and the extreme points of the unit ball of C_Lambda, to describe how the maximum modulus of T varies with respect to the arguments of its Fourier coefficients and to compute the norm of unimodular relative Fourier multipliers on C_Lambda. We obtain in particular the Sidon constant of Lambda

Fundamentals of interface phenomena in advanced bulk nanoscale materials

The review is devoted to a study of interface phenomena influencing advanced properties of nanoscale materials processed by means of severe plastic deformation, high-energy ball milling and their combinations. Interface phenomena include processes of interface defect structure relaxation from a highly nonequilibrium state to an equilibrium condition, grain boundary phase transformations and enhanced grain boundary and triple junction diffusivity. On the basis of an experimental investigation, a theoretical description of the key interfacial phenomena controlling the functional properties of advanced bulk nanoscale materials has been conducted. An interface defect structure investigation has been performed by TEM, high-resolution x-ray diffraction, atomic simulation and modeling. The problem of a transition from highly non-equilibrium state to an equilibrium one, which seems to be responsible for low thermostability of nanoscale materials, was studied. Also enhanced grain boundary diffusivity is addressed. Structure recovery and dislocation emission from grain boundaries in nanocrystalline materials have been investigated by analytical methods and modeling