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

Finite time and asymptotic behaviour of the maximal excursion of a random walk

We evaluate the limit distribution of the maximal excursion of a random walk in any dimension for homogeneous environments and for self-similar supports under the assumption of spherical symmetry. This distribution is obtained in closed form and is an approximation of the exact distribution comparable to that obtained by real space renormalization methods. Then we focus on the early time behaviour of this quantity. The instantaneous diffusion exponent $\nu_n$ exhibits a systematic overshooting of the long time exponent. Exact results are obtained in one dimension up to third order in $n^{-1/2}$. In two dimensions, on a regular lattice and on the Sierpi\'nski gasket we find numerically that the analytic scaling $\nu_n \simeq \nu+A n^{-\nu}$ holds.Comment: 9 pages, 4 figures, accepted J. Phys.

Fractional recurrence in discrete-time quantum walk

Quantum recurrence theorem holds for quantum systems with discrete energy eigenvalues and fails to hold in general for systems with continuous energy. We show that during quantum walk process dominated by interference of amplitude corresponding to different paths fail to satisfy the complete quantum recurrence theorem. Due to the revival of the fractional wave packet, a fractional recurrence characterized using quantum P\'olya number can be seen.Comment: 10 pages, 11 figure : Accepted to appear in Central European Journal of Physic

The maximum of the local time of a diffusion process in a drifted Brownian potential

We consider a one-dimensional diffusion process $X$ in a $(-\kappa/2)$-drifted Brownian potential for $\kappa\neq 0$. We are interested in the maximum of its local time, and study its almost sure asymptotic behaviour, which is proved to be different from the behaviour of the maximum local time of the transient random walk in random environment. We also obtain the convergence in law of the maximum local time of $X$ under the annealed law after suitable renormalization when $\kappa \geq 1$. Moreover, we characterize all the upper and lower classes for the hitting times of $X$, in the sense of Paul L\'evy, and provide laws of the iterated logarithm for the diffusion $X$ itself. To this aim, we use annealed technics.Comment: 38 pages, new version, merged with hal-00013040 (arXiv:math/0511053), with some additional result

Dual isotope analyses indicate efficient processing of atmospheric nitrate by forested watersheds in the northeastern U.S.

Author Posting. © Springer, 2008. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Biogeochemistry 90 (2008): 15-27, doi:10.1007/s10533-008-9227-2.Nitrogen from atmospheric deposition serves as the dominant source of new nitrogen to forested ecosystems in the northeastern U.S.. By combining isotopic data obtained using the denitrifier method, with chemistry and hydrology measurements we determined the relative importance of sources and control mechanisms on nitrate (NO3-) export from five forested watersheds in the Connecticut River watershed. Microbially produced NO3- was the dominant source (82-100%) of NO3- to the sampled streams as indicated by the δ15N and δ18O of NO3-. Seasonal variations in the δ18O-NO3- in streamwater are controlled by shifting hydrology and temperature affects on biotic processing, resulting in a relative increase in unprocessed NO3- export during winter months. Mass balance estimates find that the unprocessed atmospherically derived NO3- stream flux represents less than 3% of the atmospherically delivered wet NO3- flux to the region. This suggests that despite chronically elevated nitrogen deposition these forests are not nitrogen saturated and are retaining, removing, and reprocessing the vast majority of NO3- delivered to them throughout the year. These results confirm previous work within Northeastern U.S. forests and extend observations to watersheds not dominated by a snow-melt driven hydrology. In contrast to previous work, unprocessed atmospherically derived NO3- export is associated with the period of high recharge and low biotic activity as opposed to spring snowmelt and other large runoff events.This work was funded by an EPA STAR Fellowship (FP-91637501-1) and a grant from QLF/The Sound Conservancy to RTB

Nanomaterials by severe plastic deformation: review of historical developments and recent advances

International audienceSevere plastic deformation (SPD) is effective in producing bulk ultrafine-grained and nanostructured materials with large densities of lattice defects. This field, also known as NanoSPD, experienced a significant progress within the past two decades. Beside classic SPD methods such as high-pressure torsion, equal-channel angular pressing, accumulative roll-bonding, twist extrusion, and multi-directional forging, various continuous techniques were introduced to produce upscaled samples. Moreover, numerous alloys, glasses, semiconductors, ceramics, polymers, and their composites were processed. The SPD methods were used to synthesize new materials or to stabilize metastable phases with advanced mechanical and functional properties. High strength combined with high ductility, low/room-temperature superplasticity, creep resistance, hydrogen storage, photocatalytic hydrogen production, photocatalytic CO2 conversion, superconductivity, thermoelectric performance, radiation resistance, corrosion resistance, and biocompatibility are some highlighted properties of SPD-processed materials. This article reviews recent advances in the NanoSPD field and provides a brief history regarding its progress from the ancient times to modernity

Oxidative/Nitrative Stress and Inflammation Drive Progression of Doxorubicin-Induced Renal Fibrosis in Rats as Revealed by Comparing a Normal and a Fibrosis-Resistant Rat Strain

Chronic renal fibrosis is the final common pathway of end stage renal disease caused by glomerular or tubular pathologies. Genetic background has a strong influence on the progression of chronic renal fibrosis. We recently found that Rowett black hooded rats were resistant to renal fibrosis. We aimed to investigate the role of sustained inflammation and oxidative/nitrative stress in renal fibrosis progression using this new model. Our previous data suggested the involvement of podocytes, thus we investigated renal fibrosis initiated by doxorubicin-induced (5 mg/kg) podocyte damage. Doxorubicin induced progressive glomerular sclerosis followed by increasing proteinuria and reduced bodyweight gain in fibrosis-sensitive, Charles Dawley rats during an 8-week long observation period. In comparison, the fibrosis-resistant, Rowett black hooded rats had longer survival, milder proteinuria and reduced tubular damage as assessed by neutrophil gelatinase-associated lipocalin (NGAL) excretion, reduced loss of the slit diaphragm protein, nephrin, less glomerulosclerosis, tubulointerstitial fibrosis and matrix deposition assessed by periodic acid-Schiff, Picro-Sirius-red staining and fibronectin immunostaining. Less fibrosis was associated with reduced profibrotic transforming growth factor-beta, (TGF-beta1) connective tissue growth factor (CTGF), and collagen type I alpha 1 (COL-1a1) mRNA levels. Milder inflammation demonstrated by histology was confirmed by less monocyte chemotactic protein 1 (MCP-1) mRNA. As a consequence of less inflammation, less oxidative and nitrative stress was obvious by less neutrophil cytosolic factor 1 (p47phox) and NADPH oxidase-2 (p91phox) mRNA. Reduced oxidative enzyme expression was accompanied by less lipid peroxidation as demonstrated by 4-hydroxynonenal (HNE) and less protein nitrosylation demonstrated by nitrotyrosine (NT) immunohistochemistry and quantified by Western blot. Our results demonstrate that mediators of fibrosis, inflammation and oxidative/nitrative stress were suppressed in doxorubicin nephropathy in fibrosis-resistant Rowett black hooded rats underlying the importance of these pathomechanisms in the progression of renal fibrosis initiated by glomerular podocyte damage