ON THE DIGITS OF SUMSETS

Let A, B be large subsets of {1,. .. , N }. We study the number of pairs (a, b) ∈ A × B such that the sum of binary digits of a + b is fixed

Multi-resolution Modeling of Dynamic Signal Control on Urban Streets

Dynamic signal control provides significant benefits in terms of travel time, travel time reliability, and other performance measures of transportation systems. The goal of this research is to develop and evaluate a methodology to support the planning for operations of dynamic signal control utilizing a multi-resolution analysis approach. The multi-resolution analysis modeling combines analysis, modeling, and simulation (AMS) tools to support the assessment of the impacts of dynamic traffic signal control. Dynamic signal control strategies are effective in relieving congestions during non-typical days, such as those with high demands, incidents with different attributes, and adverse weather conditions. This research recognizes the need to model the impacts of dynamic signal controls for different days representing, different demand and incident levels. Methods are identified to calibrate the utilized tools for the patterns during different days based on demands and incident conditions utilizing combinations of real-world data with different levels of details. A significant challenge addressed in this study is to ensure that the mesoscopic simulation-based dynamic traffic assignment (DTA) models produces turning movement volumes at signalized intersections with sufficient accuracy for the purpose of the analysis. Although, an important aspect when modeling incident responsive signal control is to determine the capacity impacts of incidents considering the interaction between the drop in capacity below demands at the midblock urban street segment location and the upstream and downstream signalized intersection operations. A new model is developed to estimate the drop in capacity at the incident location by considering the downstream signal control queue spillback effects. A second model is developed to estimate the reduction in the upstream intersection capacity due to the drop in capacity at the midblock incident location as estimated by the first model. These developed models are used as part of a mesoscopic simulation-based DTA modeling to set the capacity during incident conditions, when such modeling is used to estimate the diversion during incidents. To supplement the DTA-based analysis, regression models are developed to estimate the diversion rate due to urban street incidents based on real-world data. These regression models are combined with the DTA model to estimate the volume at the incident location and alternative routes. The volumes with different demands and incident levels, resulting from DTA modeling are imported to a microscopic simulation model for more detailed analysis of dynamic signal control. The microscopic model shows that the implementation of special signal plans during incidents and different demand levels can improve mobility measures

Autour d'un théorème de Piatetski-Shapiro (Nombres premiers dans la suite [n^c])

This work deals with Piatetski-Shapiro's problem: the arithmetic properties of the sequence [n^c]. It is proved that this sequence contains the expected number of primes whenever c < 1.15417 ..., thus improving Kolesnik's result with c < 1.147 .... It is also proved that this result can be extended to almost every c < 2, in the sense of Lebesgue's mesure, even with sequences of a more general type. A lower bound of the expected number of primes in the sequence, with the correct order of magnitude, is shown to hold true whenever c < 1.166 ..., using Rosser-Iwaniec's sieve. Some related problems are also tackled. A result of Balog on the repartition of p^θ modulo 1 is proved by an elementary method. It is proved that for c < 1.05851..., every sufficiently large odd integer can be written as the sum of three primes of the above sequence, thus improving the value 1.05 given by Balog and Friedlander. It is proved that the number of representations of an integer as the sum of two numbers from the above sequence has the expected order of magnitude for c < 6/5. Most of these results were obtained with exponential sums estimates, using the double large sieve of Bombieri and Iwaniec.Dans ce travail, on s'intéresse au problème de Piatetski-Shapiro, c'est-à-dire qu'on étudie diverses propriétés arithmétiques de la suite [n^c]. On démontre que cette suite contient le nombre attendu de premiers pourvu que c < 1.15147..., améliorant ainsi le résultat de Kolesnik pour c < 1.147.... On montre de plus que ce résultat peut s'étendre à presque tout c < 2, au sens de la mesure de Lebesgue, et ceci pour des suites d'un type nettement plus général que celui énoncé précédemment. On donne également une minoration du nombre attendu de premiers dans cette suite possédant le bon ordre de grandeur pour c < 1.166..., en utilisant le crible linéaire de Rosser-Iwaniec. Plusieurs problèmes voisins ont été également abordés. On donne une méthode élémentaire pour retrouver un résultat de Balog sur la répartition de p^θ modulo 1. On montre que pour c < 1.05851..., tout entier naturel impair assez grand s'écrit comme somme de trois nombres premiers de la forme [n^c], améliorant la valeur 1.05 donnée par Balog et Friedlander. On prouve enfin que le nombre de représentations d'un entier comme somme de deux nombres de la forme [n^c] a l'ordre de grandeur escompté pour c < 6/5. La plupart de ces résultats sont dus à des estimations de sommes d'exponentielles, utilisant en particulier le double grand crible de Bombieri et Iwaniec

Autour d'un theoreme de Piatetski-Shapiro (Nombres premiers dans la suite partie entiere de n puissance c)

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : TD 82270 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

The Theorem of Vinogradov

International audienceHardy and Littlewood have shown in 1922 that assuming the Riemann hypothesis, we could deduce that every large enough odd integer is the sum of three prime numbers

On the metric theory of continued fractions

International audienc

Riemann’s Zeta Function

International audienc

A. Undecomposable matrices in dimension 3 (by J. Rivat)

International audienc

Dirichlet Series

International audienc

Euler’s Gamma Function

International audienceFor proofs of the following results, see for example Chapters 12 and 13 of Whittaker and Watson (A Course of Modern Analysis. Cambridge University Press, Cambridge, 1996)