We evaluate asymptotically the variance of number squarefree integers up to $x$ in short intervals length $H < x^{6/11 - \varepsilon}$ and arithmetic progressions modulo $q$ with $q > x^{5/11 + \varepsilon}$. On assumption respectively Lindel\"of Hypothesis Generalized we show that these ranges can be improved x^{2/3 x^{1/3 Furthermore obtaining a bound sharp factors $H^{\varepsilon}$ full rang...

We provide a few natural applications of the analytic newvectors, initiated in \cite{JN} arXiv:1911.01880, to some questions automorphic forms for $\mathrm{PGL}_n(\mathbb{Z})$ with $n\ge 2$, archimedean conductor aspect. prove an orthogonality result Fourier coefficients, density estimate non-tempered forms, equidistribution Satake parameters respect Sato--Tate measure, and second moment centra...

We provide an in-depth discussion of a theoretical framework recently introduced [Lindel et al., Phys. Rev. A 102, 041701(R) (2020)] which is capable predicting the electromagnetic field emerging from nonlinear crystal through coherent laser pulse shone. This based on macroscopic quantum electrodynamics and includes dispersion absorption effects inside allows for arbitrary optical environments ...

The modified free entropy dimension of certain n-tuples of self-adjoint operators, satisfying sequential commutation, is shown to be ≤ 1. In particular the von Neumann algebras of type II1 of the groups SL(n,Z), n ≥ 3 have generators with free entropy dimension ≤ 1. The free entropy χ(X1, . . . , Xn) and the modified free entropy dimension δ0(X1, . . . , Xn) of an n-tuple of selfadjoint element...

Until recently, all known constructions of oblivious transfer protocols based on general hardness assumptions had the following form. First, the hardness assumption is used in a black-box manner (i.e., the construction uses only the input/output behavior of the primitive guaranteed by the assumption) to construct a semi-honest oblivious transfer, a protocol whose security is guaranteed to hold ...

BACTERIAL ENDOCARDITIS following intracardiac surgery for congenital defects with use of extracorporeal circulation is a new entity, as old only as open intracardiac surgery. The reported experience is therefore meager. Suggestions regarding its pathogenesis, recognition, behavior, management, and prevention are few. Heins and Lindel reported five cases of bacterial endocarditis in a series of ...

This study aims to structure and evaluate a new COVID-19 model which predicts vaccination effect in the Kingdom of Saudi Arabia (KSA) under Atangana-Baleanu-Caputo (ABC) fractional derivatives. On statistical aspect, we analyze collected data fully vaccinated people from June 01, 2021, February 15, 2022. Then apply Eviews program find best for predicting against this pandemic, based on daily se...