Results 61 to 70 of about 9,640 (238)

EXPONENTIAL SUMS OVER PRIMES IN SHORT INTERVALS AND AN APPLICATION TO THE WARING–GOLDBACH PROBLEM [PDF]

Mathematika, 2016
Let $ (n)$ be the von Mangoldt function, $x$ real and $2\leq y \leq x$. This paper improves the estimate on the exponential sum over primes in short intervals \[ S_k(x,y; ) = \sum_{x< n \leq x+y} (n) e\left( n^k \right) \] when $k\geq 3$ for $ $ in the minor arcs.
openaire   +2 more sources

Enhancing Low‐Temperature Performance of Sodium‐Ion Batteries via Anion‐Solvent Interactions

Advanced Functional Materials, EarlyView.
DOL is introduced into electrolytes as a co‐solvent, increasing slat solubility, ion conductivity, and the de‐solvent process, and forming an anion‐rich solvent shell due to its high interaction with anion. With the above virtues, the batteries using this electrolyte exhibit excellent cycling stability at low temperatures. Abstract Sodium‐ion batteries
Cheng Zheng, Qian Yao, Yanan Sun, Hongyu Lv, Zhongchao Bai, Guoliang Zhang, Nana Wang, Jian Yang   +7 more
wiley   +1 more source

Pentagonal 2D Altermagnets: Material Screening and Altermagnetic Tunneling Junction Device Application

Advanced Functional Materials, EarlyView.
From a database of 170 pentagonal 2D materials, 4 candidates exhibiting altermagnetic ordering are screened. Furthermore, the spin‐splitting and unconventional boundary states in the pentagonal 2D altermagnetic monolayer MnS2 are investigated. A MnS2‐based altermagnetic tunneling junction is designed and, through ab initio quantum transport simulations,
Jianhua Wang, Xingyue Yang, Zongmeng Yang, Jing Lu, Pin Ho, Wenhong Wang, Yee Sin Ang, Zhenxiang Cheng, Shibo Fang   +8 more
wiley   +1 more source

Estimates for the number of sums and products and for exponential sums over subgroups in fields of prime order

Comptes Rendus. Mathématique, 2003
Our first result is a ‘sum–product’ theorem for subsets A of the finite field 𝔽 p , p prime, providing a lower bound on max(|A+A|,|A·A|). As corollary, the second and main result provides new bounds on exponential sums associated to subgroups of the multiplicative group 𝔽 p * .
Bourgain, Jean, Konyagin, S. V.
openaire   +1 more source

Biodegradable and Recyclable Luminescent Mixed‐Matrix‐Membranes, Hydrogels, and Cryogels based on Nanoscale Metal‐Organic Frameworks and Biopolymers

Advanced Functional Materials, EarlyView.
The study presents biodegradable and recyclable mixed‐matrix membranes (MMMs), hydrogels, and cryogels using luminescent nanoscale metal‐organic frameworks (nMOFs) and biopolymers. These bio‐nMOF‐MMMs combine europium‐based nMOFs as probes for the status of the materials with the biopolymers agar and gelatine and present alternatives to conventional ...
Moritz Maxeiner, Julian Burkhart, Kateryna Borysova, Chiara Mazzariol, Klaus Müller‐Buschbaum   +4 more
wiley   +1 more source

Exponential sums over primes are unbounded

We prove prime exponential sums have no better than square root cancellation on average on short intervals, in the sense that $$\frac{1}{x} \sum_{-y< n\le x} \left|\sum_{\substack{n< m \le n+y\\ 1\le m \le x}} Λ(m) \mathrm{e}(αm)\right|^2 \gg y\log y$$ whenever $y \ll x^{1/3-\varepsilon}.$ This answers a question of Ramaré by proving the lower ...
openaire   +2 more sources

Generalising the Hardy-Littlewood Method for Primes

, 2006
The Hardy-Littlewood method is a well-known technique in analytic number theory. Among its spectacular applications are Vinogradov's 1937 result that every sufficiently large odd number is a sum of three primes, and a related result of Chowla and Van der
Green, Ben
core   +2 more sources

Combinatorial Synthesis of Next Generation Water‐Soluble Quaternized N‐Halamine Oligomers with Long‐Lasting Antiviral Properties

Advanced Functional Materials, EarlyView.
A combinatorial library of dual‐functional antiviral oligomers incorporating N‐halamine and quaternary ammonium functionalities is developed for long‐lasting antiviral activity. The lead materials exhibit rapid and durable antiviral activity against SARS‐CoV‐2 variants and influenza H1N1, with 4 to 5 log reduction in viral copies at 5 mg mL−1 ...
Eid Nassar‐Marjiya, Konda Reddy Kunduru, Krishanu Ghosal, Luna Rizik, Nofar Atari, Mahran Daifa, Neta Kutner, Bassma Khamaisi, Qi Wu, Simran Jindal, Merna Shaheen‐Mualim, Ranabir Majumder, Mahitosh Mandal, Michal Mandelboim, Shady Farah   +14 more
wiley   +1 more source

Vinogradov's Theorem with Fouvry-Iwaniec Primes

, 2018
We show that every sufficiently large $x\equiv 3(4)$ can be written as the sum of three primes, each of which is a sum of a square and a prime square. The main tools are a transference version of the circle method and various sieve related ideas.Comment:
Grimmelt, Lasse
core  

Demonstration of an All‐Optical AND Gate Mediated by Photochromic Molecules

Advanced Functional Materials, EarlyView.
A logic AND gate that runs on photons is demonstrated. It relies on two spatially separated photochromic molecules that work in tandem. Abstract The realization of a photonic logic AND gate, i.e. a logic AND gate that runs on photons rather than electrons, and where all steps are controlled by light, is demonstrated. In a proof‐of‐principle experiment,
Heyou Zhang, Max Gießübel, Pankaj Dharpure, Andrea Albert, Vira Niestierkina, Paul Mulvaney, Mukundan Thelakkat, Jürgen Köhler   +7 more
wiley   +1 more source