Results 91 to 100 of about 640,811 (318)
An explicit formula for the zeros of the Riemann zeta function [PDF]
arXiv, 2023 We present an explicit formula for a weighted sum over the zeros of the Riemann zeta function. This weighted sum is evaluated in terms of a sum over the prime numbers, weighted with help of the Hermite polynomials. From the explicit formula presented in this note, it follows that prime numbers determine the distribution of the zeros of the Riemann zeta
arxiv
Designing of Self‐Dispersing Soft Dendritic Microcleaners for Microplastics Capture and Recovery
Advanced Functional Materials, EarlyView.The capture and recovery of microplastics from open aquatic systems is a complex problem, which necessitates nontrivial solutions. The principles of a comprehensive multistage process based on sustainably sourced microcleaners with hierarchical morphology are demonstrated.
Haeleen Hong +3 more
wiley +1 more source
Adelic amplitudes and intricacies of infinite products
Nuclear Physics B, 2023 For every prime number p it is possible to define a p-adic version of the Veneziano amplitude and its higher-point generalizations. Multiplying together the real amplitude with all its p-adic counterparts yields the adelic amplitude.
Christian Baadsgaard Jepsen
doaj
Jacob's ladders and some unbounded decomposition of the $ζ$-oscillating systems on products of other $ζ$-oscillating systems as an $ζ$-analogue of the prime decomposition [PDF]
arXiv, 2017 In this paper we introduce new class of multiplicative interactions of the $\zeta$-oscillating systems generated by a subset of power functions. The main result obtained expresses an analogue of prime decomposition (without the property of uniqueness).
arxiv
Advanced Functional Materials, EarlyView.The fabrication of patterned transition metal dichalcogenide (TMD)/graphene heterostructures via direct laser writing reveals new interface chemistry and enables efficient, customizable assembly. Selective laser irradiation of functionalized TMD/graphene triggers localized reactions, forming chemically modified interfaces.
Xin Chen +12 more
wiley +1 more source
p-Adic open string amplitudes with Chan-Paton factors coupled to a constant B-field
Nuclear Physics B, 2020 We establish rigorously the regularization of the p-adic open string amplitudes, with Chan-Paton rules and a constant B-field, introduced by Ghoshal and Kawano.
H. García-Compeán +2 more
doaj
Counting Primes Rationally And Irrationally [PDF]
arXiv, 2019 The recent technique for estimating lower bounds of the prime counting function $\pi(x)=#\{p \leq x: p\text{ prime}\}$ by means of the irrationality measures $\mu(\zeta(s)) \geq 2$ of special values of the zeta function claims that $\pi(x) \gg \log \log x/\log \log \log x$.
arxiv
Sono‐Piezo‐Photosynthesis of Ethylene and Acetylene from Bioethanol under Ambient Conditions
Advanced Functional Materials, EarlyView.A novel sono‐piezo‐photocatalytic strategy enables the conversion of bioethanol to ethylene (C2H4) and acetylene (C2H2) under ambient conditions, addressing the limitations of conventional methods that are high‐temperature and energy‐intensive. By using an advanced graphene oxide/sodium bismuth titanate heterostructure catalyst, this work achieved ...
Yue Jiang +21 more
wiley +1 more source
Advanced Functional Materials, EarlyView.Oct4‐nanoscript, a biomimetic nanoparticle‐based artificial transcription factor, precisely regulates cellular rejuvenation by activating Oct4 target genes, restoring epigenetic marks, and reducing DNA damage. In a progeria model, it effectively rescued aging‐associated pathologies and extended lifespan.
Hongwon Kim +8 more
wiley +1 more source
On the Existence and Frequency Distribution of the Shell Primes
, 2016 This research presents the results of a study on the existence and frequency distribution of the shell primes defined herein as prime numbers that result from the calculation of the "half-shell" of an p-dimensional entity of the form $n^p-(n-1)^p$ where ...
May, Michael P.
core