Riemann hypothesis from the Dedekind psi function
, 2010 Let $\mathcal{P}$ be the set of all primes and $ (n)=n\prod_{n\in \mathcal{P},p|n}(1+1/p)$ be the Dedekind psi function. We show that the Riemann hypothesis is satisfied if and only if $f(n)= (n)/n-e^ \log \log n <0$ for all integers $n>n_0=30$ (D), where $ \approx 0.577$ is Euler's constant.
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Pattern Formation in Non‐Equilibrium Architected Materials
Advanced Materials Technologies, EarlyView.This article demonstrates an artificial mechanical system ‐ a robotic metamaterial ‐ as an accessible and versatile platform within which to explore and prescribe the reaction‐diffusion driven pattern formation hitherto associated with comparatively less accessible and versatile non‐equilibrium biological and chemical systems.
Vinod Ramakrishnan, Michael J. Frazier
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Microwave‐Assisted Aqueous Synthesis of Gelatin‐Norbornene for Hydrogel Crosslinking and Bioprinting
Advanced Materials Technologies, EarlyView.A microwave‐assisted reaction is utilized to synthesize gelatin‐norbornene (GelNB), achieving a high degree of norbornene functionalization while reducing the macromer's upper critical solution temperature. The resulting GelNB macromer has high solubility at room temperature, facilitating light‐based 3‐dimensional (3D) printing of thiol‐norbornene ...
Jonathan B. Bryan, Chien‐Chi Lin
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Transverse momentum dependent gluon fragmentation functions from $J/\psi\ \pi$ production at $e^+ e^-$ colliders [PDF]
, 2015 Guang-Peng Zhang
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A fractional Borel–Pompeiu type formula and a related fractional ψ−$$ \psi - $$Fueter operator with respect to a vector‐valued function [PDF]
, 2022 José Óscar González-Cervantes +1 more
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Fully Inkjet‐Printed Organic Electrochemical Transistors: A Path Toward All‐Organic Electronics
Advanced Materials Technologies, EarlyView.Fully printed organic electrochemical transistors eliminate the metal electrodes used in conventional printed organic electronics. This work demonstrates the state of the art in three applications using PBFDO and PEDOT:PSS materials: a single‐material strain sensor for real‐time detection of finger flexion, an ion sensor for monitoring aqueous NaCl ...
Ali Solgi +5 more
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Infinite sums of psi functions [PDF]
Bulletin of the American Mathematical Society, 1973 openaire +2 more sources
Laser Micromachining of Liquid Metal Patterns for Stretchable Electronic Circuits
Advanced Materials Technologies, EarlyView.A cleanroom‐free fabrication strategy combines UV‐laser micromachining with a copper foil wetting layer to rapidly produce high resolution, liquid metal based stretchable electronic circuits on diverse substrates. The scalable, maskless process enables complex circuit designs (<$<$3 h, ∼$\sim$15/device) with excellent electrical stability under strain,
Merjen Palvanova +3 more
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A Completely Monotonic Function Involving Divided Differences of Psi and Polygamma Functions and an Application [PDF]
, 2006 Feng Qi
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Approximations for the Psi (Digamma) Function [PDF]
Mathematics of Computation, 1967 openaire +1 more source