Results 41 to 50 of about 16,861 (262)
RETRACTED: On the Nature of Some Euler’s Double Equations Equivalent to Fermat’s Last Theorem
Mathematics, 2022 In this work, I provide a new rephrasing of Fermat’s Last Theorem, based on an earlier work by Euler on the ternary quadratic forms. Effectively, Fermat’s Last Theorem can be derived from an appropriate use of the concordant forms of Euler and from an ...
Andrea Ossicini
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Nanodiamond Sensing in Dynamic Environments With Fast‐Tracking Through Four‐Point Positioning
Advanced Functional Materials, EarlyView.A four‐point positioning tracking (4PPT) platform enables fast 3D feedback translational tracking of fluorescent nanodiamonds while simultaneously recording ODMR spectra. By integrating real‐time translational tracking with quantum sensing, mobile nanodiamonds are used for in‐situ nanothermometry, nanorheometry, and 6D translation–rotation tracking in ...
Guoli Zhu +10 more
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Advanced Materials, EarlyView.Stacked nanoflake assembly (SNA) membranes can oscillate autonomously, offering opportunities for soft actuation and energy harvesting. This work uncovers the physical mechanism behind the sustained oscillation of SNA membranes in gradient humidity and identifies three governing dimensionless parameters, enabling rational design for optimizing SNA ...
Zijing Zhang +5 more
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On Approximate Euler Differential Equations
Abstract and Applied Analysis, 2009 We solve the inhomogeneous Euler differential equations of the form x2y′′(x)+αxy′(x)+βy(x)=∑m=0∞amxm and apply this result to the approximation of analytic functions of a special type by the solutions of Euler differential equations.
Soon-Mo Jung, Seungwook Min
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Mittag-Leffler Euler ∇-differences for Caputo fractional-order systems
Results in Physics, 2022 Exponential Euler differences have got rapid development recently for integer-order differential equations. But there are few papers focusing on this difference to fractional differential equations.
Tianwei Zhang, Yongkun Li, Jianwen Zhou
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Advanced Materials Technologies, EarlyView.The study considers the use of polymer/dielectric‐based multilayers piezoelectric Energy Harvesters (EH) to produce an output voltage and current, by exploiting the mechanical energy provided by human organs movements. In particular, the heart motion is considered from the kinematic viewpoint, and a multiphysics theoretical model is developed to assess
Hamdi Ezzin +5 more
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Variational Integrals of a Class of Nonhomogeneous 𝒜-Harmonic Equations
Abstract and Applied Analysis, 2014 We introduce a class of variational integrals whose Euler equations are nonhomogeneous 𝒜-harmonic equations. We investigate the relationship between the minimization problem and the Euler equation and give a simple proof of the existence of some ...
Guanfeng Li, Yong Wang, Gejun Bao
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Mathematics, 2019 The present paper recalls a formulation of non-conservative system dynamics through the Lagrange−d’Alembert principle expressed through a generalized Euler−Poincaré form of the system equation on a Lie group.
Simone Fiori
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Fabrication of Fibers With Complex Features Using Thermal Drawing of 3D‐Printed Preforms
Advanced Materials Technologies, EarlyView.3D printing enables rapid fabrication of macroscale polymer preforms with complex geometries. Thermal drawing then scales these structures into long fibers while preserving micron‐scale cross‐sectional features. This workflow provides a fast, low‐cost route to functional fibers with tailored geometries and material combinations for catheter, robotic ...
Ali Anil Demircali +4 more
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Rotating Fluorescent Nanodiamond Assemblies With Focused Laguerre–Gaussian Beams
Advanced Optical Materials, EarlyView.Self‐assembled fluorescent nanodiamond clusters are optically trapped and driven into controlled two‐dimensional rotation with Laguerre–Gaussian beams. With localized optical excitation, optically detected magnetic resonance spectra are collected at defined points along the orbit in a uniform external magnetic field.
Adam Stewart +5 more
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