Results 41 to 50 of about 6,644 (238)
Mathematics, 2022 In this paper, we define and study Hyers–Ulam stability of order 1 for Euler’s equation and Hyers–Ulam stability of order m−1 for the Euler–Poisson equation in the calculus of variations in two special cases, when these equations have the form y″(x)=f(x)
Daniela Marian +2 more
doaj +1 more source
A Perspective on Interactive Theorem Provers in Physics
Advanced Science, EarlyView.Into an interactive theorem provers (ITPs), one can write mathematical definitions, theorems and proofs, and the correctness of those results is automatically checked. This perspective goes over the best usage of ITPs within physics and motivates the open‐source community run project PhysLean, the aim of which is to be a library for digitalized physics
Joseph Tooby‐Smith
wiley +1 more source
Sub‐Unit‐Cell Logic Governs Transport in TPMS Architectures
Advanced Science, EarlyView.ABSTRACT Next‐generation energy, thermal, and chemical systems require architectures capable of highly efficient transport across multiple length scales. Triply periodic minimal surfaces (TPMS), first conceptualized in 1865, offer inherently scalable geometries with exceptional transport potential, yet mechanistic links between topology and performance
Haozhang Zhong +16 more
wiley +1 more source
An integration of Euler's pentagonal partition [PDF]
, 2010 A recurrent formula is presented, for the enumeration of the compositions of positive integers as sums over multisets of positive integers, that closely resembles Euler's recurrence based on the pentagonal numbers, but where the coefficients result from ...
Scollo, Giuseppe
core
Pellet Printing for Soft Robotic Devices
Advanced Science, EarlyView.Fused Granulate Fabrication (FGF) is established here as a reliable method for fabricating soft, airtight robotic devices. Through coordinated optimization of hardware, material selection, and process parameters, this approach enables high‐speed printing of thermoplastic elastomers with silicone‐like softness and modulus.
Yijia Wu +6 more
wiley +1 more source
Description of Euler bricks using Fibonacci's identity [PDF]
, 2013 We show how the Fibonacci's identity is used to obtain Euler bricks. Also,we put forward the relation between Fibonacci's identity and Euler's formula, which provides the description of Euler's bricks with noninteger spatial diagonal.
Safin, Boris
core
Developing Micro/Nanostructured Fluidic Mixing Technology for Biomedical Applications
Advanced Science, EarlyView.This review critically evaluates how micro/nanostructured mixing technologies are redefining biomedical research. By synergizing fundamental analysis, numerical modeling, structural design, and external field manipulation, these systems attain unprecedented control over mass transport.
Junkai Wang +3 more
wiley +1 more source
Euler's Exponential Formula for Semigroups [PDF]
, 2018 The aim of this paper is to show that Euler's exponential formula $\lim_{n\rightarrow\infty}\linebreak[4] (I-tA/n)^{-n}x = e^{tA}x$, well known for $C_0$ semigroups in a Banach space $X\ni x$, can be used for semigroups not of class $C_0$, the sense of ...
Cachia, Vincent
core
Quantum Barnes function as the partition function of the resolved conifold
, 2007 We suggest a new strategy for proving large $N$ duality by interpreting Gromov-Witten, Donaldson-Thomas and Chern-Simons invariants of a Calabi-Yau threefold as different characterizations of the same holomorphic function.
Koshkin, Sergiy
core +2 more sources
AIChE Journal, EarlyView.Abstract This study investigates a fault‐tolerant control (FTC) approach for continuous stirred‐tank reactors (CSTR), emphasizing the importance of timely interventions to ensure operational safety under fault conditions. A systematic methodology combining residual‐based fault estimation and Dynamic Safety Margin (DSM) monitoring is developed to guide ...
Pu Du +3 more
wiley +1 more source