Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.
About 10,000 papers for “Reference frame”
Zhiyong Wang · 1998
Solely based on the facts in relativity, we show that there is uncertainty in determining the ds2 of a free particle. The proper time of the free particle, if it is defined according to its ds2, is therefore found not to be physically definite. The way to solve the problem is proposed, and the effect of gravity on proper time is studied.
Cited by 0
Marc D. Binder, Nobutaka Hirokawa, Uwe Windhorst · 2008
Cited by 0
Muriel Gargaud, William M. Irvine, Ricardo Amils et al. · Encyclopedia of Astrobiology · 2015
Cited by 0
Muriel Gargaud, William M. Irvine, Ricardo Amils et al. · Encyclopedia of Astrobiology · 2023
Cited by 0
Raz Leib · OSF Preprints (OSF Preprints) · 2025
This project includes data and codes of the study "Error Prediction Determines the Coordinate System Used for Novel Dynamics Representation" by Raz Leib and David W. Franklin (Technical University of Munich)
Cited by 0
Data Archiving and Networked Services (DANS)
Cited by 0Open access
Andrew Hill · Zenodo (CERN European Organization for Nuclear Research) · 2026
The Reference Frame (TRF) presents a unified geometric algebra framework grounded in five ontological elements — Null, Zero, Epsilon, One, and Infinity — whose multiplicative interactions are governed by an axiomatic Cayley table encoding the boundary conditions of physical reality. From this discrete foundation, three metric signatures (i² = −1, d² = 0, j² = +1) emerge as the exhaustive classification of real 2-dimensional unital associative algebras, generating rotation, translation, and boost symmetries respectively. Together they compose the Motor operator M = (1 + (i+d+j)ε)^∞, a single expression from which the Poincaré group ISO(1,3), quantum orbital geometries, spinor decomposition, electromagnetic field structure, and cosmological expansion are derived as consequences. A radial interference equation parameterized by booster amplitude and harmonic frequency reproduces atomic orbital morphologies — s, p, d, d_z², f, and a novel golden-ratio configuration — at approximately 25 floating-point operations per vertex. The framework proposes that the exponential morphism (the Engine) is not merely a calculational tool but the structural carrier of time translation, encoding P₀ as a morphism rather than an independent spatial generator.
Cited by 0Open access
Sarah Fraser · Dalhousie Medical Journal · 2013
Cited by 0Open access
Mingying Huo (5663413), Jun Zhao (59250), Shaobiao Xie (736320) et al. · Figshare · 2015
Cited by 0Open access
The MIT Press eBooks · 2011
Cited by 0
Joseph L. Austerweil, Abram L. Friesen, Thomas L. Griffiths · 2012
Cited by 0
Marijan Marjanović, Tomislav Bašić · 2009
Tijekom 2008. godine Državna geodetska uprava uspostavila je hrvatski pozicijski sustav - CROPOS. Sustav je pusten u službenu uporabu 9. prosinca 2008. godine i tijekom prvih mjeseci rada odlicno je prihvacen od strane korisnika. Sustav se sastoji od 30 referentnih GNSS stanica koje ravnomjerno prekrivaju cijelo podrucje države. U radu je opisana obrada podataka mjerenja i izjednacenje koordinata referentnih GNSS stanica CROPOS sustava koja je obavljena u skladu s preporukama Tehnicke radne grupe EUREF-a s Bernese GPS Software Ver. 5.0. Za racunanje su koristeni podaci konacne IGS orbite i gibanja pola. U obradu su ukljuceni sedmodnevni podaci mjerenja u trajanju sesije od 24 sata za GPS tjedan 1503. Obrada podataka mjerenja obavljena je u ITRF2005 referentnom okviru, epoha 2008.83, a zatim su koordinate transformirane u ETRF00 (R05). Srednje standardno odstupanje koordinata referentnih stanica dobiveno na temelju usporedbe sedam dnevnih rjesenja i zajednickog izjednacenja je stdev(fi)= 1.2 mm, stdev(la)= 1.1 mm i stdev(h) = 3.4 mm. U svrhu ispitivanja stabilnosti referentnog okvira CROPOS sustava napravljena je obrada podataka mjerenja referentnih GNSS stanica za GPS tjedan 1527 te su dobiveni rezultati uspoređeni s prvim rjesenjem.
Cited by 0
Van Nostrand's Scientific Encyclopedia · 2007
Cited by 1
Elias G. Carayannis · 2013
Cited by 0
Rex H. Pilger · 2003
Cited by 0
Marc D. Binder, Nobutaka Hirokawa, Uwe Windhorst · 2008
Cited by 0
Bernard A. Goodman · AccessScience · 2015
AccessScience is an authoritative and dynamic online resource that contains incisively written, high-quality educational material covering all major scientific disciplines. An acclaimed gateway to scientific knowledge, AccessScience is continually expanding the ways it can demonstrate and explain core, trustworthy scientific information that inspires and guides users to deeper knowledge.
Cited by 0
C. S. Jacobs · 2013
Cited by 0
Andrew Hill · Zenodo (CERN European Organization for Nuclear Research) · 2026
The Reference Frame (TRF) presents a unified geometric algebra framework grounded in five ontological elements — Null, Zero, Epsilon, One, and Infinity — whose multiplicative interactions are governed by an axiomatic Cayley table encoding the boundary conditions of physical reality. From this discrete foundation, three metric signatures (i² = −1, d² = 0, j² = +1) emerge as the exhaustive classification of real 2-dimensional unital associative algebras, generating rotation, translation, and boost symmetries respectively. Together they compose the Motor operator M = (1 + (i+d+j)ε)^∞, a single expression from which the Poincaré group ISO(1,3), quantum orbital geometries, spinor decomposition, electromagnetic field structure, and cosmological expansion are derived as consequences. A radial interference equation parameterized by booster amplitude and harmonic frequency reproduces atomic orbital morphologies — s, p, d, d_z², f, and a novel golden-ratio configuration — at approximately 25 floating-point operations per vertex. The framework proposes that the exponential morphism (the Engine) is not merely a calculational tool but the structural carrier of time translation, encoding P₀ as a morphism rather than an independent spatial generator.
Cited by 0Open access
Nigatu Wanore Madebo (22146141) · Figshare · 2025
<div> This paper presents a novel hybrid combined neural network and fuzzy logic adaptive proportional, integral, and derivative(NNPID+FPID) control strategy that integrates neural networks and fuzzy logic for optimizing Unmanned Aerial Vehicle(UAV) dynamics by tuning the gains of a PID controller. The proposed approach leverages the strengths of each technique by applying neural networks to fine-tune the <i>y</i> and <i>ψ</i> states, while fuzzy logic enhances the performance of <i>x</i>, <i>z</i>, <i>ϕ</i>, and <i>θ</i> dynamics. A single-layer neural network with 10 hidden neurons is utilized to adjust PID gains for the <i>y</i> and <i>ψ</i> states using proportional, integral, and derivative errors () as inputs. The weights are updated through a gradient descent algorithm minimizing the mean squared error, with a nonlinear sigmoid activation function ensuring adaptability. Concurrently, fuzzy logic employs heuristic rules to dynamically tune PID gains for the remaining states, based on input errors and their derivatives. Membership functions map inputs to gains to ensure real-time adaptability. The hybrid method outperforms standalone neural network(NNPID) and fuzzy logic(FPID) approaches by significantly improving trajectory tracking performance and overall UAV control efficiency. This work demonstrates the effectiveness of combining neural networks and fuzzy logic to address the multi-dimensional control challenges of UAV systems. </div>
Cited by 0Open access