Добірка наукової літератури з теми "Parabolic motion"

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Статті в журналах з теми "Parabolic motion":

1

Klamkin, M. S. "Characterizations of Parabolic Motion." SIAM Review 30, no. 1 (March 1988): 125. http://dx.doi.org/10.1137/1030010.

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2

Okino, Takahisa. "Brownian Motion in Parabolic Space." Journal of Modern Physics 03, no. 03 (2012): 255–59. http://dx.doi.org/10.4236/jmp.2012.33034.

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3

Harm, Deborah L., and Todd T. Schlegel. "Predicting motion sickness during parabolic flight." Autonomic Neuroscience 97, no. 2 (May 2002): 116–21. http://dx.doi.org/10.1016/s1566-0702(02)00043-7.

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4

Zhu, Meijun, and Wei Guan. "Parabolic equations related to curve motion." Journal of Differential Equations 251, no. 7 (October 2011): 1727–46. http://dx.doi.org/10.1016/j.jde.2011.06.003.

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5

Salam, Badru, and Sri Latifah. "Pengembangan Projectile Launcher Sebagai Alat Praktikum Sederhana Fisika pada Materi Gerak Parabola." Indonesian Journal of Science and Mathematics Education 2, no. 2 (June 22, 2019): 177–83. http://dx.doi.org/10.24042/ijsme.v2i2.4323.

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Abstract:This research is a development research that aims to produce media product projectile launcher as a simple practical tool of physics on parabolic motion material and to know the feasibility of media projectile launcher as a simple practical tool of physics on parabolic motion material. Problems in this research, among others, is how to develop projectile launcher as a simple practical tool of physics on parabolic motion material and how is the response of learners to media projectile launcher as a simple physics practicum tool on parabolic motion material. . Subjects in this study are class IX SMA N 1 Way Tenong and SMA N 2 Way Tenong. This research is a development research using Research and Development (R & D) research method that adopt the development of Borg & Gall that has been modified by sugionoProducts are categorized very feasible based on the validation of material experts with 100% percentage and based on the validation of media experts with a percentage of 100% , as well as Projectile Launcher media are very interesting to be used as teaching materials based on teacher's assessment to get 100% score percentage and student's response in limited group trial to get 95% percentage score for SMA N 1 Way Tenong and 92% for SMA N 2 Way Tenong.Abstrak:Penelitian ini merupakan penelitian pengembangan yang bertujuan untuk menghasilkan produk media projectile launcher sebagai alat praktikum sederhana fisika pada materi gerak parabola dan untuk mengetahui kelayakan dari media projectile launcher sebagai alat praktikum sederhana fisika pada materi gerak parabola. Masalah dalam penelitian ini antara lain bagaimanakah mengembangkan projectile launcher sebagai alat praktikum sederhana fisika pada materi gerak parabola dan bagaimanakah respon peserta didik terhadap media projectile launcher sebagai alat praktikum sederhana fisika pada materi gerak parabola. . Subjek dalam penelitian ini adalah kelas IX SMA N 1 Way Tenong dan SMA N 2 Way Tenong. Penelitian ini merupakan penelitian pengembangan menggunakan metode penelitian Research and Development (R&D) yang mengadopsi pengembangan dari Borg & Gall yang telah dimodifikasi oleh sugionoProduk yang dihasilkan berkategori sangat layak berdasarkan validasi dari ahli materi dengan presentase 100% dan berdasarkan validasi dari ahli media dengan presentase 100%, serta mediaProjectile Launchersangatmenarikuntukdijadikanbahanajarberdasarkanpenilaiangurumemperolehpresentaseskor100% dan respon peserta didik pada uji coba kelompok terbatas memperoleh skor presentase 95% untuk SMA N 1 Way Tenong dan 92% untuk SMA N 2 Way Tenong
6

Pathan, Alex, and Tony Collyer. "A solution to a cubic – Barker's equation for parabolic trajectories." Mathematical Gazette 90, no. 519 (November 2006): 398–403. http://dx.doi.org/10.1017/s0025557200180192.

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Except for the circle, for which the true anomaly v is proportional to the time t, the position of a body in orbit about a central body at a given time is simplest to derive for a parabola. The classical determination of the time of flight on a parabolic trajectory is through the integration of the dynamic equations of motion. (See Appendix.)
7

Markham, Charles H., and Shirley G. Diamond. "A Predictive Test for Space Motion Sickness." Journal of Vestibular Research 3, no. 3 (September 1, 1993): 289–95. http://dx.doi.org/10.3233/ves-1993-3309.

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Eye torsion was examined in 13 astronaut subjects, tested during repeated episodes of 0 G and 1.8 G in parabolic flight aboard NASA’s KC-135. Four findings are included. 1) A strong relationship between previous history of SMS and ocular torsional disconjugacy in novel gravitational states. 2) Responses were unchanged in 4 subjects retested a year later. 3) Ocular torsional disconjugacy scores increased as exposure to 0 and 1.8 G increased. This was particularly evident in subjects who had had SMS. 4) Torsional studies during 10 to 20 parabolas are required to accurately predict SMS. The hypothesis of otolith asymmetry, compensated in 1 G but becoming unmasked in novel gravitational states, is proposed to explain the torsional disconjugacy and ensuing SMS.
8

Lv Yao-wen, 吕耀文, 王建立 WANG Jian-li, 王昊京 WANG Hao-jing, 刘维 LIU Wei, 吴量 WU Liang, and 曹景太 CAO Jing-tai. "Estimation of camera poses by parabolic motion." Optics and Precision Engineering 22, no. 4 (2014): 1078–85. http://dx.doi.org/10.3788/ope.20142204.1078.

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9

Mathis, Frank. "Characterizations of Parabolic Motion (M. S. Klamkin)." SIAM Review 31, no. 1 (March 1989): 129–31. http://dx.doi.org/10.1137/1031017.

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10

Chafi, Alhadi, Stephane Rusinek, Loris Schiaratura, Sebastien Delescluse, and Thibaut Brouillet. "Perceiving a negatively connoted stimulus imply enhanced performances: the case of a moving object." Polish Psychological Bulletin 44, no. 3 (September 1, 2013): 331–36. http://dx.doi.org/10.2478/ppb-2013-0036.

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Abstract Most studies on verticality’s embodiment showed that up positions were related to positive emotions whereas down positions were related to negative ones (Meier & Robinson, 2004). Research on motion perception found that a parabolic motion both induced animation attribution (Tremoulet & Feldman, 2000) and implied negative feelings (Chafi, Schiaratura, & Rusinek, 2012; Podevin, 2009; Podevin, Chafi, Rusinek, & Békaert, 2012). We hypothesized that seeing a parabolic downward motion will increase both the memorization for words and the execution’s speed of a serial subtraction compared to a parabolic upward motion. Results showed that the downward motion had enhancing effects both on the serial subtraction and on the number of recalled words, independently of their valence. These findings are interpreted as marking processes related to an adaptive behavior in response to a negative stimulus.

Дисертації з теми "Parabolic motion":

1

Koniski, Cyril (Cyril A. ). "Error analysis of motion transmission mechanisms : design of a parabolic solar trough." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/54497.

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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2009.
Page 47 blank. Cataloged from PDF version of thesis.
Includes bibliographical references (p. 42).
This thesis presents the error analysis pertaining to the design of an innovative solar trough for use in solar thermal energy generation fields. The research was a collaborative effort between Stacy Figueredo from Prof. Alexander Slocum's Precision Engineering Research Group at MIT and a team of students from the 2.752 Mechanical Engineering course and resulted in a final design that uses two linear actuators to rotate a monolithic parabolic trough over a 2600 range. A measure of efficiency, based on the geometric tracing of incident and reflected rays under different parabola deformations, was developed and used to determine the impact of several key parameters on the accuracy of the system. The resulting error analysis demonstrated the substantial influence of the crank arm length and actuator precision on the overall system efficiency and set an upper bound of 1 degree in permissible angular error in order to maintain 80% efficiency under sustained wind loading.
by Cyril Koniski.
S.B.
2

Pistacchio, David J. "Source/receiver motion-induced Doppler influence on the bandwidth of sinusoidal signals." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2003. http://library.nps.navy.mil/uhtbin/hyperion-image/03Dec%5FPistacchio.pdf.

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Thesis (M.S. in Engineering Acoustics)--Naval Postgraduate School, December 2003.
Thesis advisor(s): Kevin Smith, Roy Streit. Includes bibliographical references (p. 95-100). Also available online.
3

Gombi, Alessandro. "The foundational case of the parabolic motion: design of an interdisciplinary activity for the IDENTITIES project." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2020. http://amslaurea.unibo.it/21181/.

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Questa tesi si inserisce nel campo di ricerca in Didattica della Fisica. In particolare, il lavoro si colloca all’interno del progetto Erasmus+ IDENTITIES, avviato nel settembre 2019, in collaborzione con le università di Montpellier, Creta, Parma e Barcellona. IDENTITIES ha lo scopo di sviluppare moduli didattici interdisciplinari (fisica – matematica – informatica), rivolti ai futuri insegnanti. I moduli riguardano sia temi curricolari sia temi STEM come contesto in cui sviluppare competenze interdisciplinari e progettare nuovi modelli di co-teaching. I temi di IDENTITIES hanno ispirato e guidato l’attuazione di un corso rivolto a insegnanti di scuola secondaria di secondo grado, organizzato dal PLS di Fisica di Bologna assieme al PLS di Matematica e il POT di Bologna. Il corso, svoltosi tra novembre e dicembre 2019 ha rappresentato la principale fonte di materiale e di riflessioni per questo lavoro. L’obiettivo di questa tesi è contribuire al progetto tramite la creazione di un’attività didattica, rivolta ai futuri insegnanti, sul tema della parabola e del moto parabolico. L’attività è stata progettata con lo scopo di guidare attraverso i principali passaggi che hanno caratterizzato, da un punto di vista epistemologico, l’evoluzione del pensiero fisico dalla teoria sul moto del proiettile di Tartaglia fino alla dimostrazione della traiettoria parabolica del proiettile di Galileo. Nella tesi sono descritti il quadro teorico di base per il lavoro, la rielaborazione del materiale del corso PLS per costruire lenti per l’analisi dei libri di testo, l’analisi di un capitolo del libro di testo sulla cinematica bidimensionale e la conseguente progettazione dell’attività didattica. Nelle conclusioni sono discussi i principali risultati ottenuti, tra i quali la produzione delle griglie originali per l’analisi di libri di testo, l’individuazione della simmetria e dell’indipendenza dei moti come attivatori epistemologici e la produzione dell’attività.
4

Bianchi, Fabrizio. "Motions of Julia sets and dynamical stability in several complex variables." Thesis, Toulouse 3, 2016. http://www.theses.fr/2016TOU30099/document.

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Dans cette thèse, on s'intéresse aux systèmes dynamiques holomorphes dépendants de paramètres. Notre objectif est de contribuer à une théorie de la stabilité et des bifurcations en plusieurs variables complexes, généralisant celle des applications rationnelles fondées sur les travaux de Mané, Sad, Sullivan et Lyubich. Pour une famille d'applications d'allure polynomiale, on prouve l'équivalence de plusieurs notions de stabilité, entre autres une version asymptotique du mouvement holomorphe des cycles répulsifs et d'un sous-ensemble de l'ensemble de Julia de mesure pleine. Cela peut etre considéré comme une généralisation mesurable à plusieurs variables du célèbre lambda-lemme et nous permet de dégager un concept cohérent de stabilité dans ce cadre. Après avoir compris les bifurcations holomorphes, on s'intéresse à la continuité Hausdorff des ensembles de Julia. Nous relions cette propriété à l'existence de disques de Siegel dans l'ensemble de Julia, et donnons un exemple de ce phénomène. Finalement, on étudie la continuité du point de vue de l'implosion parabolique. Nous établissons un théorème de Lavaurs deux-dimensionel, ce qui nous permet d'étudier des phénomènes de discontinuité pour des perturbations d'applications tangentes à l'identité
In this thesis we study holomorphic dynamical systems depending on parameters. Our main goal is to contribute to the establishment of a theory of stability and bifurcation in several complex variables, generalizing the one for rational maps based on the seminal works of Mané, Sad, Sullivan and Lyubich. For a family of polynomial like maps, we prove the equivalence of several notions of stability, among the others an asymptotic version of the holomorphic motion of the repelling cycles and of a full-measure subset of the Julia set. This can be seen as a measurable several variables generalization of the celebrated lambda-lemma and allows us to give a coherent definition of stability in this setting. Once holomorphic bifurcations are understood, we turn our attention to the Hausdorff continuity of Julia sets. We relate this property to the existence of Siegel discs in the Julia set, and give an example of such phenomenon. Finally, we approach the continuity from the point of view of parabolic implosion and we prove a two-dimensional Lavaurs Theorem, which allows us to study discontinuities for perturbations of maps tangent to the identity
5

Lapalice, Marc-André. "La tuerie de l'Assemblée nationale (1984) comme un parricide raté : une étude du détour-parabole dans "Lortie" de Pierre Lefebvre et du Nouveau Théâtre expérimental." Master's thesis, Université Laval, 2017. http://hdl.handle.net/20.500.11794/28036.

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Cette étude s'inscrit dans le sillage de la réflexion de Jean-Pierre Sarrazac sur l'écriture dramatique du fait divers. Pour éviter de se laisser paralyser par le pouvoir de fascination que ce type de nouvelles exerce, le chercheur français suggère au dramaturge d'adopter ce qu'il nomme une « stratégie de détour ». Ce mémoire se penche sur le recours à l'une d'entre elles, soit le « détour-parabole », dans la pièce Lortie de Pierre Lefebvre et du Nouveau Théâtre Expérimental. L'œuvre de Lefebvre porte sur une tuerie de masse perpétrée à l'Assemblée nationale du Québec en 1984, par le caporal de l'armée canadienne Denis Lortie. Se fondant sur l'essai Le crime du caporal Lortie : Traité sur le Père (1989), de l'historien du droit et psychanalyste Pierre Legendre, Lortie aborde cet évènement comme un parricide raté. Ce mémoire explore les enjeux esthétiques, dramaturgiques et spectaculaires de la lecture parabolique développée dans la pièce de Lefebvre et du NTE, pour finalement chercher à dégager les nouveaux modes de perception et d'intellection du fait divers (selon l'expression de France Vernier).
6

Szavai, Dorottya. "Pêché et prière dans la poésie de János Pilinszky : le poète en dialogue (Camus, Kafka, Dostoïevski) : variations sur le thème de l'enfant prodigue." Paris 4, 2001. http://www.theses.fr/2001PA040048.

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Dewaël, Stéphanie. "Splendeur, décadence et rémission : la représentation du Fils Prodigue dans la peinture et les arts graphiques à Anvers (1520-1650)." Thesis, Paris 4, 2010. http://www.theses.fr/2010PA040109.

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Alors que la parabole du Fils Prodigue fut un support aux vives controverses religieuses du XVIe siècle qui touchèrent Anvers, les productions artistiques (peintures, gravures, dessins) restituèrent une image plus consensuelle de cette histoire. Au lieu de matérialiser les nombreuses exégèses théologiques (contradictoires) sur le message du Christ, les artistes préférèrent puiser dans la culture profane (comme les pièces de théâtre) et mettre l’accent sur la scène de la dissipation avec les courtisanes ou insister sur des détails triviaux.Cette thèse étudie les nombreuses raisons qui les ont conduits à de tels choix (poids de la censure, recherche d’une vaste clientèle, flatterie du spectateur…) et analyse les choix de mise en scène, épisode par épisode. Elle démontre comment les ateliers d’artistes ont reproduit des formules répétitives ; comment les choix iconographiques favorisèrent tour à tour la méditation spirituelle, la délectation visuelle ou les pensées condescendantes envers autrui
While the parable of the Prodigal Son was a support in the deep religious controversies which affected Antwerp during the 16th century, the artistic productions (paintings, prints and drawings) gave back a more consensual image of this history. Instead of representing the numerous contradictory theological exegeses about the message of Christ, the artists preferred to drawn their inspiration from profane culture (as plays) and to emphasize the scene of the waste with the courtesans or to insist on everyday and coarse details.This thesis studies the numerous reasons which led them to such choices (weight of censorship, search for a vast clientele, flattery of the spectator…) and analyses the choices of setting, episode by episode. It demonstrates how artist studios reproduced repetitive formulae and how the iconographic choices facilitated alternately the spiritual meditation, the visual enjoyment or the condescending thoughts to others
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Kolluru, Sethu Hareesh. "Preliminary Investigations of a Stochastic Method to solve Electrostatic and Electrodynamic Problems." 2008. https://scholarworks.umass.edu/theses/191.

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A stochastic method is developed, implemented and investigated here for solving Laplace, Poisson's, and standard parabolic wave equations. This method is based on the properties of random walk, diffusion process, Ito formula, Dynkin formula and Monte Carlo simulations. The developed method is a local method i:e: it gives the value of the solution directly at an arbitrary point rather than extracting its value from complete field solution and thus is inherently parallel. Field computation by this method is demonstrated for electrostatic and electrodynamic propagation problems by considering simple examples and numerical results are presented to validate this method. Numerical investigations are carried out to understand efficacy and limitations of this method and to provide qualitative understanding of various parameters involved in this method.

Книги з теми "Parabolic motion":

1

Benedictis, Maurizio De. Da Paisà a Salò e oltre: Parabole del grande cinema italiano. Roma: Avagliano, 2010.

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2

Imarisio, Eligio. La parabola del neorealismo nelle Cronache di poveri amanti di Carlo Lizzani. Roma: Carocci editore, 2014.

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3

Lawler, Gregory F. Random walk and the heat equation. Providence, R.I: American Mathematical Society, 2010.

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4

Nolte, David D. Galileo’s Trajectory. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805847.003.0003.

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This chapter describes the history of Galileo’s discovery of the law of fall and the parabolic trajectory, beginning with early work on the physics of motion by predecessors like the Oxford Scholars, Tartaglia and the polymath Simon Stevin who dropped lead weights from the leaning tower of Delft three years before Galileo dropped lead weights from the leaning tower of Pisa. The story of how Galileo developed his ideas of motion is described in the context of his studies of balls rolling on inclined plane and the surprising accuracy he achieved without access to modern timekeeping. Motion was always on Galileo’s mind. He saw motion in his father’s stringed instruments, vibrating in rational resonances. He saw motion in the lantern high above in the Duomo di Pisa, swinging with fixed regularity.
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Nolte, David D. Epilogue: Galileo at Home in the Multiverse. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805847.003.0012.

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This final short chapter sums up the topics of the book, showing how Galileo’s simple parabolic trajectory has matured into an overarching and grand concept that encompasses modern dynamics. Galileo achieved immortality despite his house arrest and despite the banning of his books that he feared had erased his legacy. Ironically, his house arrest gave him time to assemble and record his lifelong investigation into the science of motion—and banning his books made them immensely popular.
6

Nigal, Gedaliah. The Hasidic Tale. Littman Library of Jewish, 2008.

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Частини книг з теми "Parabolic motion":

1

Vergara Caffarelli, Roberto. "Before 1607: Parabolic trajectories." In Galileo Galilei and Motion, 163–67. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-04353-6_10.

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2

Ducomet, Bernard, and Šárka Nečasová. "On the Motion of Several Rigid Bodies in an Incompressible Viscous Fluid under the Influence of Selfgravitating Forces." In Parabolic Problems, 167–92. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0075-4_9.

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3

Erven, Matthias, and Guido Sweers. "On the Lifetime of a Conditioned Brownian Motion in Domains Connected Through Small Gaps." In Elliptic and Parabolic Equations, 77–109. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-12547-3_4.

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4

Blowey, J. F., and C. M. Elliott. "Curvature Dependent Phase Boundary Motion and Parabolic Double Obstacle Problems." In Degenerate Diffusions, 19–60. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0885-3_2.

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5

Agrati, Laura S. "Integra(c)tion of Graphic Supports. A Case-Study on Parabolic Motion for Students with Learning Difficulties." In Proceedings of the 2nd International and Interdisciplinary Conference on Image and Imagination, 166–81. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-41018-6_16.

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6

Hanlon, Robert T. "Galileo and the Law of Fall." In Block by Block: The Historical and Theoretical Foundations of Thermodynamics, 124–37. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198851547.003.0007.

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Galileo broke away from Aristotle’s incorrect theories of motion towards his own based on experimental evidence. He employed experimentation to discover the parabolic trajectory of projectile motion and also the Law of Fall. His work helped establish the scientific method and launch the scientific revolution.
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Kato, J., A. A. Martynyuk, and A. A. Shestakov. "Limiting Lyapunov Functionals for Asymptotically Autonomous Evolutionary Equations of Parabolic and Hyperbolic Type in a Banach Space." In Stability of Motion of Nonautonomous Systems (Method of Limiting Equations), 221–38. CRC Press, 2019. http://dx.doi.org/10.1201/9780203738849-9.

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8

Rigatos, G. G., and S. G. Tzafestas. "Attractors and Energy Spectrum of Neural Structures Based on the Model of the Quantum Harmonic Oscillator." In Complex-Valued Neural Networks, 376–410. IGI Global, 2009. http://dx.doi.org/10.4018/978-1-60566-214-5.ch015.

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Neural computation based on principles of quantum mechanics can provide improved models of memory processes and brain functioning and is of primary importance for the realization of quantum computing machines. To this end, this chapter studies neural structures with weights that follow the model of the quantum harmonic oscillator. The proposed neural networks have stochastic weights which are calculated from the solution of Schrödingers equation under the assumption of a parabolic (harmonic) potential. These weights correspond to diffusing particles, which interact with each other as the theory of Brownian motion (Wiener process) predicts. The learning of the stochastic weights (convergence of the diffusing particles to an equilibrium) is analyzed. In the case of associative memories the proposed neural model results in an exponential increase of patterns storage capacity (number of attractors). It is also shown that conventional neural networks and learning algorithms based on error gradient can be conceived as a subset of the proposed quantum neural structures. Thus, the complementarity between classical and quantum physics is also validated in the field of neural computation.
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Epstein, Irving R., and John A. Pojman. "Transport and External Field Effects." In An Introduction to Nonlinear Chemical Dynamics. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195096705.003.0015.

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Thus far, we have implicitly assumed that chemical species move only by diffusion. In fact, a number of external forces can affect mass transport, with significant and interesting effects on chemical waves. In this chapter, we consider three types of fields: gravitational, electric, and magnetic. These always exist, though their magnitudes are usually very small. As we shall see, small fields can have surprisingly large effects. Gravity is a ubiquitous force that all living and chemical systems experience. People largely ignored the profound effect that living with gravity has upon us until humans spent significant time in space. Bone loss and changes to the vascular systems of astronauts (Nicogossian et al., 1994) are still not well understood. Eliminating the effects of gravity is not easy. Enormous cost and effort have been expended to simulate gravity-free conditions in drop towers, parabolic airplane flights, or in Earth orbit. A simple calculation seems to suggest that gravity should have negligible influence on chemical reactions. The mass of a molecule is on the order of 10-26 kg, which translates into a gravitational force of about 10-25 N. We can compare this with the force of attraction between the electron and the proton in a hydrogen atom, which is of the order 10-8 N. Even allowing for shielding effects, the electrostatic forces that cause chemical bonds to be made and broken will always be many orders of magnitude stronger than gravitational forces. So gravity does not affect the fundamental atomic and molecular interactions, but it can drastically alter the macroscopic transport of heat and matter through convection, or macroscopic fluid motion. Natural convection is the movement of fluid as the result of differences in density, so that denser fluid sinks and less dense fluid rises. This motion is resisted by the viscosity of the medium, which acts like friction does in slowing the motion of solids. The study of convection is an entire area of physics, and we will touch only on a few aspects. The reader is referred to some excellent texts on the subject (Tritton, 1988; Turner, 1979).

Тези доповідей конференцій з теми "Parabolic motion":

1

Woodburn, D., T. X. Wu, Q. Leland, N. Rolinski, L. Chow, and B. Jordan. "Parabolic approximation to EMA motion profiles." In NAECON 2009 - IEEE National Aerospace and Electronics Conference. IEEE, 2009. http://dx.doi.org/10.1109/naecon.2009.5426646.

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2

Naumann, Joachim. "On weak solutions to the equations of non-stationary motion of heat-conducting incompressible viscous fluids: defect measure and energy equality." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-19.

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3

Cho, Taeg Sang, Anat Levin, Fredo Durand, and William T. Freeman. "Motion blur removal with orthogonal parabolic exposures." In 2010 IEEE International Conference on Computational Photography (ICCP). IEEE, 2010. http://dx.doi.org/10.1109/iccphot.2010.5585100.

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4

Gupta, D., and K. Daniilidis. "Planar motion of a parabolic catadioptric camera." In Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004. IEEE, 2004. http://dx.doi.org/10.1109/icpr.2004.1333707.

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5

Garcke, Harald, Kazuo Ito, and Yoshihito Kohsaka. "Stability analysis of phase boundary motion by surface diffusion with triple junction." In Nonlocal and Abstract Parabolic Equations and their Applications. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc86-0-5.

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6

Han, Seon. "On the Elliptic-Parabolic Motion of a Simple Pendulum in Three Dimensions." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-60672.

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The elliptic-parabolic motion of an elastic pendulum is the subject of current study. The elasticity is either provided by a single spring or an elastic cable. The motion is called elliptic-parabolic since the point mass takes the elliptical path when viewed from the top and the parabolic path when viewed from the side. Such motion can be initiated when an initial displacement and and an initial velocity are given in the perpendicular directions. The fully nonlinear analysis shows that the elliptical path precesses. In this paper, perturbation analysis is used to obtained the precession rate for the discrete and continuous pendulum.
7

Feuillebois, F., N. Ghalya, A. Sellier, L. Elasmi, Michail D. Todorov, and Christo I. Christov. "Motion of Particles in a Parabolic Flow Near a Slip Wall." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 3rd International Conference—AMiTaNS'11. AIP, 2011. http://dx.doi.org/10.1063/1.3659937.

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8

Chang-Uk Jeong and Hiroshi Watanabe. "A modified parabolic prediction based fractional pixel motion estimation using preset corrector." In 2012 18th Asia-Pacific Conference on Communications (APCC). IEEE, 2012. http://dx.doi.org/10.1109/apcc.2012.6388249.

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9

Kakue, Takashi, Takashi Nishitsuji, Tetsuya Kawashima, Tomoyoshi Shimobaba, and Tomoyoshi Ito. "Real-time electro-holography with parabolic mirrors for projecting floating 3D motion pictures." In SA'15: SIGGRAPH Asia 2015. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2820926.2820968.

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10

Gosselin, Claude, and Louis Cloutier. "The Generating Space for Parabolic Motion Error Spiral Bevel Gears Cut by the Gleason Method." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0029.

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Abstract Because of their inherent pseudo-conjugate natures, spiral bevel gears cut by the Gleason method basically transmit motion in a non uniform manner. This motion non uniformity, or motion error, repeated at each tooth engagement and at high speeds and loads, can cause vibrations in transmissions and contact-entry impact loads on gear teeth which affect the life of a gearset. It is customary to make small changes to machine settings in order to produce gear pairs with vastly improved kinematics. Therefore, machine setting changes must be carefully chosen such as to produce appropriate unloaded kinematical motion error that will cancel tooth bending deflection and contact deformation at a given load, and thus reduce noise and vibrations due to motion non-uniformity. This paper presents a study on the effects of machine settings, such as cutter tilt, machine center to back and offset, on the unloaded kinematical motion error. Applying CAD Boolean operations on the results, it is found that, for a given speed ratio, an infinite number of cutter tilt, work offset and machine center to back combinations will produce gear sets with convex parabolic motion error curve of any desired amplitude. Moreover, the amplitude of motion error curves can be linked directly to contact bias on the tooth flank. Thus, gear sets with any parabolic motion error in the unloaded state can be produced, such as to cancel tooth bending deflection and contact deformation in the loaded state.

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