Relevant bibliographies by topics / Airy's function

Academic literature on the topic 'Airy's function'

Author: Grafiati
Published: 28 July 2022
Last updated: 8 August 2022

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Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Journal articles on the topic "Airy's function":

1

Roy, Sabyasachi, N. S. Bordoloi, and D. K. Choudhury. "Isgur–Wise function within a QCD quark model with Airy's function as the wave function of heavy–light mesons." Canadian Journal of Physics 91, no. 1 (January 2013): 34–42. http://dx.doi.org/10.1139/cjp-2012-0165.

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We report a somewhat improved wave function for mesons by taking the linear confinement term in standard QCD potential as a parent and the coulombic term as a perturbation while applying quantum mechanical perturbation techniques in solving the Schrödinger equation with such a potential. We find that Airy's infinite series appears in the wave function of the mesons. We report our calculations on the Isgur–Wise function and its derivatives for heavy–light mesons within this framework.
2

ROY, SABYASACHI, and D. K. CHOUDHURY. "AN ANALYSIS OF THE ISGUR–WISE FUNCTION AND ITS DERIVATIVES WITHIN A HEAVY–LIGHT QCD QUARK MODEL." Modern Physics Letters A 27, no. 20 (June 28, 2012): 1250110. http://dx.doi.org/10.1142/s0217732312501106.

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In determining the mesonic wave function from QCD inspired potential model, if the linear confinement term is taken as parent (with Coulombic term as perturbation), Airy's function appears in the resultant wave function — which is an infinite series. In the study of Isgur–Wise function (IWF) and its derivatives with such a wave function, the infinite upper limit of integration gives rise to divergence. In this paper, we have proposed some reasonable cutoff values for the upper limit of such integrations and studied the subsequent effect on the results. We have also studied the sensitivity of the order of polynomial approximation of the infinite Airy series in calculating the derivatives of IWF.
3

THAPA, R. K., and GUNAKAR DAS. "A SIMPLE THEORY OF PHOTOFIELD EMISSION FROM THE SURFACE OF A METAL." International Journal of Modern Physics B 19, no. 19 (July 30, 2005): 3141–49. http://dx.doi.org/10.1142/s0217979205032000.

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A simple model calculation of photofield emission is presented in which the photofield emission current (PFEC) is calculated for metal W. The matrix element for photoexcitation is evaluated by using the free electron wavefunction. The transmission probability D(W) is deduced by solving Airy's differential equation. The variation of PFEC is studied as a function of parameters like the applied high electric field, the photon energy, the initial state energy with reference to the Fermi level. It is found that in addition to D(W), the matrix element Mfi also has effect on the photofield emission.
4

Bawankar, L. C., and G. D. Kedar. "MAGNETO-THERMOELASTIC PROBLEM WITH EDDY CURRENT LOSS OF A THERMOSENSITIVE CONDUCTIVE PLATE." Advances in Mathematics: Scientific Journal 10, no. 1 (January 22, 2021): 557–70. http://dx.doi.org/10.37418/amsj.10.1.55.

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In this paper a two dimensional magneto-thermoelastic problem of a thermosensitive finite conducting plate with eddy current loss is considered. It is assumed that the plate is influenced by a time-varying external magnetic field and that the heating is caused by Joule heat. The fundamental equations for magnetic field, heat conduction and elastic fields are formulated. Temperature dependent material properties and heat source as eddy current loss is considered in the heat conduction equation. Kirchhoff's variable transformation is employed to convert nonlinear to linear heat conduction equation. Integral transform technique is used to solve the magnetic field and temperature distribution. The stresses in a plane state are determined by using Airy's stress function. The numerical analysis is carried out and the results are graphically displayed.
5

Duc, Nguyen Dinh, Pham Dinh Nguyen, Nguyen Huy Cuong, Nguyen Van Sy, and Nguyen Dinh Khoa. "An analytical approach on nonlinear mechanical and thermal post-buckling of nanocomposite double-curved shallow shells reinforced by carbon nanotubes." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 11 (September 27, 2018): 3888–903. http://dx.doi.org/10.1177/0954406218802921.

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This work presents the nonlinear mechanical and thermal post-buckling of nanocomposite double-curved shallow shells reinforced by single-walled carbon nanotubes resting on elastic foundations based on the higher order shear deformation theory with geometrical nonlinearity in von Karman–Donnell sense. The composite shells are made of various amorphous polymer matrices: poly(methyl methacrylate) (PMMA) and poly{(m-phenylenevinylene)-co-[(2,5-dioctoxy-p-phenylene) vinylene]} (PmPV). The governing equations are solved by the Galerkin method and Airy's stress function to achieve mechanical and thermal post-buckling behaviors of nanocomposite double-curved shallow shells. Various types of distributions of carbon nanotubes, both uniform distributions, and functionally graded distributions are examined. The material properties of nanocomposite double-curved shallow shells are assumed to be temperature dependent. Detailed parametric studies are carried out on the effect of various types of distribution and volume fractions of carbon nanotubes, temperature increments, elastic foundations, edge to radius and edge to thickness ratios on the nonlinear mechanical and thermal post-buckling of nanocomposite double-curved shallow shells reinforced by CNTs.
6

ALIJANI, F., and M. AMABILI. "CHAOTIC VIBRATIONS IN FUNCTIONALLY GRADED DOUBLY CURVED SHELLS WITH INTERNAL RESONANCE." International Journal of Structural Stability and Dynamics 12, no. 06 (December 2012): 1250047. http://dx.doi.org/10.1142/s0219455412500472.

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Chaotic vibrations of functionally graded doubly curved shells subjected to concentrated harmonic load are investigated. It is assumed that the shell is simply supported and the edges can move freely in in-plane directions. Donnell's nonlinear shallow shell theory is used and the governing partial differential equations are obtained in terms of shell's transverse displacement and Airy's stress function. By using Galerkin's procedure, the equations of motion are reduced to a set of infinite nonlinear ordinary differential equations with cubic and quadratic nonlinearities. A bifurcation analysis is carried out and the discretized equations are integrated at (i) fixed excitation frequencies and variable excitation amplitudes and (ii) fixed excitation amplitudes and variable excitation frequencies. In particular, Gear's backward differentiation formula (BDF) is used to obtain bifurcation diagrams, Poincaré maps and time histories. Furthermore, maximum Lyapunov exponent and Lyapunov spectrum are obtained to classify the rich dynamics. It is revealed that the shell may exhibit complex behavior including sub-harmonic, quasi-periodic and chaotic response when subjected to large harmonic excitations.
7

Hamdan, M. H., S. Jayyousi Dajani, and D. C. Roach. "Asymptotic Series Evaluation of Integrals Arising in the Particular Solutions to Airy’s Inhomogeneous Equation with Special Forcing Functions." WSEAS TRANSACTIONS ON MATHEMATICS 21 (May 31, 2022): 303–8. http://dx.doi.org/10.37394/23206.2022.21.35.

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In this work, particular and general solutions to Airy’s inhomogeneous equation are obtained when the forcing function is one of Airy’s functions of the first and second kind, and the standard Nield-Kuznetsov function of the first kind. Particular solutions give rise to special integrals that involve products of Airy’s and Nield-Kuznetsov functions. Evaluation of the resulting integrals is facilitated by expressing their integrands in asymptotic series. Corresponding expressions for the Nield-Kuznetsov function of the second kind are obtained.
8

Hamdan, M. H., S. Jayyousi Dajani, and D. C. Roach. "Asymptotic Series Evaluation of Integrals Arising in the Particular Solutions to Airy’s Inhomogeneous Equation with Special Forcing Functions." PROOF 2 (June 6, 2022): 153–58. http://dx.doi.org/10.37394/232020.2022.2.19.

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In this work, particular and general solutions to Airy’s inhomogeneous equation are obtained when the forcing function is one of Airy’s functions of the first and second kind, and the standard Nield-Kuznetsov function of the first kind. Particular solutions give rise to special integrals that involve products of Airy’s and Nield-Kuznetsov functions. Evaluation of the resulting integrals is facilitated by expressing their integrands in asymptotic series. Corresponding expressions for the Nield-Kuznetsov function of the second kind are obtained.
9

Altan, BurhanettinS. "Airy's Functions in Nonlocal Elasticity." Journal of Computational and Theoretical Nanoscience 8, no. 11 (November 1, 2011): 2381–88. http://dx.doi.org/10.1166/jctn.2011.1873.

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Hamdan, M. H., S. Jayyousi Dajani, and M. S. Abu Zaytoon. "Higher Derivatives and Polynomials of the Standard Nield-Kuznetsov Function of the First Kind." International Journal of Circuits, Systems and Signal Processing 15 (December 8, 2021): 1737–43. http://dx.doi.org/10.46300/9106.2021.15.187.

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In this fundamental work, higher derivatives of the standard Nield-Kuznetsov function of the first kind, and the polynomials arising from this function and Airy’s functions, are derived and discussed. This work provides background theoretical material and computational procedures for the arising polynomials and the higher derivatives of the recently introduced Nield-Kuznetsov function, which has filled a gap that existed in the literature since the nineteenth century. The ease by which the inhomogeneous Airy’s equation can now be solved is an advantage offered by the Nield-Kuznetsov functions. The current analysis might prove to be invaluable in the study of inhomogeneous Schrodinger, Tricomi, and Spark ordinary differential equations.
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You might also be interested in the extended bibliographies on the topic 'Airy's function' for particular source types:
Journal articles Dissertations / Theses Books

Dissertations / Theses on the topic "Airy's function":

1

Bahouli, Bassem. "Caracterisations de champs de matrices, potentiels matrices et applications aux operateurs traces." Thesis, Pau, 2021. http://www.theses.fr/2021PAUU3053.

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Plusieurs auteurs ont utilisé les champs de contraintes pour résoudre l'équation d’équilibre de la mécanique des milieux continus. Airy (1863) a résolu le cas bidimensionnel, Maxwell (1870) et Morera (1892) ont étudié le cas tridimensionnel. Les solutions obtenues sont des cas particuliers de celles de Beltrami (1892). Gurtin a donné un exemple de solutions ne satisfaisant pas la représentation S = CurlCurlA de Beltrami, ce qui signifie que la représentation précédente est incomplète. De plus, il a montré que si l’ouvert est régulier, alors elle est complète dans l’espace des champs réguliers de contraintes auto-équilibrés.Dans cette thèse intitulée ”Caractérisations de champs de matrices, potentiels matrices et applications aux opérateurs traces”, on s’intéresse à diverses caractérisations de champs de vecteurs, de champs de matrices et spécialement au résultat de Gurtin dans le cas où l’ouvert et les champs de contraintes ne sont pas réguliers.Cette thèse est décomposée en cinq chapitres. Le premier chapitre expose la problématique de recherche traitée dans cette thèse. Il présente également l’origine du sujet de recherche. Dans le deuxième chapitre, on étudie l’opérateur et en particulier l’existence de potentiels vecteurs dans différents cadres fonctionnels.Dans les chapitres 3 et 4, on va montrer quelques versions de la complétude de la représentation de Beltrami et en déduire des décompositions de Helmholtz pour les champs de matrices.Le dernier chapitre est consacré à l’étude de l’image de différents opérateurs traces de fonctions W 2,p (Ω), W 3,p (Ω) lorsque Ω est un ouvert borné de R 2 lipschitzien. L’ingrédient essentiel est donné par la fonction d’Airy ou par la représentation de Beltrami
Many authors have used stress fields to solve the equilibrium equation of continuum me- chanics. Airy (1863) solved the two-dimensional case, Maxwell (1870) and Morera (1892) solved the three-dimensional case. The above solutions are special cases of those of Beltrami (1892). Gurtin gave an example of solutions that do not have Beltrami’s S = CurlCurlA representation. He showed that if the domain Ω is regular, then this representation is complete in the class of regular stress fields which are self-equilibrated.My thesis title is ”Characterizations of matrix fields, potential matrices and applications to trace operators”. In this work, we are interested by showing many characterizations ofvector fields, of matrix fields and especially by generalizing the result of Gurtin in the case when the open set and the stress fields are not regular.This thesis consists of five chapters. The first chapter presents the research problem ad- dressed in this thesis. It also presents the origin of the subject of research.In the second chapter, we study the operator . In particular, the existence of potential vectors in different functional frameworks.In Chapters 3 and 4, we will show some versions of Beltrami’s completeness and we deduce some Helmholtz decomopsitions for symmetric matrix fields.The last chapter is devoted to the study of the image of different trace operators of functions W 2,p (Ω), W 3,p (Ω) when Ω is a bounded open of R 2 with Lipschitz boundary. The essential ingredient is given by the Airy’s function or by the Beltrami representation
2

Miller, Thomas. "Verallgemeinerte Airyfunktionen." Bonn : [Math. Inst. der Univ., Bibliothek], 1989. http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&doc_number=001222832&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA.

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House, Robert Simpson. "Airy functions and the Recursive Ray Acoustics Algorithm." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1994. http://handle.dtic.mil/100.2/ADA290182.

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Thesis (M.S. in Electrical Engineering) Naval Postgraduate School, December 1994.
Thesis advisor(s): Lawrence J. Ziomek. "December 1994." Includes bibliographical references. Also available online.
4

Lladser, Manuel Eugenio. "Asymptotic enumeration via singularity analysis." Connect to this title online, 2003. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1060976912.

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Thesis (Ph. D.)--Ohio State University, 2003.
Title from first page of PDF file. Document formatted into pages; contains x, 227 p.; also includes graphics Includes bibliographical references (p. 224-227). Available online via OhioLINK's ETD Center
5

Kim, Jeong-Han. "Optical display of the Airy function and transient wave propagation in a dispersive medium." Thesis, This resource online, 1996. http://scholar.lib.vt.edu/theses/available/etd-02132009-172038/.

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Hinton, Jantzen L. "A Study on the Effects of Coil Wedge During Rewinding of Thin Gauge Metals." Wright State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=wright1312580769.

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Rochefort, Nathalie. "Functional specificity of callosal connections in the cat visual cortex." Paris 6, 2007. http://www.theses.fr/2007PA066054.

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Le transfert inter hémisphérique des informations visuelles a été étudié au niveau des aires visuelles 17 et 18 (A17 et A18) du chat par imagerie optique. La localization et l’organisation rétinotopique des régions activées par le corps calleux (CC) ont été étudiées chez des chats chiasmotomisés. Des domaines d’orientation activés par le CC sont apparus tout le long de la zone de transition (TZ) entre A17 et A18. La portion ipsilatérale du champ visuel jusqu’à 8° d’azimuth était représentée dans des patchs, dans la TZ. Cette représentation est transférée principalement par l’intermédiaire des projections non croisées de la rétine temporale et du CC. Les distributions des terminaisons de huit axones calleux dans les cartes fonctionnelles du cortex visuel ont été comparées aux caractéristiques fonctionnelles des sites d’injection dans l’hémisphère opposé. Ces résultats démontrent que les connexions calleuses relient principalement des régions corticales de même préférence d’orientation.
8

Svoboda, Petr. "Popis rozložení napětí v okolí ostrého vrubu." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-382552.

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The presented diploma thesis deals with the problem of determining the stress singularity exponent of the V-notch. This task can be divided into two parts. The first deals with the theoretical background, that means the basic relations of mechanics and the basic concepts of fracture mechanics. The second part deals with the elaboration of the Williams method and the creation of a program for calculating the stress singularity exponent.
9

Thulasi, Sunita. "Theory of the two-dimensional airy electron gas Hartee-Fock and density-functional studies /." Diss., Columbia, Mo. : University of Missouri-Columbia, 2006. http://hdl.handle.net/10355/4111.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2006.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (May 17, 2007) Vita. n following parenthesis in formula (LaTiO₃) should be subscript. Includes bibliographical references.
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Salgado, Filipe Ferraz. "Uma implementação paralela do AIRS em Scala." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/45/45134/tde-19032012-094158/.

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Com o avanço tecnológico dos últimos anos passou a ser normal vermos microprocessadores com múltiplos núcleos (cores). A expectativa é de que o crescimento da quantidade de núcleos passe a ser maior do que o crescimento da velocidade desses núcleos. Assim, além de se preocuparem em otimizar algoritmos sequenciais, os programadores começaram a dar mais atenção às possibilidades de aproveitamento de toda a capacidade oferecida pelos diversos cores. Existem alguns modelos de programação que permitem uma abordagem concorrente. O modelo de programação concorrente mais adotado atualmente é o baseado em threads, que utiliza memória compartilhada e é adotado em Java. Um outro modelo é o baseado em troca de mensagens, no qual as entidades computacionais ativas são denominadas atores. Nesse trabalho, estudamos a linguagem Scala e seu modelo de atores. Além disso, implementamos em Scala uma versão paralela de um algoritmo de classicação que simula o sistema imunológico dos animais, o AIRS paralelo, e comparamos seu desempenho com a versão em Java.
With the technological advance of the last years it has been normal to see microprocessors with multiple cores. The expectation is that the growth of number of cores becomes greater than the growth of the speed of these cores. This way, besides worrying about optimizing sequential algorithms, developers started to give more attention to the possibilities of proting from all capacity offered by the cores. There exists a few programming models that allow a concurrent approach. In these days, the most adopted concurrent programming model is the one based on threads, which uses shared memory and is adopted in Java. Other model is based on message passing, on which the active computational entities are called actors. In this project, we studied Scala language and its model based on actors. Besides that, we implemented in Scala a parallel version of a classification algorithm that simules the immune system of the animals, parallel AIRS, and compared its performance with the Java version.
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Books on the topic "Airy's function":

1

Vallée, Olivier. Airy functions and applications to physics. Hackensack, NJ: World Scientific, 2004.

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Vallée, Olivier. Airy functions and applications to physics. 2nd ed. Hackensack, NJ: World Scientific, 2010.

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Ghatak, A. K. Modified Airy function and WKB solutions to the wave equation. [Gaithersburg, Md.]: National Institute of Standards and Technology, 1991.

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Argentina) Luis Santaló Winter School-CIMPA Research School Topics in Noncommutative Geometry (3rd 2010 Buenos Aires. Topics in noncommutative geometry: Third Luis Santaló Winter School-CIMPA Research School Topics in Noncommutative Geometry, Universidad de Buenos Aires, Buenos Aires, Argentina, July 26-August 6, 2010. Edited by Cortiñas, Guillermo, editor of compilation. Providence, RI: American Mathematical Society, 2012.

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Zemanian, A. H. Realizability theory for continuous linear systems. New York: Dover, 1995.

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Numerical evaluation of the incomplete airy functions and their application to high frequency scattering and diffraction. Columbus, Ohio: Ohio State University, ElectroScience Laboratory, 1992.

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Vallee, Olivier, and manuel Soares. Airy Functions And Applications To Physics. Imperial College Press, 2004.

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Vallée, Olivier, and Manuel Soares. Airy Functions and Applications to Physics. IMPERIAL COLLEGE PRESS, 2004. http://dx.doi.org/10.1142/p345.

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Vallée, Olivier, and Manuel Soares. Airy Functions and Applications to Physics. IMPERIAL COLLEGE PRESS, 2010. http://dx.doi.org/10.1142/p709.

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Kanzieper, Eugene. Painlevé transcendents. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.9.

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This article discusses the history and modern theory of Painlevé transcendents, with particular emphasis on the Riemann–Hilbert method. In random matrix theory (RMT), the Painlevé equations describe either the eigenvalue distribution functions in the classical ensembles for finite N or the universal eigenvalue distribution functions in the large N limit. This article examines the latter. It first considers the main features of the Riemann–Hilbert method in the theory of Painlevé equations using the second Painlevé equation as a case study before analysing the two most celebrated universal distribution functions of RMT in terms of the Painlevé transcendents using the theory of integrable Fredholm operators as well as the Riemann–Hilbert technique: the sine kernel and the Airy kernel determinants.
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Book chapters on the topic "Airy's function":

1

Gdoutos, E. E. "Airy Stress Function Method." In Problems of Fracture Mechanics and Fatigue, 3–9. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-2774-7_1.

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Schweizer, Wolfgang. "Bessel and Airy Functions." In Special Functions in Physics with MATLAB, 65–80. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-64232-7_4.

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Oldham, Keith B., Jan C. Myland, and Jerome Spanier. "The Airy Functions Ai(x) and Bi(x)." In An Atlas of Functions, 585–92. New York, NY: Springer US, 2008. http://dx.doi.org/10.1007/978-0-387-48807-3_57.

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Kohn, W. "Edge Electronic Structure: The Airy Gas." In Electronic Density Functional Theory, 295–97. Boston, MA: Springer US, 1998. http://dx.doi.org/10.1007/978-1-4899-0316-7_20.

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Lubinsky, Doron S. "Mean Convergence of Interpolation at Zeros of Airy Functions." In Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, 889–909. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-72456-0_39.

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Alshaya, A., John M. Considine, and R. Rowlands. "Determination of Constitutive Properties in Inverse Problem Using Airy Stress Function." In Conference Proceedings of the Society for Experimental Mechanics Series, 73–81. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-62899-8_12.

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Lubinsky, D. S. "On Marcinkiewicz-Zygmund Inequalities at Hermite Zeros and Their Airy Function Cousins." In Trigonometric Sums and Their Applications, 119–47. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-37904-9_6.

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Bisi, Elia, and Nikos Zygouras. "GOE and $${\mathrm{Airy}}_{2\rightarrow 1}$$ Marginal Distribution via Symplectic Schur Functions." In Probability and Analysis in Interacting Physical Systems, 191–213. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15338-0_7.

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Minh, Nguyen-Hoang, and Wilfried Becker. "Open Circular Hole in a Finite Plate Under Tension Treated by Airy Stress Function Method." In Analysis of Shells, Plates, and Beams, 311–30. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-47491-1_16.

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Guzev, Mikhail A. "The Airy Stress Function for Non-Euclidean Model of a Continuous Medium and Description of Residual Stresses." In Smart Modelling For Engineering Systems, 75–85. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-33-4709-0_7.

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Conference papers on the topic "Airy's function":

1

Walker, D. G., and T. S. Fisher. "Modeling of Carbon Nanotube Emission Using Airy Functions." In ASME 2003 Heat Transfer Summer Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/ht2003-47276.

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Modeling of electron field emission has not advanced significantly since Fowler and Nordheim described the phenomenon eighty years ago. While their approach provides remarkable agreement with experiments for a large number of cases, the theory is strictly valid for planar geometries and low temperatures. Carbon nanotubes have been considered for field emission energy conversion devices. Under high-temperature conditions and significant field enhancement, the approximations used in the Fowler-Nordheim formalism become invalid. The present work predicts electron current densities emitted from carbon nanotubes using Airy functions to predict transmission and temperature dependent supply functions. Results indicate that Fowler-Nordheim compares favorably with the Airy function model for materials with large work function (φ ≈ 5eV, in the present study) at room temperatures. However, for materials with smaller work functions, the difference between the Airy function model and Fowler-Nordheim can be significant.
2

Wang, Fengfei, David Singh, Ping Yu, and Guohai Situ. "Wigner Distribution Function of Airy Beam." In Frontiers in Optics. Washington, D.C.: OSA, 2017. http://dx.doi.org/10.1364/fio.2017.fm4b.7.

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Yanovsky, Igor, Thomas S. Pagano, Evan M. Manning, Steven E. Broberg, Hartmut H. Aumann, and Luminita A. Vese. "Airs Point Spread Function Reconstruction Using Airs and Modis Data." In IGARSS 2021 - 2021 IEEE International Geoscience and Remote Sensing Symposium. IEEE, 2021. http://dx.doi.org/10.1109/igarss47720.2021.9555019.

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4

Abdelkhalek, Rihab. "Towards New Optimized Artificial Immune Recognition Systems under the Belief Function Theory." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/821.

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Abstract:
Artificial Immune Recognition Systems (AIRS) are powerful machine learning techniques, which aim to solve real world problems. A number of AIRS versions have produced successful prediction results. Nevertheless, these methods are unable to handle the uncertainty that could spread out at any stage of the AIRS approach. This issue is considered as a huge obstacle for having accurate and effective classification outputs. Therefore, our main objective is to handle this uncertainty using the belief function theory. We opt also in this article for an optimization over the classical AIRS approaches in order to enhance the classification performance.
5

Albertin, Uwe K. "Turning ray migration via airy functions." In SEG Technical Program Expanded Abstracts 1992. Society of Exploration Geophysicists, 1992. http://dx.doi.org/10.1190/1.1821891.

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6

Held, Susanne, Wolfgang Dornisch, and Nima Azizi. "An Isogeometric Element Formulation for Linear Two-Dimensional Elasticity Based on the Airy Equation." In VI ECCOMAS Young Investigators Conference. València: Editorial Universitat Politècnica de València, 2021. http://dx.doi.org/10.4995/yic2021.2021.12598.

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The aim of this work is to derive a formulation for linear two-dimensional elasticity using just one degree of freedom. With the Airy stress function, a measure without further physical meaning is chosen to this single degree of freedom. The corresponding Airy equation requires higher order basis functions for the discretization of the formulation [1]. Isogeometric structural analysis (IGA) is based on shape functions of the system in Computer-Aided design (CAD) software [2]. These shape functions can fulfill the requirement of high continuity and therefore the formulation is obtained through IGA methods. Non-Uniform Rational B-splines (NURBS) are used to discretize the domain and to solve the occurring differential equations within the Galerkin method [3]. The received one-degree of freedom formulation allows to compute stresses as direct solution of the underlying system of equations. Numerical examples demonstrate the accuracy for a quadratic plate under standard, but also under complex loading. For constant or linear loading functions only one element is sufficient to receive the exact solution – a general advantage of using higher order basis functions. The correct convergence behaviour of the proposed formulation is proved by the -error norm for a complex load situation. Here, only a few refinement steps yield a good approximation with a very small error of the stresses.
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Fedotov, A., and F. Klopp. "Difference equations, uniform quasiclassical asymptotics and Airy functions." In 2018 Days on Diffraction (DD). IEEE, 2018. http://dx.doi.org/10.1109/dd.2018.8553493.

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van Delst, Paul F. W., Henry E. Revercomb, Robert O. Knuteson, Hartmut H. Aumann, and Kenneth Overoye. "Simulations of AIRS spectral response function measurement with an FTS." In Optical Science, Engineering and Instrumentation '97, edited by William L. Barnes. SPIE, 1997. http://dx.doi.org/10.1117/12.283809.

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Chevillard, S., and M. Mezzarobba. "Multiple-Precision Evaluation of the Airy Ai Function with Reduced Cancellation." In 2013 IEEE 21st Symposium on Computer Arithmetic (ARITH). IEEE, 2013. http://dx.doi.org/10.1109/arith.2013.33.

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Shugan, Igor, Sergei Kuznetsov, Yana Saprykina, and Yang-Yih Chen. "Nonlinear Airy Wave Pulses on the Sea Surface." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-96298.

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Abstract The possibility of self-acceleration of the water-wave pulse with a permanent envelope in the form of the nonlinear Airy function during its long propagation in deep water is experimentally and theoretically analyzed. This wave packet has amazing properties — accelerates without any external force, and preserves shape in a dispersive medium. The inverted Airy envelope wave function can propagate at velocity that is faster than the group velocity. We experimentally study the behavior of Airy water-wave pulses in a super-tank and long scaled propagation, to investigate its main properties, nonlinear effects and stability. Theoretical modeling analysis is based on the nonlinear Schrodinger equation. We investigate the scope of applicability, feasibility and stability conditions of nonlinear Airy wave trains in the deep water conditions; defining regimes of self-acceleration of the main pulse, immutability shape of Airy envelope; assessing the impact of nonlinearity and dissipation on the propagation of Airy waves. We analyzed the influence of the initial pulse characteristics on self-acceleration of wave packet and the stability of the envelope form. The anticipated results allow extending the physical understanding of the evolution of nonlinear dispersive waves in a wide range of initial conditions and at different spatial and temporal scales, from both theoretical and experimental points of view. Steep waves start to become an unstable, we observe spectrum widening and downshifting. Wave propagation is accompained by the intensive wave breaking and the generation of water-wave solitons.

Reports on the topic "Airy's function":

1

Goldstein, Marvin J. Computation of Complex Airy Functions. Fort Belvoir, VA: Defense Technical Information Center, March 1986. http://dx.doi.org/10.21236/ada630527.

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2

Ghatak, A. K., R. L. Gallawa, and I. C. Goyal. Modified airy function and WKB solutions to the wave equation. Gaithersburg, MD: National Institute of Standards and Technology, 1991. http://dx.doi.org/10.6028/nist.mono.176.

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