Relevant bibliographies by topics / Generalised Integrals

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

Academic literature on the topic 'Generalised Integrals'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Generalised Integrals"

1

Muldowney. "INFINITE-DIMENSIONAL GENERALISED RIEMANN INTEGRALS." Real Analysis Exchange 14, no. 1 (1988): 14. http://dx.doi.org/10.2307/44153611.

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El-Gabali, M., and S. Kalla. "Some generalised radiation field integrals." Computers & Mathematics with Applications 32, no. 12 (December 1996): 121–28. http://dx.doi.org/10.1016/s0898-1221(96)00212-x.

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Kumar, Ravindra. "Numerical approximations of certain generalised integrals." Mathematical and Computer Modelling 11 (1988): 679–82. http://dx.doi.org/10.1016/0895-7177(88)90579-1.

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Angelantonj, Carlo, Ioannis Florakis, and Boris Pioline. "Threshold corrections, generalised prepotentials and Eichler integrals." Nuclear Physics B 897 (August 2015): 781–820. http://dx.doi.org/10.1016/j.nuclphysb.2015.06.009.

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Kaminski, D., and R. B. Paris. "Asymptotics via iterated Mellin–Barnes integrals: Application to the generalised Faxén integral." Methods and Applications of Analysis 4, no. 3 (1997): 311–25. http://dx.doi.org/10.4310/maa.1997.v4.n3.a5.

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Dragomir, S. S., and A. Sofo. "Approximating the Stieltjes integral via the Darst-Pollard inequality." Filomat 21, no. 2 (2007): 63–75. http://dx.doi.org/10.2298/fil0702063d.

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An approximation of the Stieltjes integral of bounded integrals and continuous integrators via the Darst-Pollard inequality is given. Applications for the generalised trapezoid formula and the Ostrowski inequality for functions of bounded variation are also provided. .
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De Sarkar, S., and A. G. Das. "Riemann derivatives and general integrals." Bulletin of the Australian Mathematical Society 35, no. 2 (April 1987): 187–211. http://dx.doi.org/10.1017/s0004972700013174.

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Sargent and later Bullen and Mukhopadhyay obtained a definition of absolutely continuous functions, functions, that is related to kth Peano derivatives. The generalised notions of ACkG*, [ACkG*], ACkG* above, etcetera functions led Bullen and Mukhopadhyay to define certain general integrals of the kth order.The present work is concerned with a further simplification of the definitions of such functions by the use of divided differences but still retaining similar fundamental properties. These concepts lead to the introduction of Denjoy and Ridder type integrals which are shown to be equivalent to a Perron type integral that corresponds to kth Riemann* derivatives. All three of these integrals are shown to be equivalent to the three integrals of Bullen and Mukhopadhyay.
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Cleary, Paul. "Integrability of Motions in Galactic Potentials." Publications of the Astronomical Society of Australia 6, no. 4 (1986): 453–58. http://dx.doi.org/10.1017/s1323358000018361.

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AbstractThe dynamics exhibited by systems, such as galaxies, are dominated by the isolating integrals of the motion. The most common are the energy and angular momentum integrals. The motions in a system with a full complement of isolating integrals are regular, that is, periodic or quasi-periodic. Such a system is integrable. If there is a deficiency in the number of integrals, then the motions are chaotic. There is a fundamental quantative difference in the motion, depending on the number of integrals. A technique, called Generalised Painlevé analysis, based on complex variable theory allows the user to determine if a system is integrable. Two new integrable cases of the Henon-Heiles system are presented, bringing the total number of such integrable potentials to five. It is highly probable that there are no further integrable cases of the Henon-Heiles potential. Five cases of the quartic Verhulst potential, defined by certain restrictions on the coefficients, which are found to be integrable are summarised.
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Feigin, M. V., M. A. Hallnäs, and A. P. Veselov. "Baker-Akhiezer functions and generalised Macdonald-Mehta integrals." Journal of Mathematical Physics 54, no. 5 (May 2013): 052106. http://dx.doi.org/10.1063/1.4804615.

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MacLeod, Allan J. "The efficient computation of some generalised exponential integrals." Journal of Computational and Applied Mathematics 148, no. 2 (November 2002): 363–74. http://dx.doi.org/10.1016/s0377-0427(02)00556-3.

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Dissertations / Theses on the topic "Generalised Integrals"

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Feigin, Mikhail V. "Rings of quantum integrals for generalised Calogero-Moser problems." Thesis, Loughborough University, 2002. https://dspace.lboro.ac.uk/2134/35847.

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The rings of quantum integrals for generalised Calogero-Moser problems are studied in the special case when all the parameters are integers. The problem is reduced to the description of the rings of polynomials satisfying a certain quasi-invariance property (quasi-invariants). The quasi-invariants of dihedral groups are fully described. It is shown that they form a free module over invariants generated by m-harmonic polynomials. The m-harmonic polynomials for general Coxeter group are introduced and investigated. For the non-Coxeter generalisations of Calogero-Moser problems related to the systems An(m), Cn+1(m, l), the rings of quantum integrals are considered. The Poincare series for the quasi-invariants of two-dimensional deformations are computed. It is shown that the rings of quasi-invariants are Gorenstein like in the Coxeter case.
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Bär, Christian. "Renormalized integrals and a path integral formula for the heat kernel on a manifold." Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/6005/.

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We introduce renormalized integrals which generalize conventional measure theoretic integrals. One approximates the integration domain by measure spaces and defines the integral as the limit of integrals over the approximating spaces. This concept is implicitly present in many mathematical contexts such as Cauchy's principal value, the determinant of operators on a Hilbert space and the Fourier transform of an L^p function. We use renormalized integrals to define a path integral on manifolds by approximation via geodesic polygons. The main part of the paper is dedicated to the proof of a path integral formula for the heat kernel of any self-adjoint generalized Laplace operator acting on sections of a vector bundle over a compact Riemannian manifold.
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Larsson, David. "Generalized Riemann Integration : Killing Two Birds with One Stone?" Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-96661.

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Since the time of Cauchy, integration theory has in the main been an attempt to regain the Eden of Newton. In that idyllic time [. . . ] derivatives and integrals were [. . . ] different aspects of the same thing. -Peter Bullen, as quoted in [24] The theory of integration has gone through many changes in the past centuries and, in particular, there has been a tension between the Riemann and the Lebesgue approach to integration. Riemann's definition is often the first integral to be introduced in undergraduate studies, while Lebesgue's integral is more powerful but also more complicated and its methods are often postponed until graduate or advanced undergraduate studies. The integral presented in this paper is due to the work of Ralph Henstock and Jaroslav Kurzweil. By a simple exchange of the criterion for integrability in Riemann's definition a powerful integral with many properties of the Lebesgue integral was found. Further, the generalized Riemann integral expands the class of integrable functions with respect to Lebesgue integrals, while there is a characterization of the Lebesgue integral in terms of absolute integrability. As this definition expands the class of functions beyond absolutely integrable functions, some theorems become more cumbersome to prove in contrast to elegant results in Lebesgue's theory and some important properties in composition are lost. Further, it is not as easily abstracted as the Lebesgue integral. Therefore, the generalized Riemann integral should be thought of as a complement to Lebesgue's definition and not as a replacement.
Ända sedan Cauchys tid har integrationsteori i huvudsak varit ett försök att åter finna Newtons Eden. Under den idylliska perioden [. . . ] var derivator och integraler [. . . ] olika sidor av samma mynt.-Peter Bullen, citerad i [24] Under de senaste århundradena har integrationsteori genomgått många förändringar och framförallt har det funnits en spänning mellan Riemanns och Lebesgues respektive angreppssätt till integration. Riemanns definition är ofta den första integral som möter en student pa grundutbildningen, medan Lebesgues integral är kraftfullare. Eftersom Lebesgues definition är mer komplicerad introduceras den först i forskarutbildnings- eller avancerade grundutbildningskurser. Integralen som framställs i det här examensarbetet utvecklades av Ralph Henstock och Jaroslav Kurzweil. Genom att på ett enkelt sätt ändra kriteriet for integrerbarhet i Riemanns definition finner vi en kraftfull integral med många av Lebesgueintegralens egenskaper. Vidare utvidgar den generaliserade Riemannintegralen klassen av integrerbara funktioner i jämförelse med Lebesgueintegralen, medan vi samtidigt erhåller en karaktärisering av Lebesgueintegralen i termer av absolutintegrerbarhet. Eftersom klassen av generaliserat Riemannintegrerbara funktioner är större än de absolutintegrerbara funktionerna blir vissa satser mer omständiga att bevisa i jämforelse med eleganta resultat i Lebesgues teori. Därtill förloras vissa viktiga egenskaper vid sammansättning av funktioner och även möjligheten till abstraktion försvåras. Integralen ska alltså ses som ett komplement till Lebesgues definition och inte en ersättning.
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Taylor, C. James. "Generalised proportional-integral-plus control." Thesis, Lancaster University, 1996. http://eprints.lancs.ac.uk/49452/.

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This thesis is concerned with the True Digital Control (TDC) design philosophy and its practical embodiment in the non-minimal state space (NMSS) approach to control design, for systems described by discrete time transfer function models in the backward shift operator. This yields Proportional-Integral-Plus (PIP) controllers that are particularly easy to implement in practice, since the state variables are defined only in terms of the sampled input and output signals. The basic PIP algorithm is extended and enhanced in various ways to form a more sophisticated Generalised PIP controller. This includes an investigation into the importance of structure in PIP control design, the development of a command input anticipation technique and the introduction of two stochastic formulations of the problem, namely Kalman Filtering and risk sensitive optimal control. Finally, the thesis discusses the relationship between PIP and predictive control, in particular Generalised Predictive Control (GPC) and the Smith Predictor. The power of the approach is illustrated by the design of PIP controllers for a number of difficult applications also described in the thesis, including the control of a large horticultural greenhouse at Silsoe Research Institute; the control of carbon dioxide in crop growth experiments; the control of a Statistical Traffic Model simulation of interurban traffic networks; and, finally, the control of the multivariable Shell heavy oil fractionator simulation.
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Katugampola, Don Udita Nalin. "ON GENERALIZED FRACTIONAL INTEGRALS AND DERIVATIVES." OpenSIUC, 2011. https://opensiuc.lib.siu.edu/dissertations/387.

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In this paper we present a generalization to two existing fractional integrals and derivatives, namely, the Riemann-Liouville and Hadamard fractional operators. The existence and uniqueness results for single term fractional differential equations (FDE) have also been established. We also obtain the Mellin transforms of such generalized fractional operators which are important in solving fractional differential equations.
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Delaney, Christopher. "Generalized Differential and Integral Categories." Thesis, Université d'Ottawa / University of Ottawa, 2018. http://hdl.handle.net/10393/37136.

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This paper provides two generalizations of differential and integral categories: Leibniz and generalized Rota-Baxter categories, which capture certain algebraic structures, and q-categories, which capture structures of quantum calculus. In the search for new examples of differential and integral categories, it was observed that many structures were not quite examples but satisfied certain properties and not others. This leads us to the definition of Leibniz, Rota-Baxter and proto-FTC categories. In generalizing Rota-Baxter categories further to an arbitrary weight, we show that we recapture Ribenboim's generalized power series as a monad on vector spaces with a generalized integral transformation. This also subsumes the renormalization operator on Laurent series, which has applications in the quantum realm. Finally, we define quantum differential and quantum integral categories, show that they recapture the usual notions of quantum calculus on polynomials, and construct a new example to indicate their potential usefulness outside of that specific setting
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Tang, W. "A generalized approach for transforming domain integrals into boundary integrals in boundary element methods." Thesis, University of Southampton, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.378981.

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Dunn, Thomas Boyd. "Integral Closure and the Generalized Multiplicity Sequence." Diss., North Dakota State University, 2015. https://hdl.handle.net/10365/27935.

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Wilson, Julia Carol. "Generalized Dedekind sums and their connection with Franel integrals." Thesis, University of York, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.358339.

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Wilson, Michael. "Integral modelling of jets of variable composition in generalised crossflows." Thesis, University of Bath, 1986. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382563.

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Books on the topic "Generalised Integrals"

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Nicolas Bourbaki. Integration. Berlin: Springer, 2004.

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Nicolas Bourbaki. Integration. Berlin: Springer, 2004.

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Lee, Tuo Yeong. Henstock-Kurzweil integration on Euclidean spaces. Singapore: World Scientific, 2011.

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Intégration. Paris: Hermann, 1988.

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Rana, Inder K. An introduction to measure and integration. New Delhi: Narosa, 1997.

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Rana, Inder K. An introduction to measure and integration. 2nd ed. Providence, R.I: American Mathematical Society, 2002.

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Guoju, Ye, ed. Topics in Banach space integration. Hackensack, NJ: World Scientific, 2005.

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Zemanian, A. H. Generalized integral transformations. New York: Dover, 1987.

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Generalized integral transformations. New York: Dover, 1987.

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1932-, Klir George J., ed. Generalized measure theory. New York: Springer, 2009.

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Book chapters on the topic "Generalised Integrals"

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Muldowney, P. "Infinite-dimensional generalised Riemann integrals." In Lecture Notes in Mathematics, 131–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0083104.

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Akopov, N. "HERMES Results on the Generalised GDH Integrals." In Spin Structure of the Nucleon, 121–31. Dordrecht: Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-010-0165-6_11.

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Erickson, K. Bruce, and Ross A. Maller. "Generalised Ornstein-Uhlenbeck Processes and the Convergence of Lévy Integrals." In Lecture Notes in Mathematics, 70–94. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-31449-3_6.

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Kanwal, Ram P. "Distributions Defined by Divergent Integrals." In Generalized Functions, 71–98. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8174-6_4.

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Dubois, Didier, Henri Prade, Agnès Rico, and Bruno Teheux. "Generalized Sugeno Integrals." In Information Processing and Management of Uncertainty in Knowledge-Based Systems, 363–74. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-40596-4_31.

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Anastassiou, George A. "M-Fractional Integral Type Inequalities." In Generalized Fractional Calculus, 277–82. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56962-4_13.

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Klement, Erich Peter, Radko Mesiar, and Endre Pap. "Generalized measures and integrals." In Trends in Logic, 283–312. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-015-9540-7_14.

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Davies, B. "Generalized Functions." In Integral Transforms and their Applications, 130–54. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4899-2691-3_9.

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Kanwal, Ram P. "Distributions Defined by Divergent Integrals." In Generalized Functions Theory and Technique, 71–98. Boston, MA: Birkhäuser Boston, 1998. http://dx.doi.org/10.1007/978-1-4684-0035-9_4.

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Anastassiou, George A. "Caputo Generalized $$\psi $$-Fractional Integral Type Inequalities." In Generalized Fractional Calculus, 113–33. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-56962-4_6.

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Conference papers on the topic "Generalised Integrals"

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Malik, Pradeep, Saiful R. Mondal, and A. Swaminathan. "Fractional Integration of Generalized Bessel Function of the First Kind." In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48950.

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Generalizing the classical Riemann-Liouville and Erde´yi-Kober fractional integral operators two integral transforms involving Gaussian hypergeometric functions in the kernel are considered. Formulas for composition of such integrals with generalized Bessel function of the first kind are obtained. Special cases involving trigonometric functions such as sine, cosine, hyperbolic sine and hyperbolic cosine are deduced. These results are established in terms of generalized Wright function and generalized hypergeometric functions.
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Zhang, De-Li, and Cai-Mei Guo. "N-dimensional generalized fuzzy integrals." In 2010 International Conference on Machine Learning and Cybernetics (ICMLC). IEEE, 2010. http://dx.doi.org/10.1109/icmlc.2010.5581005.

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De-Li Zhang, Cai-Mei Guo, and Da-You Liu. "Lattice-valued generalized fuzzy integrals." In 2008 International Conference on Machine Learning and Cybernetics (ICMLC). IEEE, 2008. http://dx.doi.org/10.1109/icmlc.2008.4620464.

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Boag, Amir, and Vitaliy Lomakin. "Generalized equivalence integral equations." In 2012 6th European Conference on Antennas and Propagation (EuCAP). IEEE, 2012. http://dx.doi.org/10.1109/eucap.2012.6206074.

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Sharshevsky, A., Y. Brick, and A. Boag. "Generalized source integral equation." In 2017 International Conference on Electromagnetics in Advanced Applications (ICEAA). IEEE, 2017. http://dx.doi.org/10.1109/iceaa.2017.8065455.

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Ibrahim, Rabha W., and Maslina Darus. "Generalized the Pommerenke integral operators." In PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4882559.

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Achar, B. N. Narahari, Tanya Prozny, and John W. Hanneken. "Linear Chain of Coupled Fractional Oscillators: Response Dynamics and Its Continuum Limit." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35403.

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The standard model of a chain of simple harmonic oscillators of Condensed Matter Physics is generalized to a model of linear chain of coupled fractional oscillators in fractional dynamics. The set of integral equations of motion pertaining to the chain of harmonic oscillators is generalized by taking the integrals to be of arbitrary order according to the methods of fractional calculus to yield the equations of motion of a chain of coupled fractional oscillators. The solution is obtained by using Laplace transforms. The continuum limit of the equations is shown to yield the fractional diffusion-wave equation in one dimension. The solution and numerical application of the set of equations and the continuum limit there of are discussed.
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Cuesta, Eduardo, Alfonso Fernandez-Manso, and Carmen Quintano. "Generalized fractional integrals in advanced remote sensing." In 2016 12th IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications (MESA). IEEE, 2016. http://dx.doi.org/10.1109/mesa.2016.7587128.

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Borwein, Jonathan M., and Armin Straub. "Special values of generalized log-sine integrals." In the 36th international symposium. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/1993886.1993899.

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Yasuo Narukawa and Vicenc Torra. "Domain extension for multidimensional generalized fuzzy integrals." In 2008 IEEE 16th International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, 2008. http://dx.doi.org/10.1109/fuzzy.2008.4630602.

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Reports on the topic "Generalised Integrals"

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Klein, Clara. Orthogonal, Left-Null, Integral Lines in generalized Budabara equations. Web of Open Science, March 2020. http://dx.doi.org/10.37686/emj.v1i1.21.

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Sulkosky, Vincent. The Spin Structure of 3He and the Neutron at Low Q2: A Measurement of the Generalized GDH Integrand. Office of Scientific and Technical Information (OSTI), August 2007. http://dx.doi.org/10.2172/913561.

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Ostashev, Vladimir, Michael Muhlestein, and D. Wilson. Extra-wide-angle parabolic equations in motionless and moving media. Engineer Research and Development Center (U.S.), September 2021. http://dx.doi.org/10.21079/11681/42043.

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Wide-angle parabolic equations (WAPEs) play an important role in physics. They are derived by an expansion of a square-root pseudo-differential operator in one-way wave equations, and then solved by finite-difference techniques. In the present paper, a different approach is suggested. The starting point is an extra-wide-angle parabolic equation (EWAPE) valid for small variations of the refractive index of a medium. This equation is written in an integral form, solved by a perturbation technique, and transformed to the spectral domain. The resulting split-step spectral algorithm for the EWAPE accounts for the propagation angles up to 90° with respect to the nominal direction. This EWAPE is also generalized to large variations in the refractive index. It is shown that WAPEs known in the literature are particular cases of the two EWAPEs. This provides an alternative derivation of the WAPEs, enables a better understanding of the underlying physics and ranges of their applicability, and opens an opportunity for innovative algorithms. Sound propagation in both motionless and moving media is considered. The split-step spectral algorithm is particularly useful in the latter case since complicated partial derivatives of the sound pressure and medium velocity reduce to wave vectors (essentially, propagation angles) in the spectral domain.
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