Relevant bibliographies by topics / Multiple integrals

Contents

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

Academic literature on the topic 'Multiple integrals'

Author: Grafiati
Published: 4 June 2021
Last updated: 28 July 2024

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Journal articles on the topic "Multiple integrals"

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Bandyrskii, B., L. Hoshko, I. Lazurchak, and M. Melnyk. "Optimal algorithms for computing multiple integrals." Mathematical Modeling and Computing 4, no. 1 (July 1, 2017): 1–9. http://dx.doi.org/10.23939/mmc2017.01.001.

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Greaves, G. R. H., R. R. Hall, M. N. Huxley, and J. C. Wilson. "Multiple Franel integrals." Mathematika 40, no. 1 (June 1993): 51–70. http://dx.doi.org/10.1112/s0025579300013711.

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Dynkin, E. B. "Multiple path integrals." Advances in Applied Mathematics 7, no. 2 (June 1986): 205–19. http://dx.doi.org/10.1016/0196-8858(86)90032-1.

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Dasgupta, A., and G. Kallianpur. "Multiple fractional integrals." Probability Theory and Related Fields 115, no. 4 (November 1, 1999): 505–25. http://dx.doi.org/10.1007/s004400050247.

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Papp, F. J. "Expressing certain multiple integrals as single integrals." International Journal of Mathematical Education in Science and Technology 21, no. 1 (March 1990): 137–39. http://dx.doi.org/10.1080/0020739900210120.

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Benabidallah, A., Y. Cherruault, and Y. Tourbier. "Approximation of multiple integrals by simple integrals." Kybernetes 30, no. 9/10 (December 2001): 1223–39. http://dx.doi.org/10.1108/03684920110405836.

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Malyutin, V. B., and B. O. Nurjanov. "The semiclassical approximation of multiple functional integrals." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 59, no. 4 (January 5, 2024): 302–7. http://dx.doi.org/10.29235/1561-2430-2023-59-4-302-307.

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In this paper, we study the semiclassical approximation of multiple functional integrals. The integrals are defined through the Lagrangian and the action. Of all possible trajectories, the greatest contribution to the integral is given by the classical trajectory x̅cl for which the action S takes an extremal value. The classical trajectory is found as a solution of the multidimensional Euler – Lagrange equation. To calculate the functional integrals, the expansion of the action with respect to the classical trajectory is used, which can be interpreted as an expansion in powers of Planck’s constant. The numerical results for the semiclassical approximation of double functional integrals are given.
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Greaves, G. R. H., R. R. Hall, M. N. Huxley, and J. C. Wilson. "Multiple Franel integrals: Corrigendum." Mathematika 41, no. 2 (December 1994): 401. http://dx.doi.org/10.1112/s0025579300007476.

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Grosjean, C. C. "Two Trigonometric Multiple Integrals." SIAM Review 33, no. 1 (March 1991): 114. http://dx.doi.org/10.1137/1033008.

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Podol’skii, A. A. "Identities for multiple integrals." Mathematical Notes 98, no. 3-4 (September 2015): 624–30. http://dx.doi.org/10.1134/s0001434615090291.

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Dissertations / Theses on the topic "Multiple integrals"

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Rindone, Fabio. "New non-additive integrals in Multiple Criteria Decision Analysis." Doctoral thesis, Università di Catania, 2013. http://hdl.handle.net/10761/1315.

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The proposal and the axiomatization of new fuzzy integrals has a central role in modern Multiple Criteria Decision Analysis. In this thesis we propose some generalizations of well known fuzzy integrals (Choquet, Shilkret and Sugeno). We propose and characterize bipolar fuzzy integrals, which are generalization of the most famous fuzzy integrals to the case of bipolar scale, i.e. those symmetric scale where it is possible for each value to find the opposite. We also deal with the generalization of the concept of universal integral (recently proposed to generalize several fuzzy integrals) to the case of bipolar scales. We also provide the characterization of the bipolar universal integral with respect to a level dependent bi-capacity. Finally, we consider the problem to adapt classical definitions of fuzzy integrals to the case of imprecise interval evaluations. More precisely, standard fuzzy integrals used in MCDA request that the starting evaluations of a choice on various criteria must be expressed in terms of exact-evaluations. We present the robust Choquet, Shilkret and Sugeno integrals, computed with respect to an interval capacity. These are quite natural generalizations of the Choquet, Shilkret and Sugeno integrals, useful to aggregate interval-evaluations of choice alternatives into a single overall evaluation.
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Zhang, Chengdian. "Calculus of variations with multiple integration." Bonn : [s.n.], 1989. http://catalog.hathitrust.org/api/volumes/oclc/20436929.html.

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Hu, Dehui. "Understanding introductory students’ application of integrals in physics from multiple perspectives." Diss., Kansas State University, 2013. http://hdl.handle.net/2097/16190.

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Doctor of Philosophy
Department of Physics
N. Sanjay Rebello
Calculus is used across many physics topics from introductory to upper-division level college courses. The concepts of differentiation and integration are important tools for solving real world problems. Using calculus or any mathematical tool in physics is much more complex than the straightforward application of the equations and algorithms that students often encounter in math classes. Research in physics education has reported students’ lack of ability to transfer their calculus knowledge to physics problem solving. In the past, studies often focused on what students fail to do with less focus on their underlying cognition. However, when solving physics problems requiring the use of integration, their reasoning about mathematics and physics concepts has not yet been carefully and systematically studied. Hence the main purpose of this qualitative study is to investigate student thinking in-depth and provide deeper insights into student reasoning in physics problem solving from multiple perspectives. I propose a conceptual framework by integrating aspects of several theoretical constructs from the literature to help us understand our observations of student work as they solve physics problems that require the use of integration. I combined elements of three important theoretical constructs: mathematical resources or symbolic forms, which are the small pieces of knowledge elements associated with students’ use of mathematical ideas; conceptual metaphors, which describe the systematic mapping of knowledge across multiple conceptual domains – typically from concrete source domain to abstract target domain; and conceptual blending, which describes the construction of new learning by integrating knowledge in different mental spaces. I collected data from group teaching/learning interviews as students solved physics problems requiring setting up integrals. Participants were recruited from a second-semester calculus-based physics course. I conducted qualitative analysis of the videotaped student conversations and their written work. The main contributions of this research include (1) providing evidence for the existence of symbolic forms in students’ reasoning about differentials and integrals, (2) identifying conceptual metaphors involved in student reasoning about differentials and integrals, (3) categorizing the different ways in which students integrate their mathematics and physics knowledge in the context of solving physics integration problems, (4)exploring the use of hypothetical debate problems in shifting students’ framing of physics problem solving requiring mathematics.
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Richter, Gregor. "Iterated Integrals and genus-one open-string amplitudes." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19309.

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In den vergangenen Jahrzehnten rückte das häufige Auftreten von multiplen Polylogarithmen und multiplen Zeta-Werten, in Feynman-Diagramm Rechnungen niedriger Ordnung, verstärkt in den wissenschaftlichen Fokus. Hierbei offenbarte sich eine Verbindung zu den mathematischen Theorien der Perioden und der iterierten Integrale von Chen. Eine ähnliche Allgegenwärtigkeit von multiplen Zeta-Werten wurde jüngst auch in der α'-Entwicklung von Genus-Null Stringtheorie Amplituden beobachtet. Davon inspiriert befasst sich diese Arbeit mit der Systematik der iterierten Integralen in den Streuamplituden der offenen Stringtheorie. Unser Fokus liegt insbesondere auf der Genus-Eins Amplitude, welche sich vollständig durch iterierte Integrale, die bezüglich einer punktierten elliptischen Kurve definiert sind, ausdrücken lässt. Wir führen den Begriff der getwisteten elliptischen multiplen Zeta-Werte ein. Dieser Begriff beschreibt eine Klasse von iterierten Integralen, die auf einer elliptischen Kurve definiert sind, bei welcher ein rationales Gitter entfernt wurde. Anschließend zeigen wir, dass die Entwicklung eines jeden getwisteten elliptischen multiplen Zeta-Wertes, bezüglich des modularen Parameters τ, durch ein Anfangswertproblem beschrieben wird. Weiterhin präsentieren wir ein Argument dafür, dass sich im Limes τ→i∞ jeder getwistete elliptische multiple Zeta-Wert durch zyklotomische multiple Zeta-Werte ausdrücken lässt. Schließlich beschreiben wir wie sich Genus-Eins Amplituden in offener Stringtheorie mithilfe von getwisteten elliptischen multiplen Zeta-Werten ausdrücken lassen und illustrieren dies für die Vier-Punkt Amplitude. Hierbei zeigt es sich, dass bis zu dritter Ordnung in α' alle Beiträge durch die Unterklasse der elliptischen multiplen Zeta-Werte ausgedrückt werden können, was wiederum äquivalent zu der Abwesenheit unphysikalischer Pole in Gliozzi-Scherk-Olive projizierter Superstringtheorie ist.
Over the last few decades the prevalence of multiple polylogarithms and multiple zeta values in low order Feynman diagram computations of quantum field theory has received increased attention, revealing a link to the mathematical theories of Chen’s iterated integrals and periods. More recently, a similar ubiquity of multiple zeta values was observed in the α'-expansion of genus-zero string theory amplitudes. Inspired by these developments, this work is concerned with the systematic appearance of iterated integrals in scattering amplitudes of open superstring theory. In particular, the focus will be on studying the genus-one amplitude, which requires the notion of iterated integrals defined on punctured elliptic curves. We introduce the notion of twisted elliptic multiple zeta values that are defined as a class of iterated integrals naturally associated to an elliptic curve with a rational lattice removed. Subsequently, we establish an initial value problem that determines the expansions of twisted elliptic multiple zeta values in terms of the modular parameter τ of the elliptic curve. Any twisted elliptic multiple zeta value degenerates to cyclotomic multiple zeta values at the cusp τ → i∞, with the corresponding limit serving as the initial condition of the initial value problem. Finally, we describe how to express genus-one open-string amplitudes in terms of twisted elliptic multiple zeta values and study the four-point genus-one open-string amplitude as an example. For this example we find that up to third order in α' all possible contributions in fact belong to the subclass formed by elliptic multiple zeta values, which is equivalent to the absence of unphysical poles in Gliozzi-Scherk-Olive projected superstring theory.
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Yam, Sheung Chi Phillip. "Analytical and topological aspects of signatures." Thesis, University of Oxford, 2008. http://ora.ox.ac.uk/objects/uuid:87892930-f329-4431-bcdc-bf32b0b1a7c6.

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In both physical and social sciences, we usually use controlled differential equation to model various continuous evolving system; describing how a response y relates to another process x called control. For regular controls x, the unique existence of the response y is guaranteed while it would never be the case for non-smooth controls via the classical approach. Besides, uniform closeness of controls may not imply closeness of their corresponding responses. Theory of rough paths provides a solution to both concerns. Since the creation of rough path theory, it enjoys a fruitful development and finds wide applications in stochastic analysis. In particular, rough path theory provides an effective method to study irregularity of curves and its geometric consequences in relation to integration of differential forms. In the chapter 2, we demonstrate the power of rough path theory in classical complex analysis by showing the rough path nature of the boundaries of a class of Holder's domains; as an immediate application, we extend the classical Gauss-Green's theorem. Until recently, there has been only limited research on applications of theory of rough paths to high dimensional geometry. It is clear to us that many geometric objects, in some senses appearing as solids, are actually comprised of filaments. In the chapter 3, two basic results in the theory of rough paths which will motivate later development of my thesis has been included. In the chapters 4 and 5, we identify a sensible way to do geometric calculus via those filaments (more precisely, space-filling rough paths) in dimension 3. In a recent joint work of Hambly and Lyons, they have shown that every rectifiable path can be completely characterized, up to tree-like deformation, by an algebraic object called the signature, tensor of all iterated integrals, of the path. It is clear that all tree-like deformation of the path would not change its topological features. For instance, the number of times a planar loop of finite length winds around a point (not lying on the path) is unaltered if one deforms the path in tree-like ways. Therefore, it should be plausible to extract this topological information out from the signature of the loop since the signature is a complete algebraic invariant. In the chapter 6, we express the winding number of a nice loop (respectively linking number of a pair of nice loops) as a linear functional of the signature of the loop (respectively signatures of the pair of loops).
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Shahrokhi-Dehkordi, Mohammad Sadegh. "Topological methods for strong local minimizers and extremals of multiple integrals in the calculus of variations." Thesis, University of Sussex, 2011. http://sro.sussex.ac.uk/id/eprint/6913/.

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Let Ω ⊂ Rn be a bounded Lipschitz domain and consider the energy functional F[u, Ω] := ∫ Ω F(∇u(x)) dx, over the space Ap(Ω) := {u ∈ W 1,p(Ω, Rn): u|∂Ω = x, det ∇u> 0 a.e. in Ω}, where the integrand F : Mn×n → R is quasiconvex, sufficiently regular and satisfies a p-coercivity and p-growth for some exponent p ∈ [1, ∞[. A motivation for the study of above energy functional comes from nonlinear elasticity where F represents the elastic energy of a homogeneous hyperelastic material and Ap(Ω) represents the space of orientation preserving deformations of Ω fixing the boundary pointwise. The aim of this thesis is to discuss the question of multiplicity versus uniqueness for extremals and strong local minimizers of F and the relation it bares to the domain topology. Our work, building upon previous works of others, explicitly and quantitatively confirms the significant role of domain topology, and provides explicit and new examples as well as methods for constructing such maps. Our approach for constructing strong local minimizers is topological in nature and is based on defining suitable homotopy classes in Ap(Ω) (for p ≥ n), whereby minimizing F on each class results in, modulo technicalities, a strong local minimizer. Here we work on a prototypical example of a topologically non-trivial domain, namely, a generalised annulus, Ω= {x ∈ Rn : a< |x|
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Sinescu, Vasile. "Construction of lattice rules for multiple integration based on a weighted discrepancy." The University of Waikato, 2008. http://hdl.handle.net/10289/2542.

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High-dimensional integrals arise in a variety of areas, including quantum physics, the physics and chemistry of molecules, statistical mechanics and more recently, in financial applications. In order to approximate multidimensional integrals, one may use Monte Carlo methods in which the quadrature points are generated randomly or quasi-Monte Carlo methods, in which points are generated deterministically. One particular class of quasi-Monte Carlo methods for multivariate integration is represented by lattice rules. Lattice rules constructed throughout this thesis allow good approximations to integrals of functions belonging to certain weighted function spaces. These function spaces were proposed as an explanation as to why integrals in many variables appear to be successfully approximated although the standard theory indicates that the number of quadrature points required for reasonable accuracy would be astronomical because of the large number of variables. The purpose of this thesis is to contribute to theoretical results regarding the construction of lattice rules for multiple integration. We consider both lattice rules for integrals over the unit cube and lattice rules suitable for integrals over Euclidean space. The research reported throughout the thesis is devoted to finding the generating vector required to produce lattice rules that have what is termed a low weighted discrepancy . In simple terms, the discrepancy is a measure of the uniformity of the distribution of the quadrature points or in other settings, a worst-case error. One of the assumptions used in these weighted function spaces is that variables are arranged in the decreasing order of their importance and the assignment of weights in this situation results in so-called product weights . In other applications it is rather the importance of group of variables that matters. This situation is modelled by using function spaces in which the weights are general . In the weighted settings mentioned above, the quality of the lattice rules is assessed by the weighted discrepancy mentioned earlier. Under appropriate conditions on the weights, the lattice rules constructed here produce a convergence rate of the error that ranges from O(n−1/2) to the (believed) optimal O(n−1+δ) for any δ gt 0, with the involved constant independent of the dimension.
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Hanna, George T. "Cubature rules from a generalized Taylor perspective." Thesis, full-text, 2009. https://vuir.vu.edu.au/1922/.

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The accuracy and efficiency of computing multiple integrals is a very important problem that arises in many scientific, financial and engineering applications. The research conducted in this thesis is designed to build on past work and develop and analyze new numerical methods to evaluate double integrals efficiently. The fundamental aim is to develop and assess techniques for (numerically) evaluating double integrals with high accuracy. The general approach presented in this thesis involves the development of new multivariate approximations from a generalaised Taylor perspective in terms of Appell type polynomials and to study their use in multi-dimensional integration. The expectation is that the new methods will provide polynomial and polynomial-like approximations that can be used for application in a straight forward manner with better accuracy. That is, we aim to devise and investigate new multiple integration formulae and as well as provide information on a priori error bounds. A further major contribution of the work builds on the research conducted in the field of Grüss type inequalities and leads to a new approximation of the one and two dimensional finite Fourier transform. The approximations are in terms of the complex exponential mean and estimate of the error of approximation for different classes of functions of bounded variation defined on finite intervals. It is believed that this work will also have an impact in the area of numerical multidimensional integral evaluation for other integral operators.
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Hanna, George T. "Cubature rules from a generalized Taylor perspective." full-text, 2009. http://eprints.vu.edu.au/1922/1/hanna.pdf.

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The accuracy and efficiency of computing multiple integrals is a very important problem that arises in many scientific, financial and engineering applications. The research conducted in this thesis is designed to build on past work and develop and analyze new numerical methods to evaluate double integrals efficiently. The fundamental aim is to develop and assess techniques for (numerically) evaluating double integrals with high accuracy. The general approach presented in this thesis involves the development of new multivariate approximations from a generalaised Taylor perspective in terms of Appell type polynomials and to study their use in multi-dimensional integration. The expectation is that the new methods will provide polynomial and polynomial-like approximations that can be used for application in a straight forward manner with better accuracy. That is, we aim to devise and investigate new multiple integration formulae and as well as provide information on a priori error bounds. A further major contribution of the work builds on the research conducted in the field of Grüss type inequalities and leads to a new approximation of the one and two dimensional finite Fourier transform. The approximations are in terms of the complex exponential mean and estimate of the error of approximation for different classes of functions of bounded variation defined on finite intervals. It is believed that this work will also have an impact in the area of numerical multidimensional integral evaluation for other integral operators.
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Coine, Clément. "Continuous linear and bilinear Schur multipliers and applications to perturbation theory." Thesis, Bourgogne Franche-Comté, 2017. http://www.theses.fr/2017UBFCD074/document.

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Dans le premier chapitre, nous commençons par définir certains produits tensoriels et identifions leur dual. Nous donnons ensuite quelques propriétés des classes de Schatten. La fin du chapitre est dédiée à l’étude des espaces de Bochner à valeurs dans l'espace des opérateurs factorisables par un espace de Hilbert. Le deuxième chapitre est consacré aux multiplicateurs de Schur linéaires. Nous caractérisons les multiplicateurs bornés sur B(Lp, Lq) lorsque p est inférieur à q puis appliquons ce résultat pour obtenir de nouvelles relations d'inclusion entre espaces de multiplicateurs. Dans le troisième chapitre, nous caractérisons, au moyen de multiplicateurs de Schur linéaires, les multiplicateurs de Schur bilinéaires continus à valeurs dans l'espace des opérateurs à trace. Dans le quatrième chapitre, nous donnons divers résultats concernant les opérateurs intégraux multiples. En particulier, nous caractérisons les opérateurs intégraux triples à valeurs dans l'espace des opérateurs à trace puis nous donnons une condition nécessaire et suffisante pour qu'un opérateur intégral triple définisse une application complètement bornée sur le produit de Haagerup de l'espace des opérateurs compacts. Enfin, le cinquième chapitre est dédié à la résolution des problèmes de Peller. Nous commençons par étudier le lien entre opérateurs intégraux multiples et théorie de la perturbation pour le calcul fonctionnel des opérateurs autoadjoints pour finir par la construction de contre-exemples à ces problèmes
In the first chapter, we define some tensor products and we identify their dual space. Then, we give some properties of Schatten classes. The end of the chapter is dedicated to the study of Bochner spaces valued in the space of operators that can be factorized by a Hilbert space.The second chapter is dedicated to linear Schur multipliers. We characterize bounded multipliers on B(Lp, Lq) when p is less than q and then apply this result to obtain new inclusion relationships among spaces of multipliers.In the third chapter, we characterize, by means of linear Schur multipliers, continuous bilinear Schur multipliers valued in the space of trace class operators. In the fourth chapter, we give several results concerning multiple operator integrals. In particular, we characterize triple operator integrals mapping valued in trace class operators and then we give a necessary and sufficient condition for a triple operator integral to define a completely bounded map on the Haagerup tensor product of compact operators. Finally, the fifth chapter is dedicated to the resolution of Peller's problems. We first study the connection between multiple operator integrals and perturbation theory for functional calculus of selfadjoint operators and we finish with the construction of counter-examples for those problems
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Books on the topic "Multiple integrals"

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Major, Péter. Multiple Wiener-Itô Integrals. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02642-8.

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Braides, Andrea. Homogenization of multiple integrals. Oxford: Clarendon Press, 1998.

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Spandagos, Vaggelēs. Oloklērōtikos logismos: Theōria-methodologia, 1600 lymenes askēseis. Athēna: Aithra, 1988.

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Smirnov, V. A. Analytic tools for Feynman integrals. Heidelberg: Springer, 2012.

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Sloan, I. H. Lattice methods for multiple integration. Oxford: Clarendon Press, 1994.

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service), SpringerLink (Online, ed. Multiple Integrals in the Calculus of Variations. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2008.

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Raphael, Höegh-Krohn, and Mazzucchi Sonia, eds. Mathematical theory of Feynman path integrals: An introduction. 2nd ed. Berlin: Springer, 2008.

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Kwapień, Stanisław, and Wojbor A. Woyczyński. Random Series and Stochastic Integrals: Single and Multiple. Boston, MA: Birkhäuser Boston, 1992. http://dx.doi.org/10.1007/978-1-4612-0425-1.

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1943-, Woyczyński W. A., ed. Random series and stochastic integrals: Single and multiple. Boston: Birkhäuser, 1992.

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Korobov, N. M. Teoretikochislovye metody v priblizhennom analize. 2nd ed. Moskva: MT︠S︡NMO, 2004.

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Book chapters on the topic "Multiple integrals"

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Coombes, Kevin R., Ronald L. Lipsman, and Jonathan M. Rosenberg. "Multiple Integrals." In Multivariable Calculus and Mattiematica®, 153–83. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1698-8_8.

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Shakarchi, Rami. "Multiple Integrals." In Problems and Solutions for Undergraduate Analysis, 337–58. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1738-1_21.

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Lang, Serge. "Multiple Integrals." In Undergraduate Analysis, 565–606. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4757-2698-5_21.

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Courant, Richard, and Fritz John. "Multiple Integrals." In Introduction to Calculus and Analysis Volume II/1, 367–542. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-642-57149-7_4.

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Marshall, Gordon S. "Multiple Integrals." In Springer Undergraduate Mathematics Series, 127–36. London: Springer London, 1998. http://dx.doi.org/10.1007/978-1-4471-3412-1_8.

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Eriksson, Kenneth, Claes Johnson, and Donald Estep. "Multiple Integrals." In Applied Mathematics: Body and Soul, 939–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-05800-8_13.

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Courant, Richard, and Fritz John. "Multiple Integrals." In Introduction to Calculus and Analysis, 367–542. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4613-8958-3_4.

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Stroud, K. A. "Multiple Integrals." In Further Engineering Mathematics, 433–96. London: Palgrave Macmillan UK, 1990. http://dx.doi.org/10.1007/978-1-349-20731-2_9.

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Zorich, Vladimir A. "Multiple Integrals." In Universitext, 109–61. Berlin, Heidelberg: Springer Berlin Heidelberg, 2016. http://dx.doi.org/10.1007/978-3-662-48993-2_3.

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Stroud, K. A. "Multiple Integrals." In Engineering Mathematics, 662–88. London: Palgrave Macmillan UK, 1987. http://dx.doi.org/10.1007/978-1-349-18708-9_23.

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Conference papers on the topic "Multiple integrals"

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Georgiev, S. "Multiple iso-integrals." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4912715.

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Shakeshaft, Robin. "Theoretical aspects of above-threshold absorption." In Multiple Excitations of Atoms. Washington, D.C.: Optica Publishing Group, 1986. http://dx.doi.org/10.1364/mea.1986.mb1.

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We will review computational and physical aspects of the ionization of an atom by N photons with N>P, where P is the minimum number of photons required to ionize the atom. In perturbation theory the matrix element, M(N), for N-photon absorption can be decomposed as M+(N) + M−(N), which results from the decomposition of the stationary wave of the emergent photoelectron into its outgoing ( + ) and ingoing (−) parts. Each of the M±(N)are N-dimensional integrals over N radial coordinates ri, i=1,…,N. Although these integrals are not formally convergent for N>P, the integrand of M+(N) consists of functions that either decay exponentially or are outgoing waves for ri~∞.
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Lequn Hu, Derek T. Anderson, and Timothy C. Havens. "Multiple kernel aggregation using fuzzy integrals." In 2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE). IEEE, 2013. http://dx.doi.org/10.1109/fuzz-ieee.2013.6622312.

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Chaloupka, Jan, Jiří Kunovský, Václav Šátek, Petr Veigend, and Alžbeta Martinkovičová. "Numerical Integration of Multiple Integrals using Taylor Polynomial." In 5th International Conference on Simulation and Modeling Methodologies, Technologies and Applications. SCITEPRESS - Science and and Technology Publications, 2015. http://dx.doi.org/10.5220/0005539701630171.

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Weinzierl, Stefan, Luise Adams, Christian Bogner, Ekta Chaubey, and Armin Schweitzer. "Differential equations for Feynman integrals beyond multiple polylogarithms." In 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology). Trieste, Italy: Sissa Medialab, 2018. http://dx.doi.org/10.22323/1.290.0015.

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Yu, Chii-Huei. "Application of maple on evaluating multiple improper integrals." In 2013 6th International Conference on Advanced Infocomm Technology (ICAIT). IEEE, 2013. http://dx.doi.org/10.1109/icait.2013.6621489.

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Knockaert, L. "On the analytic calculation of multiple integrals in electromagnetics." In Propagation in Wireless Communications (ICEAA). IEEE, 2011. http://dx.doi.org/10.1109/iceaa.2011.6046406.

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Bonaventura, A., L. Coluccio, and G. Fedele. "Frequency estimation of multi-sinusoidal signal by multiple integrals." In 2007 IEEE International Symposium on Signal Processing and Information Technology. IEEE, 2007. http://dx.doi.org/10.1109/isspit.2007.4458175.

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Broedel, Johannes. "From elliptic iterated integrals to elliptic multiple zeta values." In Loops and Legs in Quantum Field Theory. Trieste, Italy: Sissa Medialab, 2016. http://dx.doi.org/10.22323/1.260.0081.

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Gluza, Janusz. "Non-planar Feynman integrals, Mellin-Barnes representations, multiple sums." In Loops and Legs in Quantum Field Theory. Trieste, Italy: Sissa Medialab, 2014. http://dx.doi.org/10.22323/1.211.0052.

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Reports on the topic "Multiple integrals"

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Perez-Abreu, Victor. Multiple Wiener Integrals and Nonlinear Functionals of a Nuclear Space Valued Wiener Process. Fort Belvoir, VA: Defense Technical Information Center, October 1986. http://dx.doi.org/10.21236/ada177227.

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Brigola, R. Remark on the Multiple Wiener Integral. Fort Belvoir, VA: Defense Technical Information Center, March 1987. http://dx.doi.org/10.21236/ada186015.

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Bright, Gerald D., Robert S. Mandry, and Mark D. Barnell. Innovative Approach to Fusion Testbed to Integrate Multiple Sensor Data. Fort Belvoir, VA: Defense Technical Information Center, July 1995. http://dx.doi.org/10.21236/ada299800.

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Samorodnitsky, Gennady, and Jerzy Szulga. An Asymptotic Evaluation of the Tail of a Multiple Symmetric Alpha-Stable Integral. Fort Belvoir, VA: Defense Technical Information Center, February 1988. http://dx.doi.org/10.21236/ada194570.

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Landweber, Louis. Residues of Integrals with Three-Dimensional Multipole Singularities, with Application to the Lagally Theorem. Fort Belvoir, VA: Defense Technical Information Center, July 1985. http://dx.doi.org/10.21236/ada158771.

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Harris and Edlund. L51766 Instantaneous Rotational Velocity Development. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), May 1997. http://dx.doi.org/10.55274/r0010119.

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Considerable effort has been put forth to develop an automated method for balancing the power cylinders of reciprocating integral engines used in the natural gas industry. The benefits to power cylinder balance include reducted emissions and improved cylinder component mechanical integrity (which should lead to reductions in repair costs). The current approach to automate engine balancing uses pressure transducers to measure cylinder pressure, then integrate the signals into the engine fuel /timing management controller to achieve engine balance. Each power cylinder must be instrumented, which quickly leads to an expensive installation package. For large units (12 to 16 power cylinders), the likelihood of transducer failure and / or calibration changes will be problematic to reliable operation of this autobalancing system. A potential alternative to multiple transducers measuring power cylinder pressure is to use a single transducer to measure instantaneous shaft rotational velocity. Instantaneous shaft rotational velocity is driven by engine / compressor torque loads, and therefore is sensitive to changes in both power and compressor cylinder operation. This report summarizes the results of an investigation into the possible use of the flywheel rotational velocity as a surrogate for power cylinder pressure measurements in an autobalancing arrangement, or as a balanced/need-to-balance indicator for integral engines. A fundamental model of the rotational kinetics/dynamics was developed and used to predict the flywheel rotational acceleration. The model was validated and enhanced with data acquired as part of this study. The model was then extended to establish a sensitivity matrix, which established the change in predicted torque as a function of power cylinder imbalance. Using the sensitivity matrix, an algorithm was developed to predict the change in power cylinder peak pressures as a function of the change in the measured shaft rotational velocity.
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Brakarz, José, and Laura Jaitman. Evaluation of Slum Upgrading Programs: Literature Review and Methodological Approaches. Inter-American Development Bank, December 2013. http://dx.doi.org/10.18235/0009149.

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This technical note analyzes the methodologies used to evaluate neighborhood upgrading programs, describes their results, and suggests approaches for future evaluations. Local and central governments are increasingly utilizing slum or neighborhood upgrading programs to deal with the multiple problems of urban poverty. These programs employ a methodology of integral interventions, combining of both infrastructure works and social services targeted to specific neighborhoods. Due to this variety of interventions the assessment of their impact is complicated and requires a comprehensive approach. This document analyzes the methods used in the evaluation of a number of upgrading programs either looking at individual interventions or their combined outcomes. It proposes a methodological approach for their assessment based on three categories of outcomes: housing, neighborhood, and individual. For each type of outcome, the authors present a literature review of common interventions and their evaluation results. The document also suggests relevant indicators for evaluating slum upgrading programs according to these three types of outcomes, and finally, it presents methodological issues to take into consideration when designing the evaluations of integral programs.
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Moeyaert, Mariola. Introduction to Meta-Analysis. Instats Inc., 2023. http://dx.doi.org/10.61700/9egp6tqy3koga469.

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This seminar provides hands-on instruction covering the process of conducting a meta-analysis, from the planning stage through the selection of appropriate statistical techniques, the issues involved in analyzing data, and the interpretation of results. During the seminar you will learn how to use meta-analytic techniques to combine evidence across different research studies; integrate multiple studies into a single statistical framework; obtain precise and generalizable estimates of effect sizes; and explain differences arising from conflicting study results. An official Instats certificate of completion is provided at the conclusion of the seminar. For European PhD students, each seminar offers 2 ECTS Equivalent points.
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Moeyaert, Mariola. Introduction to Meta-Analysis. Instats Inc., 2023. http://dx.doi.org/10.61700/z1ui6nlaom67q469.

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This seminar provides hands-on instruction covering the process of conducting a meta-analysis, from the planning stage through the selection of appropriate statistical techniques, the issues involved in analyzing data, and the interpretation of results. During the seminar you will learn how to use meta-analytic techniques to combine evidence across different research studies; integrate multiple studies into a single statistical framework; obtain precise and generalizable estimates of effect sizes; and explain differences arising from conflicting study results. An official Instats certificate of completion is provided at the conclusion of the seminar. For European PhD students, each seminar offers 2 ECTS Equivalent points.
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Lee, Jin-Kyu, Amir Naser, Osama Ennasr, Ahmet Soylemezoglu,, and Garry Glaspell. Unmanned ground vehicle (UGV) full coverage planning with negative obstacles. Engineer Research and Development Center (U.S.), August 2023. http://dx.doi.org/10.21079/11681/47527.

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We explored approaches that offer full coverage path planning while simultaneously avoiding negative obstacles. These approaches are specific to unmanned ground vehicles (UGVs), which need to constantly interact with a traversable ground surface. We tested multiple potential solutions in simulation, and the results are presented herein. Full coverage path planner (FCPP) approaches were evaluated based on their ability to discretize their paths, use waypoints effectively, and be easily integrated with our current robot platform. For negative obstacles, we explored approaches that will integrate with our current navigation stack. The preferred solution will allow for teleoperation, waypoint navigation, and full autonomy while avoiding positive and negative obstacles.
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