Relevant bibliographies by topics / Multiples 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 'Multiples integrals'

Author: Grafiati
Published: 2 November 2024

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Journal articles on the topic "Multiples integrals"

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Song, Jiang Yong. "An Elliptic Integral Solution to the Multiple Inflections Large Deflection Beams in Compliant Mechanisms." Advanced Materials Research 971-973 (June 2014): 349–52. http://dx.doi.org/10.4028/www.scientific.net/amr.971-973.349.

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In this paper, a solution based on the elliptic integrals is proposed for solving multiples inflection points large deflection. Application of the Bernoulli Euler equations of compliant mechanisms with large deflection equation of beam is obtained ,there is no inflection point and inflection points in two cases respectively. The elliptic integral solution which is the most accurate method at present for analyzing large deflections of cantilever beams in compliant mechanisms.
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van der Neut, Joost, and Kees Wapenaar. "Adaptive overburden elimination with the multidimensional Marchenko equation." GEOPHYSICS 81, no. 5 (September 2016): T265—T284. http://dx.doi.org/10.1190/geo2016-0024.1.

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Iterative substitution of the multidimensional Marchenko equation has been introduced recently to integrate internal multiple reflections in the seismic imaging process. In so-called Marchenko imaging, a macro velocity model of the subsurface is required to meet this objective. The model is used to back-propagate the data during the first iteration and to truncate integrals in time during all successive iterations. In case of an erroneous model, the image will be blurred (akin to conventional imaging) and artifacts may arise from inaccurate integral truncations. However, the scheme is still successful in removing artifacts from internal multiple reflections. Inspired by these observations, we rewrote the Marchenko equation, such that it can be applied early in a processing flow, without the need of a macro velocity model. Instead, we have required an estimate of the two-way traveltime surface of a selected horizon in the subsurface. We have introduced an approximation, such that adaptive subtraction can be applied. As a solution, we obtained a new data set, in which all interactions (primaries and multiples) with the part of the medium above the picked horizon had been eliminated. Unlike various other internal multiple elimination algorithms, the method can be applied at any specified target horizon, without having to resolve for internal multiples from shallower horizons. We successfully applied the method on synthetic data, where limitations were reported due to thin layers, diffraction-like discontinuities, and a finite acquisition aperture. A field data test was also performed, in which the kinematics of the predicted updates were demonstrated to match with internal multiples in the recorded data, but it appeared difficult to subtract them.
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Saouter, Yannick. "New pancake series for π." Mathematical Gazette 104, no. 560 (June 18, 2020): 296–303. http://dx.doi.org/10.1017/mag.2020.53.

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In [1], Dalzell proved that $\pi = \frac{{22}}{7} - \int_0^1 {\frac{{{t^4}{{(1 - t)}^4}}}{{1 + {t^2}}}}$ . He then used this equation to derive a new series converging to π. In [2], Backhouse studied the general case of integrals of the form $\int_0^1 {\frac{{{t^m}{{(1 - t)}^m}}}{{1 + {t^2}}}dt}$ and derived conditions on m and n so that they could be used to evaluate π. As a sequel, he derived accurate rational approximations of π. This work was extended in [3] where new rational approximations of π are obtained. Some related integrals of the forms $\int_0^1 {\frac{{{t^m}{{(1 - t)}^m}}}{{1 + {t^2}}}P(t)\,dt}$ and $\int_0^1 {\frac{{{t^m}{{(1 - t)}^m}}}{{\sqrt {1 - {t^2}} }}P(t)dt}$ with P(t) being of polynomial form are also investigated. In [4] the author gives more new approximations and new series for the case m = n = 4k. In [5] new series for π are obtained with the integral $\int_0^a {\frac{{{t^{12m}}{{(a - t)}^{12m}}}}{{1 + {t^2}}}dt}$ where $a = 2 - \sqrt 3$ . The general problem of improving the convergence speed of the arctan series by transformation of the argument has also been considered in [6, 7]. In the present work the author considers an alternative form for the denominators in integrals. As a result, new series are obtained for multiples of π by some algebraic numbers.
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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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Fleury, Clement, and Ivan Vasconcelos. "Imaging condition for nonlinear scattering-based imaging: Estimate of power loss in scattering." GEOPHYSICS 77, no. 1 (January 2012): S1—S18. http://dx.doi.org/10.1190/geo2011-0135.1.

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Imaging highly complex subsurface structures is a challenging problem because it must ultimately deal with nonlinear multiple-scattering effects (e.g., migration of multiples, wavefield extrapolation with nonlinear model interactions, amplitude-preserving migration) to overcome the limitations of linear imaging. Most of the current migration techniques rely on the linear single-scattering assumption, and therefore, fail to handle these complex scattering effects. Recently, seismic imaging has been related to scattering-based image-domain interferometry to address the fully nonlinear imaging problem. Building on this connection between imaging and interferometry, we define the seismic image as a locally scattered wavefield and introduce a new imaging condition that is suitable and practical for nonlinear imaging. A previous formulation of nonlinear scattering-based imaging requires the evaluation of volume integrals that cannot easily be incorporated in current imaging algorithms. Our method consisted of adapting the conventional crosscorrelation imaging condition to account for the interference mechanisms that ensure power conservation in the scattering of wavefields. To do so, we added the zero-lag autocorrelation of scattered wavefields to the zero-lag crosscorrelation of reference and scattered wavefields. In our development, we demonstrated that this autocorrelation of scattered fields fully replaces the volume scattering term required by the previous formulation. We also found that this replacement follows from the application of the generalized optical theorem. The resulting imaging condition accounts for nonlinear multiple-scattering effects, reduces imaging artifacts and improves amplitude preservation and illumination in the images. We addressed the principles of our nonlinear imaging condition and demonstrated its importance in ideal nonlinear imaging experiments, i.e., we presented synthetic data examples assuming ideal scattered wavefield extrapolation and studied the influence of different scattering regimes and aperture limitation.
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Král, Josef. "Note on generalized multiple Perron integral." Časopis pro pěstování matematiky 110, no. 4 (1985): 371–74. http://dx.doi.org/10.21136/cpm.1985.118252.

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Haddad, Roudy El. "Repeated integration and explicit formula for the \(n\)-th integral of \(x^m(\ln x)^{m'}\)." Open Journal of Mathematical Sciences 6, no. 1 (June 10, 2022): 51–75. http://dx.doi.org/10.30538/oms2022.0178.

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Repeated integration is a major topic of integral calculus. In this article, we study repeated integration. In particular, we study repeated integrals and recurrent integrals. For each of these integrals, we develop reduction formulae for both the definite as well as indefinite form. These reduction formulae express these repetitive integrals in terms of single integrals. We also derive a generalization of the fundamental theorem of calculus that expresses a definite integral in terms of an indefinite integral for repeated and recurrent integrals. From the recurrent integral formulae, we derive some partition identities. Then we provide an explicit formula for the \(n\)-th integral of \(x^m(\ln x)^{m'}\) in terms of a shifted multiple harmonic star sum. Additionally, we use this integral to derive new expressions for the harmonic sum and repeated harmonic sum.
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Shao, Zijia, Shuohao Wang, and Hetian Yu. "Application of the Residue Theorem to Euler Integral, Gaussian Integral, and Beyond." Highlights in Science, Engineering and Technology 38 (March 16, 2023): 311–16. http://dx.doi.org/10.54097/hset.v38i.5821.

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The paper is divided into three different parts, which use the residue theorem to solve several different integrals, namely, the Euler integral, the Gaussian integral, the Fresnel integral, and so forth. The process of using the resiude theorem to determine these integrals is to first turn the integrals into convenient forms of complex integrals, and then find integral perimeters so that any integral on one of the curves is the required integral, through the drawing observation of the contour to write the original integral into the form of multiple integral. By studying the resiude theorem to solve the problem of complex integrals, it is demonstrated that the resiude theorem is actually a process that makes the calculation easier. These solved integrals have a wide range of applications including the study of the refraction of light, analytics, probability theory, combinatorial mathematics, and unification of the continuous Fourier transform.
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Bajic, Tatjana. "On relation between one multiple and a corresponding one-dimensional integral with applications." Yugoslav Journal of Operations Research 28, no. 1 (2018): 79–92. http://dx.doi.org/10.2298/yjor160916020b.

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For a given finite positive measure on an interval I ? R, a multiple stochastic integral of a Volterra kernel with respect to a product of a corresponding Gaussian orthogonal stochastic measure is introduced. The Volterra kernel is taken such that the multiple stochastic integral is a multiple iterated stochastic integral related to a parameterized Hermite polynomial, where parameter depends on Gaussian distribution of an underlying one-dimensional stochastic integral. Considering that there exists a connection between stochastic and deterministic integrals, we expose some properties of parameterized Hermite polynomials of Gaussian random variable in order to prove that one multiple integral can be expressed by a corresponding one-dimensional integral. Having in mind the obtained result, we show that a system of multiple integrals, as well as a collection of conditional expectations can be calculated exactly by generalized Gaussian quadrature rule.
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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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Dissertations / Theses on the topic "Multiples integrals"

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Dworaczek, Guera Charlie. "Analyse asymptotiques d'intégrales multiples : au-delà des beta-ensembles classiques." Electronic Thesis or Diss., Lyon, École normale supérieure, 2024. http://www.theses.fr/2024ENSL0036.

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Cette thèse vise à étendre les techniques mathématiques qui permettent d’extraire le comportement asymptotique de certaines intégrales multiples quand le nombre d’intégrales tend vers l’infini. Un cas très bien compris est celui de la fonction de partition des beta-ensembles classiques. Les techniques probabilistes de grandes déviations et d’analyse des équations de boucles forment l’arsenal classique pour son étude et permettent de comprendre son comportement asymptotique dans une large généralité. Des généralisations non-triviales de cette intégrale multiple sont étudiés dans ce manuscrit: le régime haute température des beta-ensembles et le modèle sinh. Dans ce premier modèle, la température proportionnelle au nombre de particules permet de rendre l’entropie du même ordre que le potentiel confinant et l’interaction à deux corps. Cela a de multiples conséquences: un support non-borné pour la mesure d’équilibre contrairement au régime classique des beta-ensembles et un opérateur master beaucoup plus délicat à gérer. Une étude fine de son comportement permet de démontrer un théorème central limite et le comportement asymptotique à toute du logarithme de sa fonction de partition. Ce premier résultat permet d’étudier certains aspects de systèmes physiques dits intégrables comme la chaîne de Toda et plus particulièrement sa limite hydrodynamique. Ce deuxième résultat permet enfin d’étendre l’application de la méthode des équations de boucle dans le cas où les particules ne se concentrent pas sur un compact. Finalement, un dernier modèle est étudié, le modèle sinh. L’étude de ce modèle est motivée par la méthode de séparation des variables quantique où ce genre d’intégrales apparaît. Il constitue une généralisation des beta-ensembles classiques où l’effet confinant est plus faible que l’interaction et où cette dernière est plus compliqué. La mesure d’équilibre y est étudié et permet d’obtenir une certaine vérification d’une conjecture de Lukyanov sur le modèle sinh-Gordon quantique en 1+1 dimensions et volume fini
This thesis aims to extend mathematical techniques that extract the asymptotic behavior of certain multiple integrals as the number of integrals tends to infinity. A well-understood case is the partition function of classical beta-ensembles. Probabilistic techniques of large deviations and analysis of loop equations form the classical arsenal for its study and allow for a broad understanding of its asymptotic behavior. Non-trivial generalizations of this multiple integral are studied in this manuscript: the high-temperature regime of beta-ensembles and the sinh model. In the first model, the temperature proportional to the number of particles makes the entropy of the same order as the confining potential and the two-body interaction. This has multiple consequences: an unbounded support for the equilibrium measure contrary to the classical regime of beta-ensembles, and a much more delicate master operator to handle. A detailed study of its behavior allows for the demonstration of a central limit theorem and the asymptotic behavior of the logarithm of its partition function. This first result permits the study of certain aspects of so-called integrable physical systems like the Toda chain, and more specifically, its hydrodynamic limit. This second result finally extends the application of the method of loop equations to cases where particles do not concentrate on a compact set. Lastly, another model is studied, the sinh model. The study of this model is motivated by the quantum separation of variables method where such integrals appear. It constitutes a generalization of classical beta-ensembles where the confining effect is weaker than the interaction, and the latter is more complicated. The equilibrium measure is studied, leading to a certain verification of Lukyanov's conjecture on the quantum sinh-Gordon model in 1+1 dimensions and finite volume
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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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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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Beiraghi, Shapour. "Multiple classifier fusion using the fuzzy integral." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0008/MQ52513.pdf.

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Ren, Deqing. "New techniques of multiple integral field spectroscopy." Thesis, Durham University, 2001. http://etheses.dur.ac.uk/3800/.

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The work of this thesis is to investigate new techniques for Integral Field Spectroscopy (IPS) to make the most efficient use of modem large telescopes. Most of the work described is aimed at the FMOS for the SUBARU 8m telescope. Although this is primarily a system for Multiple Object Spectroscopy (MOS) employing single fibres, there is an option to include a multiple-IFS (MIPS) system. Much of this thesis is therefore aimed at the design and prototyping of critical systems for both the IPS and MOS modes of this instrument. The basic theory of IFU design is discussed first. Some particular problems are described and their soludons presented. The design of the MIPS system is described together with the construction and testing of a prototype deployable IFU. The assembly of the pickoff/fore-optics, microlens array and fibre bundle and their testing are described in detail. The estimated performance of the complete module is presented together with suggestions for improving the system efficiency which is currently limited by the performance of the microlens array. The prototyping of the MIPS system is supported by an extensive programme of testing of candidate microlens arrays. Another critical aspect of the instrument is the ability to disconnect the (IPS and MOS) fibre input which is installed on a removable prime focus top-end ring from the spectrographs which are mounted elsewhere on the telescope. This requires high-performance multiple fibre connectors. The designs of connectors for the MOS and IPS modes are described. Results from the testing of a prototype for the MOS mode are presented. This work is supported by a mathematical model of the coupling efficiency which takes into account optical aberrations and alignment errors. The final critical aspect of FMOS which has been investigated is the design of the spectrographs. The baseline system operates in the near-infrared (NIR) but an additional visible channel is an option. Efficient designs for both the visible and NIR systems are presented. The design of the NIR spectrograph presents challenges in the choice of materials for the doublet and triplet lenses employed. The choice of material and the combinations in which they can be used are described. This thesis shows that all these critical aspects of FMOS have good solutions that will result in good performance of the whole instrument. For the multiple IFU system, the prototype demonstrates acceptable performance which can be made excellent by the use of a better microlens array. The multiple fibre connector prototype already indicates excellent performance. Finally, the spectrograph designs presented should result in high efficiency and good image quality.
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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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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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Rey, Neto Edgard Casal de [UNESP]. "Reduções perturbativas com multiplos tempos e hierarquias de equações integraveis." Universidade Estadual Paulista (UNESP), 1996. http://hdl.handle.net/11449/132674.

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Made available in DSpace on 2016-01-13T13:27:35Z (GMT). No. of bitstreams: 0 Previous issue date: 1996. Added 1 bitstream(s) on 2016-01-13T13:33:02Z : No. of bitstreams: 1 000027513.pdf: 1370459 bytes, checksum: 5612c0331fff63058c1c40db8af96668 (MD5)
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Rey, Neto Edgard Casal de. "Reduções perturbativas com multiplos tempos e hierarquias de equações integraveis /." São Paulo : [s.n.], 1996. http://hdl.handle.net/11449/132674.

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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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Books on the topic "Multiples integrals"

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

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

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Kuznet︠s︡ov, D. F. Strong approximation of multiple Ito and Stratonovich stochastic integrals: Multple Fourier series approach. Saint-Peterburg: Politechnical University Publishing House, 2011.

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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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Book chapters on the topic "Multiples 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 "Multiples integrals"

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Banik, Sumit, and Samuel Friot. "Analytic Evaluation of Multiple Mellin-Barnes Integrals." In Loops and Legs in Quantum Field Theory, 039. Trieste, Italy: Sissa Medialab, 2024. http://dx.doi.org/10.22323/1.467.0039.

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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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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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Chaloupka, Jan, Filip Kocina, Petr Veigend, Gabriela Nečasová, Jiří Kunovský, and Václav Šátek. "Multiple integral computations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2016). Author(s), 2017. http://dx.doi.org/10.1063/1.4992650.

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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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Zelikin, M. I., Piotr Kielanowski, Victor Buchstaber, Anatol Odzijewicz, Martin Schlichenmaier, and Theodore Voronov. "On Multiple Integral Minimization Problems." In XXIX WORKSHOP ON GEOMETRIC METHODS IN PHYSICS. AIP, 2010. http://dx.doi.org/10.1063/1.3527421.

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Orszulik, Ryan, and Jinjun Shan. "Integral plus double integral synchronization control for multiple piezoelectric actuators." In 2015 European Control Conference (ECC). IEEE, 2015. http://dx.doi.org/10.1109/ecc.2015.7330684.

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Chaloupka, Jan, Jiří Kunovský, Alžběta Martinkovičová, Václav Šátek, and Elvira Thonhofer. "Multiple integral computations using Taylor series." In PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2014 (ICNAAM-2014). AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4913137.

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Okaichi, Naoto, Masato Miura, Jun Arai, and Tomoyuki Mishina. "Integral 3D display using multiple LCDs." In SPIE/IS&T Electronic Imaging, edited by Nicolas S. Holliman, Andrew J. Woods, Gregg E. Favalora, and Takashi Kawai. SPIE, 2015. http://dx.doi.org/10.1117/12.2077514.

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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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Reports on the topic "Multiples integrals"

1

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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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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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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