Journal articles: 'Generalised Integrals'

1

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

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

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3

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

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4

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

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5

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

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6

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

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An approximation of the Stieltjes integral of bounded integrals and continuous integrators via the Darst-Pollard inequality is given. Applications for the generalised trapezoid formula and the Ostrowski inequality for functions of bounded variation are also provided. .

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7

De Sarkar, S., and A. G. Das. "Riemann derivatives and general integrals." Bulletin of the Australian Mathematical Society 35, no. 2 (April 1987): 187–211. http://dx.doi.org/10.1017/s0004972700013174.

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Sargent and later Bullen and Mukhopadhyay obtained a definition of absolutely continuous functions, functions, that is related to kth Peano derivatives. The generalised notions of ACkG*, [ACkG*], ACkG* above, etcetera functions led Bullen and Mukhopadhyay to define certain general integrals of the kth order.The present work is concerned with a further simplification of the definitions of such functions by the use of divided differences but still retaining similar fundamental properties. These concepts lead to the introduction of Denjoy and Ridder type integrals which are shown to be equivalent to a Perron type integral that corresponds to kth Riemann* derivatives. All three of these integrals are shown to be equivalent to the three integrals of Bullen and Mukhopadhyay.

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8

Cleary, Paul. "Integrability of Motions in Galactic Potentials." Publications of the Astronomical Society of Australia 6, no. 4 (1986): 453–58. http://dx.doi.org/10.1017/s1323358000018361.

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AbstractThe dynamics exhibited by systems, such as galaxies, are dominated by the isolating integrals of the motion. The most common are the energy and angular momentum integrals. The motions in a system with a full complement of isolating integrals are regular, that is, periodic or quasi-periodic. Such a system is integrable. If there is a deficiency in the number of integrals, then the motions are chaotic. There is a fundamental quantative difference in the motion, depending on the number of integrals. A technique, called Generalised Painlevé analysis, based on complex variable theory allows the user to determine if a system is integrable. Two new integrable cases of the Henon-Heiles system are presented, bringing the total number of such integrable potentials to five. It is highly probable that there are no further integrable cases of the Henon-Heiles potential. Five cases of the quartic Verhulst potential, defined by certain restrictions on the coefficients, which are found to be integrable are summarised.

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9

Feigin, M. V., M. A. Hallnäs, and A. P. Veselov. "Baker-Akhiezer functions and generalised Macdonald-Mehta integrals." Journal of Mathematical Physics 54, no. 5 (May 2013): 052106. http://dx.doi.org/10.1063/1.4804615.

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10

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

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11

Cui, Guolong, Lingjiang Kong, Xiaobo Yang, and Dan Ran. "Two useful integrals involving generalised Marcum Q-function." Electronics Letters 48, no. 16 (August 2, 2012): 1017–18. http://dx.doi.org/10.1049/el.2012.1115.

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12

Cheung, W. S., and S. S. Dragomir. "Two Ostrowski type inequalities for the Stieltjes integral of monotonic functions." Bulletin of the Australian Mathematical Society 75, no. 2 (April 2007): 299–311. http://dx.doi.org/10.1017/s0004972700039228.

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Two integral inequalities of Ostrowski type for the Stieltjes integral are given. The first is for monotonic integrators and Hölder continuous integrands while the second considers the dual case, that is, for monotonic integrands and Hölder continuous integrators. Applications for the mid-point inequality that are useful in the numerical analysis of Stieltjes integrals are exhibited. Some connections with the generalised trapezoidal rule are also presented.

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13

Seng, Chew Tuan. "On the generalised dominated convergence theorem." Bulletin of the Australian Mathematical Society 37, no. 2 (April 1988): 165–71. http://dx.doi.org/10.1017/s0004972700026691.

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In this paper we give another version of the generalised dominated convergence theorem, which is better than other convergence theorems for Perron integrals in the sense that it can be applied more easily.

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14

Mawhin. "MULTIPLE GENERALISED RIEMANN INTEGRALS ON COMPACT INTERVALS AND APPLICATIONS." Real Analysis Exchange 14, no. 1 (1988): 51. http://dx.doi.org/10.2307/44153620.

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15

Evans, G. A., and K. C. Chung. "Evaluating infinite range oscillatory integrals using generalised quadrature methods." Applied Numerical Mathematics 57, no. 1 (January 2007): 73–79. http://dx.doi.org/10.1016/j.apnum.2005.12.003.

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16

Lowndes, J. S. "On some fractional integrals and their applications." Proceedings of the Edinburgh Mathematical Society 28, no. 1 (February 1985): 97–105. http://dx.doi.org/10.1017/s0013091500003230.

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In previous papers [3, 4] the author has discussed the symmetric generalised Erdélyi–Kober operators of fractional integration defined bywhere α>0, γ≧0 and the operators ℑiγ(η,α) and defined as in equations (1) and (2) respectively but with Jα−1, the Bessel function of the first kind replaced by Iα−1, the modified Bessel function of the first kind.

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17

Paris, Richard. "Asymptotic Expansion of the Modified Exponential Integral Involving the Mittag-Leffler Function." Mathematics 8, no. 3 (March 16, 2020): 428. http://dx.doi.org/10.3390/math8030428.

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We consider the asymptotic expansion of the generalised exponential integral involving the Mittag-Leffler function introduced recently by Mainardi and Masina [Fract. Calc. Appl. Anal. 21 (2018) 1156–1169]. We extend the definition of this function using the two-parameter Mittag-Leffler function. The expansions of the similarly extended sine and cosine integrals are also discussed. Numerical examples are presented to illustrate the accuracy of each type of expansion obtained.

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18

Lindner, Alexander, and Ross Maller. "Lévy integrals and the stationarity of generalised Ornstein–Uhlenbeck processes." Stochastic Processes and their Applications 115, no. 10 (October 2005): 1701–22. http://dx.doi.org/10.1016/j.spa.2005.05.004.

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19

El-Gabali, M. "Efficient multiple-term approximations for the generalised elliptic-type integrals." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 38, no. 3 (January 1997): 411–26. http://dx.doi.org/10.1017/s0334270000000758.

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AbstractThe generalised elliptic-type integral Rμ(k, α, γ)where 0 ≤ k < 1, Re(γ) > Re(α) > 0, Re(μ) ≥ −0.5, is represented in terms of the Gauss hypergeometric function by Kalla, Conde and Hubbell [8]. In 1987, Kalla, Lubner and Hubbell derived a simple-structured single-term approximation for this function in the neighbourhood of k2 = 1 in some range of the parameters α, γ and μ. Another formula which complements the parameter range was recently derived by the author. In this paper a novel technique is used in deriving multiple-term efficient approximations (in the neighbourhood of k2 = 1) which may be considered as a generalisation to the concept of the single-term approximations mentioned above. Two non-overlapping expressions which almost cover the entire range of parameters (α, γ, μ) are derived. Closed-form solutions are obtained for single- and double-term approximations (in the neighbourhood of k2 = 1). Results show that the proposed technique is superior to existing approximations for the same number of terms. Our formulation has potential application for a wide class of special functions.

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20

Natarajan, A., and N. Mohan Kumar. "On the numerical evaluation of the generalised Fermi-Dirac integrals." Computer Physics Communications 76, no. 1 (June 1993): 48–50. http://dx.doi.org/10.1016/0010-4655(93)90118-v.

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21

Aoki, Arata, Tsuyoshi Houri, and Kentaro Tomoda. "Rational first integrals of geodesic equations and generalised hidden symmetries." Classical and Quantum Gravity 33, no. 19 (September 7, 2016): 195003. http://dx.doi.org/10.1088/0264-9381/33/19/195003.

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22

Tong, Jingcheng. "90.20 Mean value theorem for integrals generalised to involve two functions." Mathematical Gazette 90, no. 517 (March 2006): 126–27. http://dx.doi.org/10.1017/s0025557200179239.

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23

Lamb, W. "A distributional theory of fractional calculus." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 99, no. 3-4 (1985): 347–57. http://dx.doi.org/10.1017/s0308210500014360.

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SynopsisIn this paper, a theory of fractional calculus is developed for certain spacesD′p,μof generalised functions. The theory is based on the construction of fractionalpowers of certain simple differential and integral operators. With the parameter μ suitably restricted, these fractional powers are shown to coincide with the Riemann-Liouville and Weyl operators of fractional integration and differentiation. Standard properties associated with fractional integrals and derivatives follow immediately from results obtained previously by the author on fractional powers of operators; see [6], [7]. Some spectral properties are also obtained.

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24

Smits, Lieven. "Moments of certain stochastic integrals occurring in mathematical physics." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 120, no. 3-4 (1992): 267–82. http://dx.doi.org/10.1017/s0308210500032133.

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SynopsisWe give an expression for the n-th moment of certain Itô integrals. The integrands considered are nonanticipating functionals of the form s↦a(s, Xs), where a is a measurable time-dependent vector field in space satisfying mild regularity conditions, and Xs is standard translated Brownian motion. The expressions are similar to the Dyson-Phillips terms for magnetic Schrödinger semigroups.We use these expressions to establish properties of the solutions of certain Cauchy problems and we relate our results to the framework of generalised Dyson expansions as set up by Johnson and Lapidus.

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25

Gronchi, G. F., and A. Milani. "Averaging of Earth-Crossing Orbits." International Astronomical Union Colloquium 172 (1999): 433–34. http://dx.doi.org/10.1017/s0252921100073036.

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The orbits of planet-crossing asteroids (and comets) can undergo close approaches and collisions with some major planet. This introduces a singularity in the N-body Hamiltonian, and the averaging of the equations of motion, traditionally used to compute secular perturbations, is undefined. We have shown (Gronchi and Milani, 1998) that it is possible to define in a rigorous way some generalised averaged equations of motion, in such a way that the generalised solutions are unique and piecewise smooth, with corners on the node crossing lines.The model is the averaged equations of motion first introduced by Kozai (1962): the perturbing planets are assumed to move in circular, coplanar orbits, and the equations of motion are averaged over the anomalies of the asteroid and of the planets. In the non-crossing case the averaging is integrable; in the planet-crossing case there is a polar singularity of order two in the equations of motion, and averaging is not possible. To define a generalized solution, we decrease the order of the polar singularity by the method of extraction of the singularities by Kantorovich. The singularity of the perturbing function is approximated by a modified inverse distance, the one between the straight lines tangent to the two orbits at the nodal points. In this approximation the averaged perturbing function has an analytical expression, allowing explicit computation with elliptic integrals and elementary functions.

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26

Zhukovsky, K. "Solution of Some Types of Differential Equations: Operational Calculus and Inverse Differential Operators." Scientific World Journal 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/454865.

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We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

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27

Hall, Peter, and Rodney Carl Wolff. "Properties of distributions and correlation integrals for generalised versions of the logistic map." Stochastic Processes and their Applications 77, no. 1 (September 1998): 123–37. http://dx.doi.org/10.1016/s0304-4149(98)00010-6.

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28

SERGEEV, A. N., and A. P. VESELOV. "JACK–LAURENT SYMMETRIC FUNCTIONS FOR SPECIAL VALUES OF PARAMETERS." Glasgow Mathematical Journal 58, no. 3 (July 21, 2015): 599–616. http://dx.doi.org/10.1017/s0017089515000361.

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AbstractWe consider the Jack–Laurent symmetric functions for special values of parametersp0=n+k−1m, wherekis not rational andmandnare natural numbers. In general, the coefficients of such functions may have poles at these values ofp0. The action of the corresponding algebra of quantum Calogero–Moser integrals$\mathcal{D}$(k,p0) on the space of Laurent symmetric functions defines the decomposition into generalised eigenspaces. We construct a basis in each generalised eigenspace as certain linear combinations of the Jack–Laurent symmetric functions, which are regular atp0=n+k−1m, and describe the action of$\mathcal{D}$(k,p0) in these eigenspaces.

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29

Cunningham, Clifton. "Characters of Depth-Zero, Supercuspidal Representations of the Rank-2 Symplectic Group." Canadian Journal of Mathematics 52, no. 2 (April 1, 2000): 306–31. http://dx.doi.org/10.4153/cjm-2000-014-3.

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AbstractThis paper expresses the character of certain depth-zero supercuspidal representations of the rank-2 symplectic group as the Fourier transform of a finite linear combination of regular elliptic orbital integrals—an expression which is ideally suited for the study of the stability of those characters. Building on work of F. Murnaghan, our proof involves Lusztig’s Generalised Springer Correspondence in a fundamental way, and also makes use of some results on elliptic orbital integrals proved elsewhere by the author using Moy-Prasad filtrations of p-adic Lie algebras. Two applications of the main result are considered toward the end of the paper.

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Muatjetjeja, Ben, and Chaudry Masood Khalique. "Lie Group Classification for a Generalised Coupled Lane-Emden System in Dimension One." East Asian Journal on Applied Mathematics 4, no. 4 (November 2014): 301–11. http://dx.doi.org/10.4208/eajam.080214.230814a.

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AbstractIn this article, we discuss the generalised coupled Lane-Emden system u” + H(v) = 0, v” + G(u) = 0 that applies to several physical phenomena. The Lie group classification of the underlying system shows that it admits a ten-dimensional equivalence Lie algebra. We also show that the principal Lie algebra in one dimension has several possible extensions, and obtain an exact solution for an interesting particular case via Noether integrals.

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31

Ermolova, N. Y. "Useful integrals for performance evaluation of communication systems in generalised −μ and −μ fading channels." IET Communications 3, no. 2 (2009): 303. http://dx.doi.org/10.1049/iet-com:20080189.

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32

Tanabé, Susumu. "On monodromy representation of period integrals associated to an algebraic curve with bi-degree (2,2)." Analele Universitatii "Ovidius" Constanta - Seria Matematica 25, no. 1 (January 26, 2017): 207–31. http://dx.doi.org/10.1515/auom-2017-0016.

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AbstractWe study a problem related to Kontsevich's homological mirror symmetry conjecture for the case of a generic curve Y with bi-degree (2,2) in a product of projective lines ℙ1× ℙ1. We calculate two differenent monodromy representations of period integrals for the affine variety X(2,2)obtained by the dual polyhedron mirror variety construction from Y. The first method that gives a full representation of the fundamental group of the complement to singular loci relies on the generalised Picard-Lefschetz theorem. The second method uses the analytic continuation of the Mellin-Barnes integrals that gives us a proper subgroup of the monodromy group. It turns out both representations admit a Hermitian quadratic invariant form that is given by a Gram matrix of a split generator of the derived category of coherent sheaves on on Y with respect to the Euler form.

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33

Bienaymé, O., J. Leca, and A. C. Robin. "A new dynamically self-consistent version of the Besançon Galaxy model." Astronomy & Astrophysics 620 (December 2018): A103. http://dx.doi.org/10.1051/0004-6361/201833395.

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Context. Dynamically self-consistent galactic models are necessary for analysing and interpreting star counts, stellar density distributions, and stellar kinematics in order to understand the formation and the evolution of our Galaxy. Aims. We modify and improve the dynamical self-consistency of the Besançon Galaxy model in the case of a stationary and axisymmetric gravitational potential. Methods. Each stellar orbit is modelled by determining a Stäckel approximate integral of motion. Generalised Shu distribution functions (DFs) with three integrals of motion are used to model the stellar distribution functions. Results. This new version of the Besançon model is compared with the previous axisymmetric BGM2014 version and we find that the two versions have similar densities for each stellar component. The dynamically self-consistency is improved and can be tested by recovering the forces and the potential through the Jeans equations applied to each stellar distribution function. Forces are recovered with an accuracy better than one per cent over most of the volume of the Galaxy.

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Davies, I. M., and A. Truman. "Laplace asymptotic expansions of conditional Wiener integrals and generalised Mehler kernel formulae for Hamiltonians on L2(Rn)." Journal of Physics A: Mathematical and General 22, no. 9 (May 1989): 1467. http://dx.doi.org/10.1088/0305-4470/22/9/533.

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35

Leipnik, Roy B. "Partial differential equations for Eigenvalues: sensitivity and perturbation analysis." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 34, no. 4 (April 1993): 439–70. http://dx.doi.org/10.1017/s0334270000009024.

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AbstractThe well-known Wilkinson expressions for the first derivatives of (ordinary) eigen-values and eigenvectors of simple matrices, in terms of the set of eigenvalues and eigenvectors, are redifferentiated and combined to obtain partial differential equations for the eigenvalues. Analogous expressions are obtained for the first derivatives of generalised eigenvalues and eigenvectors of simple pairs of matrices (A, B), defined by . Again, redifferentiation and combination yields slightly more complicated partial differential equations for the generalised eigenvalues. When the matrices depend on a few parameters θ1, θ2, …, the resulting differential equations for the eigenvalues, with those parameters as independent variables, can easily be derived. These parametric equations are explicit representations of analytic perturbation results of Kato, expressed by him as rather abstract complex matrix integrals. Connections with bounds for eigenvalues derived by Stewart and Sun can also be made. Two applications are exhibited, the first being to a broken symmetry problem, the second being to working out the second-order perturbations for a classical problem in the theory of waves in cold plasmas.

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Lewandowski, Jerzy. "Non-abelian path integrals and generalised quantum mechanics in the external field of the 't Hooft-Polyakov monopole." Physics Letters A 121, no. 7 (May 1987): 325–28. http://dx.doi.org/10.1016/0375-9601(87)90298-2.

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37

Bhutani, O. P., and K. Vijayakumar. "On certain new and exact solutions of the Emden-Fowler equation and Emden equation via invariant variational principles and group invariance." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 32, no. 4 (April 1991): 457–68. http://dx.doi.org/10.1017/s0334270000008535.

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AbstractAfter formulating the alternate potential principle for the nonlinear differential equation corresponding to the generalised Emden-Fowler equation, the invariance identities of Rund [14] involving the Lagrangian and the generators of the infinitesimal Lie group are used for writing down the first integrals of the said equation via the Noether theorem. Further, for physical realisable forms of the parameters involved and through repeated application of invariance under the transformation obtained, a number of exact solutions are arrived at both for the Emden-Fowler equation and classical Emden equations. A comparative study with Bluman-Cole and scale-invariant techniques reveals quite a number of remarkable features of the techniques used here.

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Osler, Thomas J. "Bisecting and trisecting the arc of the lemniscate." Mathematical Gazette 100, no. 549 (October 17, 2016): 471–81. http://dx.doi.org/10.1017/mag.2016.112.

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In this paper we will discuss the lemniscate curve and show that its arc length can be bisected and trisected using classical ruler and compasses construction. The method dates back to 1718 when Count Giulio Fagnano (1682-1766) first published these constructions [1]. Fagnano was self-educated in mathematics and treated the subject as a hobby. Euler was impressed by his work on this topic and recommended his admission to the Berlin Academy of Science. Euler then generalised Fagnano's work on integrals. In addition, Fagnano was employed to assist in reinforcing the dome of Saint Peter's which was in danger of collapse. Pope Benedict IV rewarded him for his work by publishing his mathematical papers. Fagnano achieved considerable international fame as a mathematician, and rightly so given the outstanding contributions which he made on a number of different topics.

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Garetto, Claudia, Günther Hörmann, and Michael Oberguggenberger. "Generalized oscillatory integrals and Fourier integral operators." Proceedings of the Edinburgh Mathematical Society 52, no. 2 (May 28, 2009): 351–86. http://dx.doi.org/10.1017/s0013091506000915.

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AbstractIn this paper, a theory is developed of generalized oscillatory integrals (OIs) whose phase functions and amplitudes may be generalized functions of Colombeau type. Based on this, generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is motivated by the need for a general framework for partial differential operators with non-smooth coefficients and distribution dataffi The mapping properties of these FIOs are studied, as is microlocal Colombeau regularity for OIs and the influence of the FIO action on generalized wavefront sets.

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Mawhin, Jean. "Nonstandard analysis and generalized Riemann integrals." Časopis pro pěstování matematiky 111, no. 1 (1986): 34–47. http://dx.doi.org/10.21136/cpm.1986.118262.

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41

Chang, Seung Jun, Soon Ja Kang, and David Skoug. "Conditional generalized analytic Feynman integrals and a generalized integral equation." International Journal of Mathematics and Mathematical Sciences 23, no. 11 (2000): 759–76. http://dx.doi.org/10.1155/s0161171200002775.

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We use a generalized Brownian motion process to define a generalized Feynman integral and a conditional generalized Feynman integral. We then establish the existence of these integrals for various functionals. Finally we use the conditional generalized Feynman integral to derive a Schrödinger integral equation.

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Iftikhar, Sabah, Poom Kumam, and Samet Erden. "NEWTON’S-TYPE INTEGRAL INEQUALITIES VIA LOCAL FRACTIONAL INTEGRALS." Fractals 28, no. 03 (May 2020): 2050037. http://dx.doi.org/10.1142/s0218348x20500371.

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We firstly establish an identity involving local fractional integrals. Then, with the help of this equality, some new Newton-type inequalities for functions whose the local fractional derivatives in modulus and their some powers are generalized convex are obtained. Some applications of these inequalities for Simpson’s quadrature rules and generalized special means are also given.

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El-Ganaini, Shoukry Ibrahim Atia. "New Exact Solutions of Some Nonlinear Systems of Partial Differential Equations Using the First Integral Method." Abstract and Applied Analysis 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/693076.

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The first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including classical Drinfel'd-Sokolov-Wilson system (DSWE), (2 + 1)-dimensional Davey-Stewartson system, and generalized Hirota-Satsuma coupled KdV system. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner. This method can also be applied to nonintegrable equations as well as integrable ones.

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Carrillo, M. Diaz, and H. Günzler. "Local integral metrics and Daniell-Loomis integrals." Bulletin of the Australian Mathematical Society 48, no. 3 (December 1993): 411–26. http://dx.doi.org/10.1017/s0004972700015872.

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Recently Guerrero and the first author (Diaz Carrillo) proved an anologue to Daniell's extension process which works for arbitrary nonnegative linear functionals, without any continuity conditions. With the aid of Schäfke's local integral metrics we generalise this extension process and prove convergence theorems using a suitable local mean convergence, which can be traced back to Loomis.

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Shao, Yabin, and Huanhuan Zhang. "Fuzzy Integral Equations and Strong Fuzzy Henstock Integrals." Abstract and Applied Analysis 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/932696.

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Cho, Dong Hyun. "Integral Transforms on a Function Space with Change of Scales Using Multivariate Normal Distributions." Journal of Function Spaces 2016 (2016): 1–9. http://dx.doi.org/10.1155/2016/9235960.

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Using simple formulas for generalized conditional Wiener integrals on a function space which is an analogue of Wiener space, we evaluate two generalized analytic conditional Wiener integrals of a generalized cylinder function which is useful in Feynman integration theories and quantum mechanics. We then establish various integral transforms over continuous paths with change of scales for the generalized analytic conditional Wiener integrals. In these evaluation formulas and integral transforms we use multivariate normal distributions so that the orthonormalization process of projection vectors which are needed to establish the conditional Wiener integrals can be removed in the existing change of scale transforms. Consequently the transforms in the present paper can be expressed in terms of the generalized cylinder function itself.

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Safouhi, Hassan. "A Generalized Technique in Numerical Integration." EPJ Web of Conferences 173 (2018): 01011. http://dx.doi.org/10.1051/epjconf/201817301011.

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Integration by parts is one of the most popular techniques in the analysis of integrals and is one of the simplest methods to generate asymptotic expansions of integral representations. The product of the technique is usually a divergent series formed from evaluating boundary terms; however, sometimes the remaining integral is also evaluated. Due to the successive differentiation and anti-differentiation required to form the series or the remaining integral, the technique is difficult to apply to problems more complicated than the simplest. In this contribution, we explore a generalized and formalized integration by parts to create equivalent representations to some challenging integrals.As a demonstrative archetype, we examine Bessel integrals, Fresnel integrals and Airy functions.

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48

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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Akkurt, Abdullah, Mehmet Zeki Sarikaya, Hüseyin Budak, and Hüseyin Yildirim. "Generalized Ostrowski type integral inequalities involving generalized moments via local fractional integrals." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 111, no. 3 (August 30, 2016): 797–807. http://dx.doi.org/10.1007/s13398-016-0336-9.

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Zeki Sarikaya, Mehmet. "On the Generalized Weighted Integral Inequality for Double Integrals." Annals of the Alexandru Ioan Cuza University - Mathematics 61, no. 1 (January 1, 2015): 169–79. http://dx.doi.org/10.2478/aicu-2014-0008.

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Abstract:

Abstract In this paper, we obtain weighted Montgomery’s identities for function of two variables and apply them to give new generalization weighted integral inequality for double integrals involving functions of two independent variables by using fairly elementary analysis.

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Journal articles on the topic 'Generalised Integrals'

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