Academic literature on the topic 'Integral and its inverse operator'

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Journal articles on the topic "Integral and its inverse operator"

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Ali, Rana Safdar, Saba Batool, Shahid Mubeen, et al. "On generalized fractional integral operator associated with generalized Bessel-Maitland function." AIMS Mathematics 7, no. 2 (2022): 3027–46. http://dx.doi.org/10.3934/math.2022167.

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<abstract><p>In this paper, we describe generalized fractional integral operator and its inverse with generalized Bessel-Maitland function (BMF-Ⅴ) as its kernel. We discuss its convergence, boundedness, its relation with other well known fractional operators (Saigo fractional integral operator, Riemann-Liouville fractional operator), and establish its integral transform. Moreover, we have given the relationship of BMF-Ⅴ with Mittag-Leffler functions.</p></abstract>
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Ali, R. S., S. Mubeen, I. Nayab, Serkan Araci, G. Rahman, and K. S. Nisar. "Some Fractional Operators with the Generalized Bessel–Maitland Function." Discrete Dynamics in Nature and Society 2020 (July 24, 2020): 1–15. http://dx.doi.org/10.1155/2020/1378457.

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In this paper, we aim to determine some results of the generalized Bessel–Maitland function in the field of fractional calculus. Here, some relations of the generalized Bessel–Maitland functions and the Mittag-Leffler functions are considered. We develop Saigo and Riemann–Liouville fractional integral operators by using the generalized Bessel–Maitland function, and results can be seen in the form of Fox–Wright functions. We establish a new operator Zν,η,ρ,γ,w,a+μ,ξ,m,σϕ and its inverse operator Dν,η,ρ,γ,w,a+μ,ξ,m,σϕ, involving the generalized Bessel–Maitland function as its kernel, and also di
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Buterin, S. A. "Inverse Spectral Problem for Integrodifferential Sturm-Liouville Operators with Discontinuity Conditions". Contemporary Mathematics. Fundamental Directions 64, № 3 (2018): 427–58. http://dx.doi.org/10.22363/2413-3639-2018-64-3-427-458.

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We consider the Sturm-Liouville operator perturbed by a convolution integral operator on a finite interval with Dirichlet boundary-value conditions and discontinuity conditions in the middle of the interval. We study the inverse problem of restoration of the convolution term by the spectrum. The problem is reduced to solution of the so-called main nonlinear integral equation with a singularity. To derive and investigate this equations, we do detailed analysis of kernels of transformation operators for the integrodifferential expression under consideration. We prove the global solvability of the
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Baleanu, Dumitru, Arran Fernandez, and Ali Akgül. "On a Fractional Operator Combining Proportional and Classical Differintegrals." Mathematics 8, no. 3 (2020): 360. http://dx.doi.org/10.3390/math8030360.

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The Caputo fractional derivative has been one of the most useful operators for modelling non-local behaviours by fractional differential equations. It is defined, for a differentiable function f ( t ) , by a fractional integral operator applied to the derivative f ′ ( t ) . We define a new fractional operator by substituting for this f ′ ( t ) a more general proportional derivative. This new operator can also be written as a Riemann–Liouville integral of a proportional derivative, or in some important special cases as a linear combination of a Riemann–Liouville integral and a Caputo derivative
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Mayer, F. F., M. G. Tastanov, and A. A. Utemisova. "GEOMETRIC PROPERTIES OF THE BERNATSKY INTEGRAL OPERATOR." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 14, no. 4 (2022): 12–19. http://dx.doi.org/10.14529/mmph220402.

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In the geometric theory of complex variable functions, the study of mapping of classes of regular functions using various operators has now become an independent trend. The connection f(z)∈S o⇔ g(z) = zf'(z) ∈ S * of the classes S o and S * of convex and star-shaped functions can be considered as mapping using the differential operator G[f](x) = zf'(z) of class S o to class S * , that is, G: S o → S * or G(S o ) = S * . The impetus for studying this range of issues was M. Bernatsky's assumption that the inverse operator G –1 [f](x), which translates S * → S o and thereby “improves” the propert
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Tarasov, Vasily E. "Fractional Dynamics with Depreciation and Obsolescence: Equations with Prabhakar Fractional Derivatives." Mathematics 10, no. 9 (2022): 1540. http://dx.doi.org/10.3390/math10091540.

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In economics, depreciation functions (operator kernels) are certain decreasing functions, which are assumed to be equal to unity at zero. Usually, an exponential function is used as a depreciation function. However, exponential functions in operator kernels do not allow simultaneous consideration of memory effects and depreciation effects. In this paper, it is proposed to consider depreciation of a non-exponential type, and simultaneously take into account memory effects by using the Prabhakar fractional derivatives and integrals. Integro-differential operators with the Prabhakar (generalized
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Luchko, Yuri. "On a Generic Fractional Derivative Associated with the Riemann–Liouville Fractional Integral." Axioms 13, no. 9 (2024): 604. http://dx.doi.org/10.3390/axioms13090604.

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In this paper, a generic fractional derivative is defined as a set of the linear operators left-inverse to the Riemann–Liouville fractional integral. Then, the theory of the left-invertible operators developed by Przeworska-Rolewicz is applied to deduce its properties. In particular, we characterize its domain, null-space, and projector operator; establish the interrelations between its different realizations; and present a generalized fractional Taylor formula involving the generic fractional derivative. Then, we consider the fractional relaxation equation containing the generic fractional de
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Ezquerro, José Antonio, and Miguel Ángel Hernández-Verón. "Using Chebyshev’s polynomials for solving Fredholm integral equations of the second kind." Mathematical Modelling and Analysis 30, no. 1 (2025): 36–51. https://doi.org/10.3846/mma.2025.21036.

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The main problem with the Newton method is the computation of the inverse of the first derivative of the operator involved at each iteration step. Thus, when we want to apply the Newton method directly to solve an integral equation, the existence of the inverse of the first derivative is guaranteed, when the kernel is sufficiently differentiable into any of its two components, through its approximation by Taylor’s polynomial. In this paper, we study the case in which the kernel is not differentiable in any of its two components. So, we present a strategy that consists of approximating the kern
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Mika, J., and D. C. Pack. "Approximation to inverses of normal operators." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 103, no. 3-4 (1986): 335–45. http://dx.doi.org/10.1017/s0308210500018989.

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SynopsisFor many purposes, and in particular for the calculation of upper and lower bounds to bilinear forms 〈g0,f〉, where f is the solution to an operator equation and g0 is known, it isuseful to obtain an approximation to the inverse of the operator.For a normal operator A acting in a complex Hilbert space with bounded inverse A−1, we use a direct approach through fundamental results in functional analysis and derive a recipe for the ‘best formula’ for A−1 of form B = βI with β constant and I the identity operator. Examples illustrate that this leads to improved results for certain classes o
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Dhaouadi, Lazhar. "Spectral Theory from the Second-Orderq-Difference Operator." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–14. http://dx.doi.org/10.1155/2007/16595.

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Spectral theory from the second-orderq-difference operatorΔqis developed. We give an integral representation of its inverse, and the resolvent operator is obtained. As application, we give an analogue of the Poincare inequality. We introduce the Zeta function for the operatorΔqand we formulate some of its properties. In the end, we obtain the spectral measure.
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Dissertations / Theses on the topic "Integral and its inverse operator"

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Hofmann, B. "On Ill-Posedness and Local Ill-Posedness of Operator Equations in Hilbert Spaces." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801185.

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In this paper, we study ill-posedness concepts of nonlinear and linear inverse problems in a Hilbert space setting. We define local ill-posedness of a nonlinear operator equation $F(x) = y_0$ in a solution point $x_0$ and the interplay between the nonlinear problem and its linearization using the Frechet derivative $F\acent(x_0)$ . To find an appropriate ill-posedness concept for the linarized equation we define intrinsic ill-posedness for linear operator equations $Ax = y$ and compare this approach with the ill-posedness definitions due to Hadamard and Nashed.
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Assaad, Joyce. "Transformées de Riesz associées aux opérateurs de Schrödinger avec des potentiels négatifs." Thesis, Bordeaux 1, 2010. http://www.theses.fr/2010BOR14106/document.

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Dans cette thèse nous étudions la bornitude des transformées de Riesz associées aux opérateurs de Schrödinger avec des potentiels qui admettent des parties négatives.Cette étude a lieu dans un premier temps sur les espaces de Lebesgue Lp(RN, dx), puissur les espaces Lp(M, dx) où M est une variété Riemannienne de type homogène et dans un dernier temps sur les espaces à poids Lp(RN,wdx). Nous considérons également,sur ces espaces à poids, la bornitude du calcul fonctionnel holomorphe associé et la bornitude des puissances négatives de l’opérateur de Schrödinger<br>In this thesis we study the bou
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Júnior, Antônio Espósito. "Equações integrais via teoria de domínios: problemas direto e inverso." Universidade do Estado do Rio de Janeiro, 2008. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=772.

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Apresenta-se um estudo em Teoria de Domínios das equações integrais da forma geral f (x) = h(x)+g Z b(x) a(x) g(x, y, f (y))dy com h, a e b definidas para x &#8712; [a0,b0], a0 &#8804;a(x)&#8804;b(x)&#8804;b0 e g definida para x, y &#8712; [a0,b0], cujo lado direito define uma contração sobre o espaço métrico de funções reais contínuas limitadas. O ponto de partida desse trabalho é a reescrita da Análise Intervalar para Teoria de Domínios do problema de valor incial em equações diferenciais ordinárias que possuem solução como ponto fixo do operador de Picard. Com o conjunto dos números reais
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Yu, Zhiru. "A CG-FFT Based Fast Full Wave Imaging Method and its Potential Industrial Applications." Diss., 2015. http://hdl.handle.net/10161/11344.

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<p>This dissertation focuses on a FFT based forward EM solver and its application in inverse problems. The main contributions of this work are two folded. On the one hand, it presents the first scaled lab experiment system in the oil and gas industry for through casing hydraulic fracture evaluation. This system is established to validate the feasibility of contrasts enhanced fractures evaluation. On the other hand, this work proposes a FFT based VIE solver for hydraulic fracture evaluation. This efficient solver is needed for numerical analysis of such problem. The solver is then generalized t
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Books on the topic "Integral and its inverse operator"

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Novitsky, Igor M. Simultaneous unitary equivalence of operator families to integral operators with smooth kernels and its applications. Far-Eastern Branch of the Academy of Sciences of the USSR, 1990.

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1928-, Gohberg I., Kaashoek M. A, Seatzu Sebastiano, and Mee, C. V. M. van der, eds. Recent advances in operator theory and its applications: The Israel Gohberg anniversary volume : International Workshop on Operator Theory and its Applications, IWOTA 2003, Cagliari, Italy. Birkhäuser Verlag, 2005.

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Maeda, Yoshiaki. Noncommutative Differential Geometry and Its Applications to Physics: Proceedings of the Workshop at Shonan, Japan, June 1999. Springer Netherlands, 2001.

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V, Vasin V., and Tanana Vitaliĭ Pavlovich, eds. Theory of linear ill-posed problems and its applications. 2nd ed. VSP, 2002.

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W, Begehr Heinrich G., Celebi A. Okay, Gilbert Robert P. 1932-, and Kaptanoğlu H. T, eds. Further progress in analysis: Proceedings of the 6th International ISAAC Congress, Middle East Technical University, Ankara Turkey, 13-18 August 2007. World Scientific, 2009.

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Fonseca, Carlos M. da. A panorama of mathematics: Pure and applied : Conference on Mathematics and Its Applications, November 14-17, 2014, Kuwait University, Safat, Kuwait. American Mathematical Society, 2016.

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Samoilenko, A. M., and A. A. Boichuk. Generalized Inverse Operators and Fredholm Boundary-Value Problems. Brill Academic Publishers, 2004.

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Boichuk, A. A., and Anatolii M. Samoilenko. Generalized Inverse Operators and Fredholm Boundary-Value Problems. de Gruyter GmbH, Walter, 2012.

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Rajeev, S. G. Fluid Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805021.001.0001.

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Starting with a review of vector fields and their integral curves, the book presents the basic equations of the subject: Euler and Navier–Stokes. Some solutions are studied next: ideal flows using conformal transformations, viscous flows such as Couette and Stokes flow around a sphere, shocks in the Burgers equation. Prandtl’s boundary layer theory and the Blasius solution are presented. Rayleigh–Taylor instability is studied in analogy with the inverted pendulum, with a digression on Kapitza’s stabilization. The possibility of transients in a linearly stable system with a non-normal operator
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Mathematical and Computational Methods in Photonics and Phononics. American Mathematical Society, 2018.

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Book chapters on the topic "Integral and its inverse operator"

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Arov, Damir Z., and Harry Dym. "Inverse Spectral Problems for Integral and Differential Systems." In Operator Theory: Advances and Applications. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-70262-9_6.

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Cohen, Leon. "Path Integral Approach." In The Weyl Operator and its Generalization. Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0294-9_8.

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Aktosun, Tuncay. "Inverse Scattering Transform, KdV, and Solitons." In Current Trends in Operator Theory and its Applications. Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7881-4_1.

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Böttcher, A., and Yu I. Karlovich. "Cauchy’s Singular Integral Operator and Its Beautiful Spectrum." In Systems, Approximation, Singular Integral Operators, and Related Topics. Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8362-7_5.

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Widom, Harold. "The Heat Expansion for Systems of Integral Equations." In Contributions to Operator Theory and its Applications. Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-9284-1_19.

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Cappiello, Marco. "Fourier Integral Operators and Gelfand-Shilov Spaces." In Recent Advances in Operator Theory and its Applications. Birkhäuser Basel, 2005. http://dx.doi.org/10.1007/3-7643-7398-9_5.

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van der Mee, Cornelis. "Direct and Inverse Scattering for Skewselfadjoint Hamiltonian Systems." In Current Trends in Operator Theory and its Applications. Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7881-4_17.

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Rochberg, Richard, and Stephen Semmes. "End Point Results for Estimates of Singular Values of Singular Integral Operators." In Contributions to Operator Theory and its Applications. Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-9284-1_9.

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Karlovich, Yu I., and V. A. Mozel. "On Nonlocal C *-algebras of Two-dimensional Singular Integral Operators." In Recent Progress in Operator Theory and Its Applications. Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0346-5_7.

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Aktosun, Tuncay, Michael H. Borkowski, Alyssa J. Cramer, and Lance C. Pittman. "Inverse Scattering with Rational Scattering Coefficients and Wave Propagation in Nonhomogeneous Media." In Recent Advances in Operator Theory and its Applications. Birkhäuser Basel, 2005. http://dx.doi.org/10.1007/3-7643-7398-9_1.

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Conference papers on the topic "Integral and its inverse operator"

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Ghafarirad, Hamed, Seyed Mehdi Rezaei, Amir Abdullah, Mohammad Zareinejad, and Mozafar Saadat. "Observer-Based Robust Control With Adaptive Perturbation Estimation for a Piezoelectric Actuator." In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-40167.

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Control of piezoelectric actuators is under the effects of hysteresis that could affect actuators micropositioning accuracy. In this paper a modified Prandtl-Ishlinskii (PI) operator and its inverse is utilized for both identification and real time compensation of the hysteresis effect. As a result, the actuator dynamic model would be transformed to the second order linear dynamic model. Considering the parametric uncertainties, PI estimation error and probably unmodeled dynamics, a variable structure controller coupled with adaptive perturbation estimation is proposed for trajectory tracking
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Zhu, Guang-Yu, Hou-Xing Zhou, and Wei Hong. "Sparse Representation of Inverse Integral Operator Using Neumann Series and Skeletonization." In 2019 IEEE International Conference on Computational Electromagnetics (ICCEM). IEEE, 2019. http://dx.doi.org/10.1109/compem.2019.8779134.

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Caponetto, R., G. Dongola, and A. Gallo. "Fractional Integrative Operator and Its FPGA Implementation." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87406.

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In this paper the fractional order integrative operator s−m, where m is a real positive number, is approximated via a mathematical formula and then an hardware implementation of fractional integral operator is proposed using Field Programmable Gate Array (FPGA). Digital hardware implementation of fractional-order integral operator requires careful consideration of issue of system performance, hardware cost, and hardware speed. FPGA-based implementation are up to one hundred times faster than implementations based on micro-processors; this extra speed can be exploited to allow higher performanc
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Kinoshita, Yuma, Sayaka Shiota, and Hitoshi Kiya. "Reinhard's global operator based inverse tone mapping with one parameter." In 2017 Eighth International Workshop on Signal Design and its Applications in Communications (IWSDA). IEEE, 2017. http://dx.doi.org/10.1109/iwsda.2017.8095734.

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Tripathy, Srinibas, Mithun Babu M., Kanupriya M., and Mayank Mittal. "A Machine Learning Based Numerical Approach for Valve Seating Velocity Control in an Electromagnetic Camless System." In ASME 2021 Internal Combustion Engine Division Fall Technical Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/icef2021-67594.

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Abstract Improving internal combustion engine performance is a significant concern over the past few decades for engine researchers and automobile manufacturers. One of the promising methods for improving the engine performance is variable valve actuation system with camless technology. In the camless system, the conventional spring-operated valve actuation mechanism is removed, and an actuator is used to independently control the valve events (lift, timing, and duration). Among different camless systems, electromagnetic variable valve actuation (EMVA) becomes more viable because of its faster
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Salim, Daniel, Wono Setya Budhi, and Yudi Soeharyadi. "Boundedness of fractional integral operator with rough kernel on generalized Morrey space." In INTERNATIONAL CONFERENCE AND WORKSHOP ON MATHEMATICAL ANALYSIS AND ITS APPLICATIONS (ICWOMAA 2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5016646.

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Obaiys, Suzan J., and Rabha W. Ibrahim. "On a new fractional integral operator convoluted with a fractional k-symbol Raina function: stability." In 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA). IEEE, 2023. http://dx.doi.org/10.1109/icfda58234.2023.10153363.

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Lamm, Patricia K. "On the Local Regularization of Inverse Problems of Volterra Type." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0664.

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Abstract We consider a local regularization method for the solution of first-kind Volterra integral equations with convolution kernel. The local regularization is based on a splitting of the original Volterra operator into “local” and “global” parts, and a use of Tikhonov regularization to stabilize the inversion of the local operator only. The regularization parameters for the local procedure include the standard Tikhonov parameter, as well as a parameter that represents the length of the local regularization interval. We present a convergence theory for the infinite-dimensional regularizatio
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Hofmann, Bernd, Thomas F. Eibert, Francesco P. Andriulli, and Simon B. Adrian. "Investigations on the Low-Frequency Stability of Inverse Surface Source Field Transformations Based on the Electric Field Integral Operator." In 2023 17th European Conference on Antennas and Propagation (EuCAP). IEEE, 2023. http://dx.doi.org/10.23919/eucap57121.2023.10133154.

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Bhambri, Sameer, Vivek Shrivastava, and Manoj Kumawat. "An Analytical Design Approach for Inverter Output Impedance in Parallel Operation of Micro Source Inverters." In International Conference on Energy Transition and Innovation in Green Technology. REGIONAL ENERGY RESOURCES INFORMATION CENTER (RERIC), 2025. https://doi.org/10.64289/rericproc.25.0105.1328475.

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This paper proposes an analytical framework to design an inverter output impedance in microgrid applications to meet the requirements of proportional load sharing and low total harmonic distortion in the output voltage. In the proposed work, an integral controller is designed in order to make the overall impedance of an inverter to be capacitive in nature. The optimum design of overall capacitive impedance at the harmonic frequencies ensures low THD levels in the output voltage without affecting proportional load sharing, which is determined by an inverter impedance at fundamental frequency co
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Reports on the topic "Integral and its inverse operator"

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Rao, Menaka, Kushagra Merchant, and Shantanu Menon. Good Business Lab: Designing for Wellbeing. Indian School Of Development Management, 2023. http://dx.doi.org/10.58178/2303.1019.

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This case study engages with the journey of Good Business Lab (GBL), a non-profit registered in Bengaluru in 2017 that today has offices across India, as well as the USA and Latin America. Good Business Lab aims to apply research to steer businesses (primarily in labor-intensive industries such as manufacturing), to invest in the wellbeing of their workers. Through its ability to marry rigorous research techniques to its concerted intent to strike the balance between business and worker, GBL today occupies a notable niche within the Indian social sector ecosystem. The case study explores the e
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