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Journal articles on the topic 'Termes de Fourier'

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Published: 25 January 2025

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1

Révész, Sz Gy. "Rearrangement of Fourier series and fourier series whose terms have random signs." Acta Mathematica Hungarica 63, no. 4 (December 1994): 395–402. http://dx.doi.org/10.1007/bf01874464.

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2

Au-Yeung, Enrico, and John J. Benedetto. "Generalized Fourier Frames in Terms of Balayage." Journal of Fourier Analysis and Applications 21, no. 3 (December 4, 2014): 472–508. http://dx.doi.org/10.1007/s00041-014-9369-7.

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3

Zozulya, V. V. "A High Order Theory for Linear Thermoelastic Shells: Comparison with Classical Theories." Journal of Engineering 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/590480.

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A high order theory for linear thermoelasticity and heat conductivity of shells has been developed. The proposed theory is based on expansion of the 3-D equations of theory of thermoelasticity and heat conductivity into Fourier series in terms of Legendre polynomials. The first physical quantities that describe thermodynamic state have been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate. Thereby all equations of elasticity and heat conductivity including generalized Hooke's and Fourier's laws have been transformed to the corresponding equations for coefficients of the polynomial expansion. Then in the same way as in the 3D theories system of differential equations in terms of displacements and boundary conditions for Fourier coefficients has been obtained. First approximation theory is considered in more detail. The obtained equations for the first approximation theory are compared with the corresponding equations for Timoshenko's and Kirchhoff-Love's theories. Special case of plates and cylindrical shell is also considered, and corresponding equations in displacements are presented.

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4

Zhang, Zhihua. "Fourier Expansions with Polynomial Terms for Random Processes." Journal of Function Spaces 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/763075.

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Based on calculus of random processes, we present a kind of Fourier expansions with simple polynomial terms via our decomposition method of random processes. Using our method, the expectations and variances of the corresponding coefficients decay fast and partial sum approximations attain the best approximation order. Moreover, since we remove boundary effect in our decomposition of random process, these coefficients can discover the instinct frequency information of this random process. Therefore, our method has an obvious advantage over traditional Fourier expansion. These results are also new for deterministic functions.

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5

Hasanah, Dahliatul. "On continuity properties of the improved conformable fractional derivatives." Jurnal Fourier 11, no. 2 (October 31, 2022): 88–96. http://dx.doi.org/10.14421/fourier.2022.112.88-96.

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The conformable fractional derivative has been introduced to extend the familiar limit definition of the classical derivative. Despite having many advantages compared to other fractional derivatives such as satisfying nice properties as classical derivative and easy to solve numerically, it also has disadvantages as it gives large error compared to Riemann-Liouville and Caputo fractional derivatives. Modified types of conformable derivatives have been proposed to overcome the shortcoming. The improved conformal fractional derivatives are declared to be better approximations of Riemann-Liouville and Caputo derivatives in terms of physical behavior. In this paper, properties concerning continuity of the improved conformable fractional derivative are investigated. We prove the relation between -differentiable and continuity of a function and corresponding interior extremum theorem. We also prove the properties close to Rolle’s Theorem and Mean Value Theorem for the improved conformable fractional derivatives.

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6

Dukhnovsky, Sergey Anatolievich. "Secular Terms for the Kinetic Mckean Model." Differential Equations and Control Processes, no. 1 (2023): 125–36. http://dx.doi.org/10.21638/11701/spbu35.2023.108.

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In this article, we investigate the kinetic McKean model. The perturbed solution of the Cauchy problem is sought in the form of Fourier series. The Fourier coefficients for the zero and nonzero modes are written out, respectively. The original system is reduced to an infinite system of differential equations. An approximation for the systems is constructed. Under certain assumptions, we find secular terms (non-integrable part). This, in turn, will allow us to prove for the first time the exponential stabilization of the solution in the future.

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7

Nunes de Oliveira, João Francisco, Roberta Veloso Garcia, Hélio Koiti Kuga, and Estaner Claro Romão. "Efficiency of Solution Methods for Kepler’s Equation." Applied Mechanics and Materials 851 (August 2016): 587–92. http://dx.doi.org/10.4028/www.scientific.net/amm.851.587.

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This article discusses, in the case of eccentric orbits, some solution methods for Kepler's equation, for instance: Newton's method, Halley method and the solution by Fourire-Bessel expansion. The efficiency of solution methods is evaluated according to the number of iterations that each method needs to lead to a solution within the specified tolerance. The solution using Fourier-Bessel series is not an iterative method, however, it was analyzed the number of terms required to achieve the accuracy of the prescribed solution.

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8

Lü, Baida, Fanlong Kong, and Bin Zhang. "Optical systems expressed in terms of fractional Fourier transforms." Optics Communications 137, no. 1-3 (April 1997): 13–16. http://dx.doi.org/10.1016/s0030-4018(96)00775-4.

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9

Getsadze, Rostom. "Divergence of Spherical General Terms of Double Fourier Series." Journal of Fourier Analysis and Applications 12, no. 5 (October 2006): 597–604. http://dx.doi.org/10.1007/s00041-006-6045-6.

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10

Angelika, Venthy, and Joko Harianto. "Analisis Sensitivitas Model SEIV pada Kasus Penularan Penyakit Polio." Jurnal Fourier 12, no. 2 (October 31, 2023): 60–68. http://dx.doi.org/10.14421/fourier.2023.122.60-68.

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The trend of polio transmission cases until 2023 is still fluctuating and does not tend to decrease monotonically. This incident is important to discuss, especially about the factors that influence cases of polio transmission. One of the studies used to describe the incidence of polio transmission is through mathematical model analysis. One of the mathematical models used to represent the incidence of polio transmission is a dynamic model with the Susceptible-Exposed-Infected-Vaccinated (SEIV) compartment. The SEIV model analyzed in this study involves seven parameters. If the value of each parameter fluctuates, it will affect cases of polio transmission. Therefore, this research aims to analyze the influence of each parameter in the SEIV model on cases of polio transmission. The method used in this research is the literature study method. Secondary data in this study was used to create a SEIV model simulation. The findings of this research are that two parameters have the greatest influence on cases of polio transmission. The infection transmission rate parameter is the most influential parameter in terms of increasing cases of polio transmission because the sensitivity index value is the highest among the other six parameters. Meanwhile, the natural death rate parameter is the parameter that has the most influence on reducing cases of polio transmission. This is because based on the sensitivity index value, the death rate parameter has the lowest sensitivity index value among the other six parameters.

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11

Poizat, Bruno. "Une dualité entre fonctions booléennes." Journal of the Institute of Mathematics of Jussieu 9, no. 3 (April 26, 2010): 633–52. http://dx.doi.org/10.1017/s1474748010000083.

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RésuméSi k est un corps fini, toute fonction f(x1, … , xm) de {0, 1}m dans k s'écrit de manière unique comme un polynôme, à coefficients dans k, de degré un ou zéro en chacune de ses variables ; on peut donc lui associer une fonction f*(x1, … , xm), sa duale inverse, qui exprime les coefficients de son polynôme canonique. Nous considérons l'improbable hypothèse que la classe P(k), formée des suites de fonctions calculables en un nombre d'opérations (additions et multiplications) de croissance polynomialement bornée, soit close par dualité ; nous montrons qu'elle équivaut à une hypothèse bien connue en Théorie de la Complexité sous le nom de P = #pP, où p est la caractéristique de k.Dans une première section, nous exposons ce résultat lorsque k = ℤ/2ℤ, c'est-à-dire dans le cadre des calculs booléens classiques ; sa démonstration évite l'emploi d'un polynôme universel comme le hamiltonien : ses ingrédients sont d'une part la réduction parcimonieuse des circuits aux termes, et d'autre part la constatation que les expressions arithmétiques ont une duale très facile à calculer.Dans la deuxième section, nous traitons le cas général, en introduisant une classe SP(k) obtenue par sommation à partir de la classe P(k) ; nous vérifierons dans la quatrième section l'équivalence des hypothèses SP(k) = P(k) et #pP = P. Nous y définissons également une notion de transformation, dont la dualité est un cas particulier. Les transformations forment un groupe isomorphe à GL2(k), avec un sous-groupe B(k) de transformations que nous qualifions de bénignes, car elles n'ont que peu d'effet sur la complexité des fonctions ; nous montrons que toutes les transformations non-bénignes ont à peu près la même influence sur la complexité des fonctions, sauf si k = F3 ou k = F5 ; dans ces deux cas exceptionnels, la transformation de Fourier joue un rôle particulier.Dans la troisième section, nous considérons des fonctions de km dans k ; nous n'y trouvons pas des classes de complexité vraiment nouvelles, mais seulement un groupe de transformations plus riche.La quatrième section introduit l'égalité #P = P dans le paysage ; quant à la cinquième et dernière, elle examine le lien entre nos résultats et ceux de Guillaume Malod concernant la clôture par fonction-coefficient de diverses classes de complexité pour le calcul des polynômes à la manière de Valiant.Nous nous sommes efforcés de rédiger cet article de manière à ce qu'il puisse être lu par des personnes non spécialisées en algorithmie.

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12

Tang, Cong, Li-Yun Fu, Wenyong Pan, Qingqing Li, and Jianping Huang. "Optimized Pseudo-Padé Fourier Migrator in Terms of Propagation Angles." IEEE Access 8 (2020): 32054–65. http://dx.doi.org/10.1109/access.2020.2973042.

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13

Roginskaya, Maria, and Michal Wojciechowski. "Singularity of Vector Valued Measures in Terms of Fourier Transform." Journal of Fourier Analysis and Applications 12, no. 2 (April 2006): 213–23. http://dx.doi.org/10.1007/s00041-005-5030-9.

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14

Bobkov, S. G. "Proximity of probability distributions in terms of Fourier-Stieltjes transforms." Russian Mathematical Surveys 71, no. 6 (December 31, 2016): 1021–79. http://dx.doi.org/10.1070/rm9749.

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15

Williams, Earl G. "Fourier acoustics: Uncovering the origins of sound." Journal of the Acoustical Society of America 153, no. 3_supplement (March 1, 2023): A208. http://dx.doi.org/10.1121/10.0018675.

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No doubt, Jean-Baptiste Joseph Fourier has had a great impact in science. At the root of Fourier Acoustics, the Fourier series, when employed as a starting point and manipulated, allows us to uncover the origins of sound in a simple and elegant way, not only in acoustics but also in electromagnetics. A well-known stepping stone on the path is nearfield acoustical holography (NAH) and its theory can be recast almost completely, and simply, in terms of two-dimensional (2D) Fourier series and applied to any geometry. For separable coordinate systems, each of the components of the series can be propagated to a surface conformal to the measurement surface using an analytically defined propagator. But even when the surfaces are not part of a separable system, the spirit of Fourier’s expansions is mirrored with the singular value decomposition, applied to a numerically derived propagator constructed using the equivalent source method. A comprehensive demonstration of Fourier acoustics applied to aeroacoustics was in the cabin of a Boeing aircraft, in flight, using a two-dimensional spherical array. Reconstructions of vector intensity in a volume from correlations of the measured pressure to panel accelerometers showed the direction and location of the dominant fuselage sources of noise—uncovering the origin of sound. [Work supported by the Office of Naval Research.]

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16

Wang, Wei, Jianping Yuan, Yanbin Zhao, Zheng Chen, and Changchun Chen. "Fourier Series Approximations toJ2-Bounded Equatorial Orbits." Mathematical Problems in Engineering 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/568318.

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The current paper offers a comprehensive dynamical analysis and Fourier series approximations ofJ2-bounded equatorial orbits. The initial conditions of heterogeneous families ofJ2-perturbed equatorial orbits are determined first. Then the characteristics of two types ofJ2-bounded orbits, namely, pseudo-elliptic orbit and critical circular orbit, are studied. Due to the ambiguity of the closed-form solutions which comprise the elliptic integrals and Jacobian elliptic functions, showing little physical insight into the problem, a new scheme, termed Fourier series expansion, is adopted for approximation herein. Based on least-squares fitting to the coefficients, the solutions are expressed with arbitrary high-order Fourier series, since the radius and the flight time vary periodically as a function of the polar angle. As a consequence, the solutions can be written in terms of elementary functions such as cosines, rather than complex mathematical functions. Simulations enhance the proposed approximation method, showing bounded and negligible deviations. The approximation results show a promising prospect in preliminary orbits design, determination, and transfers for low-altitude spacecrafts.

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17

YAMANE, Hideshi. "Fourier integral representation of harmonic functions in terms of a current." Journal of the Mathematical Society of Japan 54, no. 4 (October 2002): 901–9. http://dx.doi.org/10.2969/jmsj/1191591996.

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18

King, Roy W., and Kathryn R. Williams. "The Fourier transform in chemistry—NMR: A glossary of NMR terms." Journal of Chemical Education 67, no. 4 (April 1990): A100. http://dx.doi.org/10.1021/ed067pa100.

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19

Erden, M. Fatih, David Mendlovic, and Haldun M. Ozaktas. "Propagation of mutual intensity expressed in terms of the fractional Fourier transform." Journal of the Optical Society of America A 13, no. 5 (May 1, 1996): 1068. http://dx.doi.org/10.1364/josaa.13.001068.

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20

Getsadze, Rostom. "On divergence of the general terms of the double Fourier-Haar series." Archiv der Mathematik 86, no. 4 (April 2006): 331–39. http://dx.doi.org/10.1007/s00013-005-1577-6.

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21

Akama, Hachiro. "An extension of the fourier convolution theorem in terms of poisson brackets." Physica A: Statistical Mechanics and its Applications 149, no. 3 (April 1988): 631–37. http://dx.doi.org/10.1016/0378-4371(88)90124-0.

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22

Matlam, Prof Jayprakash, Prof Suniilkumar Shende, and Dr Dipak G. Lanjewar. "Applications of Fourier series and Fourier Transform in Electrical and Electronics Devices." International Journal for Research in Applied Science and Engineering Technology 11, no. 4 (April 30, 2023): 1657–67. http://dx.doi.org/10.22214/ijraset.2023.50376.

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Abstract: Fourier series are of great importance in both theoretical and ap plied mathematics. For orthonormal families of complexvalued functions Fourier Series are sums of the φn that can approximate periodic, complexvalued functions with arbitrary precision. This paper will focus on the Fourier Series of the complex exponentials. Of the many possi ble methods of estimating complexvalued functions, Fourier series are especially attractive because uniform convergence of the Fourier series (as more terms are added) is guaranteed for continuous, bounded functions. Furthermore, the Fourier coefficients are designed to minimize the square of the error from the actual function. Finally, complex exponentials are relatively simple to deal with and ubiquitous in physical phenomena. This paper first defines generalized Fourier series, with an emphasis on the se ries with complex exponentials. Then, important properties of Fourier series are described and proved, and their relevance is explained. A complete example is then given, and the paper concludes by briefly mentioning some of the applications of Fourier series and the generalization of Fourier series, Fourier transforms. In the mideighteenth century, physical problems such as the conduction pat terns of heat and the study of vibrations and oscillations led to the study of Fourier series. Of central interest was the problem of how arbitrary realvalued functions could be represented by sums of simpler functions. As we shall see later, a Fourier series is an infinite sum of trigonometric functions that can be used to model realvalued, periodic functions. We shall begin by giving a brief description of the trigonometric polynomials,and especially of their relation to the complex exponentials. The Fourier series, the founding principle behind the field of Fourier analysis, is an infinite expansion of function in terms sine’s and cosines. Fourier transform provides a continuous complex frequency of a function. It is useful in the study of frequency response of a filter, solution PDE, Discrete Fourier transform and FFT in the signals analysis. The advent of Fourier transformation method has greatly extended our ability to implement Fourier methods on digital multimedia visualization system. It covers the mathematical foundations of Digital signal processing (DSP), classical sound, synthesis algorithms and multi-time frequency domain analysis associated musical sound. In this paper, we are analysis of square wave in terms of Fourier component, may occur in electric circuits designed to handle sharply rising pulses and how to convert analog to digital system by using Fourier transform and its applications in electronics and digital multimedia visualization signal process of communication system.

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23

Zhang, Xindan, and Haoyuan Zheng. "Signal Enhancement Methods Based on Wavelet Transform, Fractional Fourier Transform and Short-time Fourier Transform." Highlights in Science, Engineering and Technology 76 (December 31, 2023): 222–30. http://dx.doi.org/10.54097/eyfndn07.

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This review paper mainly focuses on different signal enhancement methods such as wavelet transform, fractional Fourier transform (FrFT) and short-time Fourier transform (STFT). First, this paper introduces the concept and importance of signal enhancement, as well as some current issues and challenges. Then, in recent years, the application of the three methods in wavelet transform, fractional Fourier transform and short-time Fourier transform is described. In terms of wavelet transform, this paper discusses the application of wavelet function to image enhancement and the specific steps, and analyzes its advantages and application in signal enhancement. In terms of fractional Fourier transform, this paper introduces its difference from traditional Fourier transform, and discusses its application in combination with adaptive filtering technology and the application of multi-level FrFT in the field of speech enhancement. Finally, in terms of short-time Fourier transform, this paper discusses its application in the fields of image enhancement and speech enhancement. The review paper finally discusses the characteristics, advantages and limitations of these three methods in signal enhancement, and looks forward to the future research directions. Through the research of this review paper, it can provide some reference and guidance for the research in the field of signal enhancement.

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24

WANG, RUI, YUESHENG XU, and HAIZHANG ZHANG. "FAST NONLINEAR FOURIER EXPANSIONS." Advances in Adaptive Data Analysis 01, no. 03 (July 2009): 373–405. http://dx.doi.org/10.1142/s1793536909000163.

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Motivated by the analytic signal approach and general construction methods by Qian et al. (accepted by Adv. Comput. Math.), we construct a class of orthonormal bases for the real signal space [Formula: see text], which have nonconstant physically meaningful instantaneous frequencies. We develop a fast algorithm for computing the Hilbert–Fourier expansion of a given function in terms of the orthonormal bases. Moreover, we study the approximation properties of the Hilbert–Fourier expansion. A numerical example is presented to demonstrate an adaptive Fourier expansion based on an optimal selection of the parameter a in the orthonormal bases according to the approximation error.

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25

Strungaru, Nicolae. "On the Fourier Transformability of Strongly Almost Periodic Measures." Canadian Journal of Mathematics 72, no. 4 (January 29, 2019): 900–927. http://dx.doi.org/10.4153/s0008414x19000075.

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AbstractIn this paper we characterize the Fourier transformability of strongly almost periodic measures in terms of an integrability condition for their Fourier–Bohr series. We also provide a necessary and sufficient condition for a strongly almost periodic measure to be the Fourier transform of a measure. We discuss the Fourier transformability of a measure on $\mathbb{R}^{d}$ in terms of its Fourier transform as a tempered distribution. We conclude by looking at a large class of such measures coming from the cut and project formalism.

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26

Ouadih, Salah El, and Radouan Daher. "Characterization of Dini Lipschitz Functions in Terms of Their Helgason Transform." Annals of West University of Timisoara - Mathematics and Computer Science 54, no. 2 (December 1, 2016): 117–30. http://dx.doi.org/10.1515/awutm-2016-0018.

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Abstract In this paper, using a generalized translation operator, we obtain an analog of Younis Theorem 5.2 in [6] for the Helgason Fourier transform of a set of functions satisfying the Dini Lipschitz condition in the space L2 for functions on noncompact rank one Riemannian symmetric spaces.

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27

Belov, A. S., M. I. Dyachenko, and S. Yu Tikhonov. "Functions with general monotone Fourier coefficients." Russian Mathematical Surveys 76, no. 6 (December 1, 2021): 951–1017. http://dx.doi.org/10.1070/rm10003.

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Abstract This paper is a study of trigonometric series with general monotone coefficients in the class with . Sharp estimates are proved for the Fourier coefficients of integrable and continuous functions. Also obtained are optimal results in terms of coefficients for various types of convergence of Fourier series. For two-sided estimates are obtained for the -moduli of smoothness of sums of series with -coefficients, as well as for the (quasi-)norms of such sums in Lebesgue, Lorentz, Besov, and Sobolev spaces in terms of Fourier coefficients. Bibliography: 99 titles.

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28

Kendirli, Barış. "Fourier Coefficients of a Class of Eta Quotients of Weight 4." International Journal of Advanced Mathematical Sciences 4, no. 1 (February 2, 2016): 4. http://dx.doi.org/10.14419/ijams.v4i1.5737.

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<p>Recently, there have been several works on the coefficients of the Fourier series expansions of a class of eta quotients by Williams, Yao, Xia and Jin, Kendirli, and Alaca. Some important explicit formulas have been discovered. Williams expressed all coefficients of one hundred and twenty-six eta quotients in terms of and and Yao, Xia and Jin, following the method of proof of Williams, expressed only even coefficients of one hundred and four eta quotients in terms of and The author has expressed the even and odd coefficients of the Fourier series expansions of a class of eta quotients in terms of and for Meanwhile, Alaca has obtained the coefficients of the Fourier series expansions of a class of eta quotients in in terms of and Here, we will express the coefficients of the Fourier series expansions of a class of eta quotients in in terms of and Fourier coefficients of the four eta quotients.</p>

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29

Kannan, Ravi. "A High Order Spectral Volume Formulation for Solving Equations Containing Higher Spatial Derivative Terms: Formulation and Analysis for Third Derivative Spatial Terms Using the LDG Discretization Procedure." Communications in Computational Physics 10, no. 5 (November 2011): 1257–79. http://dx.doi.org/10.4208/cicp.070710.100111a.

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AbstractIn this paper, we develop a formulation for solving equations containing higher spatial derivative terms in a spectral volume (SV) context; more specifically the emphasis is on handling equations containing third derivative terms. This formulation is based on the LDG (Local Discontinuous Galerkin) flux discretization method, originally employed for viscous equations containing second derivatives. A linear Fourier analysis was performed to study the dispersion and the dissipation properties of the new formulation. The Fourier analysis was utilized for two purposes: firstly to eliminate all the unstable SV partitions, secondly to obtain the optimal SV partition. Numerical experiments are performed to illustrate the capability of this formulation. Since this formulation is extremely local, it can be easily parallelized and a h-p adaptation is relatively straightforward to implement. In general, the numerical results are very promising and indicate that the approach has a great potential for higher dimension Korteweg-de Vries (KdV) type problems.

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30

GERNOTH, K. A. "QUASICLASSICAL FOURIER PATH INTEGRAL QUANTUM CORRECTION TERMS TO THE KINETIC ENERGY OF INTERACTING QUANTUM MANY-BODY SYSTEMS." International Journal of Modern Physics B 23, no. 20n21 (August 20, 2009): 3979–91. http://dx.doi.org/10.1142/s0217979209063201.

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A quasiclassical expression for the kinetic energy of interacting quantum many-body systems is derived from the full quantum expression for the kinetic energy as derived by means of the Fourier path integral representation of the canonical many-body density matrix of such systems. This quasiclassical form of the kinetic energy may be cast in the shape of thermodynamic expectation values w.r.t. to the classical Boltzmann distribution of the many-body system, which involves only the many-body interaction in contrast to the full Fourier path integral quantum distribution, which carries contributions also from the many-body kinetic energy operator. The quasiclassical quantum correction terms to the classical Boltzmann equipartition value are valid when the product of temperature and particle mass is large and then lead to significant technical simplifications and increase of speed of Monte Carlo computations of the quantum kinetic energy. The formal findings are tested numerically in quantum Fourier path integral versus classical Monte Carlo simulations.

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31

QIAN, TAO, and YANBO WANG. "REMARKS ON ADAPTIVE FOURIER DECOMPOSITION." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 01 (January 2013): 1350007. http://dx.doi.org/10.1142/s0219691313500070.

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This is a continuation of the study of adaptive Fourier decomposition (AFD).15 Under a mild condition not in terms of smoothness, a convergence rate is provided. We prove that the selection of the parameters corresponding to Fourier series in the average sense is optimal. We also present the transformation matrices between the adaptive rational orthogonal system and the related sequence of the shifted Cauchy kernels and their derivatives.

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32

Herwig, H., and K. Beckert. "Fourier Versus Non-Fourier Heat Conduction in Materials With a Nonhomogeneous Inner Structure." Journal of Heat Transfer 122, no. 2 (November 17, 1999): 363–65. http://dx.doi.org/10.1115/1.521471.

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Distinct non-Fourier behavior in terms of finite propagation velocity and a hyperbolic wave like character of heat conduction has been reported for certain materials in several studies published recently. However, there is some doubt concerning these findings. The objective of this note is to present experimental evidence for a perfectly Fourier-like behavior of heat conduction in those materials with nonhomogeneous inner structure that have been under investigation in the other studies. This controversy needs to be settled in order to understand the physics of heat conduction in these materials. [S0022-1481(00)00102-X]

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33

Zhao, Tieyu, and Yingying Chi. "Multiweighted-Type Fractional Fourier Transform: Unitarity." Fractal and Fractional 5, no. 4 (November 8, 2021): 205. http://dx.doi.org/10.3390/fractalfract5040205.

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The definition of the discrete fractional Fourier transform (DFRFT) varies, and the multiweighted-type fractional Fourier transform (M-WFRFT) is its extended definition. It is not easy to prove its unitarity. We use the weighted-type fractional Fourier transform, fractional-order matrix and eigendecomposition-type fractional Fourier transform as basic functions to prove and discuss the unitarity. Thanks to the growing body of research, we found that the effective weighting term of the M-WFRFT is only four terms, none of which are extended to M terms, as described in the definition. Furthermore, the program code is analyzed, and the result shows that the previous work (Digit Signal Process 2020: 104: 18) based on MATLAB for unitary verification is inaccurate.

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34

fryant, A., and H. Shankar. "Fourier coefficients and growth of harmonic functions." International Journal of Mathematics and Mathematical Sciences 10, no. 3 (1987): 443–52. http://dx.doi.org/10.1155/s0161171287000528.

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We consider Harmonic Functions,Hof several variables. We obtain necessary and sufficient conditions on its Fourier coefficients so thatHis an entire harmonic (that is, has no finite singularities) function; the radius of harmonicity in terms of its Fourier coefficients in caseHis not entire. Further, we obtain, in terms of its Fourier coefficients, the Order and Type growth measures, both in caseHis entire or non-entire.

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35

Uchiyama, Akihito. "On the Characterization of H p (R n ) in Terms of Fourier Multipliers." Proceedings of the American Mathematical Society 109, no. 1 (May 1990): 117. http://dx.doi.org/10.2307/2048370.

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36

Morales, Y., L. Díaz, and C. Torres. "Radial Hilbert Transform in terms of the Fourier Transform applied to Image Encryption." Journal of Physics: Conference Series 582 (January 14, 2015): 012063. http://dx.doi.org/10.1088/1742-6596/582/1/012063.

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Yu, Dansheng, Ping Zhou, and Songping Zhou. "On determination of jumps in terms of Abel–Poisson mean of Fourier series." Journal of Mathematical Analysis and Applications 341, no. 1 (May 2008): 12–23. http://dx.doi.org/10.1016/j.jmaa.2007.09.055.

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Artamonov, S. Yu. "Quality of approximation by fourier means in terms of general moduli of smoothness." Mathematical Notes 98, no. 1-2 (July 2015): 3–10. http://dx.doi.org/10.1134/s0001434615070019.

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García-Cuerva, José, and Víctor I. Kolyada. "Rearrangement Estimates for Fourier Transforms inLp andHp in Terms of Moduli of Continuity." Mathematische Nachrichten 228, no. 1 (August 2001): 123–44. http://dx.doi.org/10.1002/1522-2616(200108)228:1<123::aid-mana123>3.0.co;2-a.

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Maksimovic, Snjezana, Stevan Pilipovic, Petar Sokoloski, and Jasson Vindas. "Wave fronts via Fourier series coefficients." Publications de l'Institut Math?matique (Belgrade) 97, no. 111 (2015): 1–10. http://dx.doi.org/10.2298/pim150107001m.

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Stokke, Ross. "Amenable representations and coefficient subspaces of Fourier-Stieltjes algebras." MATHEMATICA SCANDINAVICA 98, no. 2 (June 1, 2006): 182. http://dx.doi.org/10.7146/math.scand.a-14990.

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Amenable unitary representations of a locally compact group, $G$, are studied in terms of associated coefficient subspaces of the Fourier-Stieltjes algebra $B(G)$, and in terms of the existence of invariant and multiplicative states on associated von Neumann and $C^*$-algebras. We introduce Fourier algebras and reduced Fourier-Stieltjes algebras associated to arbitrary representations, and study amenable representations in relation to these algebras.

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Toscani, Giuseppe. "On Fourier-Based Inequality Indices." Entropy 24, no. 10 (September 29, 2022): 1393. http://dx.doi.org/10.3390/e24101393.

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Inequality indices are quantitative scores that take values in the unit interval, with a zero score denoting complete equality. They were originally created to measure the heterogeneity of wealth metrics. In this study, we focus on a new inequality index based on the Fourier transform that demonstrates a number of intriguing characteristics and shows great potential for applications. By extension, it is demonstrated that other inequality measures, such as the Gini and Pietra indices, can be usefully stated in terms of the Fourier transform, allowing us to illuminate characteristics in a novel and straightforward manner.

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Gogoladze, L. "On Estimating Integral Moduli of Continuity of Functions of Several Variables in Terms of Fourier Coefficients." gmj 6, no. 4 (August 1999): 307–22. http://dx.doi.org/10.1515/gmj.1999.307.

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Jena, Bidu Bhusan, Susanta Kumar Paikray, and Umakanta Misra. "Strong Riesz summability of Fourier series." Proyecciones (Antofagasta) 39, no. 6 (December 1, 2020): 1615–26. http://dx.doi.org/10.22199/issn.0717-6279-2020-06-0096.

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The notion of strong summability was introduced by Fekete (Math. És Termesz Ertesitö, 34 (1916), 759-786). Dealing with Nörlund summability of Fourier series Mittal (J. Math. Anal. Appl. 314 (2006), 75-84) has established a result on strong summability. We have established a new result on sufficient condition for strong Riesz summability of Fourier series.

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Manjarekar, S. D., and A. P. Bhadane. "Approximations to the Solution of R-L Space Fractional Heat Equation in Terms of Kummers Hyper Geometric Functions by Using Fourier Transform Method: A New Approach." International Journal of Advanced Research in Mathematics 5 (June 2016): 32–34. http://dx.doi.org/10.18052/www.scipress.com/ijarm.5.32.

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The purpose of this paper is to give applications of Fourier Transform to solve the Riemann – Liouville Space Fractional Heat equation by using Fourier Transform Method approximated by Kummers Hyper geometric functions.

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Lynes, JA. "Fourier components of cylindrical illuminance." Lighting Research & Technology 51, no. 8 (March 21, 2019): 1224–36. http://dx.doi.org/10.1177/1477153519837317.

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Fourier analysis is applied to the profile of illuminance around the curved surface of a small cylinder, due to one, two and three point sources of light and due to an extended source. This reveals only one odd harmonic, whose amplitude is equal to half that of the illumination vector. Lighting can also generate a diminishing series of even harmonics. The lighting at any point in open space can be expressed in terms of the harmonics of illuminance around three mutually perpendicular cylinders. Visual discomfort is often associated with the presence of even harmonics. The photometry of cylindrical and semi-cylindrical illuminance, and of cylindrical harmonics, is discussed.

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Rizvi, Saad, Jie Cao, Kaiyu Zhang, and Qun Hao. "Improving Imaging Quality of Real-time Fourier Single-pixel Imaging via Deep Learning." Sensors 19, no. 19 (September 27, 2019): 4190. http://dx.doi.org/10.3390/s19194190.

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Fourier single pixel imaging (FSPI) is well known for reconstructing high quality images but only at the cost of long imaging time. For real-time applications, FSPI relies on under-sampled reconstructions, failing to provide high quality images. In order to improve imaging quality of real-time FSPI, a fast image reconstruction framework based on deep learning (DL) is proposed. More specifically, a deep convolutional autoencoder network with symmetric skip connection architecture for real time 96 × 96 imaging at very low sampling rates (5–8%) is employed. The network is trained on a large image set and is able to reconstruct diverse images unseen during training. The promising experimental results show that the proposed FSPI coupled with DL (termed DL-FSPI) outperforms conventional FSPI in terms of image quality at very low sampling rates.

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CRUZ JORDÁN., VANESA, FERNANDO MONCAYO ANASLEMA, and MARCIA BELTRAN ALEJANDRO. "GANGRENA DE FOURNIER COMPLICADA, EN HOSPITAL DE TERCER NIVEL." REVISTA FACULTAD DE CIENCIAS MÉDICAS 3, no. 2 (November 18, 2022): 26–31. http://dx.doi.org/10.53591/revfcm.v3i2.1820.

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Es un proceso infeccioso potencialmente fatal, súbito, progresiva, de etiología multibacteriana, pero de baja virulencia (E. coli, Klebsiella, Proteus, Staphylococco, clostridium, bacteroides, fusobacterium, etc) que provoca afección de tejido celular subcutáneo, fascias y piel (fascitis necrotizante) de la región perineal y genitales. Es poco frecuente pero su condición se incrementa en pacientes inmunocomprometidos, diabetes (disminución de fagocitosis y quimiotaxis), neoplasias, alcoholismo, insuficiencia renal, desnutrición, obesidad, terapias crónicas con corticoides, donde las bacterias se vuelven muy agresivas y destructivas de tejidos, llegando a provoca cuadro sistémico como shock séptico que compromete la vida. El origen por lo común es un absceso perianal, fistulas anales, lesiones rectales, hemorroides, o ligaduras de hemorroides, ulceras por presión, episiotomía en las mujeres, bartolinitis, etc. El presente trabajo incluyó 4 casos para su análisis. La edad promedio de los pacientes fue de 56 años de edad (rango de 33 – 83 años), 4 pacientes tenían algún antecedente patológico personal. Entre los factores de riesgo que presentaban fue la diabetes mellitus todos 4 pacientes; de estos 1 con cáncer anal en quimioterapia, 1 con obesidad mórbida, hipertensión con insuficiencia respiratoria restrictiva, 1 con hernia inguino escrotal encarcelada más insuficiencia renal crónica y doble amputación de extremidades inferiores (imposibilidad para la deambulación) y 1 con ruptura de uretra traumática por sondaje más insuficiencia renal crónica y ecv con imposibilidad para la deambulación.

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Gourevitch, Dmitry, Henrik P. A. Gustafsson, Axel Kleinschmidt, Daniel Persson, and Siddhartha Sahi. "A reduction principle for Fourier coefficients of automorphic forms." Mathematische Zeitschrift 300, no. 3 (October 15, 2021): 2679–717. http://dx.doi.org/10.1007/s00209-021-02784-w.

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AbstractWe consider a special class of unipotent periods for automorphic forms on a finite cover of a reductive adelic group $$\mathbf {G}(\mathbb {A}_\mathbb {K})$$ G ( A K ) , which we refer to as Fourier coefficients associated to the data of a ‘Whittaker pair’. We describe a quasi-order on Fourier coefficients, and an algorithm that gives an explicit formula for any coefficient in terms of integrals and sums involving higher coefficients. The maximal elements for the quasi-order are ‘Levi-distinguished’ Fourier coefficients, which correspond to taking the constant term along the unipotent radical of a parabolic subgroup, and then further taking a Fourier coefficient with respect to a $${\mathbb K}$$ K -distinguished nilpotent orbit in the Levi quotient. Thus one can express any Fourier coefficient, including the form itself, in terms of higher Levi-distinguished coefficients. In companion papers we use this result to determine explicit Fourier expansions of minimal and next-to-minimal automorphic forms on split simply-laced reductive groups, and to obtain Euler product decompositions of certain Fourier coefficients.

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LI, WENXIN, DAVID ZHANG, and ZHUOQUN XU. "PALMPRINT IDENTIFICATION BY FOURIER TRANSFORM." International Journal of Pattern Recognition and Artificial Intelligence 16, no. 04 (June 2002): 417–32. http://dx.doi.org/10.1142/s0218001402001757.

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Palmprint identification refers to searching in a database for the palmprint template, which is from the same palm as a given palmprint input. The identification process involves preprocessing, feature extraction, feature matching and decision-making. As a key step in the process, in this paper, we propose a new feature extraction method by converting a palmprint image from a spatial domain to a frequency domain using Fourier Transform. The features extracted in the frequency domain are used as indexes to the palmprint templates in the database and the searching process for the best match is conducted by a layered fashion. The experimental results show that palmprint identification based on feature extraction in the frequency domain is effective in terms of accuracy and efficiency.

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