Relevant bibliographies by topics / Sum Fourier

Academic literature on the topic 'Sum Fourier'

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Published: 30 May 2022
Last updated: 31 May 2022

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Journal articles on the topic "Sum Fourier"

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Leindler, László. "Relations among Fourier coefficients and sum-functions." Acta Mathematica Hungarica 104, no. 1/2 (2004): 171–83. http://dx.doi.org/10.1023/b:amhu.0000034370.78464.82.

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Yu, Dansheng, and Songping Zhou. "On relations among Fourier coefficients and sum-functions." Studia Scientiarum Mathematicarum Hungarica 45, no. 3 (September 1, 2008): 301–19. http://dx.doi.org/10.1556/sscmath.2008.1052.

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Maidanik, G., and K. J. Becker. "Double-sum technique for performing a Fourier transformation." Journal of the Acoustical Society of America 101, no. 5 (May 1997): 2448–51. http://dx.doi.org/10.1121/1.418487.

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Chen, Chang-Pao. "L1-convergence of Fourier series." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 41, no. 3 (December 1986): 376–90. http://dx.doi.org/10.1017/s144678870003384x.

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AbstractFor an integrable function f on T, we introduce a modified partial sum and establish its L1-convergence property. The relation between the sum and L1-convergence classes is also established. As a corollary, a new L1-convergence class is obtained. It is shown that this class covers all known L1-convergence classes.
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Albu_Amer, Ansam Ghazi Nsaif. "Mathematical Analysis of Fourier Expansion Using Gauss Partial Sum." IOP Conference Series: Materials Science and Engineering 571 (August 8, 2019): 012033. http://dx.doi.org/10.1088/1757-899x/571/1/012033.

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Sankaranarayanan, A. "On a sum involving Fourier coefficients of cusp forms." Lithuanian Mathematical Journal 46, no. 4 (October 2006): 459–74. http://dx.doi.org/10.1007/s10986-006-0042-y.

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Alotaibi, Abdullah, and M. Mursaleen. "Applications of Hankel and Regular Matrices in Fourier Series." Abstract and Applied Analysis 2013 (2013): 1–3. http://dx.doi.org/10.1155/2013/947492.

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Recently, Alghamdi and Mursaleen (2013) used the Hankel matrix to determine the necessary and suffcient condition to find the sum of the Walsh-Fourier series. In this paper, we propose to use the Hankel matrix as well as any general nonnegative regular matrix to obtain the necessary and sufficient conditions to sum the derived Fourier series and conjugate Fourier series.
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Li, Bing-Zhao, Ran Tao, Tian-Zhou Xu, and Yue Wang. "The Poisson sum formulae associated with the fractional Fourier transform." Signal Processing 89, no. 5 (May 2009): 851–56. http://dx.doi.org/10.1016/j.sigpro.2008.10.030.

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McGuire, J. A., W. Beck, X. Wei, and Y. R. Shen. "Fourier-transform sum-frequency surface vibrational spectroscopy with femtosecond pulses." Optics Letters 24, no. 24 (December 15, 1999): 1877. http://dx.doi.org/10.1364/ol.24.001877.

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Shparlinski, Igor E. "Bounds on the Fourier coefficients of the weighted sum function." Information Processing Letters 103, no. 3 (July 2007): 83–87. http://dx.doi.org/10.1016/j.ipl.2007.02.011.

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Dissertations / Theses on the topic "Sum Fourier"

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Müllner, Clemens. "Exponential sum estimates and Fourier analytic methods for digitally based dynamical systems." Thesis, Aix-Marseille, 2017. http://www.theses.fr/2017AIXM0042/document.

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La présente thèse a été fortement influencée par deux conjectures, l'une de Gelfond et l'autre de Sarnak.En 1968, Gelfond a prouvé que la somme des chiffres modulo m est asymtotiquement équirépartie dans des progressions arithmétiques, et il a formulé trois problèmes nouveaux.Le deuxième et le troisième problèmes traitent des sommes des chiffres pour les nombres premiers et les suites polynomiales.En ce qui concerne les nombres premiers et les carrés, Mauduit et Rivat ont résolu ces problèmes en 2010 et 2009, respectivement.Drmota, Mauduit et Rivat ont réussi généraliser le résultat concernant la suite des sommes des chiffres des carrés.Ils ont démontré que chaque bloc apparaît asymptotiquement avec la même fréquence.Selon la conjecture de Sarnak, il n'y a pas de corrélation entre la fonction de Möbius et des fonctions simples.La présente thèse traite de la répartition de suites automatiques le long de sous-suites particulières ainsi que d'autres propriétés de suites automatiques.Selon l'un des résultats principaux du présent travail, toutes les suites automatiques vérifient la conjecture de Sarnak.Moyennant une approche légèrement modifiée, nous traitons également la répartition de suites automatiques le long de la suite des nombres premiers.Dans le cadre du traitement de suites automatiques générales, nous avons mis au point une nouvelle structure destinée aux automates finisdéterministes ouvrant une vision nouvelle pour les automates et/ou les suites automatiques.Nous étendons les résultat de Drmota, Mauduit et Rivat concernant les suites digitales.Cette approche peut également être considérée comme une généralisation du troisième problème de Gelfond
The present dissertation was inspired by two conjectures, one by Gelfond and one of Sarnak.In 1968 Gelfond proved that the sum of digits modulo m is asymptotically equally distributed along arithmetic progressions.Furthermore, he stated three problems which are nowadays called Gelfond problems.The second and third questions are concerned with the sum of digits of prime numbers and polynomial subsequences.Mauduit and Rivat were able to solve these problems for primes and squares in 2010 and 2009 respectively.Drmota, Mauduit and Rivat generalized the result concerning the sequence of the sum of digits of squares.They showed that each block appears asymptotically equally frequently.Sarnak conjectured in 2010 that the Mobius function does not correlate with deterministic functions.This dissertation deals with the distribution of automatic sequences along special subsequences and other properties of automatic sequences.A main result of this thesis is that all automatic sequences satisfy the Sarnak conjecture.Through a slightly modified approach, we also deal with the distribution of automatic sequences along the subsequence of primes.In the course of the treatment of general automatic sequences, a new structure for deterministic finite automata is developed,which allows a new view for automata or automatic sequences.We extend the result of Drmota, Mauduit and Rivat to digital sequences.This is also a generalization of the third Gelfond problem
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Литвин, О. М., and О. Г. Литвин. "Оптимізація кількості експериментальних даних у методі обчислення коефіцієнтів Фур’є за допомогою проекцій." Thesis, Полтава: ПУЕТ, 2017. http://openarchive.nure.ua/handle/document/3813.

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Досліджується метод розв’язання задачі реконструкції зображень на основі використання скінченних сум Фур’є, запропонований автором Литвин О. М., в якому коефіцієнти Фур’є обчислюються за допомогою проекцій, що надходять з комп’ютерного томографа. Отримано співвідношення між порядком сум Фур’є, кількістю проекцій та точністю відновлення функції. Litvin O.M., Litvin O.G .Optimizing the number of experimental data in the method of calculating Fourier coefficients using projections.We study the method of solving the problem of image reconstruction based on the use of finite Fourier sums proposed by the author O.M. Litvin, where the Fourier coefficients are calculated using projections coming from the computer tomograph. Correlations between order Fourier sums, the number of projections and accurate restoration of function are given.
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Ravindran, Hari Alangat. "On Shifted Convolution Sums Involving the Fourier Coefficients of Theta Functions Attached to Quadratic Forms." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1406039690.

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McGuire, John Andrew. "Femtosecond nonlinear spectroscopy at surfaces Second-harmonic probing of hole burning at the Si(111)7x7 surface and fourier-transform sum-frequency vibrational spectroscopy." Berkeley, Calif. : Oak Ridge, Tenn. : Lawrence Berkeley National Laboratory ; distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy, 2004. http://www.osti.gov/servlets/purl/836810-xRj01W/native/.

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Thesis (Ph.D.); Submitted to the University of California, Berkeley, CA (US); 24 Nov 2004.
Published through the Information Bridge: DOE Scientific and Technical Information. "LBNL--56751" McGuire, John Andrew. USDOE Director. Office of Science. Office of Basic Energy Sciences. Materials Science and Engineering Division (US) 11/24/2004. Report is also available in paper and microfiche from NTIS.
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Xu, Yangyi. "Frequentist-Bayesian Hybrid Tests in Semi-parametric and Non-parametric Models with Low/High-Dimensional Covariate." Diss., Virginia Tech, 2014. http://hdl.handle.net/10919/71285.

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We provide a Frequentist-Bayesian hybrid test statistic in this dissertation for two testing problems. The first one is to design a test for the significant differences between non-parametric functions and the second one is to design a test allowing any departure of predictors of high dimensional X from constant. The implementation is also given in construction of the proposal test statistics for both problems. For the first testing problem, we consider the statistical difference among massive outcomes or signals to be of interest in many diverse fields including neurophysiology, imaging, engineering, and other related fields. However, such data often have nonlinear system, including to row/column patterns, having non-normal distribution, and other hard-to-identifying internal relationship, which lead to difficulties in testing the significance in difference between them for both unknown relationship and high-dimensionality. In this dissertation, we propose an Adaptive Bayes Sum Test capable of testing the significance between two nonlinear system basing on universal non-parametric mathematical decomposition/smoothing components. Our approach is developed from adapting the Bayes sum test statistic by Hart (2009). Any internal pattern is treated through Fourier transformation. Resampling techniques are applied to construct the empirical distribution of test statistic to reduce the effect of non-normal distribution. A simulation study suggests our approach performs better than the alternative method, the Adaptive Neyman Test by Fan and Lin (1998). The usefulness of our approach is demonstrated with an application in the identification of electronic chips as well as an application to test the change of pattern of precipitations. For the second testing problem, currently numerous statistical methods have been developed for analyzing high-dimensional data. These methods mainly focus on variable selection approach, but are limited for purpose of testing with high-dimensional data, and often are required to have explicit derivative likelihood functions. In this dissertation, we propose ``Hybrid Omnibus Test'' for high-dimensional data testing purpose with much less requirements. Our Hybrid Omnibus Test is developed under semi-parametric framework where likelihood function is no longer necessary. Our Hybrid Omnibus Test is a version of Freqentist-Bayesian hybrid score-type test for a functional generalized partial linear single index model, which has link being functional of predictors through a generalized partially linear single index. We propose an efficient score based on estimating equation to the mathematical difficulty in likelihood derivation and construct our Hybrid Omnibus Test. We compare our approach with a empirical likelihood ratio test and Bayesian inference based on Bayes factor using simulation study in terms of false positive rate and true positive rate. Our simulation results suggest that our approach outperforms in terms of false positive rate, true positive rate, and computation cost in high-dimensional case and low-dimensional case. The advantage of our approach is also demonstrated by published biological results with application to a genetic pathway data of type II diabetes.
Ph. D.
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Li, Jialun. "Harmonic analysis of stationary measures." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0311/document.

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Soit μ une mesure de probabilité borélienne sur SL m+1 (R) tel que le sous-groupe engendré par le support de μ est Zariski dense. Soit V une représentation irréductible de dimension finie de SL m+1 (R). D’après un théorème de Furstenberg, il existe une unique mesure μ-stationnaire sur PV et nous nous somme intéressés à la décroissance de Fourier de cette mesure. Le résultat principal de cette thèse est que la transformée de Fourier de la mesure stationnaire a une décroissance polynomiale. À partir de ce résultat, nous obtenons un trou spectral de l’opérateur de transfert, dont les propriétés nous permettent d’établir un terme d’erreur exponentiel pour le théorème de renouvellement dans le cadre des produits de matrices aléatoires. L’ingrédient essentiel est une propriété de décroissance de Fourier des convolutions multiplicatives de mesures sur R n , qui est une généralisation d’un théorème de Bourgain en dimension 1. Nous établissons cet ingrédient en utilisant un estimée somme produit de He et de Saxcé.Dans la dernière partie, nous généralisons un résultat de Lax et Phillips et un résultat de Hamenstädt sur la finitude des petites valeurs propres de l’opérateur de Laplace sur les variétés hyperboliques géométriquement finies
Let μ be a Borel probability measure on SL m+1 (R), whose support generates a Zariski dense subgroup. Let V be a finite dimensional irreducible linear representation of SL m+1 (R). A theorem of Furstenberg says that there exists a unique μ-stationary probability measure on PV and we are interested in the Fourier decay of the stationary measure. The main result of the thesis is that the Fourier transform of the stationary measure has a power decay. From this result, we obtain a spectral gap of the transfer operator, whose properties allow us to establish an exponential error term for the renewal theorem in the context of products of random matrices. A key technical ingredient for the proof is a Fourier decay of multiplicative convolutions of measures on R n , which is a generalisation of Bourgain’s theorem on dimension 1. We establish this result by using a sum-product estimate due to He-de Saxcé. In the last part, we generalize a result of Lax-Phillips and a result of Hamenstädt on the finiteness of small eigenvalues of the Laplace operator on geometrically finite hyperbolic manifolds
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Abolarin, David. "Non-invasive Estimation of Blood Pressure using Harmonic Components of Oscillometric Pulses." Thesis, Université d'Ottawa / University of Ottawa, 2016. http://hdl.handle.net/10393/34114.

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This research presents a pulse-by-pulse analysis of Oscillometric blood pressure waveform at systolic, diastolic and mean arterial pressure points. Using a mathematical optimization technique, pulses are characterized into component harmonic by minimizing the least square error. The results at the important pressure points are analyzed and compared for different subject using different waveform extraction techniques. Blood pressure is estimated using the harmonic parameters. The approach studies changes in the parameters as oscillometric blood pressure recording is done. 8 harmonic parameters are obtained from the pulse characterization and are used to estimate Systolic arterial Blood Pressure, Mean arterial Blood Pressure, and Diastolic arterial Blood Pressure. The estimates are compared with our reference value to determine which has the best agreement. The proposed method is further compared with Maximum Amplitude Algorithm and Pulse Morphology Algorithm. The effect of oscillometric waveform extraction methods on the proposed method is observed. The experiment established the fact that the extraction technique can alter the shape of oscillometric pulses. The methods were compared and it was observed that the used extraction methods did not make any significant difference on the accuracy, using this technique.
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Del, Gatto Davide. "Analisi di Fourier sui Gruppi." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18784/.

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La tesi riguarda la generalizzazione della trasformata di Fourier per funzioni di L^1(G), dove G è un gruppo topologico localmente compatto e di Hausdroff. L'obbiettivo è di mostrare che i risultati noti per la trasformata di Fourier (come il Teorema di Inversione, il Teorema di Plancherel, ecc...) sono validi anche in questo caso e di presentare alcuni risultati classici di analisi armonica astratta nel caso di gruppi abeliani come il Teorema di Dualità di Pontryagin.
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Noorizadeh, Sahand. "SLM-based Fourier Differential Interference Contrast Microscopy." PDXScholar, 2014. https://pdxscholar.library.pdx.edu/open_access_etds/2011.

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Optical phase microscopy provides a view of objects that have minimal to no effect on the detected intensity of light that are unobservable by standard microscopy techniques. Since its inception just over 60 years ago that gave us a vision to an unseen world and earned Frits Zernike the Nobel prize in physics in 1953, phase microscopy has evolved to find various applications in biological cell imaging, crystallography, semiconductor failure analysis, and more. Two common and commercially available techniques are phase contrast and differential interference contrast (DIC). In phase contrast method, a large portion of the unscattered light that accounts for the majority of the light passing unaffected through a transparent medium is blocked to allow the scattered light due to the object to be observed with higher contrast. DIC is a self-referenced interferometer that transduces phase variation to intensity variation. While being established as fundamental tools in many scientific and engineering disciplines, the traditional implementation of these techniques lacks the ability to provide the means for quantitative and repeatable measurement without an extensive and cumbersome calibration. The rapidly growing fields in modern biology meteorology and nano-technology have emphasized the demand for a more robust and convenient quantitative phase microscopy. The recent emergence of modern optical devices such as high resolution programmable spatial light modulators (SLM) has enabled a multitude of research activities over the past decade to reinvent phase microscopy in unconventional ways. This work is concerned with an implementation of a DIC microscope containing a 4-f system at its core with a programmable SLM placed at the frequency plane of the imaging system that allows for employing Fourier pair transforms for wavefront manipulation. This configuration of microscope provides a convenient way to perform both wavefront shearing with quantifiable arbitrary shear amount and direction as well as phase stepping interferometry by programming the SLM with a series of numerically generated patterns and digitally capturing interferograms for each step which are then used to calculate the objects phase gradient map. Wavefront shearing is performed by generating a pattern for the SLM where two phase ramp patterns with opposite slopes are interleaved through a random selection process with uniform distribution in order to mimic the simultaneous presence of the ramps on the same plane. The theoretical treatment accompanied by simulations and experimental results and discussion are presented in this work.
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Potts, Daniel, and Manfred Tasche. "Parameter estimation for nonincreasing exponential sums by Prony-like methods." Universitätsbibliothek Chemnitz, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-86476.

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For noiseless sampled data, we describe the close connections between Prony--like methods, namely the classical Prony method, the matrix pencil method and the ESPRIT method. Further we present a new efficient algorithm of matrix pencil factorization based on QR decomposition of a rectangular Hankel matrix. The algorithms of parameter estimation are also applied to sparse Fourier approximation and nonlinear approximation.
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Books on the topic "Sum Fourier"

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Gottlieb, David. On the Gibbs phenomenon III: Recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.

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Gottlieb, David. On the Gibbs phenomenon 1: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function. Hampton, Va: Institute for Computer Applications in Science and Engineering, 1992.

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service), SpringerLink (Online, ed. Classical Summation in Commutative and Noncommutative Lp-Spaces. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2011.

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méditerranéennes, Université Joseph Fourier Centre d'études et de recherches sur les montagnes sèches. Centre d'études et de recherches sur les montagnes sèches et méditerranéennes (CERMOSEM). Villeneuve de-Berg: Université Joseph Fourier Grenoble I, CERMOSEM, 1994.

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Schurz, Henri, Philip J. Feinsilver, Gregory Budzban, and Harry Randolph Hughes. Probability on algebraic and geometric structures: International research conference in honor of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea, June 5-7, 2014, Southern Illinois University, Carbondale, Illinois. Edited by Mohammed Salah-Eldin 1946- and Mukherjea Arunava 1941-. Providence, Rhode Island: American Mathematical Society, 2016.

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David, Gottlieb, and Langley Research Center, eds. On the Gibbs phenomenon I: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1992.

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Allen, Michael P., and Dominic J. Tildesley. Long-range forces. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198803195.003.0006.

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A wide variety of special techniques for handling long-range forces are explained in this chapter. This includes the traditional Ewald sum, and the particle-mesh methods that use a discrete Fourier transform. A number of techniques based on spherical truncation such as the Wolf method, the isotropic periodic sum and the reaction field are also considered. Techniques for larger systems such as the fast-multipole method, the multilevel summation approach, and the direct solution of Maxwell’s equations, are explained. The advantages and disadvantages of the different approaches are reviewed, and a number of methods for tackling long-range forces in inhomogeneous systems, particularly in a slab geometry, are presented.
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Higher order Fourier analysis. 2012.

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F, Geer James, and Langley Research Center, eds. Exponential approximations using fourier series partial sums. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1997.

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125 Fournier: 1867-1992. Hawkesbury, Ont: N. Parker, 1992.

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Book chapters on the topic "Sum Fourier"

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Tymoczko, Dmitri, and Jason Yust. "Fourier Phase and Pitch-Class Sum." In Mathematics and Computation in Music, 46–58. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-21392-3_4.

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Sheng, Gong. "Partial Sum of Fourier Series on Unitary Groups." In Harmonic Analysis on Classical Groups, 65–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-58189-2_4.

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Sheng, Gong. "Partial Sum of Fourier Series on Rotation Groups." In Harmonic Analysis on Classical Groups, 155–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-642-58189-2_9.

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Grynkiewicz, David J. "Character Sum and Fourier Analytic Methods: r-Critical Pairs I." In Structural Additive Theory, 279–98. Heidelberg: Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-00416-7_19.

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Jiang, Zhongyu, Yajun Zhang, Huaqing Liu, and Xuanxuan Li. "Symplectic Elastic Solution of Multi-layer Thick-Walled Cylinder Under Different Interlayer Constraints." In Lecture Notes in Civil Engineering, 238–53. Singapore: Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-19-1260-3_21.

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AbstractMulti-layer thick-walled cylinder is a common supporting structure in engineering, which is widely used in various engineering fields. Considering the complex boundary conditions and the different interlayer constraints, it is difficult to solve the theoretical solution of multi-layer thick walled cylinder. In this paper, the general solution expressions of displacement and stress of multi-layer thick-walled cylinder are derived in Hamiltonian mechanics system. The complex boundary conditions are transformed into the form of algebraic sum by Fourier series expansion, and the complex boundary problems are solved by superimposing the special solutions of each order expansion term. At the same time, according to the characteristics of different interlayer constraints, the corresponding conditions of interlayer continuous smooth are proposed. Combined with the boundary conditions of thick-walled cylinder, the linear equations with undetermined coefficients are established. By solving the equations, the mechanical problems of multi-layer thick-walled cylinder are finally solved. By comparing the mechanical responses of multi-layer thick-walled cylinder under different constraint conditions, it is concluded that the overall mechanical performance of the tight interlayer connection is better, and the circumfluence stress component is more prominent than other stress components. Finally, the influence of lateral pressure coefficient and elastic modulus ratio on the circumferential stress of multi-layer thick-walled cylinder is discussed. These research results provide the necessary theoretical basis for solving the mechanical problems of multi-layer thick-walled cylinders.
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Calin, Ovidiu, Der-Chen Chang, Kenro Furutani, and Chisato Iwasaki. "The Fourier Transform Method." In Heat Kernels for Elliptic and Sub-elliptic Operators, 75–88. Boston: Birkhäuser Boston, 2010. http://dx.doi.org/10.1007/978-0-8176-4995-1_5.

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Boyd, John P. "A Proof, Based on the Euler Sum Acceleration, of the Recovery of an Exponential (Geometric) Rate of Convergence for the Fourier Series of a Function with Gibbs Phenomenon." In Lecture Notes in Computational Science and Engineering, 131–39. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-15337-2_10.

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Petzelt, Jan, Vladimir Železný, Stanislav Kamba, Ilja Fedorov, and Filip Kadlec. "Quantitative Infrared and Sub-millimetre Spectroscopy of Dielectric Single Crystals, Ceramics and Thin Films." In Progress in Fourier Transform Spectroscopy, 305–6. Vienna: Springer Vienna, 1997. http://dx.doi.org/10.1007/978-3-7091-6840-0_67.

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Metral, E., G. Rumolo, and W. Herr. "Impedance and Collective Effects." In Particle Physics Reference Library, 105–81. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-34245-6_4.

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AbstractAs the beam intensity increases, the beam can no longer be considered as a collection of non-interacting single particles: in addition to the “single-particle phenomena”, “collective effects” become significant. At low intensity a beam of charged particles moves around an accelerator under the Lorentz force produced by the “external” electromagnetic fields (from the guiding and focusing magnets, RF cavities, etc.). However, the charged particles also interact with themselves (leading to space charge effects) and with their environment, inducing charges and currents in the surrounding structures, which create electromagnetic fields called wake fields. In the ultra-relativistic limit, causality dictates that there can be no electromagnetic field in front of the beam, which explains the term “wake”. It is often useful to examine the frequency content of the wake field (a time domain quantity) by performing a Fourier transformation on it. This leads to the concept of impedance (a frequency domain quantity), which is a complex function of frequency. The charged particles can also interact with other charged particles present in the accelerator (leading to two-stream effects, and in particular to electron cloud effects in positron/hadron machines) and with the counter-rotating beam in a collider (leading to beam–beam effects). As the beam intensity increases, all these “perturbations” should be properly quantified and the motion of the charged particles will eventually still be governed by the Lorentz force but using the total electromagnetic fields, which are the sum of the external and perturbation fields. Note that in some cases a perturbative treatment is not sufficient and the problem has to be solved self consistently. These perturbations can lead to both incoherent (i.e. of a single particle) and coherent (i.e. of the centre of mass) effects, in the longitudinal and in one or both transverse directions, leading to beam quality degradation or even partial or total beam losses. Fortunately, stabilising mechanisms exist, such as Landau damping, electronic feedback systems and linear coupling between the transverse planes (as in the case of a transverse coherent instability, one plane is usually more critical than the other).
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Trzcińska, Beata M., and Zuzanna Brożek-Mucha. "The Possibilities of Identifying Photocopy Toners by Means of Infrared Spectroscopy (FT-IR) and Scanning Microscopy (SEM-EDX)." In Progress in Fourier Transform Spectroscopy, 235–37. Vienna: Springer Vienna, 1997. http://dx.doi.org/10.1007/978-3-7091-6840-0_43.

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Conference papers on the topic "Sum Fourier"

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Ji, Bing, Shengsuo Niu, Zhirui Liang, Yuyang Miao, and Danye Wu. "Fast Fourier transform harmonic analysis based on nine terms minimum side-lobe cosine-sum window." In 2012 Power Engineering and Automation Conference (PEAM). IEEE, 2012. http://dx.doi.org/10.1109/peam.2012.6612417.

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Zheng, Xiang Yuan, Torgeir Moan, and Ser Tong Quek. "Numerical Simulation of Non-Gaussian Wave Elevation and Kinematics Based on Two-Dimensional Fourier Transform." In 25th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/omae2006-92014.

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The one-dimensional Fast Fourier Transform (FFT) has been extensively applied to efficiently simulate Gaussian wave elevation and water particle kinematics. The actual sea elevation/kinematics exhibit non-Gaussianities that mathematically can be represented by the second-order random wave theory. The elevation/kinematics formulation contains double-summation frequency sum and difference terms which in computation make the dynamic analysis of offshore structural response prohibitive. This study aims at a direct and efficient two-dimensional FFT algorithm for simulating the frequency sum terms. For the frequency difference terms, inverse FFT and FFT are respectively implemented across the two dimensions of the wave interaction matrix. Given specified wave conditions, not only the wave elevation but kinematics and associated Morison force are simulated. Favorable agreements are achieved when the statistics of elevation/kinematics are compared with not only the empirical fits but the analytical solutions developed based on modified eigenvalue/eigenvector approach, while the computation effort is very limited. In addition, the stochastic analyses in both time-and frequency domains show that the near-surface Morison force and induced linear oscillator response exhibits stronger non-Gaussianities by involving the second-order wave effects.
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Matsuda, Koichi, Yoichi Kanemitsu, and Shinya Kijimoto. "Stability-Optimized Clearance Configuration of Fluid-Film Journal Bearings." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84671.

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A clearance configuration of fluid-film journal bearings is optimized in a sense of enhancing the stability of a full circular bearing at high rotational speeds. A performance index is chosen as the sum of the squared whirl-frequency ratios over a wide range of eccentricity ratios, and a Fourier series is used to represent an arbitrary configuration of fluid-film bearings. An optimization problem is then formulated to find the Fourier coefficients to minimize the index. The whirl-frequency ratio is inversely proportional to the stability threshold speeds of a Jeffcott rotor. The short bearing approximation is used to simplify a mathematical model that describes a pressure distribution developed in a fluid-film bearing. The designed bearing cannot destabilize the Jeffcott rotor at any high rotating speed subject to the short-bearing assumption and significantly reduces the size of the unstable region for a finite-length bearing with a small length-to-diameter ratio.
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Alford, Laura K., and Kevin J. Maki. "Effects of Third-Order Nonlinearities on the Fourier Representation of Deterministic Wave Trains." In ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/omae2015-41441.

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The accurate estimation of extreme responses for offshore platforms and supply vessels is critical to the design process. Long time Monte Carlo-type simulations can theoretically capture extreme responses, but this type of simulation is not feasible in the early design process due to the extreme computational expense. An alternative is to use shorter simulations that are tailored to create statistically equivalent extreme responses. The latter requires judicious specification of expected extreme sea conditions. Extreme responses can be estimated using a variety of processes, including the Design Loads Generator (DLG). Assuming a vessel response is Gaussian, stationary, and ergodic, a given response can be approximated as a sum of Fourier amplitudes with random phase angles. The DLG is a process that can calculate innumerable sets of random phase angles that result in a given extreme response or design event. Using linear-systems theory, the corresponding incident-wave phase angles are calculated from the response phase angles and the incident-wave-train profile is determined. A fundamental question that must be answered is how can a nonlinear seaway that produces an extreme event be described such that a wave maker or numerical wave boundary condition be controlled to recreate the nonlinear and extreme seaway. A common practice employs linear wave theory to shift the design event in space and time. The shifted phase angles can then be used to drive a wavemaker with the intent of producing the desired wave train at a given point. However, nonlinearities in wave propagation result in an inaccurately generated design wave train. This paper focuses on the role of wave nonlinearity in the evolution of the wave system and how this can be accounted for in the control of a physical or virtual wave maker.
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Sharma, Kal Renganathan. "Transient Damped Wave Conduction and Relaxation in Human Skin and Thermal Wear During Winter." In ASME 2008 Heat Transfer Summer Conference collocated with the Fluids Engineering, Energy Sustainability, and 3rd Energy Nanotechnology Conferences. ASMEDC, 2008. http://dx.doi.org/10.1115/ht2008-56119.

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Damped wave conduction and relaxation in the human skin layer and thermal fabric layer are modeled with a temperature dependent heat source in the human tissue layer. Steady state temperature profiles are derived from the Fourier heat conduction equation. The general solution for the temperature is assumed to be a sum of the transient temperature and steady state temperature. This makes the boundary conditions in space for the skin and fabric layers homogeneous for the transient temperarature. The hyperbolic PDE is solved for by the method of separation of variables. The use of final condition in time in addition to the initial temperature condition leads to bounded infinite Fourier series solutions. These solutions are bounded and does not violate second law of thermodynamics. The model can be used to interpret experimental observations of maximum heat flux that is a parameter of the warm/cool feeling of human skin in winter. For large relaxation times of human skin tissue, τrs>(1+U*)2(b−a)216π2αs, the transient temperature can be expected to undergo oscillations. These oscillations will be supercritical and grow with time for strong heat sources, U* > 1 and may be subcritical damped oscillatory for weak heat sources, U* < 1. For large thermal relaxation times of thermal fabric material, τrf>a24π2αs, the transient temperature in the thermal fabric layer may be expected to be subcritical damped oscillatory.
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Collins, Nick. "Sonification of the Riemann Zeta Function." In ICAD 2019: The 25th International Conference on Auditory Display. Newcastle upon Tyne, United Kingdom: Department of Computer and Information Sciences, Northumbria University, 2019. http://dx.doi.org/10.21785/icad2019.003.

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The Riemann zeta function is one of the great wonders of mathematics, with a deep and still not fully solved connection to the prime numbers. It is defined via an infinite sum analogous to Fourier additive synthesis, and can be calculated in various ways. It was Riemann who extended the consideration of the series to complex number arguments, and the famous Riemann hypothesis states that the non-trivial zeroes of the function all occur on the critical line 0:5 + ti, and what is more, hold a deep correspondence with the prime numbers. For the purposes of sonification, the rich set of mathematical ideas to analyse the zeta function provide strong resources for sonic experimentation. The positions of the zeroes on the critical line can be directly sonified, as can values of the zeta function in the complex plane, approximations to the prime spectrum of prime powers and the Riemann spectrum of the zeroes rendered; more abstract ideas concerning the function also provide interesting scope.
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Yang, Baisong, Jiale Tian, Jian Zhou, and Lie Yu. "A Generalized Solution on the Static Characteristics of Short Hydrodynamic Journal Bearings Using Harmonic Components." In ASME 2016 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/imece2016-65509.

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A theoretical analysis has been done to investigate the static performance of short hydrodynamic journal bearings with a generalized film thickness expression by a sum of Fourier series equation. The hydrodynamic film thickness was written into a summation of an infinite harmonic component of trigonometric function. Reynolds equation with short bearing theory is solved for steady-state operations. In this paper, the steady-state analysis of the generalized hydrodynamic bearing has been done and compared with some typical journal bearings with respect to their harmonic components of film thickness, pressure distribution and load capacity. The relationship between the k-th order harmonic component of the film thickness H0,k and the static pressure component P0,k was established. It was found that the value of P0,k is directly determined not only by the k-th order harmonic component H0,k but also the (k−1)-th order component P0,k−1 indirectly produced by the previous harmonic component H0,k−1.This new investigation method can used to improve the performance of hydrodynamic journal bearings for shape optimization of hydrodynamic journal bearings.
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Wang, Ken Xingze. "Angle-Selection with Sub-Unity Index in Solar Cells." In Fourier Transform Spectroscopy. Washington, D.C.: OSA, 2018. http://dx.doi.org/10.1364/fts.2018.jt2a.9.

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Ghirardo, G., F. Gant, F. Boudy, and M. R. Bothien. "Protection and Identification of Thermoacoustic Azimuthal Modes." In ASME Turbo Expo 2020: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/gt2020-15354.

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Abstract This paper first characterizes the acoustic field of two annular combustors by means of data from acoustic pressure sensors. In particular the amplitude, orientation, and nature of the acoustic field of azimuthal order n is characterized. The dependence of the pulsation amplitude on the azimuthal location in the chamber is discussed, and a protection scheme making use of just one sensor is proposed. The governing equations are then introduced, and a low-order model of the instabilities is discussed. The model accounts for the nonlinear response of M distinct flames, for system acoustic losses by means of an acoustic damping coefficient α and for the turbulent combustion noise, modelled by means of the background noise coefficient σ. Keeping the response of the flames arbitrary and in principle different from flame to flame, we show that, together with α and σ, only the sum of their responses and their 2n Fourier component in the azimuthal direction affect the dynamics of the azimuthal instability. The existing result that only this 2n Fourier component affects the stability of standing limit-cycle solutions is recovered. It is found that this result applies also to the case of a non-homogeneous flame response in the annulus, and to flame responses that respond to the azimuthal acoustic velocity. Finally, a parametric flame model is proposed, depending on a linear driving gain β and a nonlinear saturation constant κ. The model is first mapped from continuous time to discrete time, and then recast as a probabilistic Markovian model. The identification of the parameters {α, β, κ, σ} is then carried out on engine timeseries data. The optimal four parameters {α, σ, β, κ} are estimated as the values that maximize the data likelihood. Once the parameters have been estimated, the phase space of the identified low-order problem is discussed on selected invariant manifolds of the dynamical system.
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Fleisher, Adam J., David A. Long, David F. Plusquellic, and Joseph T. Hodges. "Precision Doppler-broadened and Sub-Doppler Absorption Spectroscopy using Optical Frequency Comb Generators." In Fourier Transform Spectroscopy. Washington, D.C.: OSA, 2016. http://dx.doi.org/10.1364/fts.2016.fth3b.2.

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Reports on the topic "Sum Fourier"

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Maidanik, G., and K. J. Becker. A Double-Sum Technique for Performing a Fourier Transformation on an Integrand Composed of Aliased Factors. Fort Belvoir, VA: Defense Technical Information Center, May 1996. http://dx.doi.org/10.21236/ada316123.

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McGuire, John Andrew. Femtosecond nonlinear spectroscopy at surfaces: Second-harmonic probing of hole burning at the Si(111)7x7 surface and fourier-transform sum-frequency vibrational spectroscopy. Office of Scientific and Technical Information (OSTI), November 2004. http://dx.doi.org/10.2172/836810.

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Noorizadeh, Sahand. SLM-based Fourier Differential Interference Contrast Microscopy. Portland State University Library, January 2000. http://dx.doi.org/10.15760/etd.2010.

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Bylsma, Wesley. Approximating Smooth Step Functions Using Partial Fourier Series Sums. Fort Belvoir, VA: Defense Technical Information Center, September 2012. http://dx.doi.org/10.21236/ada567759.

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Kaboré, Gisele. Etude qualitative sur le mariage précoce des adolescentes: Leur vécu, leurs besoins en matière d'éducation, de santé de la reproduction et d'opportunités socio-économiques. Population Council, 2009. http://dx.doi.org/10.31899/pgy20.1002.

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La présente étude sur le mariage précoce des adolescentes à été commanditée par l’UNFPA en collaboration avec l’UNICEF et le Ministère de l’Action Sociale dans le cadre du projet « Éliminer le mariage des enfants au Burkina : un plan pour la protection, le renforcement et l’action communautaire ». Elle vise à fournir des informations relatives à la pratique du mariage précoce sur les zones d’intervention du projet, afin de faciliter les interventions visant à améliorer les conditions de vie des adolescentes mariées ou non. Il s’agissait d’analyser le contexte socioculturel du mariage des adolescentes ainsi que leur vécu et leurs besoins en matière de santé, d’éducation et d’opportunités économiques. L’étude a révélé que la majorité des adolescentes mariées vivent dans des conditions de précarité. Cet environnement présente des risques pour leur vie (grossesse précoce, immaturité à assumer pleinement un nouveau statut et des rôles et responsabilités). Ces jeunes femmes affrontent généralement seules cette nouvelle situation, sans être au préalable préparées. Tous ces obstacles entraînent des conséquences sur l’épanouissement de l’adolescente à plusieurs niveaux.
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Enquête sur la contraception d'urgence (CU) au niveau des pharmacies. Population Council, 2009. http://dx.doi.org/10.31899/rh17.1000.

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La Division de la santé de la reproduction (DRH) avec l’aide du Population Council a mené ces dernières années un programme de recherche opérationnelle sur la contraception d’urgence (CU). L’objectif de cette recherche a été de fournir des informations de base à utiliser dans l’élaboration d’une stratégie pour la promotion de l’utilisation de la CU au Sénégal. Des études ont montré qu’un accès rapide à une méthode de CU entraînerait une réduction significative de l’étendue des grossesses non désirées et des avortements chez les femmes. Cependant, malgré le fait que l’OMS ait recommandé l’intégration de la CU dans les programmes nationaux de santé, l’accès à cette méthode est encore très limité pour la grande majorité des femmes dans le monde. Au Sénégal, des études menées en 2003 et 2006 ont révélé que la CU était peu connue du public et que les pharmacies restaient le principal débouché par lequel cette méthode était proposée.
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Guide pour les pilules de contraception d'urgence : Introduire et développer l'offre des pilules de contraception d'urgence dans les pays en voie de développement. Population Council, 2009. http://dx.doi.org/10.31899/rh17.1001.

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La Division de la santé de la reproduction (DRH) avec l’aide du Population Council a mené ces dernières années un programme de recherche opérationnelle sur la contraception d’urgence (CU). L’objectif de cette recherche a été de fournir des informations de base à utiliser dans l’élaboration d’une stratégie pour la promotion de l’utilisation de la CU au Sénégal. Des études ont montré qu’un accès rapide à une méthode de CU entraînerait une réduction significative de l’étendue des grossesses non désirées et des avortements chez les femmes. Cependant, malgré le fait que l’OMS ait recommandé l’intégration de la CU dans les programmes nationaux de santé, l’accès à cette méthode est encore très limité pour la grande majorité des femmes dans le monde. Au Sénégal, des études menées en 2003 et 2006 ont révélé que la CU était peu connue du public et que les pharmacies restaient le principal débouché par lequel cette méthode était proposée.
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