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Статті в журналах з теми "Bessel"

Автор: Grafiati

Опубліковано: 4 червня 2021

Оновлено: 1 червня 2024

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1

Novelli, Jean-Christophe, and Jean-Yves Thibon. "Noncommutative Symmetric Bessel Functions." Canadian Mathematical Bulletin 51, no. 3 (September 1, 2008): 424–38. http://dx.doi.org/10.4153/cmb-2008-043-3.

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AbstractThe consideration of tensor products of 0-Hecke algebramodules leads to natural analogs of the BesselJ-functions in the algebra of noncommutative symmetric functions. This provides a simple explanation of various combinatorial properties of Bessel functions.

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2

Daher, Radouan, and Mohamed El Hamma. "Bessel Transform of -Bessel Lipschitz Functions." Journal of Mathematics 2013 (2013): 1–3. http://dx.doi.org/10.1155/2013/418546.

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3

Lenyuk, M. P. "Hybrid integral transformations (Bessel, Legendre, Bessel)." Ukrainian Mathematical Journal 43, no. 6 (June 1991): 719–28. http://dx.doi.org/10.1007/bf01058939.

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4

Joshi, C. M., and S. K. Bissu. "Some inequalities of Bessel and modified Bessel functions." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 50, no. 2 (April 1991): 333–42. http://dx.doi.org/10.1017/s1446788700032791.

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AbstractTwo-sided inequalties for the ratio of modified Bessel functions of first kind are given, which provide sharper upper and lower bounds than had been known earlier. Wronskian type inequalities for Bessel functions are proved, and in the sequel alternative proofs of Turan-type inequalities for Bessel and modified Bessel functions are also discussed. These then lead to a two-sided inequality for Bessel functions. Also incorporated in the discussion is an inequality for the ratio of two Bessel functions for 0 < x < 1. Verifications of these inequalities are pointed out numerically.

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5

Ifantis, E. K., and P. D. Siafarikas. "Inequalities involving Bessel and modified Bessel functions." Journal of Mathematical Analysis and Applications 147, no. 1 (March 1990): 214–27. http://dx.doi.org/10.1016/0022-247x(90)90394-u.

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6

Nahid, Tabinda, and Mahvish Ali. "Several characterizations of Bessel functions and their applications." Georgian Mathematical Journal 29, no. 1 (October 10, 2021): 83–93. http://dx.doi.org/10.1515/gmj-2021-2108.

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Abstract The present work deals with the mathematical investigation of some generalizations of Bessel functions. The main motive of this paper is to show that the generating function can be employed efficiently to obtain certain results for special functions. The complex form of Bessel functions is introduced by means of the generating function. Certain enthralling properties for complex Bessel functions are investigated using the generating function method. By considering separately the real and the imaginary part of complex Bessel functions, we get respectively cosine-Bessel functions and sine-Bessel functions for which several novel identities and Jacobi–Anger expansions are established. Also, the generating function of degenerate Bessel functions is investigated and certain novel identities are obtained for them. A hybrid form of degenerate Bessel functions, namely, of degenerate Fubini–Bessel functions, is constructed using the replacement technique. Finally, the explicit forms of the real and the imaginary part of complex Bessel functions are established by a hypergeometric approach.

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7

Satsanit. "On the Bessel Operator Related to Bessel Wave Equation and Laplace Bessel Equation." Journal of Advanced Research in Applied Mathematics 6, no. 2 (March 1, 2014): 82–98. http://dx.doi.org/10.5373/jaram.1730.041513.

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8

Dixit, M. M., C. P. Pandey, and Deepanjan Das. "The continuous generalized wavelet transform associated with q-Bessel operator." Boletim da Sociedade Paranaense de Matemática 41 (December 21, 2022): 1–10. http://dx.doi.org/10.5269/bspm.52810.

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Анотація:

The continuous generalized wavelet transform associated with -Bessel operator is defined, which will invariably be called continuous -Bessel wavelet transform . Certain and boundedness results and inversion formula for continuous -Bessel wavelet transform are obtained. Discrete -Bessel wavelet transform is defined and a reconstruction formula is derived for discrete- Bessel wavelet.

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9

Hu, X., H. Wang, and D. S. Guo. "Phased Bessel functions." Canadian Journal of Physics 86, no. 7 (July 1, 2008): 863–70. http://dx.doi.org/10.1139/p08-009.

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Анотація:

In the study of photon-state transitions, we found a natural extension of the first kind of Bessel functions that extends both the range and domain of the Bessel functions from the real number field to the complex number field. We term the extended Bessel functions as phased Bessel functions. This extension is completely different from the traditional “analytical extension”. The new complex Bessel functions satisfy addition, subtraction, and recurrence theorems in a complex range and a complex domain. These theorems provide short cuts in calculations. The single-phased Bessel functions are generalized to multiple-phased Bessel functions to describe various photon-state transitions.PACS Nos.: 02.30.Gp, 32.80.Rm, 42.50.Hz

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10

Upadhyay, S. K., Reshma Singh, and Alok Tripathi. "The relation between Bessel wavelet convolution product and Hankel convolution product involving Hankel transform." International Journal of Wavelets, Multiresolution and Information Processing 15, no. 04 (March 21, 2017): 1750030. http://dx.doi.org/10.1142/s0219691317500308.

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In this paper, the relation between Bessel wavelet convolution product and Hankel convolution product is obtained by using the Bessel wavelet transform and the Hankel transform. Approximation results of the Bessel wavelet convolution product are investigated by exploiting the Hankel transformation tool. Motivated from the results of Pinsky, heuristic treatment of the Bessel wavelet transform is introduced and other properties of the Bessel wavelet transform are studied.

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11

Xiang, Zhong-Qi. "Some Properties of Canonical Dual K-Bessel Sequences for Parseval K-Frames." Journal of Function Spaces 2019 (July 29, 2019): 1–6. http://dx.doi.org/10.1155/2019/9862369.

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The concept of canonical dual K-Bessel sequences was recently introduced, a deep study of which is helpful in further developing and enriching the duality theory of K-frames. In this paper we pay attention to investigating the structure of the canonical dual K-Bessel sequence of a Parseval K-frame and some derived properties. We present the exact form of the canonical dual K-Bessel sequence of a Parseval K-frame, and a necessary and sufficient condition for a dual K-Bessel sequence of a given Parseval K-frame to be the canonical dual K-Bessel sequence is investigated. We also give a necessary and sufficient condition for a Parseval K-frame to have a unique dual K-Bessel sequence and equivalently characterize the condition under which the canonical dual K-Bessel sequence of a Parseval K-frame admits a unique dual K⁎-Bessel sequence. Finally, we obtain a minimal norm property on expansion coefficients of elements in the range of K resulting from the canonical dual K-Bessel sequence of a Parseval K-frame.

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12

Won, Rachel. "Bessel beamformer." Nature Photonics 9, no. 3 (February 27, 2015): 141. http://dx.doi.org/10.1038/nphoton.2015.32.

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13

Liu, Lei, Xianwei Zheng, Jingwen Yan, and Xiaodong Niu. "Bessel Sequences and Its F-Scalability." Advances in Applied Mathematics and Mechanics 7, no. 4 (May 29, 2015): 441–53. http://dx.doi.org/10.4208/aamm.2014.m652.

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AbstractFrame theory, which contains wavelet analysis and Gabor analysis, has become a powerful tool for many applications of mathematics, engineering and quantum mechanics. The study of extension principles of Bessel sequences to frames is important in frame theory. This paper studies transformations on Bessel sequences to generate frames and Riesz bases in terms of operators and scalability. Some characterizations of operators that mapping Bessel sequences to frames and Riesz bases are given. We introduce the definitions of F-scalable and P-scalable Bessel sequences. F-scalability and P-scalability of Bessel sequences are discussed in this paper, then characterizations of scalings of F-scalable or P-scalable Bessel sequences are established. Finally, a perturbation result on F-scalable Bessel sequences is derived.

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14

Mitri, F. G. "Nonparaxial Bessel and Bessel–Gauss pincers light-sheets." Physics Letters A 381, no. 3 (January 2017): 171–75. http://dx.doi.org/10.1016/j.physleta.2016.10.055.

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15

Herman, R. M., and T. A. Wiggins. "Propagation and focusing of Bessel–Gauss, generalized Bessel–Gauss, and modified Bessel–Gauss beams." Journal of the Optical Society of America A 18, no. 1 (January 1, 2001): 170. http://dx.doi.org/10.1364/josaa.18.000170.

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16

Yilmazer, Resat, and Okkes Ozturk. "On nabla discrete fractional calculus operator for a modified Bessel equation." Thermal Science 22, Suppl. 1 (2018): 203–9. http://dx.doi.org/10.2298/tsci170614287y.

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In thermal sciences, it is possible to encounter topics such as Bessel beams, Bessel functions or Bessel equations. In this work, we also present new discrete fractional solutions of the modified Bessel differential equation by means of the nabla-discrete fractional calculus operator. We consider homogeneous and non-homogeneous modified Bessel differential equation. So, we acquire four new solutions of these equations in the discrete fractional forms via a newly developed method

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17

Cavanşir Həsənov, Əfsanə Abdullayeva, Cavanşir Həsənov, Əfsanə Abdullayeva. "BESSEL FUNKSİYALARININ BİRLƏŞMƏSİNİN SIFIRLARININ TƏDQİQİ." PAHTEI-Procedings of Azerbaijan High Technical Educational Institutions 38, no. 03 (March 28, 2024): 06–12. http://dx.doi.org/10.36962/pahtei38032024-06.

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Bessel və hiperhəndəsi funksiyalar ehtimal, statistika, riyazi fizika və mühəndislik elmlərində çox tez-tez istifadə olunur. Bundan əlavə, digər tətbiq sahələri kimi Bessel funksiyası nəzəriyyəsi də elektrik, hidrodinamika, radiofizika, rabitə nəzəriyyəsi, atom və nüvə fizikası kimi bir çox problemin həllində son zamanlar istifadə edilmişdir. Klassik mənada Bessel və Modifikasiya olunmuş Bessel funksiyaları sinus, kosinus, hiperbolik sinus və hiperbolik kosinus funksiyalarının ümumiləşdirilməsi kimi göstərilə bilər. Onların qrafikləri təxminən sinus və kosinus qrafiklərinə bənzəyir, lakin onlar ümumiyyətlə dövri deyil. Triqonometrik funksiyaları əhatə edən bir çox bərabərsizliklər və eyniliklər Bessel funksiyalarına qədər genişləndirilə bilər. Bu tip bərabərsizliklər son vaxtlar mühəndislik elmlərində, informasiya və kommunikasiya nəzəriyyələrində çox tez-tez istifadə olunur. Tədqiqat işində Bessel funksiyalarının məhsul birləşmələri üzrə sıfır funksiyalarını nəzərdən keçiririk. Açar sözlər: Bessel funksiyaları, hiperhəndəsi funksiyalar, funksiya sıfırları, müsbət sıfırlar, sıfırlar çoxluğu.

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18

Mirzaee, Azandaryania. "Invertibility of multipliers in Hilbert C*-modules." Filomat 32, no. 17 (2018): 6073–85. http://dx.doi.org/10.2298/fil1817073m.

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In this paper, we present some sufficient conditions under which Bessel multipliers in Hilbert C*-modules with semi-normalized symbols are invertible and we calculate the inverses. Especially we consider the invertibility of Bessel multipliers when the elements of their symbols are positive and when their Bessel sequences are equivalent, duals, modular Riesz bases or stable under small perturbations. We show that in these cases the inverse of a Bessel multiplier can be represented as a Bessel multiplier.

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19

Zeinal Zadeh Farhadi, Fariba, Mohammad Sadegh Asgari, Mohammad Reza Mardanbeigi, and Mahdi Azhini. "GENERALIZED BESSEL AND FRAME MEASURES." Facta Universitatis, Series: Mathematics and Informatics 35, no. 1 (April 6, 2020): 217. http://dx.doi.org/10.22190/fumi2001217z.

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Considering a finite Borel measure $ \mu $ on $ \mathbb{R}^d $, a pair of conjugate exponents $ p, q $, and a compatible semi-inner product on $ L^p(\mu) $, we have introduced $ (p,q) $-Bessel and $ (p,q) $-frame measures as a generalization of the concepts of Bessel and frame measures. In addition, we have defined the notions of $ q $-Bessel sequence and $ q$-frame in the semi-inner product space $ L^p(\mu) $. Every finite Borel measure $\nu$ is a $(p,q)$-Bessel measure for a finite measure $ \mu $. We have constructed a large number of examples of finite measures $ \mu $ which admit infinite $ (p,q) $-Bessel measures $ \nu $. We have showed that if $ \nu $ is a $ (p,q) $-Bessel/frame measure for $ \mu $, then $ \nu $ is $ \sigma $-finite and it is not unique. In fact, by using the convolutions of probability measures, one can obtain other $ (p,q) $-Bessel/frame measures for $ \mu $. We have presented a general way of constructing a $ (p,q) $-Bessel/frame measure for a given measure.

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20

Ávila, Salvador, Óscar Trigueros, and Roberto Chinchilla. "Funciones de Bessel y Neumann." Revista de la Escuela de Física 2, no. 1 (September 3, 2019): 62–65. http://dx.doi.org/10.5377/ref.v2i1.8293.

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En este trabajo, trataremos la función Bessel generalizada, que es la solución a la ecuación diferencial de Bessel de segundo orden , originándose del desarrollo de la ecuación de Laplace y la ecuación de Helmholtz en coordenadas cilíndricas y esféricas. Iniciaremos con la función de Bessel de primera clase solución linealmente independiente de la ecuación diferencial de Bessel, usando principios de simetría y condiciones de convergencia, para demostrar su valides. Veremos también las funciones de Bessel de segunda y tercera clase, denominadas respectivamente función de Neumann y la función de Hankel. Las funciones Bessel tienen diversas aplicaciones, como en: ondas electromagnéticas en guías de onda, conducción de calor en objetos cilíndricos, difusión en una red, entre muchas otras.

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21

CAMPOLIETI, GIUSEPPE, and ROMAN MAKAROV. "PRICING PATH-DEPENDENT OPTIONS ON STATE DEPENDENT VOLATILITY MODELS WITH A BESSEL BRIDGE." International Journal of Theoretical and Applied Finance 10, no. 01 (February 2007): 51–88. http://dx.doi.org/10.1142/s0219024907004081.

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This paper develops bridge sampling path integral algorithms for pricing path-dependent options under a new class of nonlinear state dependent volatility models. Path-dependent option pricing is considered within a new (dual) Bessel family of semimartingale diffusion models, as well as the constant elasticity of variance (CEV) diffusion model, arising as a particular case of these models. The transition p.d.f.s or pricing kernels are mapped onto an underlying simpler squared Bessel process and are expressed analytically in terms of modified Bessel functions. We establish precise links between pricing kernels of such models and the randomized gamma distributions, and thereby demonstrate how a squared Bessel bridge process can be used for exact sampling of the Bessel family of paths. A Bessel bridge algorithm is presented which is based on explicit conditional distributions for the Bessel family of volatility models and is similar in spirit to the Brownian bridge algorithm. A special rearrangement and splitting of the path integral variables allows us to combine the Bessel bridge sampling algorithm with either adaptive Monte Carlo algorithms, or quasi-Monte Carlo techniques for significant numerical efficiency improvement. The algorithms are illustrated by pricing Asian-style and lookback options under the Bessel family of volatility models as well as the CEV diffusion model.

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22

Baricz, Árpád, and Róbert Szász. "The radius of convexity of normalized Bessel functions of the first kind." Analysis and Applications 12, no. 05 (August 28, 2014): 485–509. http://dx.doi.org/10.1142/s0219530514500316.

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In this paper, we determine the radius of convexity for three kinds of normalized Bessel functions of the first kind. In the mentioned cases the normalized Bessel functions are starlike-univalent and convex-univalent, respectively, on the determined disks. The key tools in the proofs of the main results are some new Mittag-Leffler expansions for quotients of Bessel functions of the first kind, special properties of the zeros of Bessel functions of the first kind and their derivative, and the fact that the smallest positive zeros of some Dini functions are less than the first positive zero of the Bessel function of the first kind. Moreover, we find the optimal parameters for which these normalized Bessel functions are convex in the open unit disk. In addition, we disprove a conjecture of Baricz and Ponnusamy concerning the convexity of the Bessel function of the first kind.

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23

Nazir, Maryam, Syed Zakar Hussain Bukhari, Imtiaz Ahmad, Muhammad Ashfaq, and Malik Ali Raza. "Starlikeness of Normalized Bessel Functions with Symmetric Points." Journal of Function Spaces 2021 (November 20, 2021): 1–6. http://dx.doi.org/10.1155/2021/9451999.

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Анотація:

Bessel functions are related with the known Bessel differential equation. In this paper, we determine the radius of starlikeness for starlike functions with symmetric points involving Bessel functions of the first kind for some kinds of normalized conditions. Our prime tool in these investigations is the Mittag-Leffler representation of Bessel functions of the first kind.

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24

YASMIN, GHAZALA, and ABDULGHANI MUHYI. "ON A FAMILY OF (p, q)-HYBRID POLYNOMIALS." Kragujevac Journal of Mathematics 45, no. 03 (May 2021): 409–26. http://dx.doi.org/10.46793/kgjmat2103.409y.

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In this paper, the class of (p,q)-Bessel-Appell polynomials is introduced. The generating function, series deﬁnition and determinant deﬁnition of this class are established. Certain members of (p,q)-Bessel-Appell polynomials are considered and some properties of these members are also derived. Further, the class of 2D (p,q)-Bessel-Appell polynomials is introduced by means of the generating function and series deﬁnition. In addition, the graphical representations of some members of (p,q)-Bessel-Appell polynomials and 2D (p,q)-Bessel-Appell polynomials are plotted with the help of Matlab.

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25

Srivastava, Hari Mohan. "An Introductory Overview of Bessel Polynomials, the Generalized Bessel Polynomials and the q-Bessel Polynomials." Symmetry 15, no. 4 (March 29, 2023): 822. http://dx.doi.org/10.3390/sym15040822.

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Named essentially after their close relationship with the modified Bessel function Kν(z) of the second kind, which is known also as the Macdonald function (or, with a slightly different definition, the Basset function), the so-called Bessel polynomials yn(x) and the generalized Bessel polynomials yn(x;α,β) stemmed naturally in some systematic investigations of the classical wave equation in spherical polar coordinates. Our main purpose in this invited survey-cum-expository review article is to present an introductory overview of the Bessel polynomials yn(x) and the generalized Bessel polynomials yn(x;α,β) involving the asymmetric parameters α and β. Each of these polynomial systems, as well as their reversed forms θn(x) and θn(x;α,β), has been widely and extensively investigated and applied in the existing literature on the subject. We also briefly consider some recent developments based upon the basic (or quantum or q-) extensions of the Bessel polynomials. Several general families of hypergeometric polynomials, which are actually the truncated or terminating forms of the series representing the generalized hypergeometric function rFs with r symmetric numerator parameters and s symmetric denominator parameters, are also investigated, together with the corresponding basic (or quantum or q-) hypergeometric functions and the basic (or quantum or q-) hypergeometric polynomials associated with rΦs which also involves r symmetric numerator parameters and s symmetric denominator parameters.

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26

Nairat, Mazen. "Axial Angular Momentum of Bessel Light." Photonics Letters of Poland 10, no. 1 (March 31, 2018): 23. http://dx.doi.org/10.4302/plp.v10i1.787.

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Both linear and angular momentum densities of Bessel, Gaussian-Bessel, and Hankel-Bessel lasers are determined. Angular momentum of the three Bessel beams is illustrated at linear and circular polarization. Axial Angular momentum is resolved in particular interpretation: the harmonic order of the physical light momentum. Full Text: PDF ReferencesG. Molina-Terriza, J. Torres, and L. Torner, "Twisted photons", Nature Physics 3, 305 - 310 (2007). CrossRef J Arlt, V Garces-Chavez, W Sibbett, and K Dholakia "Optical micromanipulation using a Bessel light beam", Opt. Commun., 197, 4-6, (2001). CrossRef L. Ambrosio and H. Hernández-Figueroa, "Gradient forces on double-negative particles in optical tweezers using Bessel beams in the ray optics regime", Opt Exp, 18, 23 (2010). CrossRef I. Litvin, A. Dudley and A. Forbes, "Poynting vector and orbital angular momentum density of superpositions of Bessel beams", Opt Exp, 19, 18 (2011). CrossRef K Volke-Sepulveda, V Garcés-Chávez, S Chávez-Cerda, J Arlt and K Dholakia "Orbital angular momentum of a high-order Bessel light beam" , JOP B 4 (2). 2002. CrossRef M. Verma, S. Pal, S. Joshi, P. Senthilkumaran, J. Joseph, and H Kandpal, "Singularities in cylindrical vector beams", Jou. of Mod. Opt., 62 (13), 2015. CrossRef R. Borghi, M. Santarsiero, and M. Porras, "Nonparaxial Bessel?Gauss beams", J. Opt. Soc. Am. A, 18 (7) (2011). CrossRef L. Allen, M. Beijersbergen, R. Spreeuw, and J. Woerdman, "Orbital angular momentum of light and the transformation of Laguerre-Gaussian Laser modes", Phys Rev A, 45 (11): 8185-8189 (1992). CrossRef D. Mcglion and K. Dholakia, "Bessel beams: diffraction in a new light", Cont. Phys, 46(1) 15 ? 28. (2005). CrossRef F. Gori, G. Guattari and C. Padovani," Bessel-Gauss Beams", Opt. Commun., 64, 491, (1987). CrossRef V. Kotlyar, A. Kovalev, and A. Soifer, "Hankel?Bessel laser beams" J. Opt. Soc. Am. A, 29 (5) (2012). CrossRef L. Allen and M. Babiker "Spin-orbit coupling in free-space Laguerre-Gaussian light beams", Phys. Rev. A 53, R2937. CrossRef

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27

Soni, Amit, and Deepak Bansal. "Certain geometric properties of generalized Bessel-Maitland function." Studia Universitatis Babes-Bolyai Matematica 68, no. 4 (December 30, 2023): 789–98. http://dx.doi.org/10.24193/subbmath.2023.4.08.

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Анотація:

"In the present study, we first introduce Generalized Bessel-Maitland function $\mathbb{J}^{\xi }_{\zeta,a}(z)$ and then derive sufficient conditions under which the Generalized Bessel-Maitland function $\mathbb{J}^{\xi}_{\zeta,a}(z)$ have geometric properties like univalency, starlikeness and convexity in the open unit disk $\mathscr{D}$. Keywords: Univalent, starlike, convex and close-to-convex function, subordination, Bessel functions, Bessel-Maitland functions."

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28

Fuscaldo, Walter, and Santi C. Pavone. "Tunable Terahertz Bessel-Beam Launchers." Reviews of Electromagnetics 1 (September 13, 2022): 1–4. http://dx.doi.org/10.53792/roe/2022.1/22002.

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Анотація:

Bessel-beam launchers are planar devices capable of focusing electromagnetic energy in their radiative near-field region in the form of Bessel beams. Bessel-beam launchers are typically designed to have certain static beam features over a given operating bandwidth in the microwave/millimeter-wave range. Here, taking cues from some recent advancements in the field, we propose innovative architectures capable of generating Bessel beams at terahertz frequencies and featuring a dynamic control of the cover distance. The ideas outlined in this Vision are expected to pave the way for the realization of the first tunable terahertz Bessel-beam launchers.

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29

Bakhet, Ahmed, Shahid Hussain, Mohamed Niyaz, Mohammed Zakarya, and Ghada AlNemer. "On the Two-Variable Analogue Matrix of Bessel Polynomials and Their Properties." Axioms 13, no. 3 (March 17, 2024): 202. http://dx.doi.org/10.3390/axioms13030202.

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In this paper, we explore a study focused on a two-variable extension of matrix Bessel polynomials. We initiate the discussion by introducing the matrix Bessel polynomials involving two variables and derive specific differential formulas and recurrence relations associated with them. Additionally, we present a segment detailing integral formulas for the extended matrix Bessel polynomials. Lastly, we introduce the Laplace–Carson transform for the two-variable matrix Bessel polynomial analogue.

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30

Tian, Mingdang, Baohuai Sheng, and Shuhua Wang. "Some Upper Bounds for RKHS Approximation by Bessel Functions." Axioms 11, no. 5 (May 17, 2022): 233. http://dx.doi.org/10.3390/axioms11050233.

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A reproducing kernel Hilbert space (RKHS) approximation problem arising from learning theory is investigated. Some K-functionals and moduli of smoothness with respect to RKHSs are defined with Fourier–Bessel series and Fourier–Bessel transforms, respectively. Their equivalent relation is shown, with which the upper bound estimate for the best RKHS approximation is provided. The convergence rate is bounded with the defined modulus of smoothness, which shows that the RKHS approximation can attain the same approximation ability as that of the Fourier–Bessel series and Fourier–Bessel transform. In particular, it is shown that for a RKHS produced by the Bessel operator, the convergence rate sums up to the bound of a corresponding convolution operator approximation. The investigations show some new applications of Bessel functions. The results obtained can be used to bound the approximation error in learning theory.

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31

Raza, Mohsan, Sarfraz Nawaz Malik, Qin Xin, Muhey U. Din, and Luminiţa-Ioana Cotîrlă. "On Kudriasov Conditions for Univalence of Integral Operators Defined by Generalized Bessel Functions." Mathematics 10, no. 9 (April 19, 2022): 1361. http://dx.doi.org/10.3390/math10091361.

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In this article, we studied the necessary conditions for the univalence of integral operators that involve two functions: the generalized Bessel function and a function from the well-known class of normalized analytic functions in the open unit disk. The main tools for our discussions were the Kudriasov conditions for the univalency of functions, as well as functional inequalities for the generalized Bessel functions. We included the conditions for the univalency of integral operators that involve Bessel, modified Bessel and spherical Bessel functions as special cases. Furthermore, we provided sufficient conditions for the integral operators that involve trigonometric, as well as hyperbolic, functions as an application of our results.

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32

Nadarajah, Saralees. "Product Bessel Distributions of the First and Second Kinds." International Journal of Mathematics and Mathematical Sciences 2007 (2007): 1–7. http://dx.doi.org/10.1155/2007/57956.

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A new Bessel function distribution is introduced by taking the product of a Bessel function pdf of the first kind and a Bessel function pdf of the second kind. Various particular cases and expressions for moments are derived.

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33

Ulug, Bulent, Furkan Kuruoğlu, Yeşim Yalçın, Ayşe Erol, Fahrettin Sarcan, Ali Şahin, and Ahmet Cicek. "Surface acoustic wave quasi-Bessel beams generated by symmetrically tilted interdigital transducers." Journal of Physics D: Applied Physics 55, no. 22 (March 7, 2022): 225303. http://dx.doi.org/10.1088/1361-6463/ac570c.

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Abstract Formation of surface acoustic wave (SAW) quasi-Bessel beams on a piezoelectric substrate through superposition of plane waves generated by interdigital transducers tilted symmetrically about the propagation axis is numerically and experimentally demonstrated. Acting as an axicon, the tilted transducers provide a facile way for quasi-Bessel beam generation. Finite-element method simulations reveal that non-diffracting Bessel beams, whose length and width are 193 and 1.38 wavelengths, respectively, can be obtained on a YX-128∘ lithium niobate substrate for an axicon angle of 15 degrees. The corresponding values for 20 degrees are 146 and 1.05 wavelengths, respectively. For a wavelength of approximately 300 micrometers, transmission spectra show that Bessel beam formation can be achieved at frequencies around 13.3 MHz. Bessel beam is visualized through a thin liquid film of methanol on the substrate. SAW Bessel beams can be utilized in acoustophoresis in microfluidic systems and sensing applications.

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34

Irvan, Irvan, Zahedi Zahedi, Anjar Agus, Sarmin Suparni, and Harahap Amin. "SIMPLIFIED FORMULAS FOR SOME BESSEL FUNCTIONS AND THEIR APPLICATIONS IN EXTENDED SURFACE HEAT TRANSFER." BAREKENG: Jurnal Ilmu Matematika dan Terapan 16, no. 2 (June 1, 2022): 507–14. http://dx.doi.org/10.30598/barekengvol16iss2pp507-514.

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Bessel functions find many applications in Physics and Engineering fields. Some of these applications are in the analysis of extended surface heat transfer where the cross-sections vary. Tables of various kinds of Bessel functions are available in most handbooks of mathematics. However, the use of tables is not always convenient, particularly for applications where many values must be computed. In the applications of Bessel functions in extended surface heat transfer, graphs are also available to provide quick evaluations of the values needed. However, reading these graphs always needs interpolation; this will be cumbersome and time-consuming if there are many readings to be taken. Mathematical formulas for Bessel functions are available but they are usually complicated. Software to calculate values of Bessel functions is also available. Excel, Maple, and Mathematica can also be used to compute the values of Bessel functions. A user can write a program for an application that involves Bessel functions. However, the use of Bessel functions in Excel is limited while Maple and Mathematica are expensive commercial software. In this paper, formulas for Bessel functions of and are simplified with adequate accuracy that can be used to easily compute values needed in the extended surface heat transfer analysis. It is found that errors for and are relatively small (maximum errors are 0.004% and 0.003%, respectively) in the range of 0.05 to 3.75 while the maximum error for is 3.678% for the same range. However, the maximum error for is reduced to 0.166 if the range is from 0.25 to 3.75.

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35

Sarıkaya, Mehmet Zeki, and Hüseyin Yıldırım. "On the Bessel diamond and the nonlinear Bessel diamond operator related to the Bessel wave equation." Nonlinear Analysis: Theory, Methods & Applications 68, no. 2 (January 2008): 430–42. http://dx.doi.org/10.1016/j.na.2006.11.009.

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36

Ahmad, Khurshid, Saima Mustafa, Muhey Din, Shafiq ur Rehman, Mohsan Raza, and Muhammad Arif. "On Geometric Properties of Normalized Hyper-Bessel Functions." Mathematics 7, no. 4 (March 28, 2019): 316. http://dx.doi.org/10.3390/math7040316.

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In this paper, the normalized hyper-Bessel functions are studied. Certain sufficient conditions are determined such that the hyper-Bessel functions are close-to-convex, starlike and convex in the open unit disc. We also study the Hardy spaces of hyper-Bessel functions.

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37

Kotlyar, V. V., A. A. Kovalev, D. S. Kalinkina, and E. S. Kozlova. "Fourier-Bessel beams of finite energy." Computer Optics 45, no. 4 (July 2021): 506–11. http://dx.doi.org/10.18287/2412-6179-co-864.

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In this paper, we consider a new type of Bessel beams having Fourier-invariance property and, therefore, called Fourier-Bessel beams. In contrast to the known Bessel beams, these beams have weak side lobes. Analytical expressions for the complex amplitude of the proposed field in the initial plane of the source and in the far field region have been obtained. It is shown that the proposed Fourier-Bessel beams have a finite energy, although they do not have a Gaussian envelope. Their complex amplitude is proportional to a fractional-order Bessel function (an odd integer divided by 6) in the initial plane and in the Fraunhofer zone. The Fourier-Bessel modes have a smaller internal dark spot compared to the Laguerre-Gauss modes with a zero radial index. The proposed beams can be generated with a spatial light modulator and may find uses in telecommunications, interferometry, and the capture of metal microparticles.

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38

Nisar, K. S., S. R. Mondal, and P. Agarwal. "Composition Formulas of Bessel-Struve Kernel Function." Mathematical Problems in Engineering 2016 (2016): 1–8. http://dx.doi.org/10.1155/2016/9560346.

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The object of this paper is to study and develop the generalized fractional calculus operators involving Appell’s functionF3(·)due to Marichev-Saigo-Maeda. Here, we establish the generalized fractional calculus formulas involving Bessel-Struve kernel functionSαλz, λ,z∈Cto obtain the results in terms of generalized Wright functions. The representations of Bessel-Struve kernel function in terms of exponential function and its relation with Bessel and Struve function are also discussed. The pathway integral representations of Bessel-Struve kernel function are also given in this study.

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39

Yang, Sheng-liang, and Sai-nan Zheng. "A Determinant Expression for the Generalized Bessel Polynomials." Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/242815.

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Using the exponential Riordan arrays, we show that a variation of the generalized Bessel polynomial sequence is of Sheffer type, and we obtain a determinant formula for the generalized Bessel polynomials. As a result, the Bessel polynomial is represented as determinant the entries of which involve Catalan numbers.

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40

Tran, Dung Anh, Hang Thi Chu, and Long Ta Bui. "Application of the Bessel function to compute the air pollutant with the stratification of the atmospheric." Science and Technology Development Journal 18, no. 2 (June 30, 2015): 14–20. http://dx.doi.org/10.32508/stdj.v18i2.1067.

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The Bessel differential equation with the Bessel function of solution has been applied. Bessel functions are the canonical solutions of Bessel's differential equation. Bessel's equation arises when finding separable solutions to Laplace's equation in cylindrical or spherical coordinates. Bessel functions are important for many problems of advection–diffusion progress and wave propagation. In this paper, authors present the analytic solutions of the atmospheric advection-diffusion equation with the stratification of the boundary condition. The solution has been found by applied the separation of variable method and Bessel’s equation.

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41

Lutz, Christian, Simon Schwarz, Jan Marx, Cemal Esen, and Ralf Hellmann. "Multi-Bessel Beams Generated by an Axicon and a Spatial Light Modulator for Drilling Applications." Photonics 10, no. 4 (April 6, 2023): 413. http://dx.doi.org/10.3390/photonics10040413.

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We report on an optical setup to generate multi-Bessel beam profiles combining a refractive axicon and a spatial light modulator. Based on their particular beam profile, Bessel beams offer advantageous properties for micro drilling processes and internal volume processing, especially for transparent materials. In addition, the laser power of industrial, ultrashort pulsed lasers has increased significantly over the last few years, offering the possibility for highly efficient processes using multi-spot profiles. Our optical concept combines the dynamic possibilities of beam splitting using a spatial light modulator with the benefits of Bessel beams, which facilitates multi-Bessel beam processing. Beside the simulation and experimental evaluation of the generated multi-Bessel beams, we exemplify the applicability of the developed module for the perforation of thin metal foils by micro drilling.

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42

Плаченов, А. Б. "Смещенные параксиальные пучки Бесселя--Гаусса. I". Журнал технической физики 126, № 3 (2019): 311. http://dx.doi.org/10.21883/os.2019.03.47372.274-18.

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AbstractWe have considered a new family of localized solutions of a parabolic (paraxial wave) equation that generalizes the well-known Bessel–Gaussian beams and includes asymmetric and noncoaxial Bessel–Gaussian beams as subfamilies. The Fourier spectra of these solutions have been found, and their expansions into nonshifted Bessel–Gaussian beams have been obtained.

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43

Houissa, Khadija, and Mohamed Sifi. "Symmetric Bessel multipliers." Colloquium Mathematicum 126, no. 2 (2012): 155–76. http://dx.doi.org/10.4064/cm126-2-2.

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44

Zapata-Rodríguez, Carlos J., Slobodan Vuković, Milivoj R. Belić, David Pastor, and Juan J. Miret. "Nondiffracting Bessel plasmons." Optics Express 19, no. 20 (September 22, 2011): 19572. http://dx.doi.org/10.1364/oe.19.019572.

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45

Nguon, Donara. "Bessel integral operators." Integral Transforms and Special Functions 25, no. 8 (March 14, 2014): 647–62. http://dx.doi.org/10.1080/10652469.2014.894040.

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46

Kotlyar, V. V., A. A. Kovalev, and V. A. Soifer. "Asymmetric Bessel modes." Optics Letters 39, no. 8 (April 9, 2014): 2395. http://dx.doi.org/10.1364/ol.39.002395.

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47

Dudley, Angela, Martin Lavery, Miles Padgett, and Andrew Forbes. "Unraveling Bessel Beams." Optics and Photonics News 24, no. 6 (June 1, 2013): 22. http://dx.doi.org/10.1364/opn.24.6.000022.

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48

MUSCH, B. U., and A. PROKUDIN. "(BESSEL-)WEIGHTED ASYMMETRIES." International Journal of Modern Physics: Conference Series 04 (January 2011): 126–34. http://dx.doi.org/10.1142/s2010194511001632.

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Semi-inclusive deep inelastic scattering experiments allow us to probe the motion of quarks inside the proton in terms of so-called transverse momentum dependent parton distribution functions (TMD PDFs), but the information is convoluted with fragmentation functions (TMD FFs) and soft factors. It has long been known that weighting the measured event counts with powers of the hadron momentum before forming angular asymmetries de-convolutes TMD PDFs and TMD FFs in an elegant way, but this also entails an undesirable sensitivity to high momentum contributions. Using Bessel functions as weights, we find a natural generalization of weighted asymmetries that preserves the de-convolution property and features soft-factor cancellation, yet allows us to be less sensitive to high transverse momenta. The formalism also relates to TMD quantities studied in lattice QCD. We briefly show preliminary lattice results from an exploratory calculation of the Boer-Mulders shift using lattices generated by the MILC and LHP collaborations at a pion mass of 500 MeV.

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49

Dachraoui, Azza. "Weyl–Bessel transforms." Journal of Computational and Applied Mathematics 133, no. 1-2 (August 2001): 263–76. http://dx.doi.org/10.1016/s0377-0427(00)00649-x.

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50

Krisch, J. P., and E. N. Glass. "Relativistic Bessel cylinders." Journal of Mathematical Physics 55, no. 10 (October 2014): 102502. http://dx.doi.org/10.1063/1.4898770.

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