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Artykuły w czasopismach na temat „Bessel”

Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 25 lipca 2025

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1

Novelli, Jean-Christophe, and Jean-Yves Thibon. "Noncommutative Symmetric Bessel Functions." Canadian Mathematical Bulletin 51, no. 3 (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 (1991): 719–28. http://dx.doi.org/10.1007/bf01058939.

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4

Nahid, Tabinda, and Mahvish Ali. "Several characterizations of Bessel functions and their applications." Georgian Mathematical Journal 29, no. 1 (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 si

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5

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 (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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6

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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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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7

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

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8

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

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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 gen

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9

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 (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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10

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

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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

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12

Liu, Lei, Xianwei Zheng, Jingwen Yan, and Xiaodong Niu. "Bessel Sequences and Its F-Scalability." Advances in Applied Mathematics and Mechanics 7, no. 4 (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-scal

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13

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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14

Cavanşir Həsənov, Əfsanə Abdullayeva, Cavanşir Həsənov, Əfsanə Abdullayeva. "BESSEL FUNKSİYALARININ BİRLƏŞMƏSİNİN SIFIRLARININ TƏDQİQİ." PAHTEI-Procedings of Azerbaijan High Technical Educational Institutions 38, no. 03 (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 onla

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15

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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16

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 (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

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17

Ávila, Salvador, Óscar Trigueros, and Roberto Chinchilla. "Funciones de Bessel y Neumann." Revista de la Escuela de Física 2, no. 1 (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

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18

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 (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

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19

Baricz, Árpád, and Róbert Szász. "The radius of convexity of normalized Bessel functions of the first kind." Analysis and Applications 12, no. 05 (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 t

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20

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

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21

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

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22

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 (2001): 170. http://dx.doi.org/10.1364/josaa.18.000170.

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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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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 (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

Ibrahim, Ibrahim S., Majeed A. Yousif, Pshtiwan Othman Mohammed, Dumitru Baleanu, Ahmad Zeeshan, and Mohamed Abdelwahed. "Bessel statistical convergence: New concepts and applications in sequence theory." PLOS ONE 19, no. 11 (2024): e0313273. http://dx.doi.org/10.1371/journal.pone.0313273.

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This research introduces novel concepts in sequence theory, including Bessel convergence, Bessel boundedness, Bessel statistical convergence, and Bessel statistical Cauchy sequences. These concepts establish new inclusion relations and related results within mathematical analysis. Additionally, we extend the first and second Korovkin-type approximation theorems by incorporating Bessel statistical convergence, providing a more robust and comprehensive framework than existing results. The practical implications of these theorems are demonstrated through examples involving the classical Bernstein

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26

Nairat, Mazen. "Axial Angular Momentum of Bessel Light." Photonics Letters of Poland 10, no. 1 (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). Cross

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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 (2023): 789–98. http://dx.doi.org/10.24193/subbmath.2023.4.08.

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"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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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

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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 (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 (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

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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 (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

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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

Sudhanshu, Aggarwal. "ELZAKI TRANSFORM OF BESSEL'S FUNCTIONS." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 5, no. 8 (2018): 45–51. https://doi.org/10.5281/zenodo.1339350.

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In the modern time, Bessel’s functions appear in solving many problems of sciences and engineering together with many equations such as heat equation, wave equation, Laplace equation, Schrodinger equation, Helmholtz equation in cylindrical or spherical coordinates. In this paper, we determine Elzaki transform of Bessel’s functions. Some applications of Elzaki transform of Bessel’s functions for evaluating the integral, which contain Bessel’s functions, are given.

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34

Srivastava, Hari Mohan. "An Introductory Overview of Bessel Polynomials, the Generalized Bessel Polynomials and the q-Bessel Polynomials." Symmetry 15, no. 4 (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 polynomia

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35

Ulug, Bulent, Furkan Kuruoğlu, Yeşim Yalçın, et al. "Surface acoustic wave quasi-Bessel beams generated by symmetrically tilted interdigital transducers." Journal of Physics D: Applied Physics 55, no. 22 (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.

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36

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 (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 interpo

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37

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 (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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38

Kazımoğlu, Sercan. "Radii of γ-Spirallike of q-Special Functions". Mathematics 12, № 14 (2024): 2261. http://dx.doi.org/10.3390/math12142261.

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The geometric properties of q-Bessel and q-Bessel-Struve functions are examined in this study. For each of them, three different normalizations are applied in such a way that the resulting functions are analytic in the unit disk of the complex plane. For these normalized functions, the radii of γ-spirallike and convex γ-spirallike of order σ are determined using their Hadamard factorization. These findings extend the known results for Bessel and Struve functions. The characterization of entire functions from the Laguerre-Pólya class plays an important role in our proofs. Additionally, the inte

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Kotlyar, V. V., A. A. Kovalev, D. S. Kalinkina, and E. S. Kozlova. "Fourier-Bessel beams of finite energy." Computer Optics 45, no. 4 (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 init

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Aktaş, İbrahim, and Luminiţa-Ioana Cotîrlâ. "Certain Geometrical Properties and Hardy Space of Generalized k-Bessel Functions." Symmetry 16, no. 12 (2024): 1597. http://dx.doi.org/10.3390/sym16121597.

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In this paper, we study certain geometric properties such as the starlikeness of order ζ and the convexity of order ζ of the generalized k-Bessel function. In addition, we establish several requirements for the parameters so that the generalized k-Bessel function belongs to some subclasses of analytic functions. Furthermore, as an application of the geometric properties, we establish certain results concerning the Hardy spaces of the generalized k-Bessel function. On the other hand, we present some corollaries concerning the classical Bessel function Jρ and the modified Bessel function Iρ. To

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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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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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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 (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 o

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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 (2008): 430–42. http://dx.doi.org/10.1016/j.na.2006.11.009.

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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 (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 sp

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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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Glukhova, S. A., and M. A. Yurkin. "Scattering of generalized Bessel beams simulated with the discrete dipole approximation." Journal of Physics: Conference Series 2015, no. 1 (2021): 012046. http://dx.doi.org/10.1088/1742-6596/2015/1/012046.

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Abstract We consider the simulation of scattering of the high-order vector Bessel beams in the discrete dipole approximation framework (DDA). For this purpose, a new general classification of all existing Bessel beam types was developed based on the superposition of transverse Hertz vector potentials. Next, we implemented these beams in ADDA code – an open-source parallel implementation of the DDA. The code enables easy and efficient simulation of Bessel beams scattering by arbitrary-shaped particles. Moreover, these results pave the way for the following research related to the Bessel beam sc

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Campos, L. M. B. C., F. Moleiro, M. J. S. Silva, and J. Paquim. "On the Regular Integral Solutions of a Generalized Bessel Differential Equation." Advances in Mathematical Physics 2018 (November 4, 2018): 1–9. http://dx.doi.org/10.1155/2018/8919516.

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The original Bessel differential equation that describes, among many others, cylindrical acoustic or vortical waves, is a particular case of zero degree of the generalized Bessel differential equation that describes coupled acoustic-vortical waves. The solutions of the generalized Bessel differential equation are obtained for all possible combinations of the two complex parameters, order and degree, and finite complex variable, as Frobenius-Fuchs series around the regular singularity at the origin; the series converge in the whole complex plane of the variable, except for the point-at-infinity

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Zheng, Xianwei, Cuiming Zou, and Shouzhi Yang. "Signal representations via SIP p-frames and SIP Bessel multipliers in separable Banach spaces." International Journal of Wavelets, Multiresolution and Information Processing 19, no. 04 (2021): 2150005. http://dx.doi.org/10.1142/s0219691321500053.

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Digital signals are often modeled as functions in Banach spaces, such as the ubiquitous [Formula: see text] spaces. The frame theory in Banach spaces induces flexible representations of signals due to the robustness and redundancy of frames. Nevertheless, the lack of inner product in general Banach spaces limits the direct representations of signals in Banach spaces under a given basis or frame. In this paper, we introduce the concept of semi-inner product (SIP) [Formula: see text]-Bessel multipliers to extend the flexibility of signal representations in separable Banach spaces, where [Formula

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Alarifi, Najla M., and Saiful R. Mondal. "On Geometric Properties of Bessel–Struve Kernel Functions in Unit Disc." Mathematics 10, no. 14 (2022): 2516. http://dx.doi.org/10.3390/math10142516.

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The Bessel–Struve kernel function defined in the unit disc is used in this study. The Bessel–Struve kernel functions are generalized in this article, and differential equations are derived. We found conditions under which the generalized Bessel–Struve function is Lemniscate convex by using a subordination technique. The relation between the Janowski class and exponential class is also derived.

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