Article
Mathematics, Applied
Mohamed Abdalla, Salah Boulaaras, Mohamed Akel
Summary: This article introduces the Fourier-Bessel matrix transform (FBMT) and its inversion formula, explores the relationship with the Laplace transform, constructs the convolution properties of the FBMT. Some applications are proposed, and significant links between previous results of specific cases and the current results are outlined.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Optics
Victor V. Kotlyar, Alexey A. Kovalev, Darya S. Kalinkina
Summary: The new set of vortex rotationally symmetric Bessel beams are characterized by low sidelobes, Fourier-invariance, and finite energy, making them suitable for applications in data transmission, interferometry, and trapping of metallic particles.
OPTICS COMMUNICATIONS
(2021)
Article
Engineering, Electrical & Electronic
Zhi-Chao Zhang, Ao Sun, Zi-Yue Liang, Jing-Chi Li, Wen-Hua Liu, Xi-Ya Shi, An-Yang Wu
Summary: Sampling theorems for the two-dimensional linear canonical transform in polar coordinates play a crucial role in medical imaging, offering superior solutions for non-bandlimited image processing problems. Two types of interpolation formulae, the LCT and the LCHT, are derived for angularly periodic and highest frequency limited functions, with the latter outperforming the former in computational complexity. The selection of interpolation formula can significantly impact the efficiency of computations in image processing.
DIGITAL SIGNAL PROCESSING
(2021)
Article
Mathematics, Applied
Kevin Burrage, Pamela Burrage, Shev MacNamara
Summary: This study examines the reflectionless properties of the wave equation at boundaries in one space dimension and time, focusing on Toeplitz waves and Hankel waves. It finds exact formulae for these waves and demonstrates their reflectionless behavior on even and odd traversals. The analysis also introduces a new method of computer simulation for controlling the number of reflections in advance.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Engineering, Geological
Kien T. Nguyen, Danilo S. Kusanovic, Domniki Asimaki
Summary: This paper presents analytical solutions for computing the frequency-domain soil impedance functions (SIFs) for an infinitely-long cylindrical structure buried horizontally in a homogeneous elastic half-space. The solutions are derived using Hankel-Fourier series expansion, image technique, and Graf's addition theorem for axial SIFs, and Hankel-and Bessel-Fourier series expansion with numerical evaluation of contour integrals for in-plane SIFs. The analytical solutions are verified using finite element simulations and parametric studies are conducted to examine the variation of frequency-dependent SIFs with changes in soil properties and burial depth.
SOIL DYNAMICS AND EARTHQUAKE ENGINEERING
(2022)
Article
Mathematics, Applied
Faouaz Saadi, Radouan Daher
Summary: The aim of this paper is to prove the analogues of classical Titchmarsh theorems on the image under the discrete Fourier-Bessel transform of a set of functions satisfying a generalized Lipschitz condition in the weighted spaces L-p([0,1],t(2 alpha+1)dt), 1 < p <= 2.
ANALYSIS AND MATHEMATICAL PHYSICS
(2022)
Article
Mathematics
Hari M. Srivastava, Kush Kumar Mishra, Santosh K. Upadhyay
Summary: This paper presents a systematic study on the characteristics and properties of continuous and discrete fractional Bessel wavelet transforms, based on the theory of fractional Hankel transform.
Article
Chemistry, Analytical
Eugeny G. Abramochkin, Victor V. Kotlyar, Alexey A. Kovalev
Summary: We have derived a transformation method that relates standard Bessel-Gaussian (BG) beams with BG beams described by a Bessel function of a half-integer order and quadratic radial dependence. We have also studied square vortex BG beams described by the square of the Bessel function and double-BG beams described by a product of two different integer-order Bessel functions. By deriving expressions as series of products of three Bessel functions, we have described the propagation of these beams in free space. Additionally, we have obtained a vortex-free power-function BG beam and explored its propagation characteristics.
Article
Mathematics, Applied
Bartosz Langowski, Adam Nowak
Summary: This study demonstrates sharp power-weighted L-p, weak type, and restricted weak type inequalities for the heat semigroup maximal operator and Riesz transforms associated with the Bessel operator B-v in the exotic parameter range -infinity < v < 1. Furthermore, it characterizes basic mapping properties for other fundamental harmonic analysis operators, including the heat semigroup based vertical g-function and fractional integrals (Riesz potential operators) within the same framework.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Mohamed Abdalla
Summary: This article focuses on the evaluation of Hankel transforms involving Bessel matrix functions in the kernel, as well as their applications in special cases. The results obtained are more general and contribute to modern integral transforms with special matrix functions.
Article
Mathematics, Applied
Jihed Sahbani, Takoua Guettiti
Summary: The purpose of this paper is to establish an extension of the prolate spheroidal wave functions as the eigenfunction of the finite canonical Fourier-Bessel transform. We examine the concentration problem, uncertainty principles regarding the essential supports, and signal recovery associated with the canonical Fourier-Bessel transform in the space of band-limited functions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Durmus Albayrak, Ahmet Dernek, Nese Dernek, Faruk Ucar
Summary: The paper introduces the generalized Bessel-Maitland transform and its kernel function, obtaining new identities for special cases. Several identities for the generalized Bessel-Maitland integral transform are derived using these relations, showing some special cases are related to the Laplace transform and the Hankel transform. Additionally, examples are provided as representations of the results presented.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
S. S. Platonov
Summary: This paper proves an analogue of a classical theorem for the Hankel transform of functions from Nikol'skii type function classes on the half-line [0,+infinity).
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
(2021)
Article
Physics, Multidisciplinary
Forouzan Habibi, Mohammad Moradi
Summary: This paper investigates the propagation properties of Mainardi beams under Fractional Fourier transforms and Fourier transforms, and finds that the characteristics of Mainardi beams can be controlled by adjusting parameters such as hyperbolic parameter, fractional order, transform order, and distance propagation. These results have practical value in signal processing and beam manipulation.
Article
Water Resources
Sajedeh Farmani, Mahnaz Ghaeini-Hessaroeyeh, Saleh Hamzehei-Javaran
Summary: In this study, the finite element method is employed to investigate water penetration in soil. By using new spherical Hankel shape functions, the method's accuracy and robustness are improved. The comparisons indicate that this method is more precise in handling seepage problems.
APPLIED WATER SCIENCE
(2023)
Editorial Material
Optics
Grover A. Swartzlander
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS
(2016)
Article
Optics
Grover A. Swartzlander
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS
(2017)
Article
Optics
Xiaopeng Peng, Garreth J. Ruane, Marco B. Quadrelli, Grover A. Swartzlander
Article
Optics
Jacob H. Wirth, Abbie T. Watnik, Grover A. Swartzlander
Article
Physics, Multidisciplinary
Ying-Ju Lucy Chu, Eric M. Jansson, Grover A. Swartzlander
PHYSICAL REVIEW LETTERS
(2018)
Editorial Material
Optics
Grover A. Swartzlander
JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS
(2018)
Article
Optics
Prateek R. Srivastava, Ying-Ju Lucy Chu, Grover A. Swartzlander
Article
Optics
Jacob H. Wirth, Abbie T. Watnik, Grover A. Swartzlander
Article
Physics, Multidisciplinary
Ying-Ju Lucy Chu, Nelson V. Tabiryan, Grover A. Swartzlander
PHYSICAL REVIEW LETTERS
(2019)
Article
Physics, Multidisciplinary
Prateek R. Srivastava, Grover A. Swartzlander
EUROPEAN PHYSICAL JOURNAL PLUS
(2020)
Review
Optics
Artur R. Davoyan, Jeremy N. Munday, Nelson Tabiryan, Grover A. Swartzlander, Les Johnson
Summary: Solar sails hold great promise for space exploration, enabling novel science missions beyond the reach of current propulsion technology. However, they face challenges in optical materials and photonic designs. A technology development roadmap is outlined to guide researchers in pioneering the space faring future.
Article
Optics
Ying-Ju Lucy Chu, Monjurul Meem, Prateek R. Srivastava, Rajesh Menon, Grover A. Swartzlander
Summary: The study discusses the principles and experimental measurements of a laser beam rider, focusing on the characteristics of a diffractive axicon film and the effects of optical momentum change. Experimental results show that continuous illumination can support harmonic motion, while modulated illumination can support parametric gain and damping.
Article
Engineering, Aerospace
Amber L. Dubill, Grover A. Jr Jr Swartzlander
Summary: This paper explores the application of solar sails based on the physics of diffracted light for in-space propulsion. By comparing trajectories of different types of sails, it is found that diffractive solar sails achieve higher solar inclination angles and smaller orbital radii compared to reflective sails. The authors envision using a constellation of diffractive solar sails for space weather monitoring and heliophysics science around the sun.
Article
Optics
Jacob H. Wirth, Abbie T. Watnik, Grover A. Swartzlander
Proceedings Paper
Engineering, Electrical & Electronic
Xiaopeng Peng, Garreth J. Ruane, Alexandra B. Artusio-Glimpse, Grover A. Swartzlander
COMPUTATIONAL IMAGING XIII
(2015)
