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Journal articles on the topic 'Integral Hankel transformation'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

Gorty, Dr V. R. Lakshmi. "Continuous Generalized Hankel-type integral wavelet transformation." JOURNAL OF ADVANCES IN MATHEMATICS 11, no. 3 (2015): 5050–58. http://dx.doi.org/10.24297/jam.v11i3.1272.

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Using the theory of Hankel-type convolution, continuous generalized Hankel-type wavelet integral transformation is defined. The generalized Hankel-type integral wavelet transformation is developed. Using the developed theory of generalized Hankel-type convolution, the generalized Hankel-type translation is introduced. Properties of the kernel are developed in the study. Using the properties of kernel,D Î¼,Î±, Î² ,v (x,y,z)the generalized Hankel-type wavelet transformation is defined. The existence of the generalized Hankel-type integral wavelet transformation is given by a theorem. The bounded

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2

Schmidt, Maxie D. "A Short Note on Integral Transformations and Conversion Formulas for Sequence Generating Functions." Axioms 8, no. 2 (2019): 62. http://dx.doi.org/10.3390/axioms8020062.

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The purpose of this note is to provide an expository introduction to some more curious integral formulas and transformations involving generating functions. We seek to generalize these results and integral representations which effectively provide a mechanism for converting between a sequence’s ordinary and exponential generating function (OGF and EGF, respectively) and vice versa. The Laplace transform provides an integral formula for the EGF-to-OGF transformation, where the reverse OGF-to-EGF operation requires more careful integration techniques. We prove two variants of the OGF-to-EGF tran

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3

Prasad, Akhilesh, and P. K. Maurya. "The fractional Hankel-type integral wavelet packet transformation." Journal of Analysis 28, no. 1 (2017): 225–34. http://dx.doi.org/10.1007/s41478-017-0068-z.

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4

Prasad, Akhilesh, and P. K. Maurya. "The wavelet transformation involving the fractional powers of Hankel-type integral transformation." Afrika Matematika 28, no. 1-2 (2016): 189–98. http://dx.doi.org/10.1007/s13370-016-0438-8.

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5

Prasad, Akhilesh, V. K. Singh, and M. M. Dixit. "PSEUDO-DIFFERENTIAL OPERATORS INVOLVING HANKEL–CLIFFORD TRANSFORMATION." Asian-European Journal of Mathematics 05, no. 03 (2012): 1250040. http://dx.doi.org/10.1142/s1793557112500404.

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Pseudo-differential operator (p.d.o) associated with the symbol a(x, y) whose derivatives satisfy certain growth condition is defined and the Zemanian-type spaces Hμ(I) and S(I) are introduced. It is shown that the p.d.o is continuous linear map of the space Hμ(I) and S(I) into itself. An integral representation of p.d.o h1, μ, a is obtained. Using the Hankel convolution it is shown that p.d.o h1, μ, a satisfies a certain [Formula: see text]-norm inequality. Properties of Sobolev-type space [Formula: see text] are studied.

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6

Key, Kerry. "Is the fast Hankel transform faster than quadrature?" GEOPHYSICS 77, no. 3 (2012): F21—F30. http://dx.doi.org/10.1190/geo2011-0237.1.

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The fast Hankel transform (FHT) implemented with digital filters has been the algorithm of choice in EM geophysics for a few decades. However, other disciplines have predominantly relied on methods that break up the Hankel transform integral into a sum of partial integrals that are each evaluated with quadrature. The convergence of the partial sums is then accelerated through a nonlinear sequence transformation. While such a method was proposed for geophysics nearly three decades ago, it was demonstrated to be much slower than the FHT. This work revisits this problem by presenting a new algori

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7

Pansare, P. D., and B. B. Waphare. "Pseudo-differential operator involving generalized Hankel–Clifford transformation." Asian-European Journal of Mathematics 09, no. 01 (2016): 1650016. http://dx.doi.org/10.1142/s1793557116500169.

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Pseudo-differential operators (p.d.os) involving generalized Hankel–Clifford transformation associated with the symbol [Formula: see text] whose derivatives satisfy certain growth condition are defined and the Zemanian type function spaces [Formula: see text] and [Formula: see text] are introduced. It is shown that p.d.o’s are continuous linear map of the space [Formula: see text] and [Formula: see text] into itself. Also an Integral representation of p.d.o is obtained.

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8

Malgonde, S. P., S. R. Bandewar, and Lokenath Debnath. "Mixed Parseval equation and generalized Hankel-type integral transformation of distributions." Integral Transforms and Special Functions 15, no. 5 (2004): 431–43. http://dx.doi.org/10.1080/10652460410001686046.

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9

Yilmaz, Oguz. "Second Order Diffraction of Water Waves by a Bottom Mounted Vertical Circular Cylinder and Some Related Numerical Problems." Journal of Offshore Mechanics and Arctic Engineering 129, no. 1 (2006): 68–70. http://dx.doi.org/10.1115/1.2355519.

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A Hankel transformation is used to obtain the second order diffraction solution of vertical cylinder of circular cross section. The improper integral over the free surface is tackled carefully. The singularity at the free surface is overcome effectively using a third order nonlinear transformation. Numerical results for free surface elevations compare well with the published data.

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10

Singh, R., and V. Kumar. "Interaction Due to Mechanical Source in Generalized Thermo Microstretch Elastic Medium." International Journal of Applied Mechanics and Engineering 19, no. 2 (2014): 347–63. http://dx.doi.org/10.2478/ijame-2014-0023.

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Abstract The eigen value approach, following the Laplace and Hankel transformation has been employed to find a general solution of the field equations in a generalized thermo microstretch elastic medium for an axisymmetric problem. An infinite space with the mechanical source has been applied to illustrate the utility of the approach. The integral transformations have been inverted by using a numerical inversion technique to obtain normal displacement, normal force stress, couple stress and microstress in the physical domain. Numerical results are shown graphically

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11

Assoudi, R., S. Bougtab, H. Allouche, K. Lamzoud, F. Feuillebois, and M. Chaoui. "High accurate method to calculate a singular integral related to Hankel transform." Mathematical Modeling and Computing 9, no. 2 (2022): 241–61. http://dx.doi.org/10.23939/mmc2022.02.241.

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In this paper we are interested in the approximation of the integral \[I_0(f,\omega)=\int_0^\infty f(t)\,e^{-t}\,J_0(\omega t)\,dt\] for fairly large $\omega$ values. This singular integral comes from the Hankel transformation of order $0$, $f(x)$ is a function with which the integral is convergent. For fairly large values of $\omega$, the classical quadrature methods are not appropriate, on the other side, these methods are applicable for relatively small values of $\omega$. Moreover, all quadrature methods are reduced to the evaluation of the function to be integrated into the nodes of the s

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12

Betancor, J. J. "A Mixed Parseval's Equation And a Generalized Hankel Transformation of Distributions." Canadian Journal of Mathematics 41, no. 2 (1989): 274–84. http://dx.doi.org/10.4153/cjm-1989-014-9.

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Let an integral transform T﹛f﹜ of a complex valued function f(x) defined over the interval (0, ∞) be defined as One of the most usual procedures to extend the classical transform (l.a) to generalized functions consists in constructing a space A of testing functions over (0, ∞) which is closed with respect to the classical transform (l.a) and then the corresponding transform of the generalized function/ of the dual space of A is defined through This approach has been followed by L. Schwartz [13] and A. H. Zemanian [20], amongst others.

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13

Singh, R., and K. Singh. "Eigen Value Approach in Micropolar Elastic Medium with Voids." International Journal of Applied Mechanics and Engineering 18, no. 2 (2013): 521–36. http://dx.doi.org/10.2478/ijame-2013-0031.

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The eigen value approach, following the Laplace and Hankel transformation has been employed to find a general solution of the field equations in a micropolar elastic medium with voids for an axisymmetric problem. An infinite space with the mechanical source has been applied to illustrate the utility of the approach. The integral transformations has been inverted by using a numerical inversion technique to get the result in physical domain. The results in the form of normal displacement, volume fraction, normal force stress, tangential force stress and tangential couple stress components have b

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14

Denysenko, Viktoriia, Iryna Kovalova, and Dina Lazarieva. "The Dynamic Problem of Torsion by a Rigid Shaft of a Nonhomogeneous Half-Space." Materials Science Forum 968 (August 2019): 396–403. http://dx.doi.org/10.4028/www.scientific.net/msf.968.396.

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An axisymmetric contact problem concerning the torsion of a circular shaft of an orthotropic-nonhomogeneous half-space is considered. By means of the technique of integral transformations of Laplace and Hankel, with the subsequent application of the orthogonal polynomial method, an approximate solution in the transformant space is constructed. Also was performed reverse transformation. Calculated formulas for the angle of rotation of the shaft and the tangential stress acting on the contact area are obtained. Numerical calculations for certain types of heterogeneity have been performed. Compar

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15

Kebli, Belkacem, and Fateh Madani. "A mixed boundary value problem of a cracked elastic medium under torsion." Theoretical and Applied Mechanics 48, no. 2 (2021): 237–55. http://dx.doi.org/10.2298/tam200923010k.

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The present work aims to investigate a penny-shaped crack problem in the interior of a homogeneous elastic material under axisymmetric torsion by a circular rigid inclusion embedded in the elastic medium. With the use of the Hankel integral transformation method, the mixed boundary value problem is reduced to a system of dual integral equations. The latter is converted into a regular system of Fredholm integral equations of the second kind which is then solved by quadrature rule. Numerical results for the displacement, stress and stress intensity factor are presented graphically in some partic

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16

Gilbert, R. P., and Zhongyan Lin. "Scattering in a Shallow Ocean with an Elastic Seabed." Journal of Computational Acoustics 05, no. 04 (1997): 403–31. http://dx.doi.org/10.1142/s0218396x9700023x.

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In this paper the boundary integral equation method is used to solve a scattering problem in a shallow ocean with an elastic seabed. The Hankel transformation and Mittag–Leffler decomposition were used to construct the propagating solution for both far-field and near-field. In particular, necessary and sufficient conditions are found for the existence of the propagating solution. Using the propagating solution, the scattering problem is recast as a boundary integral equation. A numerical algorithm is developed for solving this boundary integral equation and its implementation on a T3D parallel

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17

Tayel, Ismail M. "Heating a 2D Thermoelastic Half-Space Induced by Volumetric Absorption of a Laser Radiation." Mathematics 8, no. 11 (2020): 2094. http://dx.doi.org/10.3390/math8112094.

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In this work, the generalized theory with dual-phase-lag of thermoelasticity is employed to study the influences induced by absorbing a penetrating laser radiation inside a 2D thermoelastic semi-infinite medium. The medium’s surface is presumed to be exposed to temperature-dependent heat losses and is traction-free. The considered problem is solved using the integral transforms technique by applying the double-transformation Laplace and Hankel. A numerical fashion is applied to obtain the inverse of the Laplace transformation. The results of this problem are presented graphically for some stud

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18

Shlyahin, Dmitriy. "Analyzing calculation results of non-stationary axisymmetric thermoelasticity task for a circular isotropic plate." MATEC Web of Conferences 196 (2018): 01007. http://dx.doi.org/10.1051/matecconf/201819601007.

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The paper releases results of numerical calculation of axisymmetric dynamic thermoelasticity task for a fixed circular isotropic plate in case of temperature change on its front faces (boundary conditions of the 1st type). The calculated ratios are obtained by using the GL-theory of thermoelasticity (classical theory), which determines the dependence of the vector of heat flux on the velocity of change and temperature gradient. The mathematical model of the task in question includes differential equations of axisymmetric motion and thermal conductivity, formulated as regard to the component of

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19

Hunziker, Jürg, Jan Thorbecke, and Evert Slob. "The electromagnetic response in a layered vertical transverse isotropic medium: A new look at an old problem." GEOPHYSICS 80, no. 1 (2015): F1—F18. http://dx.doi.org/10.1190/geo2013-0411.1.

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We determined that the electromagnetic vertical transverse isotropic response in a layered earth can be obtained by solving two equivalent scalar equations, which were for the vertical electric field and for the vertical magnetic field, involving only a scalar global reflection coefficient. Besides the complete derivation of the full electromagnetic response, we also developed the corresponding computer code called EMmod, which models the full electromagnetic fields including internal multiples in the frequency-wavenumber domain and obtains the frequency-space domain solutions through a Hankel

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20

Havrysh, V. I., B. O. Bilinskyi, O. S. Korol, R. R. Shkrab, and I. O. Zimoha. "MATHEMATICAL MODELS OF HEAT TRANSFER IN ELEMENTS OF TURBO GENERATORS (CONTINUED)." Ukrainian Journal of Information Technology 2, no. 1 (2020): 21–28. http://dx.doi.org/10.23939/ujit2020.02.021.

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Previously developed [8] and presented new mathematical models for the analysis of temperature regimes in individual elements of turbo generators, which are geometrically described by isotropic half-space and space with an internal heat source of cylindrical shape. Cases are also considered for half-space, when the fuel-releasing cylinder is thin, and for space, when it is heat-sensitive. For this purpose, using the theory of generalized functions, the initial differential equations of thermal conductivity with boundary conditions are written in a convenient form. To solve the obtained boundar

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21

YANG, Yonglin, Xing LI, Shenghu DING, and Wenshuai WANG. "A Numerical Algorithm for Arbitrary Real-Order Hankel Transform." Wuhan University Journal of Natural Sciences 27, no. 1 (2022): 26–34. http://dx.doi.org/10.1051/wujns/2022271026.

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The Hankel transform is widely used to solve various engineering and physics problems, such as the representation of electromagnetic field components in the medium, the representation of dynamic stress intensity factors, vibration of axisymmetric infinite membrane and displacement intensity factors which all involve this type of integration. However, traditional numerical integration algorithms cannot be used due to the high oscillation characteristics of the Bessel function, so it is particularly important to propose a high precision and efficient numerical algorithm for calculating the integ

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22

Chebakov, Mikhail I., and Elena M. Kolosova. "Contact Problem on the Interaction of a Punch in the Form of a Paraboloid of Ro-tation and a Poroelastic Layer Fixed on an Elastic Foundation." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 2 (214) (June 30, 2022): 28–35. http://dx.doi.org/10.18522/1026-2237-2022-2-28-35.

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The contact problem of the introduction of a rigid punch in the form of a paraboloid of rotation into a poroelastic layer fixed on an elastic half-space is considered on the basis of the equations of the theory of poroelastic bodies of Cowin-Nunziato. It is assumed that there is no friction in the contact zone. With the help of the Hankel integral transformation, the problem posed is reduced to solving the integral equation for an unknown contact stress. The collocation method is used to solve the integral equation. The area of contact, the values of contact stresses are found, and the deforma

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23

Siemon, Bernhard. "Accurate 1D forward and inverse modeling of high-frequency helicopter-borne electromagnetic data." GEOPHYSICS 77, no. 4 (2012): WB71—WB87. http://dx.doi.org/10.1190/geo2011-0371.1.

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Frequency-domain helicopter-borne electromagnetic (HEM) data are commonly interpreted using quasistatic approximations in forward and inverse solutions. At high-frequencies ([Formula: see text]), the accuracy of this approach is often insufficient. Implementation of a full solution of the forward problem that includes displacement currents in both subsurface and air, however, may cause singularity problems during numerical evaluation of the secondary field integral using Hankel or Laplace transforms, particularly at high frequencies. These effects can be reduced by a wavenumber shift during nu

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24

VASILYEVA, О., and Ya KOZAK. "THERMAL PROCESSES OF FIRE DETECTORS’ HEAT-RESISTANT SENSITIVE ELEMENTS." Ukrainian Journal of Civil Engineering and Architecture, no. 1 (013) (April 14, 2023): 22–27. http://dx.doi.org/10.30838/j.bpsacea.2312.280223.22.915.

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The purpose of the article. The article deals with thermal processes in the heat-resistant sensitive element of fire detectors when an electric current flows through it. Such processes are described by an inhomogeneous equation of mathematical physics with boundary conditions of the third kind. Methodology. The Hankel integral transformation is used to solve the differential equation that describes the thermal processes in the heat-resistant sensitive element of fire detectors. As a result of the transformations, a general expression was obtained for the temperature of the heat-resistant sensi

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25

Madani, Fateh, and Belkacem Kebli. "Axisymmetric Torsion of an Elastic Layer Sandwiched between Two Elastic Half-Spaces with Two Interfaced Cracks." Studia Geotechnica et Mechanica 41, no. 2 (2019): 57–66. http://dx.doi.org/10.2478/sgem-2019-0006.

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AbstractThe present article examines the problem related to the axisymmetric torsion of an elastic layer by a circular rigid disc at the symmetry plane. The layer is sandwiched between two similar elastic half-spaces with two penny-shaped cracks symmetrically located at the interfaces between the two bonded dissimilar media. The mixed boundary-value problem is transformed, by means of the Hankel integral transformation, to dual integral equations, that are reduced, to a Fredholm integral equation of the second kind. The numerical methods are used to convert the resulting system to a system of

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26

Amundsen, Lasse. "Wavenumber‐based filtering of marine point‐source data." GEOPHYSICS 58, no. 9 (1993): 1335–48. http://dx.doi.org/10.1190/1.1443516.

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In seismic processing, plane‐wave decomposition has played a fundamental role, serving as a basis for developing sophisticated processing techniques valid for depth‐dependent models. By comparing analytical expressions for the decomposed wavefields, we review several processing algorithms of interest for the geophysicist. The algorithms may be applied to marine point‐source data acquired over a horizontally layered viscoelastic and anisotropic medium. The plane‐wave decomposition is based on the Fourier transform integral for line‐source data and the Hankel transform integral for point‐source

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27

Gutiérrez-Tovar, Y. E., and J. M. R. Méndez-Pérez. "The Kontorovich–Lebedev integral transformation with a Hankel function kernel in a space of generalized functions of doubly exponential descent." Journal of Mathematical Analysis and Applications 328, no. 1 (2007): 359–69. http://dx.doi.org/10.1016/j.jmaa.2006.05.034.

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28

Shlyahin, Dmitriy, and Olesya Ratmanova. "The task of direct piezoeffect for a bi-morth plate." MATEC Web of Conferences 196 (2018): 01006. http://dx.doi.org/10.1051/matecconf/201819601006.

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The research focuses on the dynamic axisymmetric task for a round bi-morph structure consisting of a metal support plate and a piezoceramic axially polarized plate. Its bending oscillations are carried out because of the actions of mechanical load (normal stresses) on its end surface, which is an arbitrary time and radial coordinate function. The rigid and hinged support of the plate cylindrical surface is taken into account. The value of the induced field is calculated by determining the potential on the metal support plate. To solve the task of the theory of the elasticity in a three-dimensi

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29

Zhang, Shiping, and Zhan Xu. "Elastodynamic Solutions of a Finite Soil Layer under Interior Distributed Actions." Shock and Vibration 2021 (June 30, 2021): 1–18. http://dx.doi.org/10.1155/2021/5538319.

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Through a method of displacement potentials, Fourier series, and Hankel integral transformation, the generalized solutions of an elastic layer resting on a rigid base under arbitrary, distributed, buried, and time-harmonic loads are developed in this study. With the proposed solution, the specific results for two kinds of uniform distributions as a kind of fundamental solutions in the interaction analysis of media and inclusions by the method of boundary integral equations are included as illustrations. Finally, numerical examples involving surface and buried patch loads are presented to valid

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30

Shlyakhin, D. A., and Zh M. Dauletmuratova. "Non-stationary coupled axisymmetric thermoelasticity problem for a rigidly fixed round plate." PNRPU Mechanics Bulletin, no. 4 (December 15, 2019): 191–200. http://dx.doi.org/10.15593/perm.mech/2019.4.18.

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A new closed solution is constructed for the axisymmetric dynamic problem of the classical (CTE) theory of thermoelasticity for a rigidly fixed circular isotropic plate in the case of a temperature change on its face surfaces (boundary conditions of the first kind). The mathematical formulation of the problem under consideration includes linear equations of thermal conductivity and equilibrium in a spatial setting, assuming that their inertial elastic characteristics can be neglected in the structures under study. In constructing a general solution of related non-self-conjugate equations, we u

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31

Solyar, T., and O. Solyar. "DETERMINATION OF STRESSES IN THICK PLATES UNDER LOCALIZED LOADS." Mechanics And Mathematical Methods 4, no. 1 (2022): 45–63. http://dx.doi.org/10.31650/2618-0650-2022-4-1-45-63.

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The problem of invesigating the stresses in the plates, which are subjected to the action of concentrated forces and locally distributed load is considered. The stresses were determined on the basis of the relations of the three-dimensional theory of elasticity using two methods. The first uses the symbolic Lurie method with the additional application of Vashchenko-Zakharchenko expansion formulas. The solution is constructed in the form of series, which exponentially converge at points distant from the applied forces. However, these series converge slowly in the vicinity of the applied load. I

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32

Abramov, Yuriy, Oleksii Basmanov, and Yaroslav Kozak. "Substantiating the pulse method for determining the time parameter of fire detectors with a thermoresistive sensing element." Eastern-European Journal of Enterprise Technologies 6, no. 5 (114) (2021): 49–55. http://dx.doi.org/10.15587/1729-4061.2021.244235.

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This paper substantiates the pulse method for determining the time parameter for fire detectors with a thermoresistive sensing element ‒ the time constant. The method is based on using the Joule-Lenz effect, which manifests itself when an electric current pulse passes through the thermoresistive sensing element of fire detectors. Thermal processes in such a sensing element are described by a mathematical model that belongs to the class of equations of mathematical physics. The solution to the differential equation of this class was derived using the Hankel integral transformation and is repres

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33

Yuriy, Abramov, Basmanov Oleksii, and Kozak Yaroslav. "Substantiating the pulse method for determining the time parameter of fire detectors with a thermoresistive sensing element." Eastern-European Journal of Enterprise Technologies 6, no. 5 (114) (2021): 49–55. https://doi.org/10.15587/1729-4061.2021.244235.

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This paper substantiates the pulse method for determining the time parameter for fire detectors with a thermoresistive sensing element ‒ the time constant. The method is based on using the Joule-Lenz effect, which manifests itself when an electric current pulse passes through the thermoresistive sensing element of fire detectors. Thermal processes in such a sensing element are described by a mathematical model that belongs to the class of equations of mathematical physics. The solution to the differential equation of this class was derived using the Hankel integral transformation and is repres

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34

Srigutomo, Wahyu, Cahyo Aji Hapsoro, Acep Purqon, Warsa, Doddy Sutarno, and Tsuneomi Kagiyama. "Nonlinear Inversion Using Very Fast Simulated Annealing for Horizontal Electric Dipole Time-Domain Electromagnetic Data." Journal of Electromagnetic Engineering and Science 21, no. 5 (2021): 379–90. http://dx.doi.org/10.26866/jees.2021.5.r.46.

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A nonlinear stochastic inversion scheme, called very fast simulated annealing (VFSA), was applied to the time-domain electromagnetic data generated from a horizontal electric dipole. The forward formulation of the vertical magnetic field was expressed in the Laplace domain by applying the Hankel integral transform. Time-domain transformation was performed by applying the inverse Laplace transform using the Gaver–Stehfest algorithm. In this study, for noise-free synthetic data, the VFSA scheme yielded the smallest misfit and an inverted resistivity model that resembled the test model. The addit

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35

Sadiku, Salawu. "Analysis of Combined Vertical and Radial Consolidation of Soil under Time-Dependent Loading." Civil Engineering Journal 9, no. 1 (2023): 183–96. http://dx.doi.org/10.28991/cej-2023-09-01-014.

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Fine-grained compressible soils are usually associated with strength challenges in the course of carrying structures, roadways, embankments, and other civil engineering facilities. In addition, due to their low permeabilities, compressible soils take an awfully long duration to achieve optimal consolidation, with its attendant negative effects on the facilities supported by the soils. Engineering practitioners and researchers have established the efficacy of vertical drains for accelerating the consolidation process of such soils through the shortening of horizontal flow distances, thereby sta

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Prasad, Akhilesh, and Sumant Kumar. "Fractional wavelet packet transformations involving Hankel–Clifford integral transformations." Acta Mathematica Sinica, English Series 32, no. 7 (2016): 783–96. http://dx.doi.org/10.1007/s10114-016-5523-2.

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37

Linares, M. Linares, and J. M. R. Mendez Pérez. "Hankel complementary integral transformations of arbitrary order." International Journal of Mathematics and Mathematical Sciences 15, no. 2 (1992): 323–32. http://dx.doi.org/10.1155/s0161171292000401.

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Four selfreciprocal integral transformations of Hankel type are defined through(ℋi,μf)(y)=Fi(y)=∫0∞αi(x)ℊi,μ(xy)f(x)dx, ℋi,μ−1=ℋi,μ,wherei=1,2,3,4;μ≥0;α1(x)=x1+2μ,ℊ1,μ(x)=x−μJμ(x),Jμ(x)being the Bessel function of the first kind of orderμ;α2(x)=x1−2μ,ℊ2,μ(x)=(−1)μx2μℊ1,μ(x);α3(x)=x−1−2μ,ℊ3,μ(x)=x1+2μℊ1,μ(x), andα4(x)=x−1+2μ,ℊ4,μ(x)=(−1)μxℊ1,μ(x). The simultaneous use of transformationsℋ1,μ, andℋ2,μ, (which are denoted byℋμ) allows us to solve many problems of Mathematical Physics involving the differential operatorΔμ=D2+(1+2μ)x−1D, whereas the pair of transformationsℋ3,μandℋ4,μ, (which we expr

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Malgonde, S. P., and Lokenath Debnath. "On Hankel type integral transformations of generalized functions." Integral Transforms and Special Functions 15, no. 5 (2004): 421–30. http://dx.doi.org/10.1080/10652460410001686055.

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Havrysh, V. I. "Mathematical Models of the Temperature Field in Elements of Electronic Devices with Foreign Inclusion." Èlektronnoe modelirovanie 45, no. 5 (2023): 3–19. http://dx.doi.org/10.15407/emodel.45.05.003.

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Linear and non-linear mathematical models for the determination of the temperature field, and subsequently for the analysis of temperature regimes in isotropic media with semi-transparent foreign inclusions that are also subject to external heat load, have been developed. To solve the nonlinear boundary-value problem, a linearizing function was introduced, using which the original nonlinear heat conduction equation and nonlinear boundary conditions were linearized, and as a result, a partially linearized second-order differential equation with partial derivatives and discontinuous and singular

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Olshanskiy, V.P., M.V. Slipchenko, O.V. Olshanskiy, and O.M. Shukaieva. "On the calculation and forecast of the temperature in the core hearth by self-heating of raw materials in the silo." Engineering of nature management, no. 1(23) (March 22, 2022): 29–34. https://doi.org/10.5281/zenodo.6807632.

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An approximate method for calculating the temperature in an inhomogeneous core hearth without a clear boundary is presented, assuming a significant distance from its center from the walls of the silo, when the conditions of heat exchange on them have little effect on the temperature process in the center of the hearth. Gauss's law is adopted regarding the distribution of thermal sources along the radial coordinate. To construct analytical solutions of the unsteady axisymmetric problem of unsteady heat conduction, the integral Hankel transform is used. This solution makes sense when the cen

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Porter, D. "On some Cauchy-separable integral equations." Mathematical Proceedings of the Cambridge Philosophical Society 99, no. 3 (1986): 547–64. http://dx.doi.org/10.1017/s0305004100064495.

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In a recent paper, Porter [9] devised two generalized Volterra operators which convert integral equations with the Hankel function kernel into Cauchy singular equations. The transformations were exploited in [9], and in a subsequent paper (Porter and Chu [10]), in relation to certain wave diffraction problems.

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Prasad, Akhilesh, and Praveen Kumar. "Composition of pseudodifferential operators associated with fractional Hankel–Clifford integral transformations." Applicable Analysis 95, no. 8 (2015): 1792–807. http://dx.doi.org/10.1080/00036811.2015.1073264.

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Prasad, Akhilesh, and P. K. Maurya. "A pair of pseudo-differential operators involving Hankel-type integral transformations." Journal of Pseudo-Differential Operators and Applications 6, no. 1 (2014): 135–51. http://dx.doi.org/10.1007/s11868-014-0104-6.

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Ignatenko, M. V. "Operator interpolation formulas of Hermitе type with arbitrary multiplicity nodes based on identity transformations of function". Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 54, № 3 (2018): 263–72. http://dx.doi.org/10.29235/1561-2430-2018-54-3-263-272.

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The problem of construction and research of Hermite interpolation formulas with nodes of arbitrary multiplicity for operators given in functional spaces of one and two variables is considered. The construction of operator interpolation polynomials is based both on interpolation polynomials for scalar functions with respect to an arbitrary Chebyshev system and on identity transformations of functions. The reduced operator formulas contain the Stieltjes integrals and the Gateaux differentials of an interpolated operator and are invariant for a special class of operator polynomials of appropriate

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Prasad, Akhilesh, and P. K. Maurya. "A couple of fractional powers of Hankel-type integral transformations of arbitrary order." Bollettino dell'Unione Matematica Italiana 9, no. 3 (2015): 323–39. http://dx.doi.org/10.1007/s40574-015-0049-6.

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Prasad, Akhilesh, and P. K. Maurya. "A couple of fractional powers of Hankel-type integral transformations and pseudo-differential operators." SeMA Journal 74, no. 2 (2016): 181–211. http://dx.doi.org/10.1007/s40324-016-0087-8.

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Havrysh, V. I., and R. R. Shkrab. "Mathematical models for the determination of temperature fields in heterogeneous elements of digital devices taking thermo sensitivity into account." Ukrainian Journal of Information Technology 5, no. 1 (2023): 17–24. http://dx.doi.org/10.23939/ujit2023.01.017.

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Linear and nonlinear mathematical models for determining the temperature field and subsequently analyzing temperature regimes in isotropic spatial media with semi-through foreign inclusions subjected to internal and external thermal loads are developed. For this purpose, the heat transfer coefficient for such structures is described as a single unit using asymmetric unit functions, which makes it possible to consider boundary value problems of heat transfer with one linear and nonlinear differential equations of heat transfer with discontinuous and singular coefficients and linear and nonlinea

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Hone, A. N. W., J. A. G. Roberts, and P. Vanhaecke. "A family of integrable maps associated with the Volterra lattice." Nonlinearity 37, no. 9 (2024): 095028. http://dx.doi.org/10.1088/1361-6544/ad68ba.

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Abstract Recently Gubbiotti, Joshi, Tran and Viallet classified birational maps in four dimensions admitting two invariants (first integrals) with a particular degree structure, by considering recurrences of fourth order with a certain symmetry. The last three of the maps so obtained were shown to be Liouville integrable, in the sense of admitting a non-degenerate Poisson bracket with two first integrals in involution. Here we show how the first of these three Liouville integrable maps corresponds to genus 2 solutions of the infinite Volterra lattice, being the g = 2 case of a family of maps a

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Shah, Nehad Ali, A. Al-Zubaidi, and S. Saleem. "Study of Magnetohydrodynamic Pulsatile Blood Flow through an Inclined Porous Cylindrical Tube with Generalized Time-Nonlocal Shear Stress." Advances in Mathematical Physics 2021 (May 17, 2021): 1–11. http://dx.doi.org/10.1155/2021/5546701.

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The effects of pulsatile pressure gradient in the presence of a transverse magnetic field on unsteady blood flow through an inclined tapered cylindrical tube of porous medium are discussed in this article. The fractional calculus technique is used to provide a mathematical model of blood flow with fractional derivatives. The solution of the governing equations is found using integral transformations (Laplace and finite Hankel transforms). For the semianalytical solution, the inverse Laplace transform is found by means of Stehfest’s and Tzou’s algorithms. The numerical calculations were perform

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Alifanov, A. V., and V. M. Golub. "Solution of the Unsteady Heat-Conduction Equation for a System of Two Bounded Heterogeneous Cylinders with the Use of The Integral Transformations of Hankel and Laplace." Journal of Engineering Physics and Thermophysics 76, no. 5 (2003): 1111–18. http://dx.doi.org/10.1023/b:joep.0000003228.54812.18.

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