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In the paper, we consider the P H 2 -distribution, which is a particular case of the P H -distribution. In other words, The first service phase is exponentially distributed, and the service rate is μ. After the first service phase, the customer can to go away with probability p or continue the service with probability (1 − p) and service rate μ ′ . We study an analysis of an M / P H 2 / 1 queue model with catastrophes, which is regarded as a generalization of an M / M / 1 queue model with catastrophes. Whenever a catastrophe happens, all customers will be cleaned up immediately, and the queuing system is empty. The customers arrive at the queuing system based on a Poisson process, and the total service duration has two phases. Transient probabilities and steady-state probabilities of this queuing system are considered using practical applications of the modified Bessel function of the first kind, the Laplace transform, and probability-generating function techniques. Moreover, some important performance measures are obtained in the system. Finally, numerical illustrations are used to discuss the system's behavior, and conclusions and future directions of the model are given. [ABSTRACT FROM AUTHOR]

This paper focuses on integrals and Borel transforms concerning λ$$ \lambda $$‐Bessel and λ$$ \lambda $$‐Tricomi functions, employing an umbral perspective as a central approach. Differintegral techniques, presently utilized in calculus, offer a rich reserve of tools that can be utilized across a broad spectrum of problems encompassing the realm of special functions and beyond. Employing integral transforms akin to the Borel type and the related formalism proves to be a potent approach, facilitating a connection between umbral and operational methodologies. By integrating these perspectives, we establish a novel and effective method for deriving integrals of hybrid special functions and achieving the summation of their corresponding generating functions. [ABSTRACT FROM AUTHOR]

Suppose that A 1 is a class of analytic functions f : D = { z ∈ C : | z | < 1 } → C with normalization f (0) = 1 . Consider two functions P l (z) = 1 + z and Φ N e (z) = 1 + z − z 3 / 3 , which map the boundary of D to a cusp of lemniscate and to a twi-cusped kidney-shaped nephroid curve in the right half plane, respectively. In this article, we aim to construct functions f ∈ A 0 for which (i) f (D) ⊂ P l (D) ∩ Φ N e (D) (ii) f (D) ⊂ P l (D) , but f (D) ⊄ Φ N e (D) (iii) f (D) ⊂ Φ N e (D) , but f (D) ⊄ P l (D) . We validate the results graphically and analytically. To prove the results analytically, we use the concept of subordination. In this process, we establish the connection lemniscate (and nephroid) domain and functions, including g α (z) : = 1 + α z 2 , | α | ≤ 1 , the polynomial g α , β (z) : = 1 + α z + β z 3 , α , β ∈ R , as well as Lerch's transcendent function, Incomplete gamma function, Bessel and Modified Bessel functions, and confluent and generalized hypergeometric functions. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative fractional multidimensional Bessel transform, enhanced by a novel convolution structure. This integral transform parallels the established roles of the Fourier and multidimensional Bessel transforms, establishing a unique position in the field of fractional calculus. Its most notable feature is the seamless integration with a new class of anisotropic Riesz-Bessel potentials. [ABSTRACT FROM AUTHOR]

Properties of the Lommel polynomials $ R_{n,\nu }(z) $ R n , ν (z) which appear in the theory of the Bessel functions, are studied. New functional relations for hypergeometric and Horn functions, including reduction formulas, are derived. [ABSTRACT FROM AUTHOR]

In this paper, taking into account the intriguing recent results of Rabotnov functions, Poisson functions, Bessel functions and Wright functions, we consider a new comprehensive subclass O μ (Δ 1 , Δ 2 , Δ 3 , Δ 4) of univalent functions defined in the unit disk Λ = { τ ∈ C : τ < 1 } . More specifically, we investigate some sufficient conditions for Rabotnov functions, Poisson functions, Bessel functions and Wright functions to be in this subclass. Some corollaries of our main results are given. The novelty and the advantage of this research could inspire researchers of further studies to find new sufficient conditions to be in the subclass O μ (Δ 1 , Δ 2 , Δ 3 , Δ 4) not only for the aforementioned special functions but for different types of special functions, especially for hypergeometric functions, Dini functions, Sturve functions and others. [ABSTRACT FROM AUTHOR]

AbstractThis research reports an analytical and numerical study of thermo-solutal convection in pulsating flows between two coaxial cylinders under a pressure gradient and subject to Dirichlet-type boundary conditions for temperature and concentration along the vertical walls of the annulus. The numerical procedure used in this work is mainly based on the solution of the momentum equations and coupled with the energy and concentration equations. The finite difference method is adopted to solve governing equations using the implicit Crank-Nicolson time marching scheme in the fluid domain and the alternating direction implicit method inside the inner cylinder. The effect of the various parameters such as the fluid-solid conductivity ratio, thermal diffusivity ratio, buoyancy ratio, Lewis number, Richardson number, aspect ratio, and radius ratio on the heat and mass transfer characteristics and the flow structure is presented and discussed. The governing equations are solved analytically after separating into a steady case and an oscillatory case, where an analytical solution for velocity profile, temperature, and concentration distributions is obtained in terms of Bessel’s functions, while the analytical solutions of temperature and concentration profiles are keeping symmetry with the increase of the radius ratio. The results show that the analytical profile can reproduce the three fields obtained numerically and thus for the whole range of parameters. [ABSTRACT FROM AUTHOR]

In this article, we propose an efficient hybrid method to calculate the highly oscillatory Bessel integral ∫ 0 1 f (x) x - τ J m (ω x γ) d x with the Cauchy type singular point, where 0 < τ < 1 , m ≥ 0 , 2 γ ∈ N +. The hybrid method is established by combining the complex integration method with the Clenshaw– Curtis– Filon– type method. Based on the special transformation of the integrand and the additivity of the integration interval, we convert the integral into three integrals. The explicit formula of the first one is expressed in terms of the Meijer G function. The second is computed by using the complex integration method and the Gauss– Laguerre quadrature rule. For the third, we adopt the Clenshaw– Curtis– Filon– type method to obtain the quadrature formula. In particular, the important recursive relationship of the required modified moments is derived by utilizing the Bessel equation and the properties of Chebyshev polynomials. Importantly, the strict error analysis is performed by a large amount of theoretical analysis. Our proposed methods only require a few nodes and interpolation multiplicities to achieve very high accuracy. Finally, numerical examples are provided to verify the validity of our theoretical analysis and the accuracy of the proposed methods. [ABSTRACT FROM AUTHOR]

Under study is the Tricomi–Neumann problem for a three-dimensional mixed-type equation with three singular coefficients in a mixed domain consisting of a quarter of a cylinder and a triangular straight prism. We prove the unique solvability of the problem in the class of regular solutions by using the separation of variables in the hyperbolic part of the mixed domain, which yields the eigenvalue problems for one-dimensional and two-dimensional equations. Finding the eigenfunctions of the problems, we use the formula of the solution of the Cauchy–Goursat problem to construct a solution to the two-dimensional problem. In result, we find the solutions to eigenvalue problems for the three-dimensional equation in the hyperbolic part. Using the eigenfunctions and the gluing condition, we derive a nonlocal problem in the elliptic part of the mixed domain. To solve the problem in the elliptic part, we reformulate the problem in the cylindrical coordinate system and separating the variables leads to the eigenvalue problems for two ordinary differential equations. We prove a uniqueness theorem by using the completeness property of the systems of eigenfunctions of these problems and construct the solution to the problem as the sum of a double series. Justifying the uniform convergence of the series relies on some asymptotic estimates for the Bessel functions of the real and imaginary arguments. These estimates for each summand of the series made it possible to prove the convergence of the series and its derivatives up to the second order, as well as establish the existence theorem in the class of regular solutions. [ABSTRACT FROM AUTHOR]

The partial sums of the series expansion of the Bessel function Jα of the first kind provide lower and upper bounds on the positive real axis for order α ≥-1=2. [ABSTRACT FROM AUTHOR]

The Dirichlet problem for a multidimensional elliptic system in the half-space is considered. With the help of the Fourier transform, the problem of the solvability of the problem is reduced to the study of a second-order partial differential equation. [ABSTRACT FROM AUTHOR]

We consider Bernstein's inequality for the Riesz derivative of order of entire functions of exponential type in the uniform norm on the real line. For this operator, the corresponding interpolation formula is obtained; this formula has nonequidistant nodes. Using this formula, the sharp Bernstein inequality is obtained for all ; namely, the extremal entire function and the sharp constant are written out. [ABSTRACT FROM AUTHOR]

The two-parameter Wright special function is an interesting mathematical object that arises in the theory of the space and time-fractional diffusion equations. Moreover, many other special functions are particular instantiations of the Wright function. The article demonstrates finite representations of the Wright function in terms of sums of generalized hypergeometric functions, which in turn provide connections with the theory of the Gaussian, Airy, Bessel, and Error functions, etc. The main application of the presented results is envisioned in computer algebra for testing numerical algorithms for the evaluation of the Wright function. [ABSTRACT FROM AUTHOR]

Sufficient conditions are determined on the parameters such that the generalized and normalized Bessel function of the first kind, which is an elementary transform of the hypergeometric function and other related functions belong to subclasses of starlike and convex functions defined in the unit disk associated with the exponential mapping. Several differential subordination implications are derived for analytic functions involving Bessel function and the operator introduced by Baricz et al. [Differential subordinations involving generalized Bessel functions, Bull. Malays. Math. Sci. Soc. 38(3) (2015), 1255–1280]. These results are obtained by constructing suitable class of admissible functions. Examples involving trigonometric and hyperbolic functions are provided to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

As a powerful tool for models of quantum computing, q-calculus has drawn the attention of many researchers in the discipline of special functions. In this paper, we present new properties and characterize q-Bessel functions of the first kind using some identities of q-calculus. The results presented in this article help us to obtain new expression results related to q-special functions. New summation and integral representations for q-Bessel functions of the first kind are also established. A few examples are also provided to demonstrate the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

The present paper is devoted to derive a generalized Oberhettinger type integral formula. The derived form of an integral involving the product of the four-parameter Bessel function and Jacobi polynomial. The outcomes are expressed in terms of the Kampé de Fériet and Srivastava and Daoust functions. Also, four Corollaries of the both Theorems are derived in terms of the Kampé de Fériet and Srivastava and Daoust functions. Some of the significant particular cases are also determined. Furthermore, we drive an interesting relationship between Kampé de Fériet and Srivastava and Daoust functions. [ABSTRACT FROM AUTHOR]

This study focused on simulation and analytical models of a multidimensional random walk of many agents. At each step, any agent can rotate by an arbitrary angle and continue moving in the direction selected. The analytical model used gives the probability of finding an agent in the circular area of the radius r$$ r $$ in the given time moment. The model includes parameters that control the intensity of the walking process and the characteristics of the environment. Work on this topic mainly concerns the discrete case of a random walk. In this article, we consider the case of a random walk continuous in spatial coordinates. We obtain certain theoretical results for the analytical model with the help of the mathematical apparatus aimed at working with a generalized translation. With the help of a simulation, we reveal the meaning of the analytical model's parameters. Results can be used for modeling diffusion‐like processes such as the spread of an epidemic, mechanical vibrations, forest fires, migration, and dissemination of information over a network. [ABSTRACT FROM AUTHOR]

In the current effort, the effects of entropy generation and electro-osmotic driven peristaltic flow of non-Newtonian Williamson liquid in a curved micro-channel is investigated. Formulation of the problem is conducted in a wave frame of reference. Due to the complexity of non-Newtonian fluid, the analytical solutions of non-linear coupled equations are not easy to obtain and are very rarely found in the literature. For analytical solutions, the governing equations are reduced in the form of the Bessel function. The electric double layer is employed as a result of a zeta potential of about 25 mV. The low Reynolds number and long wavelength approximations are taken into account. Graphical analysis has been carried out for velocity, temperature and entropy for physical parameters. It is noted that the Brinkmann number enhances the temperature. The results of this model will be extremely helpful in designing electro-peristaltic pumps for thermal systems. [ABSTRACT FROM AUTHOR]

We derive an explicit formula for the fundamental solution K T q + 1 (x , x 0 ; t) to the discrete-time diffusion equation on the (q + 1) -regular tree T q + 1 in terms of the discrete I-Bessel function. We then use the formula to derive an explicit expression for the fundamental solution K X (x , x 0 ; t) to the discrete-time diffusion equation on any (q + 1) -regular graph X. Going further, we develop three applications. The first one is to derive a general trace formula that relates the spectral data on X to its topological data. Though we emphasize the results in the case when X is finite, our method also applies when X has a countably infinite number of vertices. As a second application, we obtain a closed-form expression for the return time probability distribution of the uniform random walk on any (q + 1) -regular graph. The expression is obtained by relating K X (x , x 0 ; t) to the uniform random walk on a (q + 1) -regular graph. We then show that if { X h } is a sequence of (q + 1) -regular graphs whose number of vertices goes to infinity and which satisfies a certain natural geometric condition, then the limit of the return time probability distributions from { X h } is equal to the return time probability distribution on the tree T q + 1 . As a third application, we derive formulas which express the number of distinct closed irreducible walks without tails on a finite graph X in terms of moments of the spectrum of its adjacency matrix. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new class of functions named the m-polynomial exponentially s-type convex and we study some of its algebraic properties. We investigate a new integral inequality of Hermite-Hadamard (H-H) type by using the new introduced definition. Also, we prove a new midpoint identity. By examining this identity we can deduce some integral inequalities of midpoint type for the new introduced definition. Several special cases are discussed in details which emphasize that the results accounted in this paper unify and extend various results in this field of study. Finally, we provide some applications on the Bessel functions and special means of distinct positive real numbers to demonstrate the applicability of the new results. [ABSTRACT FROM AUTHOR]

Various relations including differentiation formulas, connection with hypergeometric functions, integral representations, formulas of summation and series representations for three types of Neumann polynomials are derived. [ABSTRACT FROM AUTHOR]

In this paper, buckling of a nanowire column subjected to self-weight and tip load is investigated. One end of the nanowire is free, while the other end is attached to a rotational spring support. Considering the equilibrium equations together with the Euler–Bernoulli beam theory, the governing differential equation describing the behavior of the column can be obtained. Effect of surface stress is also incorporated into the formulations in terms of transverse distributed loading. The differential equation has been solved analytically and the general solution can be presented in the terms of Bessel function of the first kind. Applying the boundary conditions, the characteristic equations influenced by surface stress and stiffness of the rotational spring at the support can be expressed and then the critical load can be determined using the Newton–Raphson iterative scheme. From the results, they reveal that the positive surface stress could strengthen the nanowire against the buckling. Fixity at the base is also influenced to the critical load where the increase of the stiffness of the spring results in the increase of critical load as well. [ABSTRACT FROM AUTHOR]

With the extensive access of new energy and power electronic equipment, the harmonic problem of transmission lines becomes more and more prominent. In view of the obvious problems such as unclear mechanism and lack of quantitative analysis methods, a new method was proposed to evaluate the impact of harmonics on the ampacity of aluminum conductor steel reinforced (ACSR). First, the Bessel function was used to solve the Maxwell equations of the ACSR to derive the expression of distribution of current density for the ACSR, so as to analytically characterize the mechanism of action between harmonics and ampacity of ACSR. Based on it, the analytical expression of transmission line ampacity was established by using the heat balance equation, so as to quantitatively evaluate the impact of harmonic heating on ampacity. The theoretical analysis results show that the existence of harmonics will reduce the maximum ampacity of ACSR, and its mechanism is that the AC resistance under harmonics will increase the line resistance, resulting in the decrease of the heat extremum generated by the fundamental wave at the same line temperature, so as to further reduce the maximum ampacity. Finally, a two-position finite element model of ACSR was established in COMSOL to verify the effectiveness and accuracy of the proposed approach by injecting different harmonic distortion. [ABSTRACT FROM AUTHOR]

This research focuses on the Ostrowski–Mercer inequalities, which are presented as variants of Jensen's inequality for differentiable convex functions. The main findings were effectively composed of convex functions and their properties. The results were directed by Riemann–Liouville fractional integral operators. Furthermore, using special means, q-digamma functions and modified Bessel functions, some applications of the acquired results were obtained. [ABSTRACT FROM AUTHOR]

In the present work, the definition of memory dependent derivative (MDD) heat transfer in an infinite solid body was used to investigate the problem of wave characteristics in an unbounded thermoelectric viscoelastic solid caused by a continuous line heat source in the presence of a uniform magnetic field. Both Laplace and Hankel transform strategies are used to acquire the widespread answer in a closed form. Analytical findings were obtained for the distribution within the medium of various fields such as temperature, displacement, and stresses. For the inversion of the Laplace transformations, a computational approach is used. The distributions of the numerical consequences of the non-dimensional considered bodily variables are represented graphically. Detailed comparative evaluation is represented thru the numerical outcomes to estimate the results of the kernels, time-delay and magnetic number on the behavior of all variable. The effect offers a concept to research main thermoelectric viscoelastic materials as any other type of pertinent materials. [ABSTRACT FROM AUTHOR]

In this paper, the fast algorithms of the derivatives of Bessel functions with respect to the parameter are obtained. Based on these fast algorithms, we discuss the calculations of the derivatives of the functions related to the heterogeneous Bessel differential equation, such as Anger, Weber, Struve and modified Struve functions. In addition, the fast calculation of some integrals related to these functions are obtained. At last, numerical examples show the algorithms given in this paper are fast and high precision. [ABSTRACT FROM AUTHOR]

We compute the optimal constant and characterise the maximisers at all spatial scales for the Agmon–Hörmander L^2-Fourier adjoint restriction estimate on the sphere. The maximisers switch back and forth from being constants to being non-symmetric at the zeros of two Bessel functions. We also study the stability of this estimate and establish a sharpened version in the spirit of Bianchi–Egnell. The corresponding stability constant and maximisers again exhibit a curious intermittent behaviour. [ABSTRACT FROM AUTHOR]

Our purpose in the present investigation is to study certain geometric properties such as the close-to-convexity, convexity, and starlikeness of the hypergeometric function z 1 F 2 (a ; b , c ; z) in the open unit disk. The usefulness of the main results for some familiar special functions like the modified Sturve function, the modified Lommel function, the modified Bessel function, and the F 1 0 (− ; c ; z) function are also mentioned. We further consider a boundedness property of the function F 2 1 (a ; b , c ; z) in the Hardy space of analytic functions. Several corollaries and special cases of the main results are also pointed out. [ABSTRACT FROM AUTHOR]

A special class of neurons in the hippocampal formation broadly known as the spatial cells, whose subcategories include place cells, grid cells, and head direction cells, are considered to be the building blocks of the brain's map of the spatial world. We present a general, deep learning‐based modeling framework that describes the emergence of the spatial‐cell responses and can also explain responses that involve a combination of path integration and vision. The first layer of the model consists of head direction (HD) cells that code for the preferred direction of the agent. The second layer is the path integration (PI) layer with oscillatory neurons: displacement of the agent in a given direction modulates the frequency of these oscillators. Principal component analysis (PCA) of the PI‐cell responses showed the emergence of cells with grid‐like spatial periodicity. We show that the Bessel functions could describe the response of these cells. The output of the PI layer is used to train a stack of autoencoders. Neurons of both the layers exhibit responses resembling grid cells and place cells. The paper concludes by suggesting the wider applicability of the proposed modeling framework beyond the two simulated studies. [ABSTRACT FROM AUTHOR]

In this paper, we present a systematic study of the various characteristics and properties of some continuous and discrete fractional Bessel wavelet transforms. The method is based upon the theory of the fractional Hankel transform. [ABSTRACT FROM AUTHOR]

We determine in this paper new results about the radius of uniform convexity of two kinds of normalization of the Bessel function J ν in the case ν ∈ (− 2 , − 1) , and provide an alternative proof regarding the radius of convexity of order alpha. We then compare results regarding the convexity and uniform convexity of the considered functions and determine interesting connections between them. [ABSTRACT FROM AUTHOR]

In this study, we investigate MUltiple SIgnal Classification (MUSIC) operated at a fixed frequency for identifying the locations of short, linear perfectly conducting cracks in limited-aperture inverse scattering problem. At present, the so-called multi-static response (MSR) matrix whose elements are measured far-field pattern data is neither symmetric nor Hermitian, a projection operator onto the noise subspace cannot be defined using the conventional method, so the imaging function cannot be designed. Motivated by this fact, we first propose a novel MUSIC imaging function in limited-aperture inverse scattering problem. This is based on the asymptotic expansion formula for far-field patterns in the presence of small cracks and the structure of singular vectors associated with nonzero singular values of the MSR matrix. Next, the new imaging function was analyzed by establishing a relationship with an infinite series of the Bessel function of the integer order of the first kind and ranges of incident and observation directions. We then observe some properties of MUSIC in limited-aperture problems and show that the proposed imaging function is a generalization of full- and limited-view problems. We finally validate the feasibility and limitation of the proposed MUSIC imaging function through numerical simulation results using synthetic and real data. [ABSTRACT FROM AUTHOR]

In this paper, through complex analysis, the convergence rate is given on a quadrature of a Fourier integral with symmetrical Jacobi weight. The interpolation nodes of this quadrature formula are expressed by the frequency, and the coefficients can be expressed by the Bessel function. When the frequency is close to 0, the nodes are close to those in the Gauss quadrature. When the frequency tends to infinity, the nodes tend symmetrically to the two ends of the integrand. The higher the frequency is, the higher the accuracy of this quadrature will be. Numerical examples are provided to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, a physically based explicit analytical model for grain boundary (GB) barrier height ($\psi _{\text {B}}$) near the polycrystalline Si (poly-Si) channel/gate oxide interface is proposed for macaroni MOSFETs, the unit cell of 3-D NAND Flash memory. The model is derived by considering a cylindrical coordinate system and is expressed as the Lambert W function and the cosine integral. To verify our model, a computer-aided design (TCAD) simulation tool, including a carrier transport model for poly Si channel, is used and calibrated against experimental data of 3-D NAND string current. The validity of $\psi _{\text {B}}$ -model at ${V}_{\text {GS}} > {V}_{\text {FB}}$ is demonstrated by comparing the model with simulation data extracted from calibrated exponential density of states (DOS) distribution for grain boundary traps (GBTs). In the verification stage, simulations are also implemented under various exponential DOS distributions and channel hole radius, and a good agreement between the model and the simulation data is achieved. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Cogdell et al. ['Evaluating the Mahler measure of linear forms via Kronecker limit formulas on complex projective space', Trans. Amer. Math. Soc. (2021), to appear] developed infinite series representations for the logarithmic Mahler measure of a complex linear form with four or more variables. We establish the case of three variables by bounding an integral with integrand involving the random walk probability density $a\int _0^\infty tJ_0(at) \prod _{m=0}^2 J_0(r_m t)\,dt$ , where $J_0$ is the order-zero Bessel function of the first kind and a and $r_m$ are positive real numbers. To facilitate our proof we develop an alternative description of the integral's asymptotic behaviour at its known points of divergence. As a computational aid for numerical experiments, an algorithm to calculate these series is presented in the appendix. [ABSTRACT FROM AUTHOR]

The aim of the present document is to evaluate a triple integral involving the product a general class of logarithmic, special and exponential functions. Importance of our results lies in the fact that they involve the Bessel function of the First Kind, which is used in a wide range of areas spanning Science and Engineering. Further we establish some special cases. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the fractional power (− Δ ν) γ / 2 , 0 < γ < 2 , of the Bessel operator in the form Δ ν := d 2 d x 2 + 2 ν + 1 x d d x , ν > − 1 / 2. Our method uses a canonical representation for generalized Laplacian related to the structures of the Bessel–Kingman hypergroup. As a direct application, we solve the space-fractional diffusion equation. [ABSTRACT FROM AUTHOR]

Discrete analogues of the classical Fourier-Jacobi transform are introduced and investigated. It involves series and integrals with respect to parameters of the Gauss hypergeometric function 2 F 1 (a + i n / 2 , a − i n / 2 ; c ; − x 2) , x > 0 , n ∈ N , a , c > 0 , i is the imaginary unit. The corresponding inversion formulas for suitable functions and sequences in terms of these series and integrals are established. [ABSTRACT FROM AUTHOR]

By considering the Bessel functions of the first kind of order ν and convolution structure, a new subclass of univalent holomorphic functions based of differential subordination is defined. Some geometric properties related to coefficient estimate, weighted mean, convolution preserving conditions and neighborhood concept are obtained. [ABSTRACT FROM AUTHOR]

Using the admissibility condition, we obtain certain third order differential subordination results for an analytic function p with p(0) = 1 belonging to the class of Janowski functions, P[A,B]. As an application, certain second order differential inequalities involving special functions are obtained. [ABSTRACT FROM AUTHOR]

This present study deals with a novel mathematical model of generalized thermoelasticity in a fiber-reinforced, isotropic unbounded thermoelastic solid due to the presence of a continuous line heat source under the influence of magnetic field. The derivative is defined in an integral form of a common derivative on a slipping interval by incorporating memory-dependent heat transfer. Employing both Laplace and Hankel transforms as tools, analytical results for distributions of different fields have been derived with the help of potential function approach. The inversion of Hankel transform is performed analytically, whereas the numerical inversion of Laplace transform is carried out employing Zakian method and the method based on Fourier series expansion technique. According to the graphical representations corresponding to the numerical results, conclusions about the new theory to exhibit the significance of the kernel functions and the time-delay parameter is constructed. The significant differences of the two different numerical schemes have also explained. Excellent predictive capability is demonstrated due to the presence of memory-dependent derivative and presence of reinforcement and magnetic field. Also, significant differences due to the choice of linear and nonlinear kernels in the heat equation is elaborated. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the computation and analysis of the highly oscillatory Bessel transforms with endpoint singularities of algebraic and logarithmic type. Based on the modification of the numerical steepest descent method, we present a new and efficient quadrature rule. Firstly, we divide the considered integrals into two parts by J m (z) = 1 2 H m (1) (z) + H m (2) (z) , where each part can be transformed into the Fourier-type integrals. Then, we use the Cauchy's residue theorem to convert these Fourier-type integrals into the infinite integrals on [ 0 , + ∞) . Next, the resulting infinite integrals can be efficiently calculated by constructing some appropriate Gaussian quadrature rules. In addition, we conduct error analysis in inverse powers of the frequency parameter. Finally, several numerical examples are provided to show the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Let p be an analytic function defined on the open unit disc D with p (0) = 1 and 0 < α ≤ 1 . The conditions on complex valued functions C, D, and E are obtained for p to be subordinate to ((1 + z) / (1 - z)) α when C (z) z 2 p ′ ′ (z) + D (z) z p ′ (z) + E (z) p (z) = 0 . Sufficient conditions for confluent (Kummer) hypergeometric function and generalized and normalized Bessel function of the first kind of complex order to be subordinate to ((1 + z) / (1 - z)) α are obtained as applications. The conditions on α and β are derived for p to be subordinate to ((1 + z) / (1 - z)) α when 1 + β z p ′ (z) / p n (z) with n = 1 , 2 is subordinate to 1 + 4 z / 3 + 2 z 2 / 3 = : φ CAR (z) . Similar problems were investigated for Re p (z) > 0 when the function p (z) + β z p ′ (z) / p n (z) with n = 0 , 2 is subordinate to φ CAR (z) . The condition on β is determined for p to be subordinate to ((1 + z) / (1 - z)) α when p (z) + β z p ′ (z) / p n (z) with n = 0 , 1 , 2 is subordinate to ((1 + z) / (1 - z)) α . [ABSTRACT FROM AUTHOR]

A scale-shape mixtures of flexible generalized skew normal (SSMFGSN) distributions is proposed as a novel device for modeling asymmetric data. Computationally feasible EM-type algorithms derived from the selection mechanism are presented to compute maximum likelihood (ML) estimates of SSMFGSN distributions. Some characterizations and probabilistic properties of the SSMFGSN distributions are also studied. Monte Carlo simulations show that the proposed estimating procedures can provide desirable asymptotic properties of the ML estimates and demand less computational burden in comparison with other existing algorithms based on convolution representations. The usefulness of the proposed methodology is illustrated by analyzing a real dataset. [ABSTRACT FROM AUTHOR]

We illustrate the construction and application of the Maslov canonical operator with examples of Bessel functions. For real values of the argument, we derive representations of these functions in terms of a canonical operator and, as a consequence, obtain the well-known asymptotics. [ABSTRACT FROM AUTHOR]

The application of the methods of integral transforms has tremendously increased during the past many years for finding the exact solutions and the numerical solutions of many new problems arising in the fields of engineering and applied sciences. Some two years back the Upadhyaya transform (https://www.researchgate. net/publication/334033797) was introduced as the most powerful generalization and the most powerful unification of a number of existing variants of the classical Laplace transform occurring in the mathematics research literature. In this paper we apply the Upadhyaya transform for solving the Volterra integral equations of the first kind. Our analysis leads to the conclusion that the Upadhyaya transform is a very powerful tool for finding the solutions to the Volterra integral of the first kind. [ABSTRACT FROM AUTHOR]

The modeling of functional relationship between circular variables is gaining an increasing interest. The existing models assume the errors have same probability distributions, but the case of different distributional errors is not yet investigated. This paper considers the modeling of functional relationship for circular variables with different distributional errors. Two functional relationship models are proposed by assuming a combination of von Mises and wrapped Cauchy errors, with a distinction between known and unknown ratio of error concentrations. Parameters of the proposed models are estimated using the maximum likelihood method based on numerical iterative procedures. The properties of parameters' estimators are investigated via an extensive simulation study. The results show a direct relationship between the performance of parameters' estimates and the sample size, as well as the concentration parameters. For illustration, the proposed models are applied on wind directions data in two main cities in the Gaza Strip, Palestine. [ABSTRACT FROM AUTHOR]

In the paper, we study derivative estimates of the iterated spherical averages (At)N(f). We obtain the optimal range of exponents (α, N, p) to ensure the Lp boundedness of P (∂ ∂ x ) (A 1) N (f) for 1 ≤ p ≤ ∞, where P is a homogeneous polynomial of degree α. The main theorem extends some known results. As an application, we obtain the smallest N such that (A1)N: Lp(ℝn) → Lαp(ℝn). [ABSTRACT FROM AUTHOR]

This paper proposes an analytic model of a resonant MEMS mirror with electrostatic actuation based on a Fourier series approximation for both the comb drive torque and the input waveform and verifies the model by measurements using rectangular input waveforms with various duty cycles. The analytic model is derived by the perturbation method, results in slow flow evolution in amplitude and phase with dynamic influence matrices and vectors and also provides the local dynamics for each equilibrium described by a Jacobian matrix. An analysis of the dynamic influence matrices and vectors provides understanding of the mirror dynamics by frequency components of the input waveform and the comb drive capacitance. The asymptotic behavior at zero amplitude provides the transition curve in an extended dynamic model, which corresponds to the well-known Mathieu’s equation solely with the constant and fundamental frequency components of the input waveform. The measurement results verify the proposed model, showing less than ±0.06 % frequency error for large amplitudes and ±0.47 % for small amplitudes, which corresponds to ±1.2 Hz and ±9.6 Hz for the case of a mirror with 2 kHz natural frequency, respectively. Measurements of local dynamics and transition curves also show a good agreement with the proposed model, which can be used for a fast and accurate analysis of resonant MEMS mirrors for high precision applications. [2020-0387] [ABSTRACT FROM AUTHOR]