Struve Functions Research Articles

Geometrical and Computational Properties of the Generalized Struve Functions

Geometrical and Computational Properties of the Generalized Struve Functions

Third-Order Differential Subordination for Generalized Struve Function Associated with Meromorphic Functions

سابقاً تناولت العديد من الاعمال دراسة التبعية التفاضلية من الدرجة الاولى وبعد فترة وجيزة تناولت دراسات اخرى التبعية التفاضلية من الدرجة الثانية في قرص الوحدة . مؤخراً تم تقديم التبعية التفاضلية من الدرجة الثالثة من قبل بوانسامي واخرون في عام 1992 و انتونيو ميلر عام 2011 . تبحث هذة الورقة في صنف اوسع بكثير من متراجحات التبعية التفاضلية من الدرجة الثالثة . عرف المؤلفون المعايير الخلصة بصنف من الاوبريترات المسموح بها وهذا يعني ضمان وجود التبعية التفاضلية من الدرجة الثالثة. الدوال الميرومورفية في D هي دوال تحليلية في المجال D بأستثناء الرواسب اذا كانت فأن الدالة ميرومورفية وهي دوال يمكن تمثيلها كحاصل قسمة دالتين. دالة ستورف لها تطبيقات في قضايا الموجات السطحية و موجات الماء والديناميكا الهوائية غير المستقرة و الاتجاه البصري ونظرية عدم الاستقرار المقاوم ظهرت دالة ستروف مؤخرا في عدد من انظمة الجسيمات . فكرة التبعية التفاضلية في لغة هي تعميم للمتباينات في لغة R, وقد بدأت في عام 1981 من خلال اعمال ميلر و موكانو و ريد. في هذا المقال يتم معاينة الفئات المناسبة من الدوال المقبولة ويتم انشاء خصائص التبعية التفاضلية من الدرجة الثالثة باستخدام المؤثر للدوال متعددة التكافؤ التحليلية باستثناء عدد منته من النقاط( الاقطاب) المرتبطة بوظيفة ستروف المعممة . في هذة الدراسة هناك حاجة لعرض العديد من المفاهيم منها التبعية , الفوقية , المسيطر, افضل السائد, الالتواء (او منتج هادامارد) ,الدالة متعددة التكافؤ التحليلية باستثناء عدد منته من النقاط ( الاقطاب) , دالة ستروف بالاضافة الى مفهوم المضروب المزاح( او رمز بوشهامر) و الدوال المسموح بها.

Radii of γ-Spirallike of q-Special Functions

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 interlacing property of zeros of q-Bessel and q-Bessel-Struve functions and their derivatives is useful in the proof of our main theorems.

Federated quantum long short-term memory (FedQLSTM)

Quantum federated learning (QFL) can facilitate collaborative learning across multiple clients using quantum machine learning (QML) models, while preserving data privacy. Although recent advances in QFL span different tasks like classification while leveraging several data types, no prior work has focused on developing a QFL framework that utilizes temporal data to approximate functions useful to analyze the performance of distributed quantum sensing networks. In this paper, a novel QFL framework that is the first to integrate quantum long short-term memory (QLSTM) models with temporal data is proposed. The proposed federated QLSTM (FedQLSTM) framework is exploited for performing the task of function approximation. In this regard, three key use cases are presented: Bessel function approximation, sinusoidal delayed quantum feedback control function approximation, and Struve function approximation. Simulation results confirm that, for all considered use cases, the proposed FedQLSTM framework achieves a faster convergence rate under one local training epoch, minimizing the overall computations, and saving 25–33% of the number of communication rounds needed until convergence compared to an FL framework with classical LSTM models.

On The Monotony of Struve Functions

Cotîrlă and Szász (Comput Methods Funct Theory: 2023) solved a conjecture related with inclusion relation for Bessel functions, proposed by Baricz and András (Complex Var Elliptic Equ 54(7): 689–696, 2009). In this paper, we prove this conjecture for normalized Struve functions by using subordination factor sequences.

An equation for complex fractional diffusion created by the Struve function with a T-symmetric univalent solution

Abstract A T T -symmetric univalent function is a complex valued function that is conformally mapping the unit disk onto itself and satisfies the symmetry condition ϕ [ T ] ( ζ ) = [ ϕ ( ζ T ) ] 1 ∕ T {\phi }^{\left[T]}\left(\zeta )={\left[\phi \left({\zeta }^{T})]}^{1/T} for all ζ \zeta in the unit disk. In other words, it is a complex function that preserves the unit disk’s shape and orientation and is symmetric about the unit circle. They are used in the study of geometric function theory and the theory of univalent functions. In recent effort, we extend the class of fractional anomalous diffusion equations in a symmetric complex domain. we aim to present the analytic univalent solution for such a class using special functions technique. Our analysis and comparative findings are further supported by the geometric simulations for the univalent solution such as the convexity and starlikeness of the diffusion. As a consequence of illustration of a list of conditions yielding the univalent solutions (normalize analytic function in the open unit disk), the normalization of diffusion shape is achieved.

Geometric Properties of Normalized Galué Type Struve Function

The field of geometric function theory has thoroughly investigated starlike functions concerning symmetric points. The main objective of this work is to derive certain geometric properties, such as the starlikeness of order δ, convexity of order δ, k-starlikeness, k-uniform convexity, lemniscate starlikeness and convexity, exponential starlikeness and convexity, and pre-starlikeness for the Galué type Struve function (GTSF). Furthermore, the conditions for GTSF belonging to the Hardy space are also derived. The results obtained in this work generalize several results available in the literature.

Geometric Nature of Special Functions on Domain Enclosed by Nephroid and Leminscate Curve

In this work, the geometric nature of solutions to two second-order differential equations, zy′′(z)+a(z)y′(z)+b(z)y(z)=0 and z2y′′(z)+a(z)y′(z)+b(z)y(z)=d(z), is studied. Here, a(z), b(z), and d(z) are analytic functions defined on the unit disc. Using differential subordination, we established that the normalized solution F(z) (with F(0) = 1) of above differential equations maps the unit disc to the domain bounded by the leminscate curve 1+z. We construct several examples by the judicious choice of a(z), b(z), and d(z). The examples include Bessel functions, Struve functions, the Bessel–Sturve kernel, confluent hypergeometric functions, and many other special functions. We also established a connection with the nephroid domain. Directly using subordination, we construct functions that are subordinated by a nephroid function. Two open problems are also suggested in the conclusion.

Analytical integration of the heater and sensor 3ω signals of anisotropic bulk materials and thin films

We derive and analytically integrate the models for the heater and sensor 3ω signals of the temperature field of anisotropic bulk materials and thin films. This integration is done by using the Fourier transform and expressing the frequency dependence of temperature in terms of the modified Bessel and Struve functions, which are well-implemented in major computation software. The effects of the radiative losses and interface thermal resistance are also evaluated for different frequency regimes. Further, by fitting the 3ω model integrated over the heater and sensor widths to experimental data recorded up to 31 kHz, the thermal conductivity and thermal diffusivity of a quartz glass wafer are determined for temperatures ranging from 300 to 800 K. The obtained results show that the usual log-linear approximation can induce an uncertainty of about 5% on the thermal conductivity values. The exact integrated models are thus expected to facilitate the accurate determination of the thermal conductivity and thermal diffusivity of anisotropic materials through a wide spectrum of modulation frequencies and without time-consuming numerical integration.

Partial Sums of the Normalized Le Roy-Type Mittag-Leffler Function

Recently, some researchers determined lower bounds for the normalized version of some special functions to its sequence of partial sums, e.g., Struve and Dini functions, Wright functions and Miller–Ross functions. In this paper, we determine lower bounds for the normalized Le Roy-type Mittag-Leffler function Fα,βγ(z)=z+∑n=1∞Anzn+1, where An=ΓβΓα(n−1)+βγ and its sequence of partial sums (Fα,βγ(z))m(z)=z+∑n=1mAnzn+1. Several examples of the main results are also considered.

Redheffer-Type Bounds of Special Functions

In this paper, we aim to construct inequalities of the Redheffer type for certain functions defined by the infinite product involving the zeroes of these functions. The key tools used in our proofs are classical results on the monotonicity of the ratio of differentiable functions. The results are proved using the nth positive zero, denoted by bn(ν). Special cases lead to several examples involving special functions, namely, Bessel, Struve, and Hurwitz functions, as well as several other trigonometric functions.

Fast Calculation of the Derivatives of Bessel Functions with Respect to the Parameter and Applications

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.

Briot–Bouquet Differential Subordinations for Analytic Functions Involving the Struve Function

We define a new class of exponential starlike functions constructed by a linear operator involving normalized form of the generalized Struve function. Making use of a technique of differential subordination introduced by Miller and Mocanu, we investigate several new results related to the Briot–Bouquet differential subordinations for the linear operator involving the normalized form of the generalized Struve function. We also obtain univalent solutions to the Briot–Bouquet differential equations and observe that these solutions are the best dominant of the Briot–Bouquet differential subordinations for the exponential starlike function class. Moreover, we give an application of fractional integral operator for a complex-valued function associated with the generalized Struve function. The significance of this paper is due to the technique employed in proving the results and novelty of these results for the Struve functions. The approach used in this paper can lead to several new problems in geometric function theory associated with special functions.

Characterizations for Certain Subclasses of Starlike and Convex Functions Associated with Lommel, Struve and Bessel Functions

In this paper we have determined some necessary and sufficient conditions of normalized Lommel function sμ,v, Struve function hv and Bessel function jv of the first kind to be in the subclasses S(α, β, γ) and K(α, β, γ) of starlike and convex functions of order α and type β, γ, in the unit disk U.

Application of the Laplace Transform to a New Form of Fractional Kinetic Equation Involving the Composition of the Galúe Struve Function and the Mittag–Leffler Function

The great importance of the fractional kinetic equations (FKEs) can be seen in the very recent research work of proposing such new equations and finding their solutions by different analytical and numerical methods. The paramount purpose of the present work is to proffer and study new FKEs involving the composition of the generalized Galúe Struve function of first kind and k-Mittag–Leffler function and apply a very influential effective analytical approach based on Laplace transform to find their analytical solutions. The obtained solutions have been presented with some real values and the simulation done via MATLAB. Furthermore, the numerical and graphical interpretations are also mentioned to illustrate the main results. Some special cases are to be taken under consideration to get the results in simpler form.

On Geometric Properties of Bessel–Struve Kernel Functions in Unit Disc

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.

Bounds for an Integral Involving the Modified Lommel Function of the First Kind

Simple upper and lower bounds are established for the integral int _0^xmathrm {e}^{-beta u}u^nu t_{mu ,nu }(u),mathrm {d}u, where x>0, 0<beta <1, mu +nu >-2, mu -nu ge -3, and t_{mu ,nu }(x) is the modified Lommel function of the first kind. Our bounds complement and improve on existing bounds for this integral, by either being sharper or increasing the range of validity. Our bounds also generalise recent bounds for an integral involving the modified Struve function of the first kind, and in some cases more a direct approach lead to sharper bounds when our general bounds are specialised to the modified Struve case.

Theoretical Study on Non-Improvement of the Multi-Frequency Direct Sampling Method in Inverse Scattering Problems

Generally, it has been confirmed that applying multiple frequencies guarantees a successful imaging result for various non-iterative imaging algorithms in inverse scattering problems. However, the application of multiple frequencies does not yield good results for direct sampling methods (DSMs), which has been confirmed through simulation but not theoretically. This study proves this premise theoretically by showing that the indicator function with multi-frequency can be expressed by the Bessel and Struve functions and the propagation direction of the incident field. This is based on the fact that the indicator function with single frequency can be expressed by the exponential and Bessel function of order zero of the first kind. Various simulation outcomes are shown to support the theoretical result.

A Triple Integral Involving the Struve Function Hv(t) Expressed in terms of the Hurwitz-Lerch Zeta Function

The main focus of the present paper is to establish a triple integral involving the Struve function in terms of the Hurwitz-Lerch zeta function by using our contour integral method. We also consider some useful examples as special cases of this integral involving the Struve function to give the applications of our main results.

Amplitude and time-dependence of ultrasonic radiation force on modulation frequency computed from specular reflection contributions

Ever since the late 1970s, there has been interest in the modulated radiation pressure of double sideband suppressed carrier (DSSC) ultrasound, because the associated radiation pressure oscillates at a single low frequency. Recent research considers situations, where the radius of curvature of the illuminated objects greatly exceeds the wavelength at the implicit carrier frequency of the ultrasonic illumination [Marston et al., J. Acoust. Soc. Am. 149, 3042–3051 (2021); 150, 25–28 (2021)]. Furthermore, the objects of interest, cylinders, and spheres in water are taken to be sufficiently highly reflecting that the radiation force can be shown to be dominated by contributions associated with specular reflection. In such cases, it is helpful to geometrically analyze the amplitude and time dependence of the oscillatory radiation force for perfectly reflecting objects, where the relevant integrals of the stress projections can be carried out analytically. The results are expressed using Bessel and Struve functions. They explain how the amplitude and phase of the force depends on the DSSC modulation frequency in agreement with partial-wave-series based calculations. The approach is relevant in other situations. [Work supported by the U. S. Office of Naval Research.]