Search

A novel family of bi-univalent holomorphic functions is introduced by the use of the Lindelöf principle. The upper bound of the second Hankel determinant, H 2 , 2 (χ) , is evaluated. Furthermore, specific results are obtained as special cases of the main conclusion. These cases coincide with certain recently obtained results and improve or enhance specific ones. [ABSTRACT FROM AUTHOR]

This paper presents the Abdallah group transform, a new integral transform for solving differential, partial, and integral equations, which is a generalization of the Jafari and polynomial integral transforms. High accuracy, efficiency, and simplicity are demonstrated by applying the suggested integral transform. [ABSTRACT FROM AUTHOR]

New subclasses of bi-univalent functions with bounded boundary rotation are presented in this study. We acquired estimates for the initial coefficients a 2 , a 3 and a 4 . Furthermore, we have verified the specific situations satisfying the famous hypothesis of Brannan and Clunie. Additionally, we have obtained the well-known Fekete–Szegö inequality for the newly identified bi-univalent function subclasses. Our results not only improve, but also extend several existing results as particular cases. [ABSTRACT FROM AUTHOR]

This study is concerned with the class of p-valent meromorphic functions, represented by the series f (ζ) = ζ − p + ∑ k = 1 − p ∞ d k ζ k , with the domain characterized by 0 < | ζ | < 1 . We apply an Erdelyi–Kober-type integral operator to derive two recurrence relations. From this, we draw specific conclusions on differential subordination and differential superordination. By looking into suitable classes of permitted functions, we obtain various outcomes, including results analogous to sandwich-type theorems. The operator used can provide generalizations of previous operators through specific parameter choices, thus providing more corollaries. [ABSTRACT FROM AUTHOR]

A new class B Σ λ (γ , κ) of bi-starlike λ -pseudo functions related to the second Einstein function is presented in this paper. c 2 and c 3 indicate the initial Taylor coefficients of ϕ ∈ B Σ λ (γ , κ) , and the bounds for | c 2 | and | c 3 | are obtained. Additionally, for ϕ ∈ B Σ λ (γ , κ) , we calculate the Fekete–Szegö functional. [ABSTRACT FROM AUTHOR]

Over the last several years, there has been a considerable improvement in the possible methods for solving fractional-order chaotic systems; however, achieving high accuracy remains a challenge. This work proposes a new precise numerical technique for fractional-order chaotic systems. Through simulations, we obtain new types of complex and previously undiscussed dynamic behaviors.These phenomena, not recognized in prior numerical results or theoretical estimations, underscore the unique dynamics present in fractional systems. We also study the effects of the fractional parameters β 1 , β 2 , and β 3 on the system's behavior, comparing them to integer-order derivatives. It has been demonstrated via the findings that the suggested technique is consistent with conventional numerical methods for integer-order systems while simultaneously providing an even higher level of precision. It is possible to demonstrate the efficacy and precision of this technique through simulations, which demonstrates that this method is useful for the investigation of complicated chaotic models. [ABSTRACT FROM AUTHOR]

For functions of the form ϕ (ξ) = ξ + ∑ n = 2 ∞ c n ξ n , we identified two new subclasses of bi-starlike functions and bi-convex functions by using Mathieu-type series defined in the disc Δ = { ξ ∈ C : | ξ | < 1 } . We derived constraints for | c 2 | and | c 3 | , and the subclasses are connected to the shell-shaped area. The Fekete–Szegö functional properties for the aforementioned function subclasses were also investigated. Additionally, a number of related corollaries are shown. [ABSTRACT FROM AUTHOR]

This research is mainly concerned with understanding the propagation behavior of waves within complex elastic media, which leads to improving the properties of elastic materials to benefit from them practically. This research investigates the interaction between acoustic waves and thermal sources in a rotating elastic medium. The effect of the spread of the concentration of the substance through a chemical action is considered. The mathematical model was solved using the harmonic technique for waves in two dimensions to set the complete solutions of some basic physical quantities, such as temperature, displacement, and mechanical stress, as a linear solution in distance. Some appropriate boundary conditions were applied to the free surface to determine some unknown parameters. Linear solutions are represented graphically to discuss the propagation of waves for the dimensionless fundamental quantities under study. The results we obtained were discussed theoretically under the influence of some different parameters through two-dimensional graphs during some comparisons. To improve elastic material properties, specifically in their interaction with thermal sources and chemical actions within a rotating medium. [ABSTRACT FROM AUTHOR]

In this study, the impact of rotation on the transmission of optical acoustic waves, arising from the movement of the optical carrier within an elastic thermal environment, is examined through theoretical analysis. The theoretical framework incorporates the interaction between acoustic waves and thermomechanics to formulate governing equations specific to a semiconductor medium. The fundamental equations of the physical model, influenced by photothermal and thermoelastic principles, are deduced mathematically while considering the presence of rotation. The model studied the medium under a thermal shock wave from thermal stress resulting from light-induced temperature elevation that is not fixed but decaying over time. The mathematical model is solvable using the normal mode method. The model's numerical solutions provide access to all physical fields within the physical domain, encompassing displacement, temperature, acoustic pressure, mechanical stress, and carrier density diffusion. Utilizing the harmonic wave method, a two-dimensional graphical representation of the rotation parameter with and without the influence of the decay parameter is obtained. The theoretical analysis involves comparison, analysis, and discussion of the effects of these parameters investigated. [ABSTRACT FROM AUTHOR]

In this work, we consider the hyponormality of Toeplitz operators on the Bergman space of the annulus with a logarithmic weight. We give necessary conditions when the symbol is of the form φ+ψ¯\varphi +\overline{\psi }, where φ\varphi and ψ\psi are analytic on the annulus {z∈C;1/2

This work examines subordination conclusions for a specific subclass of p-valent meromorphic functions on the punctured unit disc of the complex plane where the function has a pole of order p. A new linear operator is used to define the subclass that is being studied. Furthermore, we present several corollaries with intriguing specific situations of the results. [ABSTRACT FROM AUTHOR]

In this work, we consider the hyponormality of Toeplitz operators on the Bergman space of the annulus with a general radial weight. We give necessary conditions when the symbol is of the form g1+g2‾, where g1 and g2 are analytic on the annulus z∈ℂ,1/2<|z|<1. [ABSTRACT FROM AUTHOR]

In this work, we consider the hyponormality of Toeplitz operators on the Bergman space of the annulus with a logarithmic weight. We give necessary conditions when the symbol is of the form ψ+φ‾, where ψ and φ are analytic on the annulus z∈ℂ,1/2<|z|<1. [ABSTRACT FROM AUTHOR]

The movement of bile inside ducts in a diseased state is investigated using a mathematical model that takes into account heat transport and chemical interactions. Bile is considered as a viscous fluid, geometry of ducts is assumed as finite length asymmetric channel and the flow is induced by peristaltic wave along the length of channel walls. Under the presumption of a long wave length and a low Reynolds number, the formulas for axial velocity, pressure gradient, volume flow rate, stream function, pressure increase, shear stress, and heat transfer coefficient are produced. In the end, a plot and discussion are made of how different emergent factors affect the relevant physical quantities. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel approach to the fractional power of the Laplace-Bessel operator Δv, defined as... The fractional power of this operator is introduced as a pseudo-differential operator through the multidimensional Bessel transform. Our primary contributions encompass a normalized singular integral representation, Bochner subordination, and intertwining relations. [ABSTRACT FROM AUTHOR]

We first describe commuting Toeplitz operators with harmonic symbols on weighted harmonic Bergman spaces. Then, a sufficient condition for hyponormality on weighted Bergman spaces of the punctured unit disk, when the analytic part of the symbol is a monomial, is shown. [ABSTRACT FROM AUTHOR]

The issue of Jeffrey nanofluid peristaltic flow in an asymmetric channel being affected by an induced magnetic field was studied. In addition, mixed convection and viscous dissipation were considered. Under the supposition of a long wave length and a low Reynolds number, the problem was made simpler. The system and corresponding boundary conditions were solved numerically by using the built-in package NDSolve in Mathematica software. This software ensures that the boundary value problem solution is accurate when the step size is set appropriately. It computes internally using the shooting method. Axial velocity, temperature distribution, nanoparticle concentration, axial induced magnetic field, and density distribution were all calculated numerically. An analysis was conducted using graphics to show how different factors affect the flow quantities of interest. The results showed that when the Jeffrey fluid parameter is increased, the magnitude of axial velocity increases at the upper wall of the channel, while it decreases close to the lower walls. Increasing the Hartmann number lads to increases in the axial velocity near the channel walls and in the concentration of nanoparticles. Additionally, as the Brownian motion parameter is increased, both temperature and nanoparticle concentration grow. [ABSTRACT FROM AUTHOR]

Recently, a multivariate multifractal analysis for pointwise regularities based on hierarchical multiresolution quantities was developed. General bounds between the Hausdorff dimension of the intersection of single fractal sets and that of the original sets were derived. Equalities were checked for some synthetic signals that include multiplicative cascades. In this paper, we focus on the setting supplied by simultaneous pointwise (T u i p i ) i = 1 , ... , L regularities. The T u p regularity for 1 ≤ p < ∞ was first introduced in order to better study elliptic partial differential equations where the natural function space setting is L p or a Sobolev space which includes unbounded functions. We will prove that both corresponding multivariate multifractal formalism and equalities above hold Baire generically in a given product of Besov spaces ∏ i = 1 , ... , L B t i s i , r i (R d) , s i , t i , r i > 0 , 1 ≤ p i ≤ ∞ such that s i − d t i > − d p i . We therefore extend previous results where only cases ( p i = ∞ and s i − d t i > 0 for all i) and ( p i = ∞ , s i = d t i and r i ≤ 1 for all i) for simultaneous pointwise Hölder regularities have been proved. [ABSTRACT FROM AUTHOR]

A bounded Hilbert space operator T is hyponormal if T ∗ T − T T ∗ is a positive operator. We consider the hyponormality of Toeplitz operators on a weighted Bergman space. We find a necessary condition for hyponormality in the case of a symbol of the form f + g ¯ where f and g are bounded analytic functions on the unit disk. We then find sufficient conditions when f is a monomial. [ABSTRACT FROM AUTHOR]

The t-multifractal formalism is a formula introduced by Jaffard and Mélot in order to deduce the t-spectrum of a function f from the knowledge of the (p,t)-oscillation exponent of f. The t-spectrum is the Hausdorff dimension of the set of points where f has a given value of pointwise Lt regularity. The (p,t)-oscillation exponent is measured by determining to which oscillation spaces Op,ts (defined in terms of wavelet coefficients) f belongs. In this paper, we first prove embeddings between oscillation and Besov-Sobolev spaces. We deduce a general lower bound for the (p,t)-oscillation exponent. We then show that this lower bound is actually equality generically, in the sense of Baire's categories, in a given Sobolev or Besov space. We finally investigate the Baire generic validity of the t-multifractal formalism. [ABSTRACT FROM AUTHOR]

The classical Hölder regularity is restricted to locally bounded functions and takes only positive values. The local Lp regularity covers unbounded functions and negative values. Nevertheless, it has the same apparent regularity in all directions. In the present work, we study a recent notion of directional local Lp regularity introduced by Jaffard. We provide its characterization by a supremum of a wide range oriented anisotropic Triebel wavelet coefficients and leaders. In addition, we deduce estimates on the Hausdorff dimension of the set of points where the directional local Lp regularity does not exceed a given value. The obtained results are illustrated by some examples of self-affine cascade functions. [ABSTRACT FROM AUTHOR]

The oscillating multifractal formalism is a formula conjectured by Jaffard expected to yield the spectrum d(h, β) of oscillating singularity exponents from a scaling function ζ(p, s'), for p > 0 and s' ∈ ℝ, based on wavelet leaders of fractional primitives f-s' of f. In this paper, using some results from Jaffard et al., we first show that ζ(p, s') can be extended on p ∈ ℝ to a function that is concave with respect to p ∈ ℝ and independent on orthonormal wavelet bases in the Schwartz class. We also establish its concavity with respect to s' when p > 0. Then, we prove that, under some assumptions, the extended scaling function ζ(p, s') is the Legendre transform of the wavelet leaders density of f-s'. Finally, as an application, we study the validity of the extended oscillating multifractal formalism for random wavelet series (under the assumption of independence and laws depending only on the scale). [ABSTRACT FROM AUTHOR]

The usual thermodynamic formalism is uniform in all directions and, therefore, it is not adapted to study multi-dimensional functions with various directional behaviors. It is based on a scaling function characterized in terms of isotropic Sobolev or Besov-type norms. The purpose of the present paper was twofold. Firstly, we proved wavelet criteria for a natural extended directional scaling function expressed in terms of directional Sobolev or Besov spaces. Secondly, we performed the directional multifractal formalism, i.e., we computed or estimated directional Hölder spectra, either directly or via some Legendre transforms on either directional scaling function or anisotropic scaling functions. We obtained general upper bounds for directional Hölder spectra. We also showed optimal results for two large classes of examples of deterministic and random anisotropic self-similar tools for possible modeling turbulence (or cascades) and textures in images: Sierpinski cascade functions and fractional Brownian sheets. [ABSTRACT FROM AUTHOR]