355,208 Results Found

This document represents the cummulative effort of the members of the Ad Hoc Committee on Labia/­Lingual Posturing Function: Robert M. Mason (chair), Michelle M. Ferketic (ex officio), Sheila S. Gideon, Marvin L. Hanson, Ralph L. Shelton, and Ida M....

Neurological diseases severely affect the quality of life of patients. Although existing treatments including rehabilitative therapy aim to facilitate the recovery of motor function, achieving complete recovery remains a challenge. In recent years, r...

β-glucan is a non-starch soluble polysaccharide widely present in yeast, mushrooms, bacteria, algae, barley, and oat. β-Glucan is regarded as a functional food ingredient due to its various health benefits. The high molecular weight (Mw) an...

JNK is a protein kinase, which induces transactivation of c-jun. The three isoforms of JNK, JNK1, JNK2, and JNK3, are encoded by three distinct genes. JNK1 and JNK2 are expressed ubiquitously throughout the body. By contrast, the expression of JNK3 i...

The main purpose of this paper is to study extension of the extended beta function by Shadab et al. by using 2-parameter Mittag-Leffler function given by Wiman. In particular, we study some functional relations, integral representation, Mellin transf...

The main aim of this research paper is to introduce a new extension of the Gauss hypergeometric function and confluent hypergeometric function by using an extended beta function. Some functional relations, summation relations, integral representation...

This paper aims to obtain the ${}_{\xi }\mathsf{\Psi }_{\eta }$-extended Whittaker function and its integral representations. This function is defined by using the ${}_{\xi }\mathsf{\Psi }_{\eta }$-confluent hypergeometric function, which was recently extended in terms of the Fox–W...

We calculate some infinite sums containing the digamma function in closed form. These sums are related either to the incomplete beta function or to the Bessel functions. The calculations yield interesting new results as by-products, such as parameter...

Introduction: Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been shown to cause long-term pulmonary sequelae. Objects: The aim of this study was to evaluate the consequences of the SARS-CoV-2 infection on pulmonary function and on...

In this study, the connection between certain subfamilies of harmonic univalent functions is established by utilizing a convolution operator involving the Mittag–Leffler function. The investigation reveals inclusion relations concerning harmoni...

Organic anion transporting polypeptide 1B1 (OATP1B1) is specifically expressed at the basolateral membrane of human hepatocytes and plays important roles in the uptake of various endogenous and exogenous compounds including many drugs. The proper fun...

Soil degradation and poor fertility severely constrain vegetation growth in urban ecosystems, particularly in compacted and nutrient-depleted tree pits. Mulching has emerged as an effective strategy to improve soil quality and regulate soil–mic...

Lung function in children and adolescents with obesity must consider the coexistence of two complex and related phenomena: obesity and growth. The assessment of body composition can identify changes in respiratory dynamics arising, exclusively or joi...

In this paper we will be concerned with zeta-symmetry—the functional equation for the (Riemann) zeta-function (equivalents to which are called modular relations)—and reveal the reason why so many results are intrinsic to PFE (Partial Frac...

In this paper, according to some numerical computational evidence, we investigate and prove certain identities and properties on the absolute Möbius divisor functions and Euler totient function when they are iterated. Subsequently, the relations...

In this paper, we present some new symmetric bounds for Bateman’s G-function and its derivatives, in terms of the digamma and polygamma functions, which are better than some recent results.

Archimedean copulas form a very wide subclass of symmetric copulas. Most of the popular copulas are members of the Archimedean copulas. These copulas are obtained using real functions known as Archimedean generators. In this paper, we observe that un...

We investigate a nonparametric, varying coefficient regression approach for modeling and estimating the regression effects caused by two functionally correlated datasets. Due to modern biomedical technology to measure multiple patient features during...

In this paper, we further study the generating function involving a variety of special numbers and ploynomials constructed by the second author. Applying the Mellin transformation to this generating function, we define a new class of zeta type functi...

The aim of this paper is the imputation of missing data of COVID-19 hospitalized and intensive care curves in several Spanish regions. Taking into account that the curves of cases, deceases and recovered people are completely observed, a function-on-...

Functional cognitive disorders (FCD) have become a subject of increasing clinical interest in recent years, in part because of their high prevalence amongst patients attending dedicated memory clinics. Empirical understanding of FCD based on observat...

Work-related asthma (WRA) is a very frequent condition in the occupational setting, and refers either to asthma induced (occupational asthma, OA) or worsened (work-exacerbated asthma, WEA) by exposure to allergens (or other sensitizing agents) or to...

Recently, Special Function Theory (SPFT) and Operator Theory (OPT) have acquired a lot of concern due to their considerable applications in disciplines of pure and applied mathematics. The Hurwitz-Lerch Zeta type functions, as a part of Special Funct...

This study aimed to investigate the regulatory effects of combined Bacillus subtilis (BS) and chito-oligosaccharides (COS) supplementation on growth performance, antioxidant function, immune function, and intestinal barrier function of broilers. A to...

Riemann’s method is one of the definitive ways of solving Cauchy’s problem for a second order linear hyperbolic partial differential equation in two variables. The first review of Riemann’s method was published by E.T. Copson in 195...

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 functio...

In recent years, special functions have played a significant role in the investigation of different subclasses within the class of bi-univalent functions. In this work, we present and investigate two new subclasses of bi-univalent functions defined i...

In this survey we stress the importance of the higher transcendental Mittag-Leffler function in the framework of the Fractional Calculus. We first start with the analytical properties of the classical Mittag-Leffler function as derived from being the...

Using the power series expansion technique, this paper established two new inequalities for the sine function and tangent function bounded by the functions $x^2{\left(sin(\lambda x)/(\lambda x)\right)}^{\alpha }$ and $x^2{\left(tan(\mu x)/(\mu x)\right)}^{\beta }$. These results are better than the ones in the previous li...

We prove that the function $\sigma \left(s\right)$ defined by $\beta \left(s\right)=\frac{6s^2+12s+5}{3s^2(2s+3)}-\frac{{\psi }^{\prime }\left(s\right)}{2}-\frac{\sigma \left(s\right)}{2s^5},s>0$, is strictly increasing with the sharp bounds $0<\sigma \left(s\right)<\frac{49}{120}$, where $\beta \left(s\right)$ is Nielsen’s beta function a...

This article studies the convolutional kernel function of fractal operators in bone fibers. On the basis of the micro-nano composite structure of compact bone, we abstracted the physical fractal space of bone fibers and derived the fractal operators....

The relationship between the inverse Langevin function and the proposed r₀-r₁-Lambert W function is defined. The derived relationship leads to new approximations for the inverse Langevin function with lower relative error bounds than comparable publi...

This paper examines the relationship between the classical polylogarithm function and meromorphic harmonic univalent mappings. Using a convolution operator derived from the polylogarithm function, we define a class of harmonic meromorphic functions a...

Symmetry is a fascinating property of numerous mathematical notions. In mathematical analysis a function $f:[a,b]\to \mathbf{R}$ symmetric about $\frac{a+b}{2}$ satisfies the equation $f(a+b-x)=f\left(x\right)$. In this paper, we investigate the relationship of unified Mittag&...

Lauricella, G. in 1893 defined four multidimensional hypergeometric functions $F_A$, $F_B$, $F_C$ and $F_D$. These functions depended on three variables but were later generalized to many variables. Lauricella’s functions are infinite sums of products of v...

In this paper, some coefficient problems for starlike analytic functions with respect to symmetric points are considered. Bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to f...

The normalized analytic function ${\Phi }_N\left(z\right)=1+z-{\displaystyle \frac{z^3}{3}}$, which connects the open unit disk onto a bounded domain within the right half of a nephroid-shaped region, is associated with the bounded turning of functions denoted by $R_n$. It calculates the...

Motivated by the recent work on the symmetric domains, this article investigates certain features of symmetric domain which are caused by the secant hyperbolic functions. Geometric characteristics of analytic functions associated with secant hyperbol...

Let $t_{\tau }$ be a solution to the equation $\theta \left(t\right)=(\tau -1)\pi$, $\tau >0$, where $\theta \left(t\right)$ is the increment of the argument of the function ${\pi }^{-s/2}\mathsf{\Gamma }(s/2)$ along the segment connecting points $s=1/2$ and $s=1/2+it$. $t_{\tau }$ is called...

In this paper, we find some properties of Euler’s function and Dedekind’s function. We also generalize these results, from an algebraic point of view, for extended Euler’s function and extended Dedekind’s function, in algebrai...

We define the characteristic function operator $e^{i\theta \mathbf{A}+i\tau \mathbf{B}}$, where $\mathbf{A}$ and $\mathbf{B}$ are explicit functions of the operators $\mathbf{x}$ and $\mathbf{D}$. Operators of this form arise in a wide range of applications, including quantum mechanics, evolution equations, and time...

We characterize the complete monotonicity of the Kilbas-Saigo function on the negative half-line. We also provide the exact asymptotics at $-\infty$, and uniform hyperbolic bounds are derived. The same questions are addressed for the classical Le Roy functi...

By making use of a higher-order q-derivative operator, certain families of meromorphic q-starlike functions and meromorphic q-convex functions are introduced and studied. Several sufficient conditions and coefficient inequalities for functions in the...

We apply our simultaneous contour integral method to an infinite sum in Prudnikov et al. and use it to derive the infinite sum of the Incomplete gamma function in terms of the Hurwitz zeta function. We then evaluate this formula to derive new series...

The remarkable Koebe function is the (unique) extremal of many important distortion functionals in geometric function theory. This paper provides a complete characterization of such functionals.

The composition $H\left(z\right)=f(\Phi (z\left)\right)$ is studied, where f is an entire function of a single complex variable and $\Phi$ is an entire function of n complex variables with a vanished gradient. Conditions are presented by the function $\Phi$ providing boundedn...

In the theory of special functions, finding correlations between different types of functions is of great interest as unifying results, especially when considering issues such as analytic continuation. In the present paper, the relation between Lambe...

The confluence of distributions (generalized functions) with integral transforms has become a remarkably powerful tool to address important unsolved problems. The purpose of the present study is to investigate a distributional representation of the g...

Objectives: The objective of this narrative review was to examine the available literature regarding the increasingly popular method of exercise commonly referred to as “Functional Training” and its potential implications on vestibular an...

The purpose of this research is to unify and extend the study of the well-known concept of coefficient estimates for some subclasses of analytic functions. We define the new subclass ${\mathcal{A}}_4^{r,s}$ of analytic functions related to the four-leaf domain, to inc...