355,208 Results Found

In this paper, the author derives an analytical exact form of signum function, which evidently constitutes a fundamental concept of Communication Systems and Control Theory along with digital control systems and is also involved in many other fields...

Geometric function theory has extensively explored the geometric characteristics of analytic functions within symmetric domains. This study analyzes the geometric properties of a specific class of analytic functions employing confluent hypergeometric...

In this article, we consider a unified generalized version of extended Euler’s Beta function’s integral form a involving Macdonald function in the kernel. Moreover, we establish functional upper and lower bounds for this extended Beta fun...

Recently, Network Function Virtualization (NFV) and Software Defined Networking (SDN) have attracted many mobile operators. For the flexible deployment of Network Functions (NFs) in an NFV environment, NF decompositions and control/user plane separat...

Recently, two classes of univalent functions ${\mathcal{S}}_e^{*}$ and ${\mathcal{K}}_e$ were introduced and studied. A function f is in ${\mathcal{S}}_e^{*}$ if it is analytic in the unit disk, $f\left(0\right)=f^{\prime }\left(0\right)-1=0$ and $\frac{z{f}^{\prime }\left(z\right)}{f\left(z\right)}$...

Relying on the Hurwitz formula, we find closed-form formulas for the series over sine and cosine functions through the Hurwitz zeta functions, and using them and another summation formula for trigonometric series, we obtain a finite sum for some seri...

A new class of smooth exact penalty functions, constructed using the hyperbolic tangent (tanh) function, is proposed for solving constrained global optimization problems. The tanh function is chosen because of its unique mathematical properties: it i...

In this work, the authors use their contour integral method to derive an application of the Fourier integral theorem given by ${\int }_{-\infty }^{\infty }{\int }_{-\infty }^{\infty }{e}^{mx-my-e^x-e^y+y}{(\log \left(a\right)+x-y)}^{k}dxdy$ in terms of the Lerch function. This integral formula is then used to derive closed...

The principal aim of this paper is to introduce the extended Voigt-type function ${\mathbb{V}}_{\mu ,\nu }(x,y)$ and its counterpart extension ${\mathbb{W}}_{\mu ,\nu }(x,y)$, involving the Neumann function $Y_{\nu }$ in the kernel of the representing integral. The newly defined integra...

It is difficult to determine whether lung function improves by simple abdominal strengthening exercises, and studies on the correlation of lung function and functional movement are insufficient. Therefore; we aimed to identify the correlation between...

The present paper is devoted to the study of integral properties of alpha unpredictable functions. The problem of invariance of recurrence under integration is one of the most challenging and interesting in the theory of functions. The problem was so...

The main aim of this article is to study the Fredholm-type integral equation involving the incomplete H-function (IHF) and incomplete H-function in the kernel. Firstly, we solve an integral equation associated with the IHF with the aid of the theory...

Kurepa’s function and his hypothesis have been investigated by means of numerical simulation. Particular emphasis has been given to the conjecture on its distribution, that should be one of a random uniform distribution, which has been verified...

This is a collection of definite integrals involving the logarithmic and polynomial functions in terms of special functions and fundamental constants. All the results in this work are new.

The symmetric patterns that inequalities contain are reflected in researchers’ studies in many mathematical sciences. In this paper, we prove an asymptotic expansion for the generalized gamma function ${\mathsf{\Gamma }}_{\mu }\left(v\right)$ and study the completely mon...

Patients with cognitive impairment have decreased lower limb function. Therefore, we aimed to investigate the relationship between lower limb function and cognitive disorders to determine whether lower limb function can be screened to identify cognit...

In existing models with an unknown link function, the issue of predictors containing both multiple functional data and multiple scalar data has not been studied. To fill this gap, we propose a generalized partially functional linear model, which not...

The Lerch zeta function is defined by a Dirichlet series depending on two fixed parameters. In the paper, we consider the approximation of analytic functions by discrete shifts of the Lerch zeta function, and we prove that, for arbitrary parameters a...

One-cycle control (OCC) is prized in power converter applications for its rapid dynamic response and effective disturbance suppression. While its core principle relies on the symmetry of the volt-second value of the inductor in each cycle, recent res...

Schröder approximations of the first kind, modified for the inverse function approximation case, are utilized to establish general analytical approximation forms for an inverse function. Such general forms are used to establish arbitrarily accur...

The properties of a special function which is defined by an integral is presented. The numerical values of this function are tabulated correct to twenty decimal places. The curves of this function and its complementary are plotted. Some properties of...

In this paper, we introduce some classes of univalent harmonic functions with respect to the symmetric conjugate points by means of subordination, the analytic parts of which are reciprocal starlike (or convex) functions. Further, we discuss the geom...

The paper proves a theorem about the structure of the distribution function on which the extremum of the fractionally linear functional is reached in the presence of an uncountable number of linear constraints. The problem of finding an extremal dist...

In this paper, we find some inequalities which involve Euler’s function, extended Euler’s function, the function $\tau$, and the generalized function $\tau$ in algebraic number fields.

The Lambert W function, implicitly defined by $W\left(x\right){}^{}$...

There have been many different definitions of fractional calculus presented in the literature, especially in recent years. These definitions can be classified into groups with similar properties. An important direction of research has involved provin...

Background: Patients who undergo cardiac surgery and procedures often experience functional impairments. However, few studies have compared changes in physical function, cognitive function, mental health, and sleep quality before and after the interv...

This study examines the necessary requirements for some analytic function subclasses, especially those associated with the generalized Mittag-Leffler function, to be classified as univalent function subclasses that are determined by particular geomet...

Generalization of the ordinary hyperbolic functions called hyperbolic Ateb-functions is considered. They are the inverse of incomplete Beta-function. These functions are solutions of differential equations, which describe the aperiodic vibration moti...

We proved that the Hurwitz zeta function is prime. In addition, we derived the Nevanlinna characteristic for this function.

In this article, we study scalar-on-function regression with functional covariates observed through replicated measurements subject to measurement error. Treating replicated curves as surrogates of an underlying latent process, the proposed framework...

Geometric function theory, a subfield of complex analysis that examines the geometrical characteristics of analytic functions, has seen a sharp increase in research in recent years. In particular, by employing subordination notions, the contributions...

A service function chain (SFC) is an ordered virtual network function (VNF) chain for processing traffic flows to deliver end-to-end network services in a virtual networking environment. A challenging problem for an SFC in this context is to determin...

A three directional (3-D) multi-scroll chaotic attractors based on the Jerk system with nonlinearity of the sine function and sign function is introduced in this paper. The scrolls in the X-direction are generated by the sine function, which is a mod...

Patients with long-term health sequelae of COVID-19 (post-COVID-19 condition) experience both physical and cognitive manifestations. However, there is still uncertainty about the prevalence of physical impairment in these patients and whether there i...

Determining the exact number of primes at large magnitudes is computationally intensive, making approximation methods (e.g., the logarithmic integral, prime number theorem, Riemann zeta function, Chebyshev’s estimates, etc.) particularly valuab...

Asymmetry plays a significant role in the transmission dynamics in novel discrete fractional calculus. Few studies have mathematically modeled such asymmetry properties, and none have developed discrete models that incorporate different symmetry deve...

In numerous geometric and physical applications of complex analysis, estimating the sharp bounds of coefficient-related problems of univalent functions is very important due to the fact that these coefficients describe the core inherent properties of...

To solve the problem that the traditional ambiguity function cannot well reflect the time-frequency distribution characteristics of linear frequency modulated (LFM) signals due to the presence of impulsive noise, two robust ambiguity functions: corre...

In this paper, we find sufficient conditions to be imposed on the parameters of a class of functions related to the Barnes–Mittag-Leffler function that allow us to conclude that it possesses certain geometric properties (such as starlikeness, u...

Since in many particular cases checking directly the conditions from the definitions of starlikeness or convexity of a function can be difficult, in this paper we use the theory of differential subordination and in particular the method of admissible...

Background: Video-assisted thoracoscopic surgery (VATS) has been increasingly used as an approach for lung lobectomy. However, the recovery of respiratory and physical function may be insufficient at discharge because the average length of hospital s...

By means of the generating function method and Dougall’s formulae for bilateral hypergeometric series, we examine four classes of infinite series, which may be considered as variants of Riemann zeta function. Several summation formulae are establishe...

There is evidence to suggest that hormonal migraine is associated with altered cerebrovascular function. We aimed to investigate whether the expression of genes related to endothelial function in venous blood (1) might influence cerebrovascular funct...

Nitric oxide synthases (NOS) are enzymes responsible for the cellular production of nitric oxide (NO), a highly reactive signaling molecule involved in important physiological and pathological processes. Given its remarkable capacity to diffuse acros...

Graphene is a two dimensional one atom thick allotrope of carbon that displays unusual crystal structure, electronic characteristics, charge transport behavior, optical clarity, physical & mechanical properties, thermal conductivity and much more...

Let $f\left(z\right)=z+{\displaystyle \sum }_{n=2}^{\infty }{a}_n{z}^n$ and $g_{p,b,c}\left(z\right)=z+{\displaystyle \sum }_{n=2}^{\infty }\frac{{\left(-\frac{c}{4}\right)}^{n-1}}{{\left(\frac{3}{2}\right)}_{n-1}{\left(k\right)}_{n-1}}{z}^n$ with ...

In the present paper, we present certain geometric properties, such as starlikeness, convexity of order $\eta (0\le \eta <1)$, and close-to-convexity, in an open unit disk of the normalized form of Ramanujan-type entire functions. As a consequence,...

Patients with cancer often experience changes in function during and after treatment but it is not clear what cancer types, and associated clinical factors, affect function. This study evaluated patient-reported functional impairments between specifi...

The topics studied in the geometric function theory of one variable functions are connected with the concept of Symmetry because for some special cases the analytic functions map the open unit disk onto a symmetric domain. Thus, if all the coefficien...