626 Results Found

In this paper, we obtain some new natural approaches of Shafer-Fink inequality for arc sine function and the square of arc sine function by using the power series expansions of certain functions, which generalize and strengthen those in the existing...

The main purpose of this article is to examine the q-analog of starlike functions connected with a trigonometric sine function. Further, we discuss some interesting geometric properties, such as the well-known problems of Fekete-Szegö, the neces...

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...

This manuscript addresses the feasibility and significance of using a sine function to modify the system error of a normal linear feedback control to achieve more efficient capabilities in terms of energy-saving. The associated mathematic modeling an...

Let ${\mathcal{S}}_s^{*}$ be the class of normalized functions f defined in the open unit disk $\mathbb{D}=\{z:|z|<1\}$ such that the quantity $\frac{z{f}^{\prime }\left(z\right)}{f\left(z\right)}$ lies in an eight-shaped region in the right-half plane and satisf...

In this paper, we consider the generalized sine-Gordon equation ${\psi }_{tx}=(1+a{\partial }_x^2)\sin \psi$ and the sinh-Poisson equation $u_{xx}+u_{yy}+\sigma \sinh u=0$, where a is a real parameter, and $\sigma$ is a positive parameter. Under different conditions, e.g., $a=$...

A novel chaotic system for generating multi-scroll attractors based on a Jerk circuit using a special form of a sine function (SFSF) is proposed in this paper, and the SFSF is the product of a sine function and a sign function. Although there are inf...

This paper develops two novel arcsine-type analytic approximation formulas for $\mathrm{arcsl}\left(x\right)$, the Gauss lemniscate sine function, each equipped with a monotonic and bounded remainder term of order $x^{29}$ as $x\to 0$, which demonstrates the high accuracy of t...

This study of Hankel and Hermitian Toeplitz determinants is one of the major areas of interest in Geometric function theory and has wide applications in the areas of signal processing and Applied Mathematics. In our present investigations, we define...

In multiquadratic radial basis function (MQ-RBF) interpolation, shape parameters have a direct effect on the interpolation accuracy. The paper presents an MQ-RBF interpolation technique with optimized shape parameters for estimating the parameters of...

In this paper, a circuit technique to extend the measuring range of a linear variable differential transformer (LVDT) is proposed. The transfer characteristic of the LVDT contains the odd function form of the cubic polynomial. Therefore, the measurin...

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...

This work is devoted to the hyperbolic sine function (HSF) control-based finite-time bipartite synchronization of fractional-order spatiotemporal networks and its application in image encryption. Initially, the addressed networks adequately take into...

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...

In this paper, by means of the Faà di Bruno formula, with the help of explicit formulas for partial Bell polynomials at specific arguments of two specific sequences generated by derivatives at the origin of the inverse sine and inverse cosine...

A novel kernel recursive second-order sine adaptive (KRSOSA) algorithm was devised for identifying non-linear systems, which was constructed using a symmetry squared sine function to develop a novel kernel loss function and recursive scheme. In the p...

In this paper, a fractional-order discrete map with a hyperbolic sine function has been proposed and studied. Firstly, the basic characteristics of the map in integer-order case are studied theoretically and numerically. Secondly, dynamics of the map...

The logarithmic functions have been used in a verity of areas of mathematics and other sciences. As far as we know, no one has used the coefficients of logarithmic functions to determine the bounds for the third Hankel determinant. In our present inv...

This study introduces a subclass $S_{qs}^{*}$ of starlike functions associated with the q-analogue of the sine function defined in symmetric unit disk. This article comprises the investigation of sharp coefficient bounds, and the upper bound of the third-ord...

In this research, we define a few subclasses of analytic functions which are connected to sine functions and the cardioid domain in the unit disk. We investigate initial coefficient bounds, the Fekete–Szego problem and second and third Hankel d...

In cryptography, the pseudorandom number sequences must have random appearance to be used in secure information systems. The skew tent map (STM) is an attractive map to produce pseudorandom sequences due to its easy implementation and the absence of...

We present a proof, using elementary methods, of the Euler reflection formula for the Gamma function, based on an integral computed by Laplace and on the Euler–Gauss infinite product representation of Gamma. This way, we reverse the classical p...

In the paper, the authors introduce two notions, the normalized remainders, or say, the normalized tails, of the Maclaurin power series expansions of the sine and cosine functions, derive two integral representations of the normalized tails, prove th...

We consider four infinite collections of improper integrals involving the sine and cosine functions and provide explicit values for the integrals in each of the collections. The methods used are elementary and involve the sine integral function and t...

In the paper, by virtue of a derivative formula for the ratio of two differentiable functions and with the help of a monotonicity rule, the authors expand a logarithmic expression involving the sine function into the Maclaurin power series in terms o...

In this article, our objective is to define and study a new subclass of analytic functions associated with the q-analogue of the sine function, operating in conjunction with a convolution operator. By manipulating the parameter q, we observe that the...

In digital shearography, the speckle noise of the phase fringe pattern has a negative effect on the accuracy and reliability of the phase unwrapping procedure. A novel and optimized sine–cosine transform wavelet threshold denoising method is pr...

In this article, we extensively study a family of distributions using the trigonometric function. We add an extra parameter to the sine transformation family and name it the alpha-sine-G family of distributions. Some important functional forms and pr...

To improve high motion accuracy and efficiency in the high-speed operation of a 4-DOF (4 degrees of freedom) redundant parallel robot, this paper introduces a trajectory planning of the parallel robot in joint space based on the twelve-phase sine jer...

In this paper, function approximation is utilized to establish functional series approximations to integrals. The starting point is the definition of a dual Taylor series, which is a natural extension of a Taylor series, and spline based series appro...

In this study, we introduce the new subclasses, ${\mathcal{M}}_{\alpha }(sin)$ and ${\mathcal{M}}_{\alpha }(cos)$, of $\alpha$-convex functions associated with sine and cosine functions. First, we obtain the initial coefficient bounds for the first five coefficients of the functions t...

This paper aims to improve SHA-512 security without increasing complexity; therefore, we focused on hash functions depending on DNA sequences and chaotic maps. After analysis of 45 various chaotic map types, only 5 types are selected in this proposal...

In this paper, the authors provide several sharp upper and lower bounds for the Neuman–Sándor mean in terms of the arithmetic and contra-harmonic means, and present some new sharp inequalities involving hyperbolic sine function and hyper...

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...

Control charts are widely used in quality control and industrial sectors. Because of their important role, researchers are focusing on the development of new control charts. According to our study, there is no significant amount of published work on...

Sine and cosine wave synthesis is utilized for generating sinusoidal-like values in the digital domain. While this task is commonly handled through software, dedicated hardware like Direct Digital Synthesis (DDS) is also available. However, both meth...

In the paper, the authors establish the monotonicity results of the ratios between normalized tails of the Maclaurin power series expansions of the sine and cosine functions and restate them in terms of the generalized hypergeometric functions.

The aim of this paper is to give generating functions for parametrically generalized polynomials that are related to the combinatorial numbers, the Bernoulli polynomials and numbers, the Euler polynomials and numbers, the cosine-Bernoulli polynomials...

In this paper, we introduce q-cosine and q-sine Euler polynomials and determine identities for these polynomials. From these polynomials, we obtain some special properties using a power series of q-trigonometric functions, properties of q-exponential...

This paper presents an overview of cosine and sine Apostol-type Frobenius–Euler–Fibonacci polynomials, as well as several identities that are associated with these polynomials. By applying a partial derivative operator to the generating f...

We analyze the spectral stability of travelling waves in a $\delta$-regularized dissipative sine-Gordon equation modelling refined long Josephson junction dynamics. Linearization about a wave yields a singularly perturbed fourth-order spectral problem...

We consider the asymptotic expansion of the generalised exponential integral involving the Mittag-Leffler function introduced recently by Mainardi and Masina [Fract. Calc. Appl. Anal. 21 (2018) 1156–1169]. We extend the definition of this funct...

We introduce and study an integral transform whose kernel is Dawson’s integral. The proposed transform is connected to the Fourier sine transform through a classical integral representation of Dawson’s function and to the Glasser transfor...

For the first time, we study the Fokas–Lenells equation in polarization preserving fibers with multiplicative white noise in Itô sense. Four integration algorithms are applied, namely, the method of modified simple equation (MMSE), the me...

This paper introduces a novel class of generalized contractions, termed $(\alpha ,\eta ,(Q,h),\mathcal{L})$-contraction mapping, within the context of triple controlled metric-type spaces, extending the framework of fixed point theory in controlled structures. T...

Supramolecular coordination polymers with wavelike structures have been synthesized by self-assembly and their structures analyzed using the sine trigonometric function. Slow evaporation of a methylene chloride-methanol solution of a 1:1 molar mixtur...

This paper constructs and introduces $(p,q)$ -cosine and $(p,q)$ -sine Bernoulli polynomials using $(p,q)$ -analogues of ${(x+a)}^n$ . Based on these polynomials, we discover basic properties and identities. Moreov...

Fractals are essential in representing the natural environment due to their important characteristic of self similarity. The dynamical behavior of fractals mostly depends on escape criteria using different iterative techniques. In this article, we es...

The greater cane rat algorithm (GCRA) is a swarm intelligence algorithm inspired by the discerning and intelligent foraging behavior of the greater cane rats, which facilitates mating during the rainy season and non-mating during the dry season. Howe...

The whale optimization algorithm (WOA) is constructed on a whale’s bubble-net scavenging pattern and emulates encompassing prey, bubble-net devouring prey, and stochastic capturing for prey to establish the global optimal values. Nevertheless,...