55 Results Found

Currently, algorithms to embed watermarks into digital images are increasing exponentially, for example in image copyright protection. However, when a watermarking algorithm is applied, the preservation of the image’s quality is of utmost impor...

Heart diseases are the most important causes of death in the world and over the years, the study of cardiac movement has been carried out mainly in two dimensions, however, it is important to consider that the deformations due to the movement of the...

This study focuses on analyzing the generalized HSC-KdV equations characterized by variable coefficients and Wick-type stochastic (Wt.S) elements. To derive white noise functional (WNF) solutions, we employ the Hermite transform, the homogeneous bala...

In probabilistic analysis, random variables with unknown distributions are often appeared when dealing with practical engineering problem. A Hermite normal transformation model has been proposed to conduct structural reliability assessment without th...

We introduce a multi-parameter family of bases in the Hilbert space $L^2\left(\mathbb{R}\right)$ that are associated to a set of Hermite functions, which also serve as a basis for $L^2\left(\mathbb{R}\right)$. The Hermite functions are eigenfunctions of the Fourier transform, a property that is,...

Automated skin lesion classification using machine learning techniques is crucial for early and accurate skin cancer detection. This study proposes a hybrid method combining the Hermite, Radial Fourier–Mellin, and Hilbert transform to extract c...

Uncertain variables, such as electric power system parameters, have significant impacts on dynamic simulations of power systems. As traditional uncertainty analysis methods for power system dynamic simulations, both the simulation method and the appr...

Using normalized Hermite functions, we construct bases in the space of square integrable functions on the unit circle ($L^2(\mathcal{C})$) and in $l_2(\mathbb{Z})$, which are related to each other by means of the Fourier transform and the discrete Fourier transform. These re...

We associate the stationary harmonic oscillator with time-dependent systems exhibiting non-Hermiticity by means of point transformations. The new systems are exactly solvable, with all-real spectra, and transit to the Hermitian configuration for the...

In this short communication, we present a new limit relation that reduces pseudo-Jacobi polynomials directly to Hermite polynomials. The proof of this limit relation is based upon ${}_2{F}_1$-type hypergeometric transformation formulas, which are applicable...

The present paper suggests fuel consumption modeling for HDVs based on the code from the Japanese Ministry of the Environment. Two interpolation models (inversed distance weighted (IDW) and Hermite) and three types of fuel efficiency maps (coarse, me...

Fractional order differential equations often possess inherent symmetries that play a crucial role in governing their dynamics in a variety of scientific fields. In this work, we consider numerical solutions for fractional-order linear delay differen...

In this article, we discuss the (2 + 1)-D coupled Korteweg–De Vries (KdV) equations whose coefficients are variables, and stochastic (2 + 1)-D C-KdV (C-KdV) equations with the $\chi$-Wick-type product. White noise functional solutions (WNFS) are...

The monitoring of respiratory rate is a relevant factor in medical applications and day-to-day activities. Contact sensors have been used mostly as a direct solution and they have shown their effectiveness, but with some disadvantages for example in...

The breathing rate monitoring is an important measure in medical applications and daily physical activities. The contact sensors have shown their effectiveness for breathing monitoring and have been mostly used as a standard reference, but with some...

Nowadays, medical imaging has become an indispensable tool for the diagnosis of some pathologies and as a health prevention instrument. In addition, medical images are transmitted over all types of computer networks, many of them insecure or suscepti...

Some classical texts on the Sturm–Liouville equation ${(p(x)y^{\prime })}^{\prime }-q(x)y+\lambda \rho (x)y=0$ are revised to highlight further properties of its solutions. Often, in the treatment of the ensuing integral equations, $\rho =const$ is a...

Monitoring Peripheral Oxygen Saturation (SpO₂) is an important vital sign both in Intensive Care Units (ICUs), during surgery and convalescence, and as part of remote medical consultations after of the COVID-19 pandemic. This has made the development...

The focus of the research presented in this paper is on a new generalized family of degenerate three-variable Hermite–Appell polynomials defined here using a fractional derivative. The research was motivated by the investigations on the degener...

This Special Issue contains 14 articles from the MDPI journal Symmetry on the general subject area of “Special Functions and Polynomials”, written by scholars belonging to different countries of the world. A similar number of submitted ar...

In this invited survey-cum-expository review article, we present a brief and comprehensive account of some general families of linear and bilinear generating functions which are associated with orthogonal polynomials and such other higher transcenden...

In this paper, we present recent results in harmonic analysis in the real line $\mathbb{R}$ and in the half-line ${\mathbb{R}}^{+}$ , which show a closed relation between Hermite and Laguerre functions, respectively, their symmetry groups and Fourier analysis....

In this paper, we investigate the Wick-type stochastic (3+1)-dimensional modified Benjamin–Bona–Mahony (BBM) equations. We present a generalised version of the modified tanh–coth method. Using the generalised, modified tanh–coth method, white noise t...

This paper proposes an efficient and accurate numerical framework for solving fractional Bagley–Torvik equations, which model viscoelastic and memory-dependent dynamic systems. The method combines the Hermite polynomial approximation with a lea...

This is a review paper on the generalization of Euclidean as well as pseudo-Euclidean groups of interest in quantum mechanics. The Weyl–Heisenberg groups, $H_n$, together with the Euclidean, $E_n$, and pseudo-Euclidean $E_{p,q}$, groups are two families o...

Some systems of univariate orthogonal polynomials can be mapped into other families by the Fourier transform. The most-studied example is related to the Hermite functions, which are eigenfunctions of the Fourier transform. For the multivariate case,...

The Daoist monasteries, which were first popularized in southern China in the late fifth century, reflected major changes in the structure of medieval Daoism. From the perspective of comparative religious history, the rise of Daoist monasteries bears...

Three-dimensional printing is a layer-by-layer stacking process. It can realize complex models that cannot be manufactured by traditional manufacturing technology. The most common model currently used for 3D printing is the STL model. It uses planar...

We provide a realization of fractional supersymmetry quantum mechanics of order r, where the Hamiltonian and the supercharges involve the fractional Dunkl transform as a Klein type operator. We construct several classes of functions satisfying certai...

In this work, we obtain non-Gaussian (NG) stochastic solutions to $\chi$-Wick-type stochastic ($\chi$-Wk-TS) Burgers’ equations with variable coefficients. An Exp-function method, the connection between white noise theory and hypercomplex systems...

In this paper, we show that the use of methods of an operational nature, such as umbral calculus, allows achieving a double target: on one side, the study of the Voigt function, which plays a pivotal role in spectroscopic studies and in other applica...

We propose a local feature descriptor based on moment. Although conventional scale invariant feature transform (SIFT)-based algorithms generally use difference of Gaussian (DoG) for feature extraction, they remain sensitive to more complicated deform...

This Editorial introduces the Symmetry Special Issue “Theory and Applications of Special Functions II” and summarizes the nine contributions collected therein. The papers span the analytic continuation of multivariate hypergeometric funct...

Let f be a band-limited function in $L^2(\mathbb{R})$ . Fix $T>0$ , and suppose $f^{\prime }$ exists and is integrable on $[-T,T]$ . This paper gives a concrete estimate of the error incurred when approximating f in the root mean squa...

Automated segmentation of brain tumors is a difficult procedure due to the variability and blurred boundary of the lesions. In this study, we propose an automated model based on Bendlet transform and improved Chan-Vese (CV) model for brain tumor segm...

In this paper, the coupled nonlinear KdV (CNKdV) equations are solved in a stochastic environment. Hermite transforms, generalized conformable derivative, and an algorithm that merges the white noise instruments and the $({\mathfrak{G}}^{\prime }/{\mathfrak{G}}^{\mathfrak{2}})$-expansion techni...

In this article, we introduce a novel three-step iterative algorithm with memory for finding the roots of nonlinear equations. The convergence order of an established eighth-order iterative method is elevated by transforming it into a with-memory var...

Inspired by ideas from umbral calculus and based on the two types of integrals occurring in the defining equations for the gamma and the reciprocal gamma functions, respectively, we develop a multi-variate version of umbral calculus and of the so-cal...

We studied theoretically and experimentally the propagation of structured Laguerre–Gaussian (sLG) beams through an optical system with general astigmatism based on symplectic ABCD transforms involving geometry of the second-order intensity mome...

With the increasing proportion of various unbalanced loads in the power grid, power quality is seriously challenged. It is of great significance to effectively detect, analyze, and evaluate the power quality problems. First, this paper introduces the...

New three-step with-memory iterative methods for solving nonlinear equations are presented. We have enhanced the convergence order of an existing eighth-order memory-less iterative method by transforming it into a with-memory method. Enhanced acceler...

A method for the solution of linear differential equations (DE) of non-integer order and of partial differential equations (PDE) by means of inverse differential operators is proposed. The solutions of non-integer order ordinary differential equation...

This article demonstrates the crucial importance of the symmetrization method for the formation of autofocusing beams. It is possible to impart autofocusing properties to rather arbitrary distributions, for example, truncated and inverted classical m...

Orbital angular momentum (OAM) beams may create a new paradigm for the future classical and quantum communication systems. A majority of existing OAM beam converters are bulky, slow, and cannot withstand high powers. Here, we design and experimentall...

The second virial coefficient (SVC) of the Lennard-Jones fluid is a cornerstone of molecular theory, yet its calculation has traditionally relied on the complex integration of the pair potential. This work introduces a fundamentally different approac...

The Dyson index, $\beta$, plays an essential role in random matrix theory, as it labels the so-called “three-fold way” that refers to the symmetries satisfied by ensembles under unitary transformations. As is known, its $1,$ 2, and 4 values...

A nonlinear equation $f\left(x\right)=0$ is mathematically transformed to a coupled system of quasi-linear equations in the two-dimensional space. Then, a linearized approximation renders a fractional iterative scheme $x_{n+1}=x_n-f\left(x_n\right)/[a+bf\left(x_n\right)]$, which require...

Massive heterogeneous big data residing at different sites with various types and formats need to be integrated into a single unified view before starting data mining processes. Furthermore, in most of applications and research, a single big data sou...

This article comprises the study of three-dimensional squeezing flow of (CNT-SiO₂/H₂O) hybrid nanofluid. The flow is confined inside a rotating channel whose lower wall is stretchable as well as permeable. Heat transfer with viscous dissipation is a...

Using the wavelet transform defined in the infinite domain to process the signal defined in finite interval, the wavelet transform coefficients at the boundary are usually very large. It will bring severe boundary effect, which reduces the calculatio...