In this paper, we propose a zoom auxiliary imaging lens based on the four-component mechanical zoom method for a modulation transfer function (MTF) test system. The auxiliary imaging lenses of the current MTF test system typically use fixed-focus opt...
This paper introduces the optimal auxiliary function method (OAFM) for solving a nonlinear system of Belousov–Zhabotinsky equations. The system is characterized by its complex dynamics and is treated using the Caputo operator and concepts from...
This paper presents an efficient improved generalized class of estimators for the precise estimation of the population distribution function using auxiliary information. Estimation of the population distribution function is a crucial aspect of statis...
In this paper, the delay-dependent stability of haptic systems is studied by developing a new stability criterion. Firstly, the haptic system inevitably introduces time delays by using communication networks to transmit information between the contro...
In this paper, we introduce and implement the optimal auxiliary function method to solve a system of fractional-order Whitham–Broer–Kaup equations, a class of nonlinear partial differential equations with broad applications in mathematica...
This study aims to explore the effect of spatial-fractional derivatives and the multiplicative standard Wiener process on the solutions of the stochastic fractional regularized long-wave equation (SFRLWE) and contribute to its analysis. We introduce...
In this article, we investigate the utilization of Riemann–Liouville’s fractional integral and the Caputo derivative in the application of the Optimal Auxiliary Function Method (OAFM). The extended OAFM is employed to analyze fractional n...
In this paper, a new two-step joint optimization approach based on the asynchronous subregion optimization method is proposed for training a pipeline model composed of two different models. The first-step processing of the proposed joint optimization...
Based on some geometrical properties (symmetries and global analytic first integrals) of the Rabinovich system the closed-form solutions of the equations have been established. The chaotic behaviors are excepted. Moreover, the Rabinovich system is re...
In the present work, the nonlinear oscillations of a pendulum wrapping on two cylinders is studied by means of a new analytical technique, namely the Optimal Auxiliary Functions Method (OAFM). The equation of motion is derived from the Lagrange&rsquo...
The main aim of our paper is concerning the damped oscillations of 3D dynamical systems, depending on a single physical parameter. This system does not admit Hamilton–Poisson structure but can be explicitly integrated, and the exact parametric...
Coal-based solid-waste binders provide a promising route for integrating mine backfilling with CO2 mineralization, but auxiliary components can affect flowability, strength, and mineralization response differently. In this study, coal gasification sl...
Background: Fast excitatory transmission in the central nervous system is carried out by AMPA-type glutamate receptors. Neuronal hyperexcitability and epilepsy have been associated with the dysregulation of AMPA receptor function. Modulation of the g...
The present paper treats the problem of steady laminar MHD flow of an incompressible viscous fluid for mixed convection stagnation-point flow over a vertical stretching sheet in the presence of an externally magnetic field. By means of the Optimal Au...
In this study, a new modification of the newly developed semi-analytical method, optimal auxiliary function method (OAFM) is used for fractional-order KdVs equations. This method is called the fractional optimal auxiliary function method (FOAFM). The...
In the field of new-energy electric vehicles, lithium battery cells need to be connected in series and parallel to meet the requirements of high voltage and high power. Aiming at the high cost of traditional active equalizer, a half/full-bridge conve...
Auxiliary line construction has been identified as a crucial approach to fostering mathematical creative thinking. However, existing studies have only focused on the correlations between auxiliary line construction tasks and mathematical creative thi...
Accurate estimation of population distribution characteristics is a fundamental task in survey sampling and statistical inference. This paper introduces a new family of estimators for the cumulative distribution function (CDF) under probability propo...
Estimation of the population distribution function is an important problem in survey sampling with a variety of applications in social sciences, medical studies, environmental research and economics and in industrial quality control. When auxiliary i...
This study uses the optimal auxiliary function method to approximate solutions for fractional-order non-linear partial differential equations, utilizing Riemann–Liouville’s fractional integral and the Caputo derivative. This approach elim...
This paper addresses the unconstrained global minimization of continuously differentiable functions by introducing a novel global optimization framework based on the auxiliary function approach. First, a robust auxiliary function that remains unaffec...
This paper concentrates on the stability problem for linear systems with a differentiable time-varying delay via an auxiliary equation-based method. By supposing that the second-order derivative of the system state is available, an auxiliary equation...
The singularity of Jacobian happens when we are looking for a root, with multiplicity greater than one, of a system of nonlinear equations. The purpose of this article is two-fold. Firstly, we will present a modification of an existing method that co...
In this paper, a new analytical approach is proposed to investigate the electrical and mechanical behavior of a low-power permanent magnet synchronous generator (PMSG) in the presence of a wind gust. The proposed model for the wind gust and wind powe...
The present paper focuses on nonlinear oscillations of a horizontally supported Jeffcott rotor. An approximate solution to the system of governing equations having quadratic and cubic nonlinearities is obtained in two cases of practical interest: sim...
We study Geraghty-type non-self mappings within the framework of best proximity point theory. By introducing auxiliary functions with subsequential convergence, we establish general conditions ensuring the existence and uniqueness of best proximity p...
The main objective of the present work is to find an approximate analytical solution for the nonlinear differential equation of the vibro-impact oscillator under the influence of the electromagnetic actuation near the primary resonance. The trigger o...
Based on a new kind of analytical approach, namely the Optimal Auxiliary Functions Method (OAFM), a new analytical procedure is proposed to solve the problem of the annular axisymmetric stagnation flow and heat transfer on a moving cylinder with fini...
The objective of this paper is to obtain new relation-theoretic coincidence and common fixed point results for some mappings F and g via hybrid contractions and auxiliary functions in extended rectangular b-metric spaces, which improve the existing r...
In this work, the effect of vibro-impact nonlinear, forced, and damped oscillator on the dynamics of the electromagnetic actuation (EA) near primary resonance is studied. The vibro-impact regime is given by the presence of the Hertzian contact. The E...
This paper deals with the analytical investigation of a multirotor system connected by a flexible coupling subjected to dynamic angular misalignment. A novel analytical approach is employed for this purpose, namely the optimal auxiliary functions met...
In this study, we examine the wave equation with a nontrivial boundary condition. The main target of this study is to prove the local-in-time existence and the blow-up in finite time of the energy solution. Through the construction of an auxiliary fu...
Outliers are observations that are significantly different from the other observations in a dataset. These types of observations are asymmetric in nature due to a lack of symmetry. The estimation of the cumulative distribution function (CDF) is an im...
To gain insight into various phenomena of interest, cumulative distribution functions (CDFs) can be used to analyze survey data. The purpose of this study was to present an efficient ratiocum-exponential estimator for estimating a population CDF usin...
The Shimizu–Morioka dynamical system is analytically investigated in this paper by means of the Optimal Auxiliary Functions Method (OAFM). This system has a chaotic dynamical behavior, specified for more physical applications as chaos synchroni...
This article introduces two enhanced techniques: the Natural Transform Iterative Method (NTIM) and the Optimal Auxiliary Function Method (OAFM). These approaches provide a close approximation for solving fractional-order Navier–Stokes equations...
This paper constructs a universal algebraic realization model for Hermitian parameter matrices whose entries have modulus at most one and whose diagonal entries are normalized. The entries of the parameter matrix are used as weights of oriented cross...
The present work is devoted to the study of nonlinear vibrations of an electromagnetically actuated cantilever beam subject to harmonic external excitation. The soft actuator that controls the vibratory motion of such components of a robotic structur...
In this paper, a new approach is proposed to analyze the behavior of a nonlinear two-degree-of-freedom vibro-impact oscillator subject to a harmonic perturbing force, based on a combination of analytical and numerical approaches. The nonlinear govern...
The behavior of the Rucklidge-type dynamical system was investigated, providing some semi-analytical solutions, in this paper. This system was analytically investigated by means of the Optimal Auxiliary Functions Method (OAFM) for two cases. An exact...
The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connec...
The unstable nonlinear Schrödinger equations (UNLSEs) are universal equations of the class of nonlinear integrable systems, which reveal the temporal changing of disruption in slightly stable and unstable media. In current paper, an improved aux...
Symmetry widely exists in many complex and real-world networks, with flower networks and sunflower networks being two richly symmetric networks and having many practical applications due to their special structures. The number of subtrees (the subtre...
The density functional code deMon2k employs a fitted density throughout (Auxiliary Density Functional Theory), which offers a great speed advantage without sacrificing necessary accuracy. Powerful Quantum Mechanical/Molecular Mechanical (QM/MM) appro...
The aim of present paper is to obtain approximate semi-analytical solutions for the Qi-type dynamical system, while neglecting its chaotic behaviors. These solutions are derived using the Optimal Auxiliary Functions Method (OAFM). The impact of the s...
The KPI equation is one of most well-known nonlinear evolution equations, which was first used to described two-dimensional shallow water wavs. Recently, it has found important applications in fluid mechanics, plasma ion acoustic waves, nonlinear opt...
This paper presents the optimal auxiliary function method (OAFM) implementation to solve a nonlinear fractional system of the Jaulent–Miodek Equation with the Caputo operator. The OAFM is a vital method for solving different kinds of nonlinear...
The current literature of remote sensing (RS) scene classification shows that state-of-the-art results are achieved using feature extraction methods, where convolutional neural networks (CNNs) (mostly VGG16 with 138.36 M parameters) are used as featu...
The purpose of this work is to explore the nonlinear vibration of a rub-impact Jeffcott rotor. In the first stage, the motion is not affected by the friction force, but in the second stage, the motion is influenced by the normal force and the frictio...
The Korteweg–de Vries (KDV) equation is one of the most well-known models in nonlinear physics, such as fluid physics, plasma, and ocean engineering. It is very important to obtain the exact solutions of this model in the process of studying th...
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