2,507 Results Found

The finite element method (FEM) with a special graded mesh is constructed for the Dirichlet boundary value problem with degeneration of the solution on the entire boundary of the two-dimensional domain. A comparative numerical analysis is performed f...

The positive solutions to the critical Lane–Emden equation in ${\mathbb{R}}^n$ have been classified completely by the moving plane method. Afterwards, with additional conditions such as limited energy or volume, there is proof that relies entirely on integra...

In this paper, we discuss the existence of positive radially symmetric entire solutions of the p-k-Hessian equation ${\sigma }_k^{\frac{1}{k}}\left(\lambda \left(D_i\left({\left|Du\right|}^{p-2}{D}_{j}u\right)\right)\right)={\alpha }^{\frac{1}{k}}\left(\right|x\left|\right)f\left(u\right),$ and the general p-k-Hessian system ${\sigma }_k^{\frac{1}{k}}\left(\lambda \left(D_i\left({\left|Du\right|}^{p-2}{D}_{j}u\right)\right)\right)={\mathrm{\&alph}}^{}$...

This article is to investigate the existence of entire solutions of several quadratic trinomial difference equations $f{(z+c)}^2+2\alpha f\left(z\right)f(z+c)+f{\left(z\right)}^2=e^{g\left(z\right)},$ and the partial differential difference equations $f{(z+c)}^2+2\alpha f(z+c)\frac{\partial f\left(z\right)}{\partial z_1}+{\left(\frac{\partial f\left(z\right)}{\partial z_1}\right)}^2=e^{g\left(z\right)},$$f{(z+c)}^2+$...

In this article, we consider a semilinear elliptic system involving gradient terms of the form $\left\{\begin{array}{ccc}\Delta y\left(x\right)+{\lambda }_1\left|\nabla y\left(x\right)\right|=p\left(\left|x\right|\right)f\left(y\left(x\right),z\left(x\right)\right)\hfill & if\hfill & x\in \Omega ,\hfill \\ \Delta z\left(x\right)+{\lambda }_2\left|\nabla z\left(x\right)\right|=q\left(\left|x\right|\right)g\left(y\left(x\right)\right)\hfill & if\hfill & x\in \Omega ,\hfill \end{array}\right.$ where ${\lambda }_1$, ${\lambda }_2\in \left[0,\infty \right)$, $\&Omega$...

This article is concerned with the description of the entire solutions of several Fermat type partial differential-difference equations (PDDEs) ${\left[\mu f\left(z\right)+\lambda f_{z_1}\left(z\right)\right]}^2+{[\alpha f(z+c)-\beta f\left(z\right)]}^2=1,$ and ${\left[\mu f\left(z\right)+{\lambda }_1{f}_{z_1}\left(z\right)+{\lambda }_2{f}_{z_2}\left(z\right)\right]}^{}$...

We mainly study the transcendental entire solutions of the differential equation $f^n(z)+P(f)=p_1{e}^{{\alpha }_{1}z}+p_2{e}^{{\alpha }_{2}z}$ , where $p_1$ , $p_2$ , ${\alpha }_1$ and ${\alpha }_2$ are...

This paper concerns the existence and precise expression form of entire solutions to a certain type of delay-differential equation. The significance of our results lie in that we generalize and supplement the related results obtained recently.

We revisit the problem of studying the solutions growth order in complex higher order linear differential equations with entire and meromorphic coefficients of $\left[p,q\right]$-order, proving how it is related to the growth of the coefficient of the unknown funct...

Many researchers’ attentions have been attracted to various growth properties of meromorphic solution f (of finite $\phi$-order) of the following higher order linear difference equation $A_n\left(z\right)f\left(z+n\right)+...+A_1\left(z\right)f\left(z+1\right)+A_0\left(z\right)f\left(z\right)=0$, where $A_n\left(z\right),\dots ,A_0\left(z\right)$ are entire or meromorphi...

Langevin dynamics simulations are performed to study polyelectrolytes driven through a nanopore in monovalent and divalent salt solutions. The driving electric field E is applied inside the pore, and the strength is varied to cover the four character...

Decision-making plays a pivotal role in data-driven optimization, aiming to achieve optimal results by identifying the most effective combination of input variables. Traditionally, in multi-objective data-driven optimization problems, decision-making...

Plastic anisotropy significantly affects the behavior of structures and machine parts. Given the many parameters that classify a structure made of anisotropic material, analytic and semi-analytic solutions are very useful for parametric analysis and...

The influence of biopolymer–biopolymer chain interactions on selected rheological properties of aqueous solutions from konjac (KG), xanthan gum (XG), and carboxymethyl cellulose (CMC) was investigated using viscosity measurements in extensional...

Ensuring security for modern IoT systems requires the use of complex methods to analyze their software. One of the most in-demand methods that has repeatedly been proven to be effective is static analysis. However, the progressive complication of the...

It is commonly accepted that ‘the brain computes’ and that it serves as a model for establishing principles of technical (first of all, electronic) computing. Even today, some biological implementation details inspire the implementation o...

The issue of the invariance of the unboundedness property of the solutions of the Carleman–Bers–Vekua system (generalized analytic functions) with respect to the transformation of the restriction is studied. The concept of the rating of a...

The use of automorphisms of the various Bianchi-type Lie algebras as Lie-point symmetries of the corresponding Einstein field equations entails a reduction of their order and ultimately leads to the entire solution space. When a valid reduced action...

A biharmonic boundary value problem with a singularity is one of the mathematical models of processes in fracture mechanics. It is necessary to have estimates of the function norms in the neighborhood of the singularity point to study the existence a...

In the half-plane, a solution to a two-dimensional hyperbolic equation with a translation operator in the lowest derivative with respect to a spatial variable varying along the entire real axis is constructed in an explicit form. It is proven that th...

Through transformation and utilizing a novel extended complex method combining with the Weierstrass factorization theorem, Wiman–Valiron theory and the Painlevé test, new non-constant meromorphic solutions were constructed for the predat...

In this paper, the generalized Jacobi elliptic functions expansion method with computerized symbolic computation are employed to investigate explicitly analytic solutions of the (N + 1)-dimensional generalized Boussinesq equation. The exact solutions...

Since a solution towards carbon neutrality in already highly populated territories that does not profoundly alter the territories has not yet been found, territorial acupuncture, a new methodology presented in this paper, proposes a solution to this...

This paper describes a solution for the image density classification problem (DCP) using an entirely distributed system with only local processing of information named cellular automata (CA). The proposed solution uses two cellular automata’s f...

In this research, we focus on the symmetry of an ancient solution for a fractional parabolic equation involving logarithmic Laplacian in an entire space. In the process of studying the property of a fractional parabolic equation, we obtained some max...

In this paper, using the notion of ($I_q$)–stability and the method of a priori estimates, known as the method of lower and upper solutions, the sufficient conditions guaranteeing uniform convergence of solutions to the solution of a reduced probl...

The homotopy analysis method (HAM) is a useful method to derive analytical approximate solutions of black holes in modified gravity theories. In this paper, we study the Einstein–Weyl gravity coupled with Maxwell field and obtain analytical app...

We propose a memetic algorithm for the multiple-choice multidimensional knapsack problem (MMKP). In this study, we focus on finding good solutions for the MMKP instances, for which feasible solutions rarely exist. To find good feasible solutions, we...

A novel and innovative solution addressing wind turbines’ main bearing failure predictions using SCADA data is presented. This methodology enables to cut setup times and has more flexible requirements when compared to the current predictive algorithm...

The increasing popularity of water sports—surfing, in particular—has been raising attention to its yet immature technology market. While several available solutions aim to characterise surf session events, this can still be considered an open issue,...

Land degradation through erosion processes is probably the most restrictive issue regarding the sustainable agricultural use of land resources in contemporary Romania. The socio-economic changes that occurred in Romanian society after 1990 resulted i...

This paper solves a generalized class of first-order fractional ordinary differential equations (1st-order FODEs) by means of Riemann–Liouville fractional derivative (RLFD). The principal incentive of this paper is to generalize some existing r...

In this paper, a general algebraic method based on the generalized Jacobi elliptic functions expansion method, the improved general mapping deformation method and the extended auxiliary function method with computerized symbolic computation i...

Painful castration of male piglets to avoid boar taint can potentially be replaced by three more ethical alternatives: entire male production in combination with a detection method, immunocastration (an active vaccination against the gonadotrophin-re...

In this paper, we consider the stochastic fractional-space Chiral nonlinear Schrödinger equation (S-FS-CNSE) derived via multiplicative noise. We obtain the exact solutions of the S-FS-CNSE by using the Riccati equation method. The obtained solu...

The inclusion of microgrids (MGs) in power systems, especially distribution-substation-level MGs, significantly affects power systems because of the large volumes of import and export power flows. Consequently, power dispatch has become complicated,...

In this manuscript, the Nikol’skii-Lizorkin problem with degeneracy on the entire boundary of the domain is considered. The degeneracy is caused by the behavior of the coefficients and right-hand sides of the problem on the boundary. The triang...

Rapid development and conducted experiments in the field of the introduction the fifth generation of the mobile network standard allow for the flourishing of the Internet of Things. This is one of the most important reasons to design and test systems...

The article describes solutions in the field of diagnostics of a control system based on a CNC and the cooperation with an industrial robot. The industrial robot is controlled directly from the CNC. Data exchange between the CNC and the robot control...

Chaotic evolution is generally too irregular to be captured in an analytic solution. Nonetheless, some dynamical systems do have such solutions enabling more rigorous analysis than can be achieved with numerical solutions. Here, we introduce a method...

By Lomov’s S.A. regularization method, we constructed an asymptotic solution of the singularly perturbed Cauchy problem in a two-dimensional case in the case of violation of stability conditions of the limit-operator spectrum. In particular, th...

Given an unbounded non-decreasing positive function $\phi$, we studied what the relations are between the growth order of any solution of a complex linear differential–difference equation whose coefficients are entire or meromorphic functions of...

All sectors have been affected by digital, economic, and demographic transitions. These will also be completely changing the paradigms of the construction industry, which is increasingly being pressured to implement strategic solutions in order to mi...

A health monitoring system typically collects and processes data to observe the health status of a bridge. The cost limitations imply that only the measurement point data of a few key points can be obtained; however, the entire bridge monitoring info...

Computation of the solution of the nonlinear Caputo fractional differential equation is essential for using $q,$ which is the order of the derivative, as a parameter. The value of q can be determined to enhance the mathematical model in question using...

In recent decades, artificial intelligence (AI) tools have been applied in many medical fields, opening the possibility of finding novel solutions for managing very complex and multifactorial problems, such as those commonly encountered in radiothera...

We reported the novel use of a taurolidine-containing antimicrobial solution in the successful salvage of a partially exposed and polymicrobially infected cardiac implantable electronic device pulse generator in a frail patient unfit for lead extract...

One of the currently promoted methods of counteracting climate change is nature-based climate solutions, which harness the power of nature to reduce greenhouse gas emissions. Sustainable management of ecosystems is a guarantee for sustained human wel...

The safety of existing tunnels during the entire under-crossing process of a new shield tunnel is critically important for ensuring the sustainable operation of urban transportation infrastructure. The nonlinear behavior of surrounding soils plays a...

Multi-Dimensional Optimal Power Flow (MDOPF) is a fundamental task in power systems engineering aimed at optimizing the operation of electrical networks while considering various constraints such as power generation, transmission, and distribution. T...