543 Results Found

In this paper, we study the regularity of weak solutions to the incompressible Boussinesq equations in ${\mathbb{R}}^3\times (0,T)$ . The main goal is to establish the regularity criterion in terms of one velocity component and the gradient of te...

One of the most intriguing issues in the mathematical theory of the stationary Navier–Stokes equations is the regularity of weak solutions. This problem has been deeply investigated for homogeneous fluids. In this paper, the regularity of the solutio...

Consider the time-periodic viscous incompressible fluid flow past a body with non-zero velocity at infinity. This article gives sufficient conditions such that weak solutions to this problem are smooth. Since time-periodic solutions do not have finit...

Aimed at the issue of estimating the fault component from a noisy observation, a novel detection approach based on augmented Huber non-convex penalty regularization (AHNPR) is proposed. The core objectives of the proposed method are that (1) it estim...

It is a primary challenge in the fault diagnosis community of the gearbox to extract the weak fault features under heavy background noise and nonstationary conditions. For this purpose, a novel weak fault detection approach based on majorization&ndas...

In complicated scenarios, due to the low precision of float solutions and poor reliability of fixed solutions, it is challenging to achieve a balance between accuracy and reliability of the integer least squares (ILS) estimation. To address this dile...

The class of weak pseudoorders and left weak interior hyperideals in ordered hyperstructures is a generalization of pseudoorders and interior hyperideals. In this work, we study the concept of weak pseudoorders and left weak interior hyperideals in o...

In the Heisenberg group ${\mathbb{H}}^n$ and for exponents $2\le q\le 4$, the local Lipschitz ($C^{0,1}$) regularity is demonstrated for weak solutions to a non-homogeneous highly degenerate q-Laplace equation of the form $-{\sum }_{i=1}^{2n}{X}_i\left({\lambda }_i(Xu)X_{i}u\right)=g(x)$, where ${\&}_{}$...

This article notably targets the more general (extended) function spaces by investigating the regularity of the weak solutions or turbulent solutions to the Cauchy problem of the 3D magnetic Bénard system by converting it into mathematical sym...

In this paper, we study the regularity of the weak solution of the coupled system derived from the microwave heating model with frequency variable. We first show that the weak solution $\mathbf{E}$ of the system is Hölder continuous near the boundary...

In this paper, we investigate the regularity of weak solutions to the 3D incompressible MHD equations. We provide a regularity criterion for weak solutions involving any two groups functions $({\partial }_1{u}_1,{\partial }_1{b}_1)$, $({\partial }_2{u}_2,{\partial }_2{b}_2)$ and $({\partial }_3{u}_3,{\partial }_3{b}_3)$ in anisotropic Lor...

While surface movement regularities have been sufficiently understood in the mining practices of eastern China, the case seems to be very different in western China where the super-thick and weak cementation (STWC) overburden exists. To better unders...

This paper deals with a boundary control problem for the Darcy–Brinkman–Jeffreys system describing 3D (or 2D) steady-state flows of an incompressible viscoelastic fluid through a porous medium. Applying the elliptic regularization method...

In this paper, we consider local Dirichlet problems driven by the $\left(r\right(u),s(u\left)\right)$-Laplacian operator in the principal part. We prove the existence of nontrivial weak solutions in the case where the variable exponents $r,s$ are real continuous functions and...

We consider a non-standard nonlinear singularly perturbed 2D initial-boundary value problem with Venttsel type boundary conditions, arising in homogenization of radiative-conductive heat transfer problems. We establish existence, uniqueness and regul...

In this paper, we introduce and systematically investigate several classes of localized Baer-type rings associated with a fixed idempotent element e, namely e-Baer, e-quasi-Baer, e-p.q.-Baer, e-PP, and e-APP rings. We develop a unified structural fra...

We establish a compactness theorem for three-dimensional incompressible Navier–Stokes approximations with varying regularization mechanisms. Equation residuals are measured in a negative space compatible with the velocity, pressure, and convect...

This work develops a locally adaptive isogeometric phase-field framework for two-dimensional quasi-static brittle fracture using cubic $C^1$ polynomial splines over hierarchical T-meshes (PHT-splines). The aim is not to introduce a new crack-density fun...

In this paper, we establish a structural inequality of the ∞-subLaplacian ${▵}_{0,\infty }$ in a class of the semi-simple Lie group endowed with the horizontal vector fields $X_1,\dots ,X_{2n}$. When $1<p\le 4$ with $n=1$ and $1<p<3+\frac{1}{n-1}$ w...

Sentiment classification often relies on costly in-domain annotations, while weak-supervision sources provide low-cost but inconsistent labels. We propose Multi-Source Reliability-Aware Aggregation and Cross-domain Consistency Learning (MSRA-CCL) for...

This paper studies the continuation problem for the three-dimensional compressible Navier–Stokes–Fourier system inside an admissible thermo-acoustic regime under periodic boundary conditions. The analysis considers strong solutions in the...

We discuss a black hole generated by some matter fluid, whose stress-energy tensor is known. We show that it is regular and that it satisfies the Weak Energy Condition (WEC) and the null energy condition (NEC). Finally, we look for its asymptotic beh...

In this paper, we examine the weak deflection angle and greybody bound for a magnetized regular black hole. For this purpose, we apply the Gauss–Bonnet theorem on the black hole and obtain the deflection angle in plasma and non-plasma mediums....

An asymptotic solution of the linear Cauchy problem in the presence of a “weak” turning point for the limit operator is constructed by the method of S. A. Lomov regularization. The main singularities of this problem are written out explic...

This study considers equilibrium problems, focusing on identifying finite solutions for feasible solution sequences. We introduce an innovative extension of the weak sharp minimum concept from convex programming to equilibrium problems, coining this...

Marathons are one of the ultimate challenges of human endeavor. As a consequence of the growing passion of amateur runners for this discipline, a strong need has been shown for counselling during the preparation and for advice on how to manage their...

In this article, I consider local solutions of the 3D Navier–Stokes equations and its properties such as an existence of global and smooth solution, uniform boundedness. The basic role is assigned to a special invariant class of solenoidal vect...

In order to be able to use methods of universal algebra for investigating posets, we assigned to every pseudocomplemented poset, to every relatively pseudocomplemented poset and to every sectionally pseudocomplemented poset, a certain algebra (based...

Extracting roads accurately from remote sensing images is important for map updates, traffic analysis, and infrastructure monitoring. Medium-resolution multispectral images can provide useful surface and background information, but when used alone, t...

In this paper, one-wheel and two-wheel concatenations of circular words and their languages are investigated. One-wheel concatenation is an operation that is commutative but not associative, while two-wheel concatenation is associative but not commut...

The field of probabilistic metric spaces has an intrinsic interest based on a blend of ideas drawn from metric space theory and probability theory. The goal of the present paper is to introduce and study new ideas in this field. In general terms, we...

The regularity of the n-P-V-rings and n-P-V’-rings is systematically investigated in this paper. Employing the notions of quasi-ideals, weakly left (or right) ideals, and generalized weak ideals, we focus on investigating the strong $\pi$-regula...

This paper discusses the regularity of the GP-V’-rings in conjunction with idempotent reflexivity for the first time. We mainly discuss the weak and strong regularity of the GP-V’-rings using generalized weak ideals, weakly right ideals,...

We prove the existence of weak solutions of a two-incompressible immiscible wetting and non-wetting fluids phase flow model in porous media with dynamic capillary pressure. This model is a coupled system which includes a nonlinear parabolic saturatio...

In this paper, we introduce a new class of structures called bipolar soft weak structures, which extend several notions studied in earlier works. We investigate many of the generalized properties of these structures by considering a fundamental conce...

This article investigates the inverse problem of estimating the weight function using boundary observations in a distributed-order time-fractional diffusion equation. We propose a method based on $L^2$ regularization to convert the inverse problem into...

The symmetry of hyperoperation is expressed by hypergroup, more extensive hyperalgebraic structures than hypergroups are studied in this paper. The new concepts of neutrosophic extended triplet semihypergroup (NET- semihypergroup) and neutrosophic ex...

We consider an operator ${\{S\left(t\right)\}}_{t\ge 0}$ on a Banach space X with generator A, characterized by being an $\alpha$-times-integrated C-regularized semigroup. The adjoint family $S^{*}\left(t\right):X^{*}\to X^{*}$ is introduced for analysis. ${\{S^{*}\left(t\right)\}}_{t\ge 0}$ maintains the charact...

The fluctuation and uncertainty of the electricity load bring challenges to load forecasting. Traditional point forecasting struggles to avoid errors, and pure interval forecasting may cause the problem of too wide an interval. In this paper, we comb...

We study an elliptic quasilinear fractional problem with fractional Neumann boundary conditions, proving an existence and multiplicity result without assuming the classical Ambrosetti–Rabinowitz condition. Improving previous results, we also pr...

Let $(A,\Delta )$ be a weak multiplier Hopf algebra. It is a pair of a non-degenerate algebra A, with or without identity, and a coproduct $\Delta :A⟶M(A\otimes A)$, satisfying certain properties. In this paper, we continue the study of these objects and...

Studies have examined the characteristics of individuals who use e-cigarettes, including sociodemographic and smoking characteristics, and the relationship of e-cigarette use to tobacco control policies. While most studies consider a subset of these...

In this article, we generalize the concept of group-graded modules by introducing the concept of $\mathfrak{G}$-weak graded R-modules, which are R-modules graded by a set $\mathfrak{G}$ of left coset representatives, where R is a $\mathfrak{G}$-weak graded ring. Moreover, we prove some pr...

As an extension of quasi-continuity in general topology, we define soft quasi-continuity. We show that this notion is equivalent to the known notion of soft semi-continuity. Next, we define soft weak quasi-continuity. With the help of examples, we pr...

Environmental resource management requires negotiation among state and non-state actors with conflicting goals and different levels of influence. In northwestern Argentina, forest policy implementation is described as weak, due to governance structur...

Fractional wave equations with time-dependent coefficients are natural generations of classical wave equations which can be used to characterize propagation of wave in inhomogeneous media with frequency-dependent power-law behavior. This paper discus...

The aim of this study is to determine a 3D incompressible Brinkman–Forchheimer-extended Darcy fluid flow. Based on global well-posedness and regularity of solutions with a periodic boundary condition, the determining modes for weak and regular...

In the Heisenberg group ${\mathbb{H}}^n$, we establish the local regularity theory for weak solutions to non-homogeneous degenerate nonlinear parabolic equations of the form ${\partial }_{t}u-{\displaystyle \sum _{i=1}^{2n}}{X}_i{A}_i\left(Xu\right)=K(x,t,u,Xu)$, where the nonlinear structure is modeled on...

In the Heisenberg group ${\mathbb{H}}^n$, we obtain the local second-order $H{W}_{\mathrm{loc}}^{2,2}$-regularity for the weak solution u to a class of degenerate parabolic quasi-linear equations ${\partial }_{t}u={\displaystyle \sum _{i=1}^{2n}}{X}_i{A}_i(Xu)$ modeled on the parabolic p-Laplacian equation. Specifically...

This paper concerns the viscous Boussinesq equations without a dissipation term and their relation to the temperature equation related to the exterior of a ball with a smooth boundary. We first prove the global existence of weak solutions on the boun...