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...
We study the solvability of nonlinear inverse problems of determining the low order coefficients in the second order hyperbolic equation. The overdetermination condition is specified as an integral condition with final data. Existence and uniqueness...
In this paper, the 1st-level general fractional derivatives of arbitrary order are defined and investigated for the first time. We start with a generalization of the Sonin condition for the kernels of the general fractional integrals and derivatives...
The paper investigates the regularization of solutions to nonlinear Volterra integral equations of the first kind, under the assumption that a solution exists and belongs to the space of continuous functions. The kernel of the equation is a different...
In this study, we investigate coupled real and complex dispersionless equations for curve families, even if they have singular points. Even though the connections with the differential equations and regular curves were considered in various ways in t...
Designed to mitigate the significant low-frequency vibration and noise inherent in conventional marine centrifugal pump systems, the magnetic levitation pump constitutes a novel form of centrifugal pump employing active magnetic bearing technology. W...
The dynamical interaction between binary systems is crucial in understanding the nature of orbital motion under the influence of gravitational potential. In our study, we focused on investigating the effects of dynamical forces on the regularity of b...
This article analyzes a regularized set of fuzzy differential equations with respect to an uncertain parameter. We provide sufficient conditions for the correctness of a new regularization scheme. For the resulting family of regularized fuzzy differe...
We consider the construction of a regular map from the unit square to a general four-sided domain, a problem that arises in several applications, e.g., in the numerical solution of integral equations or when dealing with trimmed surfaces in CAD. In o...
In this paper, we give an effective numerical method for the heat conduction problem connected with the Laplace equation. Through the use of a single-layer potential approach to the solution, we get the boundary integral equation about the density fu...
Recovering the relaxation spectrum, a fundamental rheological characteristic of polymers, from experiment data requires special identification methods since it is a difficult ill-posed inverse problem. Recently, a new approach relating the identifica...
This article delves into the spectral problem associated with a multiple differentiation operator that features an integral perturbation of boundary conditions of one specific type, namely, regular but not strengthened regular. The integral perturbat...
Particle size distribution is one of the important microphysical parameters to characterize the aerosol properties. The aerosol optical depth is used as the function of wavelength to study the particle size distribution of whole atmospheric column. H...
We consider a numerical approximation for stochastic fractional differential equations driven by integrated multiplicative noise. The fractional derivative is in the Caputo sense with the fractional order α∈(0,1), and the non-linear t...
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...
We consider general linear multi-term Caputo fractional integro-differential equations with weakly singular kernels subject to local or non-local boundary conditions. Using an integral equation reformulation of the proposed problem, we first study th...
This study investigates how economic growth, financial integration, social integration, and knowledge management shape CO2 emissions in Saudi Arabia using quarterly data from 1995Q1 to 2024Q4. It applies kernel-regularized quantile regression to capt...
This paper solves the inverse source problem of heat conduction in which the source term only varies with time. The application of the discrete regularization method, a kind of effective radial symmetry and axisymmetric heat conduction problem source...
The number of hologram points in near-field acoustical holography (NAH) for a vibro-acoustic system plays a vital role in conditioning the transfer function between the source and measuring points. The requirement for many overdetermined hologram poi...
In this study, we consider regular eigenvalue problems formulated by using the left and right standard fractional derivatives and extend the notion of a fractional Sturm–Liouville problem to the regular Prabhakar eigenvalue problem, which inclu...
We address the question of the electromagneticdensity and the mass function for regular rotating electrically charged compact objects as determined by dynamical equations of nonlinear electrodynamics minimally coupled to gravity. The rotating electri...
We studied, for the Kortweg–de Vries–Burgers equations on cylindrical and spherical waves, the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary. The regular profile at the vicinity of perturb...
In addressing the multifaceted problem of multiple-input multiple-output (MIMO) detection in wireless communication systems, this work highlights the pressing need for enhanced detection reliability under variable channel conditions and MIMO antenna...
The article considers third-order equations with multiple characteristics with general boundary value conditions and non-local initial data. A regular solution to the problem with known methods is constructed here. The uniqueness of the solution to t...
In this paper, we investigate the generalized Radhakrishnan–Kundu–Lakshmanan equation with polynomial law using the method of dynamical systems. By using traveling-wave transformation, the model can be converted into a singular integrable...
We present an integration condition ensuring that a stochastic differential equation dXt=μ(t,Xt)dt+σ(t,Xt)dBt, where μ and σ are sufficiently regular, has a solution of the form Xt=Z(t,Bt). By generalizing the integration condition...
In this study, a third-order linear integro-differential equation with a small parameter at two higher derivatives was considered. An asymptotic expansion of the solution to the boundary value problem for the considered equation is constructed by con...
We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation. We combine the Laguerre transform with the integral equation method and...
Damage identification plays a crucial role in the post-earthquake assessment and safety control of civil structures, which is usually an ill-posed inverse problem due to the presence of uncertainties and lack of measurement information. Regularizatio...
This paper presents the first application of the Laser Doppler Vibrometer (LDV) in non-stationary conditions within a hydropower plant powerhouse. The aim of this research is to develop a methodology to include non-contact vibration monitoring as par...
In order to develop the building blocks for future biosensing and spintronic applications, an engraving technique using electron beam lithography is employed in order to develop nanomagnetic pre-patterned structures with logic potential. The paper de...
This paper is devoted to exploring the mapping properties for the commutator μΩ,b generated by Marcinkiewicz integral μΩ with a locally integrable function b in the generalized Campanato spaces on the generalized Morrey spaces. Unde...
This paper provides a method to bound and calculate any eigenvalues and eigenfunctions of n-th order boundary value problems with sign-regular kernels subject to two-point boundary conditions. The method is based on the selection of a particular type...
A heterogeneous traffic flow consists of regular vehicles, and intelligent connected vehicles having interactive functions is updating the composition of the current urban-road network traffic flow. It has been a growing trend and will continue to be...
This paper reports a novel sensor effect in solid non-regular materials with the following formula: a previously unknown phenomenon in solid disordered structures, such as rocks and building concrete, has been experimentally established, which is exp...
Few-shot fault diagnosis (FSFD) seeks to build accurate models from scarce labeled data, a frequent challenge in industrial settings with noisy measurements and varying operating conditions. Conventional metric-based meta-learning (MBML) often assume...
This paper studies the buckling of standing columns under self-weight and tip load. An emphasis is placed on linearly tapered columns with regular polygons cross-section whose volume is constant. Five end conditions for columns are considered. The di...
We study the regularity properties of the unique solution of a generalized mean-field G-SDE. More precisely, we consider a generalized mean-field G-SDE with a square-integrable random initial condition, establish its first- and second-order Fré...
In this paper, an effective numerical method for the Dirichlet problem connected with the Helmholtz equation is proposed. We choose a single-layer potential approach to obtain the boundary integral equation with the density function, and then we deal...
The questions of the one-value solvability of an inverse boundary value problem for a mixed type integro-differential equation with Caputo operators of different fractional orders and spectral parameters are considered. The mixed type integro-differe...
The Melnikov method is applied to a class of generalized Ziegler pendulums. We find an analytical form for the separatrix of the system in terms of Jacobian elliptic integrals, holding for a large class of initial conditions and parameters. By workin...
The mesh size significantly affects the accuracy and computational efficiency of finite-element analysis (FEA) simulations. This study investigates mesh regularization to mitigate mesh dependency, align numerical results with experimental data, and o...
This paper proposes a solution to the sideways heat conduction problem (SHCP) based on the time and space integration direction. Conventional inverse problems depend highly on the available data, particularly when the observed data are contaminated w...
The study of the electromagnetic diffraction from penetrable screens with apertures and/or inhomogeneities is of great relevance today due to the huge number of modern applications in which they are involved. In this paper, the analysis of the plane...
This paper examines the tractability of multivariate approximation problems under the normalized error criterion for a zero-mean Gaussian measure in an average-case setting. The Gaussian measure is associated with a covariance kernel, which is repres...
We investigate the semi-linear, non-autonomous, first-order abstract differential equation x′(t)=A(t)x(t)+f(t,x(t),φ[α(t,x(t))]),t∈R. We obtain results on existence and uniqueness of (ω,c)-periodic (second-kind periodic) mild solutions, assuming that...
We study a bilinear optimal control problem for an evolution equation with a nonlinear term that depends on both the state and its time integral. First, we establish existence and uniqueness results for this evolution equation. Then, we derive weak m...
In the three-dimensional open rectangular domain, the problem of the identification of the redefinition function for a partial differential equation with Gerasimov–Caputo-type fractional operator, degeneration, and integral form condition is consider...
The main objective of this paper is to propose a new boundary element method (BEM) modeling for stress sensitivity of nonlocal thermo-elasto-plastic damage problems. The numerical solution of the heat conduction equation subjected to a non-local cond...
We introduce a method based on Lipschitz pointwise transformations to define a distance on a Banach function space from its norm. We show how some specific lattice geometric properties (p-convexity, p-concavity, p-regularity) or, equivalently, some t...
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