A non-local solution is obtained here in the theory of cracks, which depends on the scale parameter in the non-local theory of elasticity. The gradient solution is constructed as a regular solution of the inhomogeneous Helmholtz equation, where the f...
The phenomenon of degeneracy of energy levels is often attributed either to an underlying (super)symmetry (SUSY), or to the presence of a Kato exceptional point (EP). In our paper a conceptual bridge between the two notions is proposed to be provided...
The effects of vacuum polarization associated with a massless scalar field near pointlike source with a zero-range potential in three spatial dimensions are analyzed. The “physical” approach consists in the usage of direct delta-potential as a model...
In this paper, we prove existence and regularity results for a nonlinear elliptic problem of p-Laplacian type with a singular potential like
The inversion of potential field data has widely utilized the generalized cross-validation (GCV) and the unbiased predictive risk estimator (UPRE) methods to determine the regularization parameter. However, these two methods are time-consuming and it...
The classical Neumann–Kelvin (NK) theory of potential flow around a free-surface-piercing ship that steadily advances in calm water or through regular waves is considered. Specifically, this study presents an elementary ‘no-equation inter...
An approach is presented to address singularities in general relativity using a complex Riemannian spacetime extension. We demonstrate how this method can be applied to both black hole and cosmological singularities, specifically focusing on the Schw...
Error in the method of regularized Stokeslets is highly dependent on the choice of the blob or regularization function that is utilized to handle singularities in the flow. In this work, we develop a general framework to choose regularizations at the...
This paper presents unified counterexamples for which standard elliptic regularity results break down for linear elliptic equations with highly singular coefficients in dimensions
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...
This paper is concerned with the reconstruction of relaxation time distributions in Nuclear Magnetic Resonance (NMR) relaxometry. This is a large-scale and ill-posed inverse problem with many potential applications in biology, medicine, chemistry, an...
We outline the basic ideas and analyze the possibilities of the quantum birth of universes inside regular black holes with the de Sitter interior replacing a singularity. We compare different cases and show that the most plausible case is the birth o...
This paper is focused on developing a Galerkin finite element framework for the fractional Allen–Cahn equation with regularized logarithmic potential over the
Cutting out an infinite tube around
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...
Classical black holes contain a singularity at their core. This has prompted various researchers to propose a multitude of modified spacetimes that mimic the physically observable characteristics of classical black holes as best as possible, but that...
The aim to improve diagnosis decision systems of kidneys led to the concept of many methods of texture characterization of kidneys from ultrasound images. Here, as a first main contribution, we propose a texture characterization method based on the s...
In this paper, we propose an approach to inverse spectral problems for the n-th order
The online sequential extreme learning machine with persistent regularization and forgetting factor (OSELM-PRFF) can avoid potential singularities or ill-posed problems of online sequential regularized extreme learning machines with forgetting factor...
We briefly overview the basic properties and generic behavior of circular equatorial particle orbits and light rings around regular rotating compact objects with dark energy interiors, which are described by regular metrics of the Kerr–Schild c...
In this paper, we study the theory of second gradient electromagnetostatics as the static version of second gradient electrodynamics. The theory of second gradient electrodynamics is a linear generalization of higher order of classical Maxwell electr...
We focus on a quasi-one-dimensional Poisson–Nernst–Planck model with small permanent charges for ionic flows of two oppositely charged ion species through an ion channel. Of particular interest is to examine the dynamics of ionic flows in...
The Casimir effect for a scalar field in presence of delta-type potentials has been investigated for a long time in the case of surface delta functions, modelling semi-transparent boundaries. More recently Albeverio, Cacciapuoti, Cognola, Spreafico a...
We apply a very simple procedure to construct non-singular cosmological models for flat Friedmann universes filled with minimally coupled scalar fields or by tachyon Born–Infeld-type fields. Remarkably, for the minimally coupled scalar field an...
A generalization of the efficient interpolation of periodic Green’s functions is presented for a multilayer medium hosting transverse electric current densities and transverse equivalent magnetic current densities at different interfaces. The m...
We introduce the concept of the magnetic metapole—a theoretical extension of classical multipole theory involving a fractional j pole count (related to the harmonic degree n as j = 2n). Defined by a scalar potential with colatitudinal dependenc...
We consider the two- and n-body problems on the two-dimensional conformal sphere
Nowadays, actuator line method (ALM) has become the most potential method in wind turbine simulations, especially in wind farm simulations and fluid-structure interaction simulations. The regularization kernel, which was originally introduced to ALM...
In one of our previous papers, we obtained a general class of potentials inside the nucleus, such that the singular solution of the Dirac equation for the S-states of hydrogen atoms outside the nucleus can be matched with the corresponding regular so...
The studied configuration is a two-dimensional, very thin parabolic reflector made of graphene and illuminated by an H-polarized electromagnetic plane wave. We present basic scattering and focusing properties of such a graphene reflector depending on...
A conceptually consistent understanding is sought for the interactions sampled by the imaginary cubic oscillator with potential
This paper presents a computational study of wave–bathymetry and wave–structure interaction problems using advanced numerical techniques based on high-fidelity, two-phase Navier–Stokes (TpNS) flow and reduced-order, fully nonlinear...
The purpose of the work presented in this paper is to study the reflection and transmission coefficients resulting from the interactions of regular waves with a rectangular breakwater sited at the bottom of a tank. The present investigation is devote...
Assuming the permanent charge density is much larger than the ion concentrations on two boundaries of an open ion channel, this paper studies the impacts of large permanent charges which are positioned along the channel wall and play a significant ro...
Heterogeneous unmanned aerial vehicle–unmanned surface vehicle (UAV–USV) formations must reject disturbances while maintaining prescribed tracking performance and responding to collision risks. This study develops a mathematically consist...
This work presents a semi-classical, quantum-corrected model of gravitational collapse for a charged, spherically symmetric dust cloud, extending the classical Oppenheimer–Snyder (OS) framework through loop quantum gravity effects. Our goal is...
This study investigates the use of three different quadrature schemes, as well as an iterative quadrature methodology, to analyze vibrations in magneto-electro-thermo-elastic nanobeams. Individual MATLAB programs for each method are developed with th...
We investigate static, spherically symmetric (SS) spacetimes in covariant teleparallel
This work participates in the research for potential areas of observational evidence of quantum effects on geometry in a black hole astrophysical context. We consider properties of a family of loop quantum corrected regular black hole (BHs) solutions...
In this study, the Log-Periodic Power Law Singularity (LPPLS) model is adopted for real-time identification and monitoring of Bitcoin bubbles and crashes using different time scale data, and the modified Lagrange regularization method is proposed to...
As a multichannel signal processing method based on data-driven, multivariate empirical mode decomposition (MEMD) has attracted much attention due to its potential ability in self-adaption and multi-scale decomposition for multivariate data. Commonly...
Measurements of dust emissions and the modeling of dissipation dynamics and total values are related to great uncertainties. Agricultural activity, especially soil cultivation, may be an essential component to calculate and model local and regional d...
Breast cancer remains a major public health concern, and early detection is crucial for improving survival rates. Metabolomics offers the potential to develop non-invasive screening and diagnostic tools based on metabolic biomarkers. However, the inh...
Multi-environment trials (METs) are essential in plant breeding programs to evaluate crop productivity and adaptability in diverse environments. In this study, we demonstrated the practical use of METs to evaluate grain yield and yield-related traits...
We present a comprehensive quantum field theoretical analysis of graviton self-energy and mass generation in 3+1 dimensional BTZ black hole spacetime, incorporating axion interactions within the framework of dark matter theory. Using a novel mathemat...
Ion channels are protein pores that regulate ionic flow across cell membranes, enabling vital processes such as nerve signaling. They often conduct multiple ionic species simultaneously, leading to complex nonlinear transport phenomena. Because exper...
Wave overtopping occurring in offshore wind renewable energy structures such as tension leg platforms (TLPs) or semi-submersible platforms is a phenomenon that is worth studying and preventing in order to extend the remaining useful life of the corre...
Super-pixels represent perceptually similar visual feature vectors of the image. Super-pixels are the meaningful group of pixels of the image, bunched together based on the color and proximity of singular pixel. Computation of super-pixels is highly...