The eigenfunction approach used for discrete symmetries is deduced from the concept of quantum numbers. We show that the irreducible representations (irreps) associated with the eigenfunctions are indeed a shorthand notation for the set of eigenvalue...
A family of Schwartz functions
Soft foundation consolidation engineering applications and experimental studies have proven the effectiveness of the air–boosted vacuum preloading method (AVP). The sand well consolidation theory, a typical axisymmetric consolidation, is adapte...
The convergence of two numerical methods for solving linear water wave scattering problems, namely the eigenfunction matching method (EMM) and the singularity-respecting Galerkin approximation (SRGA), is examined. To do so, the methods are applied to...
We study the eigenfunctions and eigenvalues of the boundary value problem for the nonlocal Laplace equation with multiple involution. An explicit form of the eigenfunctions and eigenvalues for the unit ball are obtained. A theorem on the completeness...
To address the limitations of traditional analytical models in characterising multi-core coupling effects and the excessive computational cost of finite element simulations, this paper presents a high-precision analytical model for a novel T-II compo...
Microwave imaging of objects embedded in multilayer cylindrical structures is of practical importance in applications where inaccessible targets are surrounded by a known inhomogeneous host. In such problems, incorporating the known multilayer struct...
In this paper, we study the eigenfunctions to one nonlocal second-order differential operator with double involution. We give an explicit form of the eigenfunctions to the boundary value problem in the unit ball with Dirichlet conditions on the bound...
Fourier expansions employing polyharmonic–Neumann eigenfunctions have demonstrated improved convergence over those using the classical trigonometric system, due to the rapid decay of their Fourier coefficients. Building on this insight, we inve...
Designing imaging methods is one of the important issues in inverse scattering problems. In recent years, some studies have shown that the transmission eigenfunctions contain important qualitative and quantitative information about the unknown scatte...
The history of boundary value problems for differential equations starts with the well-known studies of D. Bernoulli, J. D’Alambert, C. Sturm, J. Liouville, L. Euler, G. Birkhoff and V. Steklov. The greatest success in spectral theory of ordina...
Modal expansions based on k-eigenvalues and α-eigenvalues are commonly used in order to investigate the reactor behaviour, each with a distinct point of view: the former is related to fission generations, whereas the latter is related to time. Well-k...
We give a definition of Green’s function of the general boundary value problems for non-self-adjoint second order differential equation with involution. The sufficient conditions for the basis property of system of eigenfunctions are established in t...
This work serves as a bridge between two approaches to analysis of dynamical systems: the local, geometric analysis, and the global operator theoretic Koopman analysis. We explicitly construct vector fields where the instantaneous Lyapunov exponent f...
On a compact n-dimensional Riemannian manifold without boundary
The Steklov–Zaremba problem for the Laplace operator in a bounded domain with a strictly Lipschitz boundary is considered. A homogeneous Dirichlet condition is specified on the closed part of the boundary of the domain, and the Steklov boundary...
In the present work, we investigate a
We quantized the full Einstein equations in a globally hyperbolic spacetime
The impedance change in an induction coil surrounding a metal tube adapter is investigated using the truncated region eigenfunction expansion (TREE) method. The conventional TREE method is inapplicable to this problem as a consequence of the numerica...
We quantize the Hamilton equations instead of the Hamilton condition. The resulting equation has the simple form
This paper studies the existence and uniqueness of the classical solution of inverse problems for a fourth-order hyperbolic equation with a complex-valued coefficient with Dirichlet and Neumann boundary conditions. Using the method of separation of v...
In this work, we study the spectral properties of the Laplace operator with variable dependent boundary conditions in a disk. The boundary conditions include periodic and antiperiodic boundary conditions as well as the generalized Samarskii–Ion...
An important goal in cardiology and other fields is to identify and control dynamic spiral wave patterns in reaction–diffusion partial differential equations. This research focuses on the Barkley model. The spiral wave motion is controlled and...
In the present work, two-dimensional mixed problems with the Caputo fractional order differential operator are studied using the Fourier method of separation of variables. The equation contains a linear transformation of involution in the second deri...
This article discusses the author’s version of the technology for solving a one-dimensional boundary value problem for a one-dimensional advection–diffusion equation based on the method of separation of variables, as well as the theory of...
This study investigates the combined effect of the breaking and energy dissipation of water waves by variable bottoms across the surf zone. The shoreline is set up as a partially reflecting vertical wall in the solution technique, with shelves betwee...
It is shown that if we exclude the existence of nontrivial small solutions, then a linear autonomous functional differential equation has a nontrivial nonnegative solution if and only if it has a nonnegative eigenfunction.
The solution of the eigenvalue problem in bounded domains with planar and cylindrical stratification is a necessary preliminary task for the construction of modal solutions to canonical problems with discontinuities. The computation of the complex ei...
The Bragg reflections of oblique water waves by periodic surface-piercing structures over periodic bottoms are investigated using the eigenfunction matching method (EMM). Based on the assumption of small wave amplitude, the linear wave theory is empl...
This paper investigates the scattering of oblique water waves by multiple thin barriers over undulation bottoms using the eigenfunction matching method (EMM). In the solution procedures of the EMM, the bottom topographies are sliced into shelves sepa...
In this study, the scattering of oblique water waves by multiple variable porous breakwaters near a partially reflecting wall over uneven bottoms are investigated using the eigenfunction matching method (EMM). In the solution procedure, the variable...
Score-based generative models, grounded in stochastic differential equations (SDEs), excel in producing high-quality data but suffer from slow sampling due to the extensive nonlinear computations required for iterative score function evaluations. We...
The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to c...
In this study, the Bragg resonance of water waves scattered by multiple permeable thin barriers over a series of periodic breakwaters was solved by employing the eigenfunction matching method (EMM). The geometrical configuration was divided into mult...
In this work, we deal with the autonomy issue in the perturbation expansion for the eigenfunctions of a compact Hilbert–Schmidt integral operator. Here, the autonomy points to the perturbation expansion coefficients of the relevant eigenfunction not...
This paper introduces a rigorously defined fractional Heun operator constructed through a symmetric composition of left and right Riemann–Liouville fractional derivatives. By deriving a compatible fractional Pearson-type equation, a new weight...
The paper considers the solvability of some inverse problems for fractional differential equations with a nonlocal biharmonic operator, which is introduced with the help of involutive transformations in two space variables. The considered problems ar...
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...
The present paper is concerned with the spectral theory of nonlocal Sturm–Liouville eigenvalue problems on a finite interval. The continuity, differentiability and comparison results of eigenvalues with respect to the nonlocal potentials are studied,...
Considering a representation space for a group of unimodular
Kernel-combination procedures used in classification often return only a combined kernel matrix on the training sample, rather than a kernel function that can be evaluated consistently at new points. This limitation is especially important for superv...
This paper is devoted to solving boundary value problems for differential equations with fractional derivatives by the Fourier method. The necessary information is given (in particular, theorems on the completeness of the eigenfunctions and associate...
Recent progress in autonomous vehicle technology has led to the development of accurate and efficient tools for ensuring safety, which is crucial for verifying the reliability and security of vehicles. These vehicles operate under diverse conditions,...
The paper presents an exact solution to the internal boundary value problem of the field distribution in an electrostatic lens formed by two identical semi-infinite coaxially located round cylinders separated by a slit of finite width and located ins...
In this paper, we examine the role played by topology, and some specific boundary conditions as well, on the physics of a higher-dimensional black hole. We analyze the line element of a five-dimensional non-extremal Reissner–Nordström blac...
This study deals with the peristaltic transport of non-Newtonian Jeffrey fluid with uniformly distributed identical rigid particles in a rectangular duct. The effects of a magnetohydrodynamics bio-bi-phase flow are taken into account. The governing e...
Exceptional points are parameter values at which two eigenvalues and their corresponding eigenfunctions coalesce, rendering the wave operator defective. They arise widely in non-Hermitian wave physics and disrupt the modal expansions on which semi-an...
This work presents a novel diagnostic method to localize Partial Discharges (PDs) inside Medium Voltage (MV) and High Voltage (HV) equipment. The method is well suited for that equipment presenting a bounded domain with fixed Boundary Conditions (BCs...
A fixed, concentric, cylindrical oscillating water column (OWC) wave energy converter (WEC) is proposed for shallow offshore sites. Compared with the existing shoreline OWC device, this wave energy device is not restricted by the wave directions and...
In the paper, we transform the general Sturm–Liouville problem (SLP) into two canonical forms: one with the homogeneous Dirichlet boundary conditions and another with the homogeneous Neumann boundary conditions. A boundary shape function method...
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