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Our recent work established existence and uniqueness results for $\mathcal{C}^{k,\alpha}_{\text{loc}}$ globally defined linearizing semiconjugacies for $\mathcal{C}^1$ flows having a globally attracting hyperbolic fixed point or periodic…
A stabilized version of the fundamental solution method to catch ill-conditioning effects is investigated with focus on the computation of complex-valued elastic interior transmission eigenvalues in two dimensions for homogeneous and…
The motivation of this paper is to study a second order elliptic operator which appears naturally in Riemannian geometry, for instance in the study of hypersurfaces with constant $r$-mean curvature. We prove a generalized Bochner-type…
The non-trivial zeros of the Riemann zeta function and the prime numbers can be plotted by a modified von Mangoldt function. The series of non-trivial zeta zeros and prime numbers can be given explicitly by superposition of harmonic waves.…
Using the well known approach developed in the papers of B. Davies and his co-authors we obtain inequalities for the location of possible complex eigenvalues of non-selfadjoint functional difference operators. When studying the sharpness of…
We prove the exponential decay of eigenfunctions of reductions of Brown-Ravenhall operators to arbitrary irreducible representations of rotation-reflection and permutation symmetry groups under the assumption that the corresponding…
Consider a random matrix of size $N$ as an additive deformation of the complex Ginibre ensemble under a deterministic matrix $X_0$ with a finite rank, independent of $N$. When some eigenvalues of $X_0$ separate from the unit disk, outlier…
The flow of an ideal fluid possesses a remarkable property: despite limited regularity of the velocity field, its particle trajectories are analytic curves. In our previous work, this fact was used to introduce the structure of an analytic…
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid…
We consider second order elliptic systems of partial differential equations subject to Dirichlet and Neumann boundary conditions. We prove analyticity of the elementary symmetric functions of the eigenvalues, and compute Hadamard-type…
Fully Developed Turbulence (FDT) is a theoretical asymptotic phenomenon which can only be approximated experimentally or computationally, so its defining characteristics are hypothetical. It is considered to be a chaotic stationary flow…
We discuss the existence of eigenvalues for a third order boundary value problem subject to functional boundary conditions and higher order derivative dependence in the nonlinearities. We prove the existence of positive and negative…
$f$-electron systems exhibit a subtle interplay between strong spin--orbit coupling and crystal-field effects, producing complex energy landscapes that are computationally demanding. We introduce auxiliary functions, constructed by…
The Eigendecomposition of quadratic forms (symmetric matrices) guaranteed by the spectral theorem is a foundational result in applied mathematics. Motivated by a shared structure found in inferential problems of recent interest---namely…
The differential equations satisfied by the wavefunction coefficients of conformally coupled scalars in a power-law cosmology can be recast into an iterative differential system of basis functions. These functions can be encoded within…
We give a formula for the values of automorphic Green functions on the special rational 0-cycles (big CM points) attached to certain maximal tori in the Shimura varieties associated to rational quadratic spaces of signature (2d,2). Our…
Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…
We in this paper study the hermiticity of Hamiltonian and energy spectrum for the SU(1; 1) systems. The Hermitian Hamiltonian can possess imaginary eigenvalues in contrast with the common belief that hermiticity is a suffcient condition for…
This is the first in a series of works devoted to small non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2. In the present work we treat the case when the classical flow of the unperturbed part is…
The eigenvalue problem for a linear function L centers on solving the eigen-equation Lx = rx. This paper generalizes the eigenvalue problem from a single linear function to an iterated function system F consisting of possibly an infinite…