Related papers: Triangularisation of Singularly Perturbed Logarith…
We consider constrained partial differential equations of hyperbolic type with a small parameter $\varepsilon>0$, which turn parabolic in the limit case, i.e., for $\varepsilon=0$. The well-posedness of the resulting systems is discussed…
We study the asymptotic behavior of the solutions related to a family of singularly perturbed linear partial differential equations in the complex domain. The analytic solutions obtained by means of a Borel-Laplace summation procedure are…
We consider a family of linear singularly perturbed PDE relying on a complex perturbation parameter $\epsilon$. As in a former study of the authors (A. Lastra, S. Malek, Parametric Gevrey asymptotics for some nonlinear initial value Cauchy…
Extreme-mass-ratio inspirals (EMRIs) will be key sources for LISA. However, accurately extracting system parameters from a detected EMRI waveform will require self-force calculations at second order in perturbation theory, which are still…
We study an irregular singularity of Poincar\'e rank 1 at the origin of a certain third-order linear solvable homogeneous ODE. We perturb the equation by introducing a small parameter $\varepsilon\in (\mathbb{R}_+, 0)\,(\varepsilon < 1)$…
We present a novel recursive algorithm for reducing a symmetric matrix to a triangular factorization which reveals the rank profile matrix. That is, the algorithm computes a factorization $\mathbf{P}^T\mathbf{A}\mathbf{P} =…
In this article, we discuss formal invariants of singularly-perturbed linear differential systems in neighborhood of turning points and give algorithms which allow their computation. The algorithms proposed are implemented in the computer…
We consider rank one perturbations $A_\alpha=A+\alpha(\cdot,\varphi)\varphi$ of a self-adjoint operator $A$ with cyclic vector $\varphi\in\mathcal H_{-1}(A)$ on a Hilbert space $\mathcal H$. The spectral representation of the perturbed…
First order perturbations of homogeneous and hypersurface orthogonal LRS (Locally Rotationally Symmetric) class II cosmologies with a cosmological constant are considered in the framework of the 1+1+2 covariant decomposition of spacetime.…
We study a family of singularly perturbed $q-$difference-differential equations in the complex domain. We provide sectorial holomorphic solutions in the perturbation parameter $\epsilon$. Moreover, we achieve the existence of a common…
This paper is a continuation a previous work of the authors where parametric Gevrey asymptotics for singularly perturbed nonlinear PDEs has been studied. Here, the partial differential operators are combined with particular Moebius…
We study the hybrid type of rank one perturbations in $\mathbb{R}^2$ and $\mathbb{R}^3$, where the perturbation supported by a circle/sphere is considered together with the delta potential supported by a point outside of the circle/sphere.…
The Gerlach and Sengupta (GS) formalism of coordinate-invariant, first-order, spherical and nonspherical perturbations around an arbitrary spherical spacetime is generalized to higher orders, focusing on second-order perturbation theory.…
We study a singularly perturbed PDE with cubic nonlinearity depending on a complex perturbation parameter $\epsilon$. This is the continuation of a precedent work by the first author. We construct two families of sectorial meromorphic…
Discrete differential equations appear most prominently in planar map and lattice path enumeration. In this work we consider discrete differential equations with an additional parameter $x$, where the order of the equation is $1$ for $x=0$…
A number of random matrix ensembles permitting exact determination of their eigenvalue and eigenvector statistics maintain this property under a rank $1$ perturbation. Considered in this review are the additive rank $1$ perturbation of the…
For a nonnegative self-adjoint operator $A_0$ acting on a Hilbert space $\mathfrak{H}$ singular perturbations of the form $A_0+V, \ V=\sum_{1}^{n}{b}_{ij}<\psi_j,\cdot>\psi_i$ are studied under some additional requirements of symmetry…
This paper develops a unified analytical framework for determinant identities under finite-rank perturbations of square matrices that remains valid without invertibility assumptions. In contrast to classical inverse-based formulations, the…
We show that the conditions imposed on a second order linear differential equation with rational coefficients on the complex line by requiring it to have regular singularities with fixed exponents at the points of a finite set $P$ and…
A direct solver is introduced for solving overdetermined linear systems involving nonuniform discrete Fourier transform matrices. Such matrices can be transformed into a Cauchy-like form that has hierarchical low rank structure. The rank…