Related papers: Transformations preserving the effective spectral …
We study the effective range expansion of scattering on a real Casimir-Polder potential. We use Liouville transformations which transform the potential landscape while preserving the reflection and transmission amplitudes. We decompose the…
Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…
The main purpose of this note is to illustrate how the radius in a finite-dimensional power-associative algebra over a field $\mathbb{F}$, either $\mathbb{R}$ or $\mathbb{C}$, may change when the multiplication in this algebra is modified.…
An effective radius of convergence is defined and computed for any truncated Taylor series. Applications to well known series are performed and is shown that a range of good coincidence for actual and approximative plot can always be found.…
We prove that continuous spectrum- and commutativity-preserving maps to $\mathcal{M}_n(\mathbb{C})$ from the space of normal (real or complex) $n\times n$, $n\ge 3$ matrices with spectra contained in a given continuous-injection interval…
In this note functions that transform open segments of a linear space into open segments of another linear space are studied and characterized. Assuming that the range is non-collinear, it is proved that such a map can always be expressed…
In our article we consider some algebraical methods which may be useful in some inverse spectral problems. The reconstraction of the matrix from its minors is considered.
Landen transformations are maps on the coefficients of an integral that preserve its value. We present a brief survey of their appearnce in the literature.
In this work we study the scattering and transfer matrices for electric fields defined with respect to an angular spectrum of plane waves. For these matrices, we derive the constraints that are enforced by conservation of energy,…
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
The ability to control electromagnetic fields on the subwavelength scale could open exciting new venues in many fields of science. Transformation optics provides one way to attain such control through the local variation of the permittivity…
We show that two tensor permutation matrices permutate tensor product of rectangle matrices. Some examples, in the particular case of tensor commutation matrices, for studying some linear matrix equations are given.
Accurate and fast modeling of electric fields in layered structures have a great scientific and practical value. Prevalent method for that is transfer-matrix method. However, transfer matrix method is limited to infinite plane wave…
We give an extension to a nonconvex setting of the classical radial representation result for lower semicontinuous envelope of a convex function on the boundary of its effective domain. We introduce the concept of radial uniform upper…
This study explores the relationship between hypergraph automorphisms and the spectral properties of matrices associated with hypergraphs. For an automorphism $f$, an \( f \)-compatible matrices capture aspects of the symmetry, represented…
This work is concerned with the stability of regime-switching processes under the perturbation of the transition rate matrices. From the viewpoint of application, two kinds of perturbations are studied: the size of the transition rate…
We investigate when a computable automorphism of a computable field can be effectively extended to a computable automorphism of its (computable) algebraic closure. We then apply our results and techniques to study effective embeddings of…
We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the…
Scale transformations have played an extremely successful role in studies of cosmological large-scale structure by relating the non-linear spectrum of cosmological density fluctuations to the linear primordial power at longer wavelengths.…
We give an efficient algorithm which can obtain a relative error approximation to the spectral norm of a matrix, combining the power iteration method with some techniques from matrix reconstruction which use random sampling.