Related papers: New spectral multiplicities for mixing transformat…
Collective oscillations of supernova neutrinos swap the electron neutrino and antineutrino spectra with those of another flavor in certain energy intervals bounded by sharp spectral splits. This phenomenon is far more general than…
Given a bivariate system of polynomial equations with fixed support sets $A, B$ it is natural to ask which multiplicities its solutions can have. We prove that there exists a system with a solution of multiplicity $i$ for all $i$ in the…
Mass spectrometry, especially so-called tandem mass spectrometry, is commonly used to assess the chemical diversity of samples. The resulting mass fragmentation spectra are representations of molecules of which the structure may have not…
Improper Lorentz Transformations can be retained as exact symmetries of Nature if the particle content and gauge group of the Standard Model are doubled. The resulting ``Exact Parity Model (EPM)'' sees each ordinary particle paired with a…
A set of necessary and sufficient conditions under which an isotone mapping from a subset of a poset X to a poset Y has an extension to an isotone mapping from X to Y are found.
It is shown that a finite number of conditions are {\em not} sufficient to determine the locality of transformations between two probability distributions of pure states as well as the locality of transformations between two $d\times d$…
Let R be an E_2 ring spectrum with zero odd dimensional homotopy groups. Every map of ring spectra MU to R is represented by a map of E_2 ring spectra. If 2 is invertible in pi_0(R), then every map of ring spectra MSO to R is represented by…
For any set $M$ of natural numbers there are mixing Gaussian automorphisms and non-mixing Gaussian automorphisms with singular spectrum (as well as some automorphisms which are disjoint from all Gaussian actions) such that $…
We analyze the neutrino conversions inside a supernova in the 3$\nu$ mixing scheme, and their effects on the neutrino spectra observed at the earth. We find that the observations of the energy spectra of neutrinos from a future galactic…
Let $(X, d)$ be a semimetric space. A permutation $\Phi$ of the set $X$ is a combinatorial self similarity of $(X, d)$ if there is a bijective function $f \colon d(X^2) \to d(X^2)$ such that $$ d(x, y) = f(d(\Phi(x), \Phi(y))) $$ for all…
For $E \subset \mathbb{N}$, a subset $R \subset \mathbb{N}$ is $E$-intersective if for every $A \subset E$ having positive upper relative density, we have $R \cap (A - A) \neq \varnothing$. On the other hand, $R$ is chromatically…
Given a complex nilpotent finite dimensional Lie algebra of linear transformations $L$, in a complex finite dimensional vector space $E$, we study the joint spectra $Sp(L,E)$, $\sigma_{\delta,k}(L,E)$ and $\sigma_{\pi,k}(L,E)$. We compute…
In this note, we investigate a mixture of combinatorial spectra and stratified simplicial sets, which would be thought of as a model of the spectrum objects of $(\infty, \infty)$-categories.
Given two sets of quantum states {A_1, ..., A_k} and {B_1, ..., B_k}, represented as sets of density matrices, necessary and sufficient conditions are obtained for the existence of a physical transformation T, represented as a…
We present a necessary and sufficient conditions under which the sum of two EP elements in a *-ring has core inverse. As an application, we establish the conditions under which a block complex matrix with EP sub-blocks has core inverse.
Given two combinatorial identities proved earlier, a new set of variations of these combinatorial identities is listed and proved with the integral representation method. Some identities from literature are shown to be special cases of…
Given a level set $E$ of an arbitrary multiplicative function $f$, we establish, by building on the fundamental work of Frantzikinakis and Host [13,14], a structure theorem which gives a decomposition of $\mathbb{1}_E$ into an almost…
This paper uses a construction of M. Keane to show that there exists a topologically mixing interval exchange transformation.
The energy spectrum of a system of $N_a$ atoms of $n$ levels interacting with a one-mode electromagnetic field is studied in the dipole and rotating wave approximations. We find that, under the resonant condition, it exhibits a mirror…
We provide necessary and sufficient conditions for separability of mixed states. As a result we obtain a simple criterion of separability for $2\times2$ and $2\times3$ systems. Here, the positivity of the partial transposition of a state is…