Related papers: Eigenvector-eigenvalue identities and an applicati…
Flavor transitions via the charged current interactions are parametrized by a three dimensional and unitary transformation. This so called mixing matrix requires of four mixing parameters. Here we show that under the phenomenological…
Theories of flavor operate at various scales. Recently it has been pointed out that in the context of modular flavor symmetries certain combinations of observables are highly constrained, or even uniquely fixed, by modular invariance and…
One way to study an hypergraph is to attach to it a tensor. Tensors are a generalization of matrices, and they are an efficient way to encode information in a compact form. In this paper we study how properties of weighted hypergraphs are…
The eigenvalues of the potentials $V_{1}(r)=\frac{A_{1}}{r}+\frac{A_{2}}{r^{2}}+\frac{A_{3}}{r^{3}}+\frac{A_{4 }}{r^{4}}$ and $V_{2}(r)=B_{1}r^{2}+\frac{B_{2}}{r^{2}}+\frac{B_{3}}{r^{4}}+\frac{B_{4}}{r^ {6}}$, and of the special cases of…
We characterize the relationship between the singular values of a complex Hermitian (resp., real symmetric, complex symmetric) matrix and the singular values of its off-diagonal block. We also characterize the eigenvalues of an Hermitian…
In this article we establish some constraints on the eigenvalues for the action of a self map of a proper variety on its $\ell$-adic cohomology. The essential ingredients are a trace formula due to Fujiwara, and the theory of weights.
We derive analytic expressions for three flavor neutrino oscillations in the presence of matter in the plane wave approximation using the Cayley-Hamilton formalism. Especially, we calculate the time evolution operator in both flavor and…
The Riemann curvature tensor is a central mathematical tool in Einstein's theory of general relativity. Its related eigenproblem plays an important role in mathematics and physics. We extend M-eigenvalues for the elasticity tensor to the…
The electroweak theory contains too many empirical parameters. Most of them are related to the flavor part of particle physics. In this paper we discuss a relevant simple idea: the complicated system of actual dimensionless, small versus…
Reporting about the density matrix theory for a composite quantum system of flavor eigenstates, we introduce the idea of flavor-weighted energies. It provides us with the right correlation between the energies of flavor eigenstates and…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
The eigenvector-eigenvalue identity relates the eigenvectors of a Hermitian matrix to its eigenvalues and the eigenvalues of its principal submatrices in which the jth row and column have been removed. We show that one-dimensional arrays of…
We use SU(3) flavor symmetry to analyze the $PP', VP$ and baryon-antibaryon decays of $J/\psi$. Both, the SU(3)-invariant and -violating contributions are considered. Particular attention is paid to the interference of the electromagnetic…
Current neutrino oscillation data indicate that the 3x3 lepton flavor mixing matrix V is likely to be symmetric about its V_{e3}-V_{\mu 2}-V_{\tau 1} axis. This off-diagonal symmetry corresponds to three pairs of {\it congruent} unitarity…
In this paper we discuss some relations between the eigenvalues and the diagonal entries of Hermitian matrices.
Much effort has been spent on characterizing the spectrum of the non-backtracking matrix of certain classes of graphs, with special emphasis on the leading eigenvalue or the second eigenvector. Much less attention has been paid to the…
A wealth of new data in charmed particle physics allows the testing of flavor symmetry and the extraction of key amplitudes. Information on relative strong phases is obtained.
We develop a rather general approach to entanglement characterization based on convexity properties and polynomial identities. This approach is applied to obtain simple and efficient entanglement conditions which work equally well in both…
Correlation function of complex eigenvalues of N by N random matrices drawn from non-Hermitean random matrix ensemble of symplectic symmetry is given in terms of a quaternion determinant. Spectral properties of Gaussian ensembles are…
We define two new constants associated with real eigenvalues of a P-tensor. With the help of these two constants, in the case of P-tensors, we establish upper bounds of two important quantities, whose positivity is a necessary and…