Related papers: New spectral multiplicities for mixing transformat…
The mixing of three and four massive neutrinos is considered. It is shown that the neutrino oscillation data are not compatible with a hierarchy of couplings in the three-neutrino case. In the case of four neutrinos, a hierarchy of masses…
For different classes of measure preserving transformations, we investigate collections of sets that exhibit the property of lightly mixing. Lightly mixing is a stronger property than topological mixing, and requires that a lim inf is…
A new mechanism is proposed to explain neutrino masses and their mixing via SU(1,1) horizontal symmetry breaking. Based on this mechanism smallness of neutrino masses is naturally realized and inverted hierarchical spectrum with large…
We propose that the entanglement of mixed states is characterised properly in terms of a probability density function $\mathcal{P}(\mathcal{E})$. There is a need for such a measure since the prevalent measures (such as \textit{concurrence}…
The two matrix model is considered, with measure given by the exponential of a sum of polynomials in two different variables. It is shown how to derive a sequence of pairs of ``dual'' finite size systems of ODEs for the corresponding…
A revolution in our understanding of the neutrino sector is underway, driven by observations that are interpreted in terms of changes in neutrino flavors as they propagate. Since neutrino oscillations occur only if neutrinos are massive,…
A multicomplex, also known as a twisted chain complex, has an associated spectral sequence via a filtration of its total complex. We give explicit formulas for all the differentials in this spectral sequence.
It has been known that the transition probability of the single species ASEP with $N$ particles is expressed as a sum of $N!$ $N$-fold contour integrals which are related to permutations in the symmetric group $S_N$. On other hand, the…
We show that the conditions for total neutrino conversion found in [1] are equivalent to the conditions of maximal depth (parametric resonance) and ($\pi/2 + \pi k$) - phase of parametric oscillations. Therefore the effects considered in…
We give sufficient conditions to guarantee that if two self-conformal sets E and F have Lipschitz equivalent subsets of positive measure, then there is a bilipschitz map of E into, or onto, F.
A random vector $X=(X_1,\ldots,X_n)$ with the $X_i$ taking values in an arbitrary measurable space $(S, \mathscr{S})$ is exchangeable if its law is the same as that of $(X_{\sigma(1)}, \ldots, X_{\sigma(n)})$ for any permutation $\sigma$.…
A tournament is $k$-spectrally monomorphic if all the $k\times k$ principal submatrices of its adjacency matrix have the same characteristic polynomial. Transitive $n$-tournaments are trivially $k$-spectrally monomorphic. We show that there…
We have found in [1] new conditions for a total neutrino conversion in the case of neutrino oscillations taking place in a medium, consisting of n = 2 (or 3) alternating layers with constant densities $N_1$ and $N_2$. It is claimed in [4]…
We obtain new partial results supporting the spectral set conjecture in dimension 1.
A modification of the usual extended N = 2 supersymmetry algebra implementing the two dimensional permutation group is performed. It is shown that one can found a multiplet that forms an off-shell realization of this alternative extension…
In this paper, we show that when two systems of differential equations admitting a symmetry group are related by a point transformation it is always possible to generate invariant schemes, one for each system, that are also related by the…
A normal subgroup $E$ of a group $G$ is said to be hypercyclically embedded in $G$ if either $E=1$ or $E\neq 1$ and every chief factor of $G$ below $E$ is cyclic. In this article, we present some new characterizations of a normal subgroup…
A square matrix of order $n$ with $n\geq 2$ is called a \textit{permutative matrix} or permutative when all its rows (up to the first one) are permutations of precisely its first row. In this paper, the spectra of a class of permutative…
A given density matrix may be represented in many ways as a mixture of pure states. We show how any density matrix may be realized as a uniform ensemble. It has been conjectured that one may realize all probability distributions that are…
This paper shows that mixed multiplicities and the multiplicity of Rees modules of good filtrations and that of their reductions are the same. As an application of this result, we obtain interesting results on mixed multiplicities and the…