Propose economical and stable lepton mass matrices with texture zeros

There are many viable combinations of texture zeros in lepton mass matrices. We propose an economical and stable mass texture. Analytical and numerical results on mixing parameters and the effective mass of neutrinos are obtained. These results satisfy new constraints from neutrinos oscillation experiments and cosmological observations. Our proposition reveals that in the complex forest of neutrinos mixing models, a simple and robust one is still possible.Comment: 11 pages, 2 figure

Lepton mixing patterns from the group Σ(36×3)\Sigma(36\times3) with a generalized CP transformation

The group $\Sigma(36\times3)$ with the generalized CP transformation is introduced to predict the mixing pattern of leptons. Various combinations of abelian residual flavor symmetries with CP transformations are surveyed. Six mixing patterns could accommodate the fit data of neutrinos oscillation at $3\sigma$ level. Among them, two patterns predict the nontrivial Dirac CP phase, around $\pm 57^{\circ}$ or $\pm 123^{\circ}$, which is in accordance with the result of the literature and the recent fit data. Furthermore, one pattern could satisfy the experimental constraints at $1\sigma$ level

Lepton mixing patterns from combinations of elementary correlations

Recent data of reactor neutrino experiments set more stringent constraint on leptonic mixing patterns. We examine all possible patterns on the basis of combinations of elementary correlations of elements of leptonic mixing matrix. we obtain 62 viable mixing patters at 3$\sigma$ level of mixing parameters. Most of these patterns can be paired via the {\mu}- interchange which changes the octant of $\theta_{23}$ and the sign of $\cos{\delta}$. All viable patterns can be classified into two groups: the perturbative patterns and non-perturbative patterns. The former can be obtained from perturbing TBM. The latter cannot be obtained from perturbing any mixing pattern whose $\theta_{13}$ is zero. Different predictions of Dirac CP phase $\delta$ of these two types of mixing patterns are discussed. Evolutions of mass matrices of neutrinos with small mixing parameters are discussed via special mixing patterns on the basis of flavor groups. In general cases, a small variation of $\sin\theta_{13}$ may bring about large modifications to alignment of vacuum expectation values in a mixing model. Therefore, small but nonzero $\sin\theta_{13}$ brings a severer challenge to leptonic mixing models on the basis of flavor groups than usual views.Comment: 29pages, 5 figure

A novel mathematical construct for the family of leptonic mixing patterns

In order to induce a family of mixing patterns of leptons which accommodate the experimental data with a simple mathematical construct, we construct a novel object from the hybrid of two elements of a finite group with a parameter $\theta$. This construct is an element of a mathematical structure called group-algebra. It could reduce to a generator of a cyclic group if $\theta/2\pi$ is a rational number. We discuss a specific example on the base of the group $S_{4}$. This example shows that infinite cyclic groups could give the viable mixing patterns for Dirac neutrinos.Comment: 9 pages, 2 figures, 1 tabl

Studying the baryon properties through chiral soliton model at finite temperature and denstity

We have studied the chiral soliton model in a thermal vacuum. The soliton equations are solved at finite temperature and density. The temperature or density dependent soliton solutions are presented. The physical properties of baryons are derived from the soliton solutions at finite temperature and density. The temperature or density dependent variation of the baryon properties are discussed.Comment: 7 pages, 6 figure

To understand sQGP through non-topological FL model

The non-topological FL model is studied at finite temperature and density. The soliton solutions of the FL model in deconfinement phase transition are solved and thoroughly discussed for different boundary conditions. We indicate that the solitons before and after the deconfinement have different physical meanings: the soliton before deconfinement represents hadron, while the soliton after the deconfinement represents the bound state of quarks which leads to a sQGP phase. The corresponding phase diagram is given.Comment: 7 pages, 8 figure

Interplay between Fano resonance and PT\mathcal{PT} symmetry in non-Hermitian discrete systems

We study the effect of PT-symmetric complex potentials on the transport properties of non-Hermitian systems, which consist of an infinite linear chain and two side-coupled defect points with PT-symmetric complex on-site potentials. By analytically solving the scattering problem of two typical models, which display standard Fano resonances in the absence of non-Hermitian terms, we find that the PT-symmetric imaginary potentials can lead to some pronounced effects on transport properties of our systems, including changes from the perfect reflection to perfect transmission, and rich behaviors for the absence or existence of the prefect reflection at one and two resonant frequencies. Our study can help us to understand the interplay between the Fano resonance and PT symmetry in non-Hermitian discrete systems, which may be realizable in optical waveguide experiments.Comment: 6 pages, 6 figure

The generalized connectivity of some regular graphs

The generalized $k$-connectivity $\kappa_{k}(G)$ of a graph $G$ is a parameter that can measure the reliability of a network $G$ to connect any $k$ vertices in $G$, which is proved to be NP-complete for a general graph $G$. Let $S\subseteq V(G)$ and $\kappa_{G}(S)$ denote the maximum number $r$ of edge-disjoint trees $T_{1}, T_{2}, \cdots, T_{r}$ in $G$ such that $V(T_{i})\bigcap V(T_{j})=S$ for any $i, j \in \{1, 2, \cdots, r\}$ and $i\neq j$. For an integer $k$ with $2\leq k\leq n$, the {\em generalized $k$-connectivity} of a graph $G$ is defined as $\kappa_{k}(G)= min\{\kappa_{G}(S)|S\subseteq V(G)$ and $|S|=k\}$. In this paper, we study the generalized $3$-connectivity of some general $m$-regular and $m$-connected graphs $G_{n}$ constructed recursively and obtain that $\kappa_{3}(G_{n})=m-1$, which attains the upper bound of $\kappa_{3}(G)$ [Discrete Mathematics 310 (2010) 2147-2163] given by Li {\em et al.} for $G=G_{n}$. As applications of the main result, the generalized $3$-connectivity of many famous networks such as the alternating group graph $AG_{n}$, the $k$-ary $n$-cube $Q_{n}^{k}$, the split-star network $S_{n}^{2}$ and the bubble-sort-star graph $BS_{n}$ etc. can be obtained directly.Comment: 19 pages, 6 figure

The gg-good neighbour diagnosability of hierarchical cubic networks

Let $G=(V, E)$ be a connected graph, a subset $S\subseteq V(G)$ is called an $R^{g}$-vertex-cut of $G$ if $G-F$ is disconnected and any vertex in $G-F$ has at least $g$ neighbours in $G-F$. The $R^{g}$-vertex-connectivity is the size of the minimum $R^{g}$-vertex-cut and denoted by $\kappa^{g}(G)$. Many large-scale multiprocessor or multi-computer systems take interconnection networks as underlying topologies. Fault diagnosis is especially important to identify fault tolerability of such systems. The $g$-good-neighbor diagnosability such that every fault-free node has at least $g$ fault-free neighbors is a novel measure of diagnosability. In this paper, we show that the $g$-good-neighbor diagnosability of the hierarchical cubic networks $HCN_{n}$ under the PMC model for $1\leq g\leq n-1$ and the $MM^{*}$ model for $1\leq g\leq n-1$ is $2^{g}(n+2-g)-1$, respectively

PT\mathcal{PT} symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model

We study the $\mathcal{PT}$-symmetry breaking for the scattering problem in a one-dimensional (1D) non-Hermitian tight-binding lattice model with balanced gain and loss distributed on two adjacent sites. In the scattering process the system undergoes a transition from the exact $\mathcal{PT}$-symmetry phase to the phase with spontaneously breaking $\mathcal{PT}$-symmetry as the amplitude of complex potentials increases. Using the S-matrix method, we derive an exact discriminant, which can be used to distinguish different symmetry phases, and analytically determine the exceptional point for the symmetry breaking. In the $\mathcal{PT}$-symmetry breaking region, we also confirm the appearance of the unique feature, i.e., the coherent perfect absorption Laser, in this simple non-Hermitian lattice model. The study of the scattering problem of such a simple model provides an additional way to unveil the physical effect of non-Hermitian $\mathcal{PT}$-symmetric potentials.Comment: 6 pages, 3 figure