Alternating Hamiltonian cycles in 22-edge-colored multigraphs

A path (cycle) in a $2$-edge-colored multigraph is alternating if no two consecutive edges have the same color. The problem of determining the existence of alternating Hamiltonian paths and cycles in $2$-edge-colored multigraphs is an $\mathcal{NP}$-complete problem and it has been studied by several authors. In Bang-Jensen and Gutin's book "Digraphs: Theory, Algorithms and Applications", it is devoted one chapter to survey the last results on this topic. Most results on the existence of alternating Hamiltonian paths and cycles concern on complete and bipartite complete multigraphs and a few ones on multigraphs with high monochromatic degrees or regular monochromatic subgraphs. In this work, we use a different approach imposing local conditions on the multigraphs and it is worthwhile to notice that the class of multigraphs we deal with is much larger than, and includes, complete multigraphs, and we provide a full characterization of this class. Given a $2$-edge-colored multigraph $G$, we say that $G$ is $2$-$\mathcal{M}$-closed (resp. $2$-$\mathcal{NM}$-closed)} if for every monochromatic (resp. non-monochromatic) $2$-path $P=(x_1, x_2, x_3)$, there exists an edge between $x_1$ and $x_3$. In this work we provide the following characterization: A $2$-$\mathcal{M}$-closed multigraph has an alternating Hamiltonian cycle if and only if it is color-connected and it has an alternating cycle factor. Furthermore, we construct an infinite family of $2$-$\mathcal{NM}$-closed graphs, color-connected, with an alternating cycle factor, and with no alternating Hamiltonian cycle.Comment: 15 pages, 20 figure

Neutrino mixing and masses in a left-right model with mirror fermions

In the framework of a left-right model containing mirror fermions with gauge group SU(3)$_{C} \otimes SU(2)_{L} \otimes SU(2)_{R} \otimes U(1)_{Y^\prime}$, we estimate the neutrino masses, which are found to be consistent with their experimental bounds and hierarchy. We evaluate the decay rates of the Lepton Flavor Violation (LFV) processes $\mu \rightarrow e \gamma$, $\tau \rightarrow \mu \gamma$ and $\tau \rightarrow e\gamma$. We obtain upper limits for the flavor-changing branching ratios in agreement with their present experimental bounds. We also estimate the decay rates of heavy Majorana neutrinos in the channels $N \rightarrow W^{\pm} l^{\mp}$, $N \rightarrow Z \nu_{l}$ and $N \rightarrow H \nu_{l}$, which are roughly equal for large values of the heavy neutrino mass. Starting from the most general Majorana neutrino mass matrix, the smallness of active neutrino masses turns out from the interplay of the hierarchy of the involved scales and the double application of seesaw mechanism. An appropriate parameterization on the structure of the neutrino mass matrix imposing a symmetric mixing of electron neutrino with muon and tau neutrinos leads to Tri-bimaximal mixing matrix for light neutrinos.Comment: Accepted by European Physical Journal

How sails generate forces

We propose a new paradigm of the aerodynamics of sails that reconciles our understanding of the force generation mechanisms of both upwind and downwind sails, and that is applicable to both attached and separated flow conditions. Sail experience significant flow separation. Even when the flow appears to be attached, this is sometimes only in the time averaged sense. In these conditions, the underlining as- sumptions of thin airfoil theory and lifting line theory are violated. There is therefore a need to develop an intuitive understanding of the force generation mechanisms that does not rely on these assumptions. This paper aims to address this issue by proposing a new paradigm based on the impulse theory. The force generation mechanism can be intuitively associated with the vorticity field, which can be gathered with computational fluid dynamics or particle image velocimetry. This paradigm intuitively reconciles key results of traditional wing aerodynamics, and provides sail designers a measurable objective to modify a sail shape also in separated flow conditions. It will hopefully underpin both a deeper understanding of sail aerodynamics and the development of low order models for new design tools

Neutrino masses and mixing parameters in a left-right model with mirror fermions

In this work we consider a left-right model containing mirror fermions with gauge group SU(3)$_{C} \otimes SU(2)_{L} \otimes SU(2)_{R} \otimes U(1)_{Y^\prime}$. The model has several free parameters which here we have calculated by using the recent values for the squared-neutrino mass differences. Lower bound for the mirror vacuum expectation value helped us to obtain crude estimations for some of these parameters. Also we estimate the order of magnitude of the masses of the standard and mirror neutrinos.Comment: 13 pages, version submitted to European Physical Journal