Abstract:
If neutrinos have masses, why are they so tiny? Are these masses of the Dirac type or of the Majorana type? We are already familiar with the mechanism of how to obtain a tiny Majorana neutrino mass by the famous see-saw mechanism. The question is: Can one build a model in which a tiny Dirac neutrino mass arises in a more or less "natural" way? What would be the phenomenological consequences of such a scenario, other than just merely reproducing the neutrino mass patterns for the oscillation data? In this article, a systematic and detailed analysis of a model is presented, with, as key components, the introduction of a family symmetry as well as a new SU(2) symmetry for the right-handed neutrinos. In particular, in addition to the calculations of light neutrino Dirac masses, interesting phenomenological implications of the model will be presented.

Abstract:
A systematic, rigorous, and complete investigation of the Bloch equations in time-harmonic driving classical field is performed. Our treatment is unique in that it takes full advantage of the partial fraction decomposition over real number field, which makes it possible to find and classify all analytic solutions. Torrey's analytic solution in the form of exponentially damped harmonic oscillations [Phys. Rev. {\bf 76}, 1059 (1949)] is found to dominate the parameter space, which justifies its use at numerous occasions in magnetic resonance and in quantum optics of atoms, molecules, and quantum dots. The unorthodox solutions of the Bloch equations, which do not have the form of exponentially damped harmonic oscillations, are confined to rather small detunings $\delta^2\lesssim (\gamma-\gamma_t)^2/27$ and small field strengths $\Omega^2\lesssim 8 (\gamma-\gamma_t)^2/27$, where $\gamma$ and $\gamma_t$ describe decay rates of the excited state (the total population relaxation rate) and of the coherence, respectively. The unorthodox solutions being readily accessible experimentally are characterized by rather featureless time dependence.

Abstract:
We show how leptogenesis can occur at the TeV scale with neutrinos that possess almost purely Dirac masses and negligible Majorana mass contributions as a consequence of the small wavefunction overlap in a warped fifth dimension. Lepton number violation at the Planck scale is introduced via a Majorana mass term on the Planck brane. Such a Majorana mass operator leads to the small mass splitting of otherwise degenerate Kaluza-Klein excited states on the TeV brane. This tiny mass splitting can compensate for the small Yukawa couplings to give a CP asymmetry large enough to produce the sufficient baryon asymmetry from the decay of the nearly degenerate neutrino Kaluza-Klein states. In this way the standard baryogenesis via leptogenesis scenario can naturally occur at the TeV scale without the need for a high mass scale.

Abstract:
The status of the problem of neutrino masses and mixing is shortly reviewed. Different schemes of mixing of (Dirac or Majorana) massive neutrinos are considered. The theory of neutrino oscillations in vacuum and in matter is presented. Existing indications in favor of neutrino mixing are shortly discussed.

Abstract:
We apply a result of David and Jon Borwein to evaluate a sequence of highly-oscillatory integrals whose integrands are the products of a rapidly growing number of sinc functions. The value of each integral is given in the form $\pi(1-t)/2$, where the numbers $t$ quickly become very tiny. Using the Euler-Maclaurin summation formula, we calculate these numbers to high precision. For example, the integrand of the tenth integral in the sequence is the product of 68100152 sinc functions. The corresponding $t$ is approximately $9.6492736004286844634795531209398105309232 \cdot 10^{-554381308}$.

Abstract:
In this paper we present the self-stabilizing implementation of a class of token based algorithms. In the current work we only consider interactions between weak nodes. They are uniform, they do not have unique identifiers, are static and their interactions are restricted to a subset of nodes called neighbours. While interacting, a pair of neighbouring nodes may create mobile agents (that materialize in the current work the token abstraction) that perform traversals of the network and accelerate the system stabilization. In this work we only explore the power of oblivious stateless agents. Our work shows that the agent paradigm is an elegant distributed tool for achieving self-stabilization in Tiny Interaction Protocols (TIP). Nevertheless, in order to reach the full power of classical self-stabilizing algorithms more complex classes of agents have to be considered (e.g. agents with memory, identifiers or communication skills). Interestingly, our work proposes for the first time a model that unifies the recent studies in mobile robots(agents) that evolve in a discrete space and the already established population protocols paradigm.

Abstract:
Neutrino oscillations as solutions of the solar neutrino problems and the atmospheric neutrino deficits may restrict neutrino mass squared differences and mixing angles in three-neutrino mixing scheme. Currently we have several solutions depending on the interpretations of the solar neutrino problems. Combining the neutrino oscillation solutions and a mass matrix ansatz, we investigated the neutrino mass bounds and found possible leptonic CP-violating rephasing-invariant quantity $J^{l}_{\tiny CP} \leq 0.012$ for large mixing angle MSW and just-so vacuum oscillations solutions, and $J^{l}_{\tiny CP} \leq 0.0013$ for small mixing angle MSW solution.

Abstract:
This is a review for Reports of Progress in Physics. After an introduction we start by explaining the different neutrino masses corresponding to different types of neutrinos, Dirac or Majorana, in section 2. In section 3 we discuss the main elementary particle models for neutrino masses and their distinctive phenomenological consequences. In section 4 we describe the status of direct mass searches and Majorana mass searches in neutrinoless double beta decays. In section 5 we go over the many cosmological implications of, and constraints on, neutrino properties, mainly masses and lifetimes. Sections 6, 7 and 8 review neutrino oscillations, the solar neutrino problem and the atmospheric neutrino problem, their implications and the current and future experiments. In particular, we explain oscillations in vacuum in section 6 and oscillations in matter in section 7. Section 9 summarizes the main bounds imposed by stars, mainly SN1987A. A few concluding remarks follow.

Abstract:
We consider a simple extension of the Standard Model providing dark matter and a TeV-scale seesaw mechanism that also allows for viable leptogenesis. In addition to the Standard Model degrees of freedom, the model contains a neutrinophilic Higgs doublet, a scalar singlet, and six singlet fermions (including three right-handed Majorana neutrinos) that are charged under a local $U(1)^\prime$ gauge symmetry. We show how the $U(1)^\prime$ charge assignments and the choice of scalar potential can lead to a TeV-scale seesaw mechanism and $\mathcal{O}(1)$ neutrino Yukawa couplings in a straightforward way. While this scenario has all the ingredients one would expect for significant experimental signatures, including several new TeV scale degrees of freedom, we find that most distinctive features associated with neutrino mass generation, leptogenesis and the dark sector are likely to remain inaccessible in the absence of additional lepton flavor symmetries.

Abstract:
The characteristic scale of neutral current, provided by an extension of Standard Model with a local group over the right-handed fermions, determines the smallness of neutrino masses of Dirac kind. The experimental observation of neutrino oscillations imposes the stringent limit on the $Z^\prime$ physics appearance at low energies.