Related papers: Killing Luzin and Sierpinski sets
We construct, using mild combinatorial hypotheses, a real Menger set that is not Scheepers, and two real sets that are Menger in all finite powers, with a non-Menger product. By a forcing-theoretic argument, we show that the same holds in…
We demonstrate that Abelian family symmetries allow one to enforce texture zeros in arbitrary entries of the fermion mass matrices. Placing zeros in any number of elements of all occurring mass matrices can be done with two alternative…
If the sterile neutrino mass matrix in an otherwise conventional seesaw model has a rank less than the number of flavors, it is possible to produce pseudo-Dirac neutrinos. In a two-flavor, sterile rank 1 case, we demonstrate analytic…
The Tile Assembly Model is a Turing universal model that Winfree introduced in order to study the nanoscale self-assembly of complex (typically aperiodic) DNA crystals. Winfree exhibited a self-assembly that tiles the first quadrant of the…
In this article, we provide an explicit description of a set of generators for any ideal of an ultragraph Leavitt path algebra. We provide several additional consequences of this description, including information about generating sets for…
This paper develops a Mellin-Laplace analytic framework for the fixed-shift prime correlation r_h(n) = Lambda(n) Lambda(n+h) for h not equal to 0. This sequence has no multiplicative structure, no Euler product, and no singularity at s = 1.…
As a consequence of the LSND anomaly and other hints of an eV scale sterile neutrino from particle physics and cosmology, the neutrino sector of the standard model of particle physics has to be extended and the smallest extension is the…
Stringent constraints on the interactions of dark matter with the Standard Model suggest that dark matter does not take part in gauge interactions. In this regard, the possibility of communicating between the visible and dark sectors via…
Let $\mathfrak{F}_n$ be the set of all cuspidal automorphic representations $\pi$ of $\mathrm{GL}_n$ with unitary central character over a number field $F$. We prove the first unconditional zero density estimate for the set…
We construct generating pairs of simple Lie algebras in characteristic zero. We apply this construction to exhibit infinite series of 2-generator Zariski dense subgroups that are free of rank 2 of the simple algebraic groups SL(n, C), Sp(n,…
A natural extension of the standard model to accommodate massive neutrinos is to introduce one Higgs triplet and three right-handed Majorana neutrinos, leading to a 6 \times6 neutrino mass matrix. We show that three light Majorana neutrinos…
We consider the minimal extended seesaw model which can accommodate an eV scale sterile neutrino. The scenario also includes three heavy right handed neutrinos in addition to the light sterile neutrino. In this model, the active-sterile…
We argue that a detailed analysis of semileptonic decays can test the possibility of a massive neutrino. The key observable, related to the forward-backward asymmetry, is exactly zero for a massless neutrino but becomes non-zero if the…
We show that every countable set of partial bijections from an infinite set to itself can be obtained as a composition of just two such partial bijections. This strengthens a result by Higgins, Howie, Mitchell and Ru\v{s}kuc stating that…
We prove a variety of results concerning singular sets of reals. Our results concern: Kysiak and Laver-null sets, Kocinac and gamma-k-sets, Fleissner and square Q-sets, Alikhani-Koopaei and minimal Q-like-sets, Rubin and sigma-sets, and…
We discuss two extensions of the Standard Model based on the seesaw mechanism and on non-abelian family symmetry groups O(2) and $D_4$, respectively. Both models have a twofold-degenerate neutrino Dirac mass matrix $M_D$, a Majorana mass…
On a real ($\mathbb F=\mathbb R$) or complex ($\mathbb F=\mathbb C$) analytic connected 2-manifold $M$ with empty boundary consider two vector fields $X,Y$. We say that $Y$ {\it tracks} $X$ if $[Y,X]=fX$ for some continuous function…
We compute analytically the tree-level annihilation rates of a collection of non-relativistic neutralino and chargino two-particle states in the general MSSM, including the previously unknown off-diagonal rates. The results are…
In the framework of the seesaw mechanism with three heavy right-handed Majorana neutrinos and no Higgs triplets we carry out a systematic study of the structure of the right-handed neutrino sector. Using the current low-energy neutrino data…
The negative outcome of gaugino searches at LEP has been one of the most disappointing results for fans of supersymmetric models. In the framework of minimal supersymmetric models with GUT unification assumptions, the combined absence of…