Related papers: Killing Luzin and Sierpinski sets

We construct a non-free but aleph_1-separable, torsion-free abelian group G with a pure free subgroup B such that all subgroups of G disjoint from B are free and such that G/B is divisible. This answers a question of Irwin and shows that a…

The results of many LHC searches for supersymmetric particles are interpreted using simplified models, in which one fixes the masses and couplings of most sparticles then scans over a few remaining masses of interest. We present a new…

We describe a method to construct hypersurfaces of the complex affine $n$-space with isomorphic $\mathbb{C}^*$-cylinders. Among these hypersurfaces, we find new explicit counterexamples to the Laurent Cancellation Problem, i.e.…

We propose a model based on an alternative $U(1)_{B-L}$ gauge symmetry with 5 dimensional operators in the Lagrangian, and we construct the neutrino masses at one-loop level, and discuss lepton flavor violations, dark matter, and the…

Sterile neutrinos are well-motivated extensions of the Standard Model, introduced to address fundamental questions such as the origin of neutrino masses and the nature of dark matter. Exploiting the precise data reconstruction achieved by…

A bijection from R to R is called an Erdos-Sierpinski mapping if it maps meager sets onto the first category sets and vice versa. We show that there is no Erdos-Sierpinski mapping preserving addition.

In this text we combine the notions of supergeometry and supersymmetry. We construct a special class of supermanifolds whose reduced manifolds are (pseudo) Riemannian manifolds. These supermanifolds allow us to treat vector fields on the…

A family of M-sets and null-series for the d-dimensional Walsh system is constructed if we consider convergence over rectangles, cubes, or iterated convergence. Non-empty portions of the constructed M-sets are also M-sets. The question of…

We construct a family of simple gauge models in which three sterile neutrinos become naturally light by virtue of a generalized seesaw mechanism involving a chiral gauge symmetry. Examples where the chiral gauge group is SU(5)', SU(7)',…

Utilizing an embedding theorem of Obraztsov we construct groups as described in the title. This provides an affirmative answer to a problem of D. O. Revin. The constructed groups also provide a negative answer to a question highlighted by…

We investigate SUSY of Wess-Zumino models in non(anti-)commutative Euclidean superspaces. Non(anti-)commutative deformations break 1/2 SUSY, then non(anti-)commutative Wess-Zumino models do not have full SUSY in general. However, we can…

Under MA_{omega_1} every uncountable almost disjoint family is either anti-Luzin or has an uncountable Luzin subfamily. This fails under CH. Related properties are also investigated.

Privacy laws and regulations enforce data-driven systems, e.g., recommender systems, to erase the data that concern individuals. As machine learning models potentially memorize the training data, data erasure should also unlearn the data…

For Leptogenesis based on the type-I seesaw mechanism, we present a systematic calculation of lepton-number violating and purely flavoured asymmetries within nonequilibrium Quantum Field Theory. We show that sterile neutrinos with…

Machine \emph{unlearning}, which involves erasing knowledge about a \emph{forget set} from a trained model, can prove to be costly and infeasible by existing techniques. We propose a nearly compute-free zero-shot unlearning technique based…

We consider a general, anomaly free U$(1)^\prime$ extension of the Standard Model (SM) where the neutrino mass is generated at the tree level via the inverse seesaw mechanism. The model contains three right handed neutrinos, three…

We construct model sets arising from cut and project schemes in Euclidean spaces whose associated Delone dynamical systems have positive toplogical entropy. The construction works both with windows that are proper and with windows that have…

We construct r-matrices for simple Lie superalgebras with non-degenerate Killing forms using Belavin-Drinfeld type triples. This construction gives us the standard r-matrices and some nonstandard ones.

We give a positive answer to the question of Shkarin (\emph{On universal abelian topological groups}, Mat. Sb. 190 (1999), no. 7, 127-144) whether there exists a metrically universal abelian separable group equipped with invariant metric.…

Motivated by the interpretation of the recent results on the TeV gamma radiation from the Galactic center, including the new 2004 HESS data, as a by-product of dark matter particles annihilations, we address the question of the largest…