emph{The (undirected) power graph on the conjugacy classes} $mathcal{P_C}(G)$ of a group $G$ is a simple graph in which the vertices are the conjugacy classes of $G$ and two distinct vertices $C$ and $C'$ are adjacent in $mathcal{P_C}(G)$ if one is a subset of a power of the other. In this paper, we describe groups whose associated graphs are $k$-regular for $k=5,6$.

Proving a conjecture of Talagrand, fractional version the ``expectation-threshold" Kalai and second author, we show that $p_c (\mathcal{F}) = O(q_f(\mathcal{F})\mathrm{log}\ \ell(\mathcal{F}))$ for any increasing family $\mathcal{F}$ on finite set $X$, where $p_c(\mathcal{F})$ $q_f(\mathcal{F})$ are threshold ``fractional expectation-threshold" $\mathcal{F}$, $\ell(\mathcal{F})$ is maximum size...

Let $E$ be a finite set and $\mathcal P$, $\mathcal S$, $\mathcal L$ three classes of subsets of $E$, and $r$ a function defined on $2^E$. In this paper, we give an algorithm for testing if the quadruple $(\mathcal P, \mathcal S, \mathcal L, r)$ is the locked structure of a given matroid, i.e., recognizing if $(\mathcal P, \mathcal S, \mathcal L, r)$ defines a matroid. This problem is intractab...

In this note we deal with intuitionistic modal logics over $\mathcal{M}\mathcal{I}PC$ and predicate superintuitionistic logics. We study the correspondence between the lattice of all (normal) extensions of MTPC and the lattice of all predicate superintuitionistic logics. Let $\mathrm{L}_{Prop}$ denote a propositional language which contains two modal operators $\square$ and $\mathrm{O}$ , and $...

inspired by a recent work of buchweitz and flenner, we show that, for a semidualizing bimodule $c$, $c$--perfect complexes have the ability to detect when a ring is strongly regular.it is shown that there exists a class of modules which admit minimal resolutions of $c$--projective modules.

In this article, we develop a notion of Quillen bifibration which combines the two notions of Grothendieck bifibration and of Quillen model structure. In particular, given a bifibration $p:\mathcal E\to\mathcal B$, we describe when a family of model structures on the fibers $\mathcal E_A$ and on the basis category $\mathcal B$ combines into a model structure on the total category $\mathcal E$, ...

The subalgebra membership problem is the problem of deciding if a given element belongs to an algebra given by a set of generators. This is one of the best established computational problems in algebra. We consider a variant of this problem, which is motivated by recent progress in the Constraint Satisfaction Problem, and is often referred to as the Subpower Membership Problem (SMP). In the SMP...

Abstract A method for modelling the prompt production of molecular states using hadronic rescattering framework general-purpose Pythia event generator is introduced. Production cross sections possible exotic molecules via at LHC are calculated $$\chi _{c1}(3872)$$ ? c 1</mml...

We introduce a family of mathematical objects called $\mathcal{P}$-schemes, where $\mathcal{P}$ is a poset of subgroups of a finite group $G$. A $\mathcal{P}$-scheme is a collection of partitions of the right coset spaces $H\backslash G$, indexed by $H\in\mathcal{P}$, that satisfies a list of axioms. These objects generalize the classical notion of association schemes as well as the notion of $...

Phaseless reconstruction from space-time samples is a nonlinear problem of recovering a function $x$ in a Hilbert space $\mathcal{H}$ from the modulus of linear measurements $\{\lvert \langle x, \phi_i\rangle \rvert$, $ \ldots$, $\lvert \langle A^{L_i}x, \phi_i \rangle \rvert : i \in\mathscr I\}$, where $\{\phi_i; i \in\mathscr I\}\subset \mathcal{H}$ is a set of functionals on $\mathcal{H}$, a...