In this note we show that the family of Cayley graphs a finitely generated subgroup ${\rm GL}_{n_0}(\mathbb{F}_p(t))$ modulo some admissible square-free polynomials is expanders under certain algebraic conditions. Here more precise formulation our main result. For positive integer $c_0$, say polynomial $c_0$-admissible if degree irreducible factors $f$ are distinct integers with prime at least ...

We characterise the pairs of graphs $\{ X, Y \}$ such that all \}$-free (distinct from $C_5$) are perfect. Similarly, we $\omega$-colourable (that is, their chromatic number is equal to clique number). More generally, show characterizations for perfectness and $\omega$-colourability connected which independence at least~$3$, distinct an odd cycle, order least $n_0$, similar characterisations su...

We show that for a hyperbolic knot complement, all but at most 12 Dehn fillings are irreducible with infinite word-hyperbolic fundamental group. AMS Classification numbers Primary: 57M50, 57M27 Secondary: 57M25, 57S25

the biological effects of omega-3 and omega-6 fatty acids are determined by their mutual interactions. this interaction extremely affects various functions. lower consumption of omega-3 during gestation leads to various disorders, even in hearing. we aimed to assess the effect of low omega-3/omega-6 ratios on auditory nerve conduction. in this experimental study, the auditory brainstem response...

We study the Max Partial $H$-Coloring problem: given a graph $G$, find largest induced subgraph of $G$ that admits homomorphism into $H$, where $H$ is fixed pattern without loops. Note when complete on $k$ vertices, problem reduces to finding $k$-colorable subgraph, which for $k=2$ equivalent (by complementation) Odd Cycle Transversal. prove every loops, can be solved in $\{P_5,F\}$-free graphs...

In the present work, we investigate several theoretical models of pion vector form factor and aim at getting best fit for two-pion cross sections to reduce uncertainties calculation contribution muon anomalous magnetic moment. Combined with a polynomial description factor, obtain from Gounaris-Sakurai (or K\"uhn-Santamaria) model experimental data up 1 GeV. By product, branching ratio $\omega \...

Let I be a homogeneous ideal in polynomial ring over field. $$I^{(n)}$$ the n-th symbolic power of I. Motivated by results about ordinary powers I, we study asymptotic behavior regularity function $${{\,\mathrm{reg}\,}}(I^{(n)})$$ and maximal generating degree $$\omega (I^{(n)})$$ , when is monomial ideal. It known that both functions are eventually quasi-linear. We show that, addition, sequenc...

We apply the derivative expansion of effective action in exact renormalization group equation up to fourth order $Z_2$ and $O(N)$ symmetric scalar models $d=3$ Euclidean dimensions. compute critical exponents $\nu$, $\eta$ $\omega$ using polynomial field. obtain our predictions for employing two regulators widely used ERG computations. Wynn's epsilon algorithm improve exponents, extrapolating b...