Chung, Graham, and Wilson proved that a graph is quasirandom if and only if there is a large gap between its first and second largest eigenvalue. Recently, the authors extended this characterization to coregular k-uniform hypergraphs with loops. However, for k ≥ 3 no k-uniform hypergraph is coregular. In this paper we remove the coregular requirement. Consequently, the characterization can be a...

In this paper, we show that if $M$ is a non-zero Artinian $R$-module and $\underline{x}:=x_1,\ldots,x_n$ an $M$-coregular sequence, then $x_1,\ldots,x_n$ $D(H_n^{\underline{x}}(M))$-coregular sequence. Moreover, $R$ complete with respect to $I$-adic topology $d=\mathrm{Ndim} M$, $\dim H^I_d(M) \le d$ $\mathrm{depth} H_I^d(M)\ge \min\{{2, d}\}$ whenever $H^I_d(M) \ne 0.$

Let R be a commutative Noetherian ring and let M be a nitely generated R-module. If I is an ideal of R generated by M-regular sequence, then we study the vanishing of the rst Tor functors. Moreover, for Artinian modules and coregular sequences we examine the vanishing of the rst Ext functors.

Some examples of coregular spaces were mentioned last time binary quadratic forms, binary cubic forms etc. Clearly, any pre-homogeneous space is a vector space. Coregular spaces were first classified by Littelman (1989) for semisimple irreducible representations; there are around 50 of them including infinite families. A lot of these spaces come from Vinberg theory, something that’ll be discuss...

A Hausdorff topological space X is called superconnected (resp. coregular ) if for any nonempty open sets U 1 , … n ⊆ the intersection of their closures ‾ ∩ not empty complement ∖ ( a regular space). canonical example projective Q P ∞ vector < ω = { x ∈ : | ≠ 0 } over field rationals . The quotient by equivalence relation ∼ y iff ⋅ We prove that every countable second-countable homeomorphic to ...