We show that for all k ≥ 1, there exists an integer N(k) such that for all n ≥ N(k) the k-th order jet scheme over the commuting n × n matrix pairs scheme is reducible. At the other end of the spectrum, it is known that for all k ≥ 1, the k-th order jet scheme over the commuting 2× 2 matrices is irreducible: we show that the same holds for n = 3.

defined on n-tuples of commuting elements of G and invariant under simultaneous conjugation. Thus, in [HKR00] the study of nth Morava E-theory at a prime p leads to χ(g1, ..., gn) defined on gi of p-power order. On the other hand, the construction of equivariant elliptic cohomology in [Dev96] (which corresponds to n = 2) uses functions χ(g1, g2) as above but without restrictions on the order. T...

‎in a recent paper c‎. ‎miguel proved that the diameter of the commuting graph of the matrix ring $mathrm{m}_n(mathbb{r})$ is equal to $4$ if either $n=3$ or $ngeq5$‎. ‎but the case $n=4$ remained open‎, ‎since the diameter could be $4$ or $5$‎. ‎in this work we close the problem showing that also in this case the diameter is $4$.

the non-commuting graph $nabla(g)$ of a non-abelian group $g$ is defined as follows: its vertex set is $g-z(g)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. in this paper we 'll prove that if $g$ is a finite group with $nabla(g)congnabla(bs_{n})$, then $g cong bs_{n}$, where $bs_{n}$ is the symmetric group of degre...

Using the idea of local entropy theory, we characterize sequence tuple via mean forms sensitive in both topological and measure-theoretical senses. For sense, show that for an ergodic measure-preserving system, $\mu$-sequence tuple, $\mu$-mean $\mu$-sensitive coincide, give example to ergodicity condition is necessary. a certain class minimal systems, tuple.

The result from the title is shown. Let L(H) denote the algebra of all bounded linear operators on a complex Hilbert space H. If M⊂ L(H), then we denote by M′ the commutant of M, M′ = {S ∈ L(H) : T S = S T for every T ∈ M}. The second commutant is denoted by M′′ = (M′)′. Denote further by W(M) the smallest weakly closed subalgebra of L(H) containing M and by AlgLatM the algebra of all operators...

consider the random walk among n places with n(n - 1)/2 transports. we attach an exponential random variable xij to each transport between places pi and pj and take these random variables mutually independent. if transports are possible or impossible independently with probability p and 1-p, respectively, then we give a lower bound for the distribution function of the smallest path at point log...

BACKGROUND Few studies have assessed the predictors of changes in commuting. This study investigated the associations between physical environmental characteristics and changes in active commuting. METHODS Adults from the population-based European Prospective Investigation into Cancer (EPIC)-Norfolk cohort self-reported commuting patterns in 2000 and 2007. Active commuters were defined as tho...