Nontriviality and Strong Nontriviality for Exponential Time

Nontriviality for Exponential Time w.r.t. Weak Reducibilities

A set A is nontrivial for the linear exponential time class E = DTIME(2) if A ∈ E and the sets from E which can be reduced to A are not from a single level DTIME(2) of the linear exponential hierarchy. Similarly, a set A is nontrivial for the polynomial exponential time class EXP = DTIME(2) if A ∈ EXP and the sets from EXP which can be reduced to A are not from a single level DTIME(2 k ) of the...

Nonrenormalizability and Nontriviality

A redesigned starting point for covariant φn, n ≥ 4, models is suggested that takes the form of an alternative lattice action and which may have the virtue of leading to a nontrivial quantum field theory in the continuum limit. The lack of conventional scattering for such theories is understood through an interchange of limits. Despite being perturbatively nonrenormalizable, the quantum theory ...

Nontriviality of SK1 (R [MJ)

The main result of this paper is as follows: For any commutative regular (actually even K2-regular) ring R and any finitely generated intermediate monoid ZP+ c A4 c Q’+ (for some natural r) the following conditions are equivalent: (a) A4 zE:, (b) R[M] is K,-regular, (c) M is seminormal and SK,(R) = SK,(R[M]) (i.e. the natural homomorphism SK,(R) -SK,(R[M]) is an isomorphism), and, if in additio...

Nontriviality of Rankin-Selberg L-functions and CM points

Graphical Methods Establishing Nontriviality of State Cycle Khovanov Homology Classes

We determine when certain state cycles represent nontrivial Khovanov homology classes by analyzing features of the state graph. Using this method, we are able to produce hyperbolic knots with arbitrarily many diagonals containing nontrivial state cycle homology classes. This gives lower bounds on the Khovanov width of knots whose complexity precludes computation of the full homology.