Excision in Singular Theory.

Singular perturbation theory

When we apply the steady-state approximation (SSA) in chemical kinetics, we typically argue that some of the intermediates are highly reactive, so that they are removed as fast as they are made. We then set the corresponding rates of change to zero. What we are saying is not that these rates are identically zero, of course, but that they are much smaller than the other rates of reaction. The st...

Geometric Singular Perturbation Theory

Excision in Algebraic K-theory (after Suslin)

(1) K1(A)→ K1(A/I)→ K0(I)→ K0(A)→ K0(A/I)→ K−1(I)→ · · · . Soon it was realized that in general one cannot expect this sequence to be continued on the left. This problem, known as excision in algebraic K-theory, was solved in [4] in characteristic zero and in [3] in general. In [1, Thm. 3.1] and in [2] a pro-version of excision is deduced. Theorem (Suslin–Wodzicki, Suslin) If TorIoZ i (Z,Z) = 0...

Singular continuous spectrum in ergodic theory

We prove that in the weak topology of measure preserving transformations , a dense G has purely singular continuous spectrum in the orthocomplement of the constant functions. In the uniform topology, a dense G of aperiodic transformations has singular continuous spectrum. We show that a dense G of shift-invariant measures has purely singular continuous spectrum. These results stay true for Z d ...

Singular Propositions in Two-Stage Theory

In traditional possible-worlds semantics the meaning, or intension, of an atomic empirical sentence is given as a proposition, whereby a proposition is modelled as a mapping from possible worlds to truth-values. Call such propositions ‘PWS (ie possible-worlds semantic) propositions.’ This notion of proposition, however, has been rightly found to be too coarse to handle propositional and notiona...