Remarks on the Degree Theory

Remarks on Binding Theory

We propose some reformulations of binding principle A that build on recent work by Pollard and Xue, and by Runner et al. We then turn to the thorny issue of the status of indices, in connection with the seemingly simpler Principle B. We conclude that the notion of index is fundamentally incoherent, and suggest some possible approaches to eliminating them as theoretical primitives. One possibili...

Remarks on Classical Invariant Theory

A uniform formulation, applying to all classical groups simultaneously, of the First Fundamental Theory of Classical Invariant Theory is given in terms of the Weyl algebra. The formulation also allows skew-symmetric as well as symmetric variables. Examples illustrate the scope of this formulation.

Remarks on Formal Knot Theory

Remarks on the Theory of Cosmological Perturbation

It is shown that the power spectrum defined in the Synchronous Gauge can not be directly used to calculate the predictions of cosmological models on the large-scale structure of universe, which should be calculated directly by a suitable gauge-invariant power spectrum or the power spectrum defined in the Newtonian Gauge. PACS: 98.80.-k; 98.80.Hw; 98.80.Cq

Some Remarks on Number Theory

This note contains some disconnected minor remarks on number theory . 1 . Let (1) Iz j I=1, 1<j<co be an infinite sequence of numbers on the unit circle . Put n s(k, n) _ z~, Ak = Jim sup I s(k, n) j=1 k=oo and denote by B k the upper bound of the numbers I s(k,n)j . If z j = e 2nij' a =A 0 then all the Ak 's are finite and if the continued fraction development of a has bounded denominators the...