The Hermite ring conjecture in dimension one

A short proof of the maximum conjecture in CR dimension one

In this paper and by means of the extant results in the Tanaka theory, we present a very short proof in the specific case of CR dimension one for Beloshapka's maximum conjecture. Accordingly, we prove that each totally nondegenerate model of CR dimension one and length >= 3 has rigidity. As a result, we observe that the group of CR automorphisms associated with each of such models contains onl...

Simulations of transport in one dimension

Advection-dispersion equation is solved in numerically by using combinations of differential quadrature method (DQM) and various time integration techniques covering some explicit or implicit single and multi step methods. Two different initial boundary value problems modeling conservative and nonconservative transports of some substance represented by initial data are chosen as test problems. ...

The Manin Conjecture in Dimension 2

Global Coefficient Ring in the Nilpotence Conjecture

In this note we show that the nilpotence conjecture for toric varieties is true over any regular coefficient ring containing Q. In [G] we showed that for any additive submonoid M of a rational vector space with the trivial group of units and a field k with chark = 0 the multiplicative monoid N acts nilpotently on the quotient Ki(k[M ])/Ki(k) of the ith K-groups, i ≥ 0. In other words, for any s...

The Marr Conjecture in One Dimension and Uniqueness of Wavelet Transforms

The Marr conjecture in vision theory states that an image is uniquely determined by its multiscale edges. Specifically, a locally integrable function on Rd is uniquely determined by its Gaussian edges (the zeros of its smoothed Laplacian) at dyadic scales, or equivalently, the zeros of its discrete Mexican hat wavelet transform. Though this is false in full generality (e.g. for nondecaying and ...