where η is the evaluation map. It was proved by Flenner [F] that if characteristic k = 0 then Vd is a semistable vector bundle. He uses this as an crucial ingredient to prove his restriction theorem for torsion free semistable sheaves on a normal projective variety, defined over a field of characteristic 0, to a general hypersurface of degree d, where d has a lower bound in terms of degree of t...

Abstract. It is known that the weight (that is, the number of nonzero coefficients) of a univariate polynomial over a field of characteristic zero is larger than the multiplicity of any of its nonzero roots. We extend this result to an appropriate statement in positive characteristic. Furthermore, we present a new proof of the original result, which produces also the exact number of monic polyn...

We find new lower bounds on the torsion orders of very general Fano hypersurfaces over (uncountable) fields arbitrary characteristic. Our results imply that unirational parametrizations most need to have enormously large degree. also hold in characteristic two, where they solve rationality problem for under a logarithmic degree bound, thereby extending previous result author from different two

Let F be a homogeneous real polynomial of even degree in any number of variables. We consider the problem of giving explicit conditions on the coefficients so that F is positive definite or positive semi-definite. In this note we produce a necessary condition for positivity and a sufficient condition for non-negativity, in terms of positivity or semi-positivity of a one-variable characteristic ...

Several proofs given in [2] contain significant errors or gaps, although to our knowledge all results claimed there are provable. The needed corrections are described below. All references are to [2] unless otherwise stated, and we adopt the notation and terminology of that paper. 1. Lemma 7.10 asserts that the principles D2 and SRT 2 2 are equivalent over RCA0. However, the proof that D 2 2 im...

Precisely describing the formation and evolution rules of coal-rock fracturing crack have great value on reservoir fracturing improvement and highly efficient mining of coal bed methane well. In this paper, a non-linear dynamic method is used to study crack damage evolution behavior of coal-rock fracturing. Considering distribution characteristics of natural cracks in coal-rock, and based on da...

Abstract Different methods to address the isomorphism in kinematic chains existed earlier and is well reported. In all methods, link-adjacency matrix (LAM) represents structural information of a given chain. Having gathered large collection co-spectral belonging number chain categories possessing (containing up 20 links 13 degrees freedom), present work aims at addressing by developing implemen...