Finding the mean of the total number Ntot of stationary points for N−dimensional random Gaussian landscapes can be reduced to averaging the absolute value of characteristic polynomial of the corresponding Hessian. First such a reduction is illustrated for a class of models describing energy landscapes of elastic manifolds in random environment, and a general method of attacking the problem anal...

We determine for all simple simply connected reductive linear algebraic groups defined over a finite field all irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corresponding finite simple groups. For large rank l our bound is proportional to l3 and for rank 11 m...

Here we study (in positive characteristic) integral curves X ⊂ Pr with secant degree one, i.e., for which a general P ∈ Seck−1(X) is in a unique k-secant (k − 1)-dimensional linear subspace.

The use of Toom-Cook sub-quadratic polynomial multiplication was recently shown to be possible also when the coefficient field does not have elements enough, particularly for F2[x]. This paper focus on how Toom’s strategies can be adapted to polynomials on non-binary small fields. In particular we describe the Toom-3 algorithm for Fp[x] with p ∈ {3, 5, 7}, and some other unbalanced algorithms. ...

Maoying Qiao, Jun Yu, Wei Bian, Qiang Li, and Dacheng Tao 1 School of Computer Science, Hangzhou Dianzi University 2 School of Software, FEIT, The University of Technology Sydney 3 Department of Computing, The Hong Kong Polytechnic University 4 UBTECH Sydney Artificial Intelligence Institute, School of IT, FEIT, The University of Sydney {qiaomy, yujun}@hdu.edu.cn, {brian.weibian, leetsiang.clou...

We use a sequence of blow-ups over the projective space parametrizing plane curves of degree d to obtain some enumerative results concerning smooth plane curves of arbitrary degree. For d = 4 , this gives a first modem verification of results of H. G. Zeuthen. O. INTRODUCTION The kth 'characteristic number' of the d(dt3) -dimensional family of smooth plane curves of degree d, denoted Nd(k) in t...

Let [Formula: see text] be a prime and let the complex field. We explicitly classify finite solvable irreducible monomial subgroups of up to conjugacy. That is, we give complete irredundant list text]-conjugacy class representatives as generating sets matrices. Copious structural information about non-solvable is also proved, enabling classification all such groups bar one family. explain obsta...