We prove an exponential lower bound on the size of static LovászSchrijver proofs of Tseitin tautologies. We use several techniques, namely, translating static LS+ proof into Positivstellensatz proof of Grigoriev et al., extracting a “good” expander out of a given graph by removing edges and vertices of Alekhnovich et al., and proving linear lower bound on the degree of Positivstellensatz proofs...

In this paper we give certain preserving properties of the generalized Alexander operator on some subclasses of n-uniformly functions. 2000 Mathematical Subject Classification: 30C45

By using Alexander duality on simplicial complexes we give a new and algebraic proof of Dirac’s theorem on chordal graphs.

We investigate functions f over a finite field Fq, with q prime, with the property that the map x goes to f(x) + cx is a permutation for at least 2 √ q − 1 elements c of the field. We also consider the case in which q is not prime and f is a function in many variables and pairs of functions (f, g) with the property that the map x goes to f(x) + cg(x) + dx is a permutation for many pairs (c, d) ...

BACKGROUND Randomised controlled trial evidence indicates that Alexander Technique is clinically and cost effective for chronic back pain. The aim of this mixed methods evaluation was to explore the role and perceived impact of Alexander Technique lessons in the naturalistic setting of an acute hospital Pain Management Clinic in England. METHODS To capture changes in health status and resourc...

No evidence, literary or pictorial, exists from antiquity to indicate that Alexander the Great was left-handed. Instead classical representations of Alexander show him as right-handed.

The Murphy operators in the Hecke algebra Hn of type A are explicit commuting elements whose sum generates the centre. They can be represented by simple tangles in the Homfly skein theory version of Hn. In this paper I present a single tangle which represents their sum, and which is obviously central. As a consequence it is possible to identify a natural basis for the Homfly skein of the annulu...

We study the topology of the boundary manifold of a line arrangement in CP , with emphasis on the fundamental group G and associated invariants. We determine the Alexander polynomial ∆(G), and more generally, the twisted Alexander polynomial associated to the abelianization of G and an arbitrary complex representation. We give an explicit description of the unit ball in the Alexander norm, and ...

In this paper we extend the exponential sum results from [B-K] and [B-G-K] for prime moduli to composite moduli q involving a bounded number of prime factors. In particular, we obtain nontrivial bounds on the exponential sums associated to multiplicative subgroups H of size q, for any given δ > 0. The method consists in first establishing a ‘sum-product theorem’ for general subsets A of Z. If q...