Quasi-random properties are deterministic properties which capture certain characteristics of random objects. The last decades have seen an extensive e↵ort in the study of this subject which has revealed many connections between di↵erent branches of mathematics and theoretical computer science. For graphs the systematic investigation was initiated by Thomason [27, 28] who studied deterministic ...

There is a construction of random subsets of Z in which almost every subset is Sidon (this was first done by Katznelson). More is true: almost every subset is the finite union of quasi-independent sets. Also, if every Sidon subset of Z\{0} is the finite union of quasi-independent sets, then the required number of quasi-independent sets is bounded by a function of the Sidon constant. Analogs of ...

For a locally quasi-convex (lqc) abelian group G, we describe all compatible lqc topologies on G and apply this result to the Mackey problem for groups. We characterize groups which are or admit topology provide characterization of two whose product is Mackey. convex spaces

This paper concerns curves on non-commutative schemes, hereafter called quasi-schemes. A quasi-scheme X is identiied with the category ModX of quasi-coherent sheaves on it. Let X be a quasi-scheme having a regularly embedded hypersurface Y. Let C be a curve on X which is in \good posi-tion" with respect to Y (see Deenition 5.1)|this deenition includes a requirement that X be far from commutativ...

We construct (0, 2), D = 2 gauged linear sigma model on supermanifold with both an Abelian and non-Abelian gauge symmetry. For the purpose of checking the exact supersymmetric (SUSY) invariance of the Lagrangian density, it is convenient to introduce a new operator Û for the Abelian gauge group. The Û operator provides consistency conditions for satisfying the SUSY invariance. On the other hand...

The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-)periodic solutions of various equations of mathematical physics. In this paper, algorithms for its computation are given. First, a formula is derived allowing the pointwise approximation of Riemann theta functions, with arbitrary, user-specified precision. This formula ...

In this manuscript I show how to recover some of the inertia structure of (quasi) divisors of a function field K|k over an algebraically closed base field k from its maximal mod ` abelian-by-central Galois theory of K, provided td(K|k) > 1. This is a first technical step in trying to extend Bogomolov’s birational anabelian program beyond the full pro-` situation, which corresponds to the limit ...

The moduli space of principally polarized abelian varieties with real structure and with level N = 4m structure (with m ≥ 1) is shown to coincide with the set of real points of a quasi-projective algebraic variety defined over Q, and to consist of finitely many copies of the quotient of the space GL(n, R)/O(N) (of positive definite symmetric matrices) by the principal congruence subgroup of lev...

It has been observed by different authors that QTAG-modules behave very much like torsion abelian groups. In this paper, in section 3, we characterize quasi-essential submodules (Theorem 3.9) and further find a characterization for an h-pure submodule to be a direct summand (Theorem 3.11). In section 4, we obtained a necessary and sufficient condition for a submodule to be contained in a minima...

We develop the theory of parity quasi-complexes (PQC), preparing the set up for defining derived functors using resolutions in the nonabelian case. A homotopy structure on the category of PQC is defined, yielding a 2-category structure. The nonabelian homology functor factors through the corresponding homotopy category. Following the relative homological algebra approach, resolutions are define...