On a Classical Theta-Function

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

a brief discussion on neo- classical production function

the neo- classical school on the situation of the individual and claims that individuals (consumers and producers) meet each in the market. on the supply side, there exists possibility of substitution between factors of production and, on the demand side, substitution by consumers between final goods. in the neo- classical production function capital and labor are taken as the determniants of t...

A new class of function spaces on domains of R^d and its relations to classical function spaces

On Minrank and the Lovász Theta Function

Two classical upper bounds on the Shannon capacity of graphs are the θ-function due to Lovász and the minrank parameter due to Haemers. We provide several explicit constructions of n-vertex graphs with a constant θ-function and minrank at least n for a constant δ > 0 (over various prime order fields). This implies a limitation on the θ-function-based algorithmic approach to approximating the mi...

On Ramanujan's definition of mock theta function.

In his famous "deathbed" letter, Ramanujan "defined" the notion of a mock theta function and offered some examples of functions he believed satisfied his definition. Very recently, Griffin et al. established for the first time that Ramanujan's mock theta functions actually satisfy his own definition. On the other hand, Zwegers' 2002 doctoral thesis [Zwegers S (2002) Mock theta functions. PhD th...