Random Series in Powers of Algebraic Integers: Hausdorff Dimension of the Limit Distribution

Scaling Limit of Random Planar Quadrangulations with a Boundary

We discuss the scaling limit of large planar quadrangulations with a boundary whose length is of order the square root of the number of faces. We consider a sequence (σn) of integers such that σn/ √ 2n tends to some σ ∈ [0,∞]. For every n ≥ 1, we call qn a random map uniformly distributed over the set of all rooted planar quadrangulations with a boundary having n faces and 2σn half-edges on the...

Random Series in Powers of Algebraic Integers

Infinite Subsets of Random Sets of Integers

There is an infinite subset of a Martin-Löf random set of integers that does not compute any Martin-Löf random set of integers. To prove this, we show that each real of positive effective Hausdorff dimension computes an infinite subset of a Martin-Löf random set of integers, and apply a result of Miller.

Laminar Flame Speed Prediction in Lean Mixture of Aluminum Dust Clouds by Considering the Effect of Random Distribution of Particles in Two-dimension

        In the present study, the effect of random distribution of reactants and products on laminar, 2D and steady-state flame propagation in aluminium particles has been investigated. The equations are solved only for lean mixture. The flame structure is assumed to consist of a preheat zone, a reaction zone and a post flame zone. It is presumed that in the preheat zone particles are heated an...

ALGEBRAIC INDEPENENCE OF CERTAIN FORMAL POWER SERIES (II)

We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)