Homogeneous Algebraic Distributions

Homogeneous Coordinatesfor Algebraic

Gap distributions and homogeneous dynamics

We survey the use of dynamics of SL(2,R)-actions to understand gap distributions for various sequences of subsets of [0, 1), particularly those arising from special trajectories of various two-dimensional dynamical systems. We state and prove an abstract theorem that gives a unified explanation for some of the examples we present.

One - Dimensional Associated Homogeneous Distributions

Let H′ (R) denote the set of Associated Homogeneous Distributions (AHDs) with support in R. The set H′ (R) consists of the distributional analogues of one-dimensional power-log functions. H′ (R) is an important subset of the tempered distributions S′ (R), because (i) it contains the majority of the (one-dimensional) distributions typically encountered in physics applications and (ii) recent wor...

Homogeneous Equations of Algebraic Petri Nets

Algebraic Petri nets are a formalism for modeling distributed systems and algorithms, describing control and data flow by combining Petri nets and algebraic specification. One way to specify correctness of an algebraic Petri net model N is to specify a linear equation E over the places of N based on term substitution, and coefficients from an abelian group G. Then, E is valid in N iff E is vali...

Optimal Quantization for Dyadic Homogeneous Cantor Distributions

For a large class of dyadic homogeneous Cantor distributions in R, which are not necessarily self-similar, we determine the optimal quantizers, give a characterization for the existence of the quantization dimension, and show the non-existence of the quantization coefficient. The class contains all self-similar dyadic Cantor distributions, with contraction factor less than or equal to 1 3 . For...