Geometric Generalization of the Exponential Law

investigating the feasibility of a proposed model for geometric design of deployable arch structures

deployable scissor type structures are composed of the so-called scissor-like elements (sles), which are connected to each other at an intermediate point through a pivotal connection and allow them to be folded into a compact bundle for storage or transport. several sles are connected to each other in order to form units with regular polygonal plan views. the sides and radii of the polygons are...

Characterizations of the Exponential Law

A general solution of the functional equation J f{x+y)dfii(y) = f(x) where / is a nonnegative function and ?i is a o--finite positive Borel measure on [0, oo ) is shown to be f(x) = p(x) exp (xa?) where p is a periodic function with every yep, the support of ft as a period. The solution is applied in characterizing Pareto, exponential and geometric distributions by properties of integrated lack...

Exponential Challenges, Exponential Rewards - The future of Moore's Law

The Generalized Universal Law of Generalization

It has been argued by Shepard that there is a robust psychological law that relates the distance between a pair of items in psychological space and the probability that they will be confused with each other. Specifically, the probability of confusion is a negative exponential function of the distance between the pair of items. In experimental contexts, distance is typically defined in terms of ...

Geometric Exponential Integrators

In this paper, we consider exponential integrators for semilinear Poisson systems. Two types of exponential integrators are constructed, one preserves the Poisson structure, and the other preserves energy. Numerical experiments for semilinear Possion systems obtained by semi-discretizing Hamiltonian PDEs are presented. These geometric exponential integrators exhibit better long time stability p...