Nonassociative exponential and logarithm

A Generalized Logarithm for Exponential-Linear Equations

Dan Kalman ([email protected]) joined the mathematics faculty at American University in 1993, following an eight year stint in the aerospace industry and earlier teaching positions in Wisconsin and South Dakota. He has won three MAA writing awards, is an Associate Editor of Mathematics Magazine, and served a term as Associate Executive Director of the MAA. His interests include matr...

Parameterized floating-point logarithm and exponential functions for FPGAs

As FPGAs are increasingly being used for floating-point computing, the feasibility of a library of floating-point elementary functions for FPGAs is discussed. An initial implementation of such a library contains parameterized operators for the logarithm and exponential functions. In single precision, those operators use a small fraction of the FPGA’s resources, have a smaller latency than their...

Exponential Bounds in the Law of Iterated Logarithm for Martingales

In this paper non-asymptotic exponential estimates are derived for tail of maximum martingale distribution by naturally norm-ing in the spirit of the classical Law of Iterated Logarithm.

Nonassociative Algebras

Nonassociative Valuations

In a paper entitled Noncommutative valuations, Schilling [8] proved that if an algebra of finite order over its center is relatively complete in a valuation (where the value group of the nonarchimedean, exponential valuation is not assumed to be commutative) then the value group is commutative. A similar type of theorem, proved by Albert [l], states that if an algebra of finite order over a fie...