A monoid S satisfies Condition (A) if every locally cyclic left S-act is cyclic. This condition first arose in Isbell’s work on left perfect monoids, that is, monoids such that every left S-act has a projective cover. Isbell showed that S is left perfect if and only if every cyclic left S-act has a projective cover and Condition (A) holds. Fountain built on Isbell’s work to show that S is left ...

A random walk on a lattice is one of the most fundamental models in probability theory. When the random walk is inhomogenous and its inhomogeniety comes from an ergodic stationary process, the walk is called a random walk in a random environment (RWRE). The basic questions such as the law of large numbers (LLN), the central limit theorem (CLT), and the large deviation principle (LDP) are ...

In an important paper, Amrita Dhillon [3] provided a multi-profile version of Harsanyi’s [5] single-profile theorem on utilitarianism. Like Harsanyi, she assumed that the social alternatives are lotteries. Individuals’ preferences satisfy the von Neumann-Morgenstern (vN-M) axioms, and have thus an expected utility representation. A social welfare function maps profiles of individuals’ preferenc...

Recent growth in the renewable energy industry has increased government support for alternative energy. In the United States, hydropower is the largest source of renewable energy and also one of the most efficient. Currently, there are 30,000 megawatts of potential energy capacity through smalland micro-hydro projects throughout the United States. Increased development of micro-hydro could doub...

The Command and Control theory of John Boyd, a 20 century military strategist, allow us to introduce computing techniques that are able to speed up the OODA loop (Observe–Orient–Decide–Act), especially on observing and orienteering steps. This paper introduces a low cost framework capable of monitoring people, vehicles, boats, or any other elements of interest, almost in real time. The goal of ...