We present a Monte Carlo molecular simulation method that calculates the helical twisting power of a chiral molecule by sampling intermolecular torques. The approach is applied to an achiral nematic liquid crystalline system, composed of Gay-Berne particles, that is doped with chiral molecules. Calculations are presented for six chiral dopant molecules and the results show a good correlation wi...

This paper establishes a simple model of long run economic and political development, which is driven by the inherent technical features of di¤erent production factors, and political con‡icts among factor owners on how to divide the outputs. The main capital form in economy evolves from land to physical capital and then to human capital, which enables their respective owners (landlords, capital...

Here, we show, unconditionally for k = 3, and on the prime k-tuples conjecture for k ≥ 4, that ∑∞ n=1 σk(n) n! is irrational, where σk(n) denotes the sum of the kth powers of the divisors of n.

Let H∗(Be) be the total Springer representation of W for the nilpotent element e in a simple Lie algebra g. Let ∧V denote the exterior powers of the reflection representation V of W . The focus of this paper is on the algebra of W -invariants in H∗(Be)⊗ ∧ ∗V and we show that it is an exterior algebra on the subspace (H∗(Be) ⊗ V ) in some new cases. This was known previously for e = 0 by a resul...

We give a complete characterization of so called powerful arithmetic progressions, i.e. of progressions whose kth term is a kth power for all k. We also prove that the length of any primitive arithmetic progression of powers can be bounded both by any term of the progression different from 0 and ±1, and by its common difference. In particular, such a progression can have only finite length.

A network structure metric is herein suggested for the investigation of the behaviour of epidemic spreading processes in general network-structured populations. This simple measure, based on the algebraic powers of the adjacency matrix associated with the network in question, is shown to admit a heuristic interpretation as a representation of a spreading process similar to standard epidemic mod...

Fibonacci numbers have engaged the attention of mathematicians for several centuries, and whilst many of their properties are easy to establish by very simple methods, there are several unsolved problems connected to them. In this paper we review the history of the conjecture that the only perfect powers in Fibonacci sequence are 1, 8, and 144. Afterwards we consider more stronger conjecture an...

Parliamentary and Presidential Democracies: Which One is Best? With the exception of the United States, where a system of separation of executive and legislative powers exists, all countries that are considered to be stable democracies adopt a constitution that is, at least partially, parliamentary. A parliamentary constitution is characterized by the fusion of executive and legislative powers,...