On vanishing sums of m \,m\,th roots of unity in finite fields

In an earlier work, the authors have determined all possible weights $n$ for which there exists a vanishing sum $\zeta_1+\cdots +\zeta_n=0$ of $m$th roots of unity $\zeta_i$ in characteristic 0. In this paper, the same problem is studied in finite fields of characteristic $p$. For given $m$ and $p$, results are obtained on integers $n_0$ such that all integers $n\geq n_0$ are in the ``weight set'' $W_p(m)$. The main result $(1.3)$ in this paper guarantees, under suitable conditions, the existence of solutions of $x_1^d+\cdots+x_n^d=0$ with all coordinates not equal to zero over a finite field

Using infrared thermography for monitoring thermal efficiency of buildings - case studies from Nottingham Trent University

Global warming and the continuous increase of energy cost are driving the need for reducing energy consumption. Buildings are responsible for approximately 50% of the UK energy consumption. Major part of this consumption is for heating and air conditioning of buildings. Nottingham Trent University is a leading university in the UK in relation to improving the performance of its buildings in order to improve insulation and energy consumption. The experimental case studies presented in this paper highlights some of the new measures taken to reduce energy consumption and enhance the sustainability of the University buildings. Infrared thermography is used to evaluate insulation measures and energy performance. The results indicate that enhanced insulation combined with modern sustainable technologies can significantly reduce energy consumption

Real time demonstration of high bitrate quantum random number generation with coherent laser light

We present a random number generation scheme that uses broadband measurements of the vacuum field contained in the radio-frequency sidebands of a single-mode laser. Even though the measurements may contain technical noise, we show that suitable algorithms can transform the digitized photocurrents into a string of random numbers that can be made arbitrarily correlated with a subset of the quantum fluctuations (high quantum correlation regime) or arbitrarily immune to environmental fluctuations (high environmental immunity). We demonstrate up to 2 Gbps of real time random number generation that were verified using standard randomness tests