Lacunary formal power series and the Stern-Brocot sequence

Let $F(X) = \sum_{n \geq 0} (-1)^{\varepsilon_n} X^{-\lambda_n}$ be a real lacunary formal power series, where $\varepsilon_n = 0, 1$ and $\lambda_{n+1}/\lambda_n > 2$. It is known that the denominators $Q_n(X)$ of the convergents of its continued fraction expansion are polynomials with coefficients $0, \pm 1$, and that the number of nonzero terms in $Q_n(X)$ is the $n$th term of the Stern-Brocot sequence. We show that replacing the index $n$ by any 2-adic integer $\omega$ makes sense. We prove that $Q_{\omega}(X)$ is a polynomial if and only if $\omega \in {\mathbb Z}$. In all the other cases $Q_{\omega}(X)$ is an infinite formal power series, the algebraic properties of which we discuss in the special case $\lambda_n = 2^{n+1} - 1$.Comment: to appear in Acta Arithmetic

Experimental Study of Heat Pump Thermodynamic Cycles Using CO 2 Based Mixtures -Methodology and First Results

The aim of this work is to study heat pump cycles, using CO 2 based mixtures as working fluids. Since adding other chemicals to CO 2 moves the critical point and generally equilibrium lines, it is expected that lower operating pressures as well as higher global efficiencies may be reached. A simple stage pure CO 2 cycle is used as reference, with fixed external conditions. Two scenarios are considered: water is heated from 10 {\textdegree}C to 65 {\textdegree}C for Domestic Hot Water scenario and from 30 {\textdegree}C to 35 {\textdegree}C for Central Heating scenario. In both cases, water at the evaporator inlet is set at 7 {\textdegree}C to account for such outdoor temperature conditions. In order to understand the dynamic behaviour of thermodynamic cycles with mixtures, it is essential to measure the fluid circulating composition. To this end, we have developed a non intrusive method. Online optical flow cells allow the recording of infrared spectra by means of a Fourier Transform Infra Red spectrometer. A careful calibration is performed by measuring a statistically significant number of spectra for samples of known composition. Then, a statistical model is constructed to relate spectra to compositions. After calibration, compositions are obtained by recording the spectrum in few seconds, thus allowing for a dynamic analysis. This article will describe the experimental setup and the composition measurement techniques. Then a first account of results with pure CO 2 , and with the addition of propane or R-1234yf will be given

The Review of Economic Performance and Social Progress 2001: The Longest Decade: Canada in the 1990s

In this chapter, Paul Jenkins and Brian O'Reilly survey the monetary policy developments in the 1990s, focusing on links between monetary policy and the economic well-being of Canadians. The Bank of Canada economists do admit that tight monetary policy in the early 1990s hurt growth in the short-term, but they argue that such action was necessary to ratchet down entrenched inflationary expectations. Moreover, they argue that stagnation in the early part of the decade was not simply the result of monetary policy, but also reflected a weak US economy and structural problems in the Canadian economy.Monetary Policy, Inflation, Inflation Reduction, Inflation Policy, Growth, Recession, Well-being, Wellbeing, Well Being, Canada

DNA extraction from formalin-fixed tissue: new light from the Deep-Sea

DNA samples were extracted from ethanol and formalin-fixed decapod crustacean tissue using a new method based on Tetramethylsilane (TMS)-Chelex. It is shown that neither an indigestible matrix of cross-linked protein nor soluble PCR inhibitors impede PCR success when dealing with formalin-fixed material. Instead, amplification success from formalin-fixed tissue appears to depend on the presence of unmodified DNA in the extracted sample. A staining method that facilitates the targeting of samples with a high content of unmodified DNA is provided