System for generating timing and control signals

A system capable of generating every possible data frame subperiod and delayed subperiod of a data frame of length of M clock pulse intervals (CPIs) comprised of parallel modulo-m sub i counters is presented. Each m sub i is a prime power divisor of M and a cascade of alpha sub i identical modulo-p sub i counters. The modulo-p sub i counters are feedback shift registers which cycle through p sub i distinct states. Every possible nontrivial data frame subperiod and delayed subperiod is derived and a specific CPI in the data frame is detected. The number of clock pulses required to bring every modulo-p sub i counter to a respective designated state or count is determined by the Chinese remainder theorem. This corresponds to the solution of simultaneous congruences over relatively prime moduli

On the L2−L^2-Poincar\'e duality for incomplete riemannian manifolds: a general construction with applications

Let $(M,g)$ be an open, oriented and incomplete riemannian manifold of dimension $m$. Under some general conditions we show that it is possible to build a Hilbert complex $(L^2\Omega^i(M,g),d_{\mathfrak{M},i})$ such that its cohomology groups, labeled with $H^i_{2,\mathfrak{M}}(M,g)$, satisfy the following properties: \begin{itemize} \item H^i_{2,\mathfrak{M}}(M,g)=ker(d_{max,i})/\im(d_{min,i}) \item $H^i_{2,\mathfrak{M}}(M,g)\cong H^{m-i}_{2,\mathfrak{M}}(M,g)$ (Poincar\'e duality holds) \end{itemize} Finally in the rest of the paper we study some properties of this complex with particular attention to the sufficient conditions which make it a Fredholm complex.Comment: Final version. To appear on Journal of Topology and Analysi

On the volume measure of non-smooth spaces with Ricci curvature bounded below

We prove that, given an $RCD^{*}(K,N)$-space $(X,d,m)$, then it is possible to $m$-essentially cover $X$ by measurable subsets $(R_{i})_{i\in \mathbb{N}}$ with the following property: for each $i$ there exists $k_{i} \in \mathbb{N}\cap [1,N]$ such that $m\llcorner R_{i}$ is absolutely continuous with respect to the $k_{i}$-dimensional Hausdorff measure. We also show that a Lipschitz differentiability space which is bi-Lipschitz embeddable into a euclidean space is rectifiable as a metric measure space, and we conclude with an application to Alexandrov spaces.Comment: Final version to appear in the Annali della Scuola Normale Superiore Classe di Scienz

Universal Magnetic-Field-Driven Metal-Insulator-Metal Transformations in Graphite and Bismuth

Applied magnetic field induces metal - insulator and re-entrant insulator-metal transitions in both graphite and rhombohedral bismuth. The corresponding transition boundaries plotted on the magnetic field - temperature (B - T) plane nearly coincide for these semimetals and can be best described by power laws T ~ (B - B_c)^k, where B_c is a critical field at T = 0 and k = 0.45 +/- 0.05. We show that insulator-metal-insulator (I-M-I) transformations take place in the Landau level quantization regime and illustrate how the IMT in quasi-3D graphite transforms into a cascade of I-M-I transitions, related to the quantum Hall effect in quasi-2D graphite samples. We discuss the possible coupling of superconducting and excitonic correlations with the observed phenomena, as well as the signatures of quantum phase transitions associated with the M-I and I-M transformations.Comment: 23 pages including 14 figure

The Schizophrenic Spectrum of LSR 1610-0040: a Peculiar M Dwarf/Subdwarf

We present a moderate resolution (R=2000), 0.8-4.1 micron spectrum of LSR 1610-0040, a high proper motion star classified as an early-type L subdwarf by Lepine and collaborators based on its red-optical spectrum. The near-infrared spectrum of LSR 1610-0040 does not fit into the (tentative) M/L subdwarf sequence but rather exhibits a mix of characteristics found in the spectra of both M dwarfs and M subdwarfs. In particular, the near-infrared spectrum exhibits a Na I doublet and CO overtone bandheads in the K band, and Al I and K I lines and an FeH bandhead in the H band, all of which have strengths more typical of field M dwarfs. Furthermore the spectrum of Gl 406 (M6 V) provides a reasonably good match to the 0.6-4.1 micron spectral energy distribution of LSR 1610. Nevertheless the near-infrared spectrum of LSR 1610 also exhibits features common to the spectra of M subdwarfs including a strong Ti I multiplet centered at ~0.97 microns, a weak VO band at ~1.06 microns, and possible collision-induced H_2 absorption in the H and K bands. We discuss a number of possible explanations for the appearance of the red-optical and near-infrared spectrum of LSR 1610-0040. Although we are unable to definitively classify LSR 1610-0040, the preponderance of evidence suggests that it is a mildly metal-poor M dwarf. Finally, we tentatively identify a new band of TiO at ~0.93 microns in the spectra of M dwarfs.Comment: Accepted for publication in the Astronomical Journa

Sharp weak-type inequalities for differentially subordinated martingales

Let $M,N$ be real-valued martingales such that $N$ is differentially subordinate to $M$. The paper contains the proofs of the following weak-type inequalities: (i) If $M\geq0$ and $0<p\leq1$, then $$\Vert N\Vert_{p,\infty}\leq2\Vert M\Vert_p$$ and the constant is the best possible. (ii) If $M\geq0$ and $p\geq2$, then $$\Vert N\Vert_{p,\infty}\leq\frac{p}{2}(p-1)^{-1/p}\Vert M\Vert_p$$ and the constant is the best possible. (iii) If $1\leq p\leq2$ and $M$ and $N$ are orthogonal, then $$\Vert N\Vert_{p,\infty}\leq K_p\Vert M\Vert_p,$$ where $$K_p^p=\frac{1}{\Gamma(p+1)}\cdot\biggl(\frac{\pi}{2}\biggr)^{p-1}\cdot\frac{1+1/3^2+1/5^2+1/7^2+...}{1-1/3^{p+1}+1/5^ {p+1}-1/7^{p+1}+...}.$$ The constant is the best possible. We also provide related estimates for harmonic functions on Euclidean domains.Comment: Published in at http://dx.doi.org/10.3150/08-BEJ166 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Open issues in stellar modelling

An important goal of helio- and asteroseismology is to improve the modelling of stellar evolution. Here I provide a brief discussion of some of the uncertain issues in stellar modelling, of possible relevance to asteroseismic inferences.Comment: Proc. HELAS Workshop on `New insights into the Sun', eds M. S. Cunha and M. J. Thompson (invited talk