The Omega Counter, a Frequency Counter Based on the Linear Regression

This article introduces the {\Omega} counter, a frequency counter -- or a frequency-to-digital converter, in a different jargon -- based on the Linear Regression (LR) algorithm on time stamps. We discuss the noise of the electronics. We derive the statistical properties of the {\Omega} counter on rigorous mathematical basis, including the weighted measure and the frequency response. We describe an implementation based on a SoC, under test in our laboratory, and we compare the {\Omega} counter to the traditional {\Pi} and {\Lambda} counters. The LR exhibits optimum rejection of white phase noise, superior to that of the {\Pi} and {\Lambda} counters. White noise is the major practical problem of wideband digital electronics, both in the instrument internal circuits and in the fast processes which we may want to measure. The {\Omega} counter finds a natural application in the measurement of the Parabolic Variance, described in the companion article arXiv:1506.00687 [physics.data-an].Comment: 8 pages, 6 figure, 2 table

The Parabolic variance (PVAR), a wavelet variance based on least-square fit

This article introduces the Parabolic Variance (PVAR), a wavelet variance similar to the Allan variance, based on the Linear Regression (LR) of phase data. The companion article arXiv:1506.05009 [physics.ins-det] details the $\Omega$ frequency counter, which implements the LR estimate. The PVAR combines the advantages of AVAR and MVAR. PVAR is good for long-term analysis because the wavelet spans over $2 \tau$, the same of the AVAR wavelet; and good for short-term analysis because the response to white and flicker PM is $1/\tau^3$ and $1/\tau^2$, same as the MVAR. After setting the theoretical framework, we study the degrees of freedom and the confidence interval for the most common noise types. Then, we focus on the detection of a weak noise process at the transition - or corner - where a faster process rolls off. This new perspective raises the question of which variance detects the weak process with the shortest data record. Our simulations show that PVAR is a fortunate tradeoff. PVAR is superior to MVAR in all cases, exhibits the best ability to divide between fast noise phenomena (up to flicker FM), and is almost as good as AVAR for the detection of random walk and drift

Weak and strong fillability of higher dimensional contact manifolds

For contact manifolds in dimension three, the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent. We extend these facts to higher dimensions: in particular, we define a natural generalization of weak fillings and prove that it is indeed weaker (at least in dimension five),while also being obstructed by all known manifestations of "overtwistedness". We also find the first examples of contact manifolds in all dimensions that are not symplectically fillable but also cannot be called overtwisted in any reasonable sense. These depend on a higher-dimensional analogue of Giroux torsion, which we define via the existence in all dimensions of exact symplectic manifolds with disconnected contact boundary.Comment: 68 pages, 5 figures. v2: Some attributions clarified, and other minor edits. v3: exposition improved using referee's comments. Published by Invent. Mat

Maser Oscillation in a Whispering-Gallery-Mode Microwave Resonator

We report the first observation of above-threshold maser oscillation in a whispering-gallery(WG)-mode resonator, whose quasi-transverse-magnetic, 17th azimuthal-order WG mode, at a frequency of approx. 12.038 GHz, with a loaded Q of several hundred million, is supported on a cylinder of mono-crystalline sapphire. An electron spin resonance (ESR) associated with Fe3+ ions, that are substitutively included within the sapphire at a concentration of a few parts per billion, coincides in frequency with that of the (considerably narrower) WG mode. By applying a c.w. `pump' to the resonator at a frequency of approx. 31.34 GHz, with no applied d.c. magnetic field, the WG (`signal') mode is energized through a three-level maser scheme. Preliminary measurements demonstrate a frequency stability (Allan deviation) of a few times 1e-14 for sampling intervals up to 100 s.Comment: REVTeX v.4, 3 pages, with a separate .bbl file and 3 .eps figure

Highly efficient synthesis of the tricyclic core of Taxol by cascade metathesis

An efficient enantioselective synthesis of the ABC tricyclic core of the anticancer drug Taxol is reported. The key step of this synthesis is a cascade metathesis reaction, which leads in one operation to the required tricycle if appropriate fine-tuning of the dienyne precursor is performed

Controlling the Frequency-Temperature Sensitivity of a Cryogenic Sapphire Maser Frequency Standard by Manipulating Fe3+ Spins in the Sapphire Lattice

To create a stable signal from a cryogenic sapphire maser frequency standard, the frequency-temperature dependence of the supporting Whispering Gallery mode must be annulled. We report the ability to control this dependence by manipulating the paramagnetic susceptibility of Fe3+ ions in the sapphire lattice. We show that the maser signal depends on other Whispering Gallery modes tuned to the pump signal near 31 GHz, and the annulment point can be controlled to exist between 5 to 10 K depending on the Fe3+ ion concentration and the frequency of the pump. This level of control has not been achieved previously, and will allow improvements in the stability of such devices.Comment: 17 pages, 10 figure

Ultra-Low Noise Microwave Extraction from Fiber-Based Optical Frequency Comb

In this letter, we report on all-optical fiber approach to the generation of ultra-low noise microwave signals. We make use of two erbium fiber mode-locked lasers phase locked to a common ultra-stable laser source to generate an 11.55 GHz signal with an unprecedented relative phase noise of -111 dBc/Hz at 1 Hz from the carrier.The residual frequency instability of the microwave signals derived from the two optical frequency combs is below 2.3 10^(-16) at 1s and about 4 10^(-19) at 6.5 10^(4)s (in 5 Hz bandwidth, three days continuous operation).Comment: 12 pages, 3 figure

Nuclear break-up of 11Be

The break-up of 11Be was studied at 41AMeV using a secondary beam of 11Be from the GANIL facility on a 48Ti target by measuring correlations between the 10Be core, the emitted neutrons and gamma rays. The nuclear break-up leading to the emission of a neutron at large angle in the laboratory frame is identified with the towing mode through its characteristic n-fragment correlation. The experimental spectra are compared with a model where the time dependent Schrodinger equation (TDSE) is solved for the neutron initially in the 11 Be. A good agreement is found between experiment and theory for the shapes of neutron experimental energies and angular distributions. The spectroscopic factor of the 2s orbital is tentatively extracted to be 0.46+-0.15. The neutron emission from the 1p and 1d orbitals is also studied

Distribution and lability of land-derived organic matter in the surface sediments of the Rhône prodelta and the adjacent shelf (Mediterranean Sea, France): a multi proxy study

The Gulf of Lions is a river-dominated ocean margin that receives high loads of nutrients and particulate matter from the Rhône River but most particulate materials settle rapidly on the nearshore seafloor. One question is raised on the fate of these large quantities of organic carbon delivered by the river to the coastal marine environment. Surface sediments (0–0.5 cm) were collected in the Rhône prodelta and its adjacent shelf during a period of low river discharge (April 2007, 16 stations). The sources, distribution and lability of sedimentary organic matter were examined using bulk (organic carbon, total nitrogen, stable carbon isotope ratios, and grain size) and molecular-level (pigments, amino acids, fatty acids, and δ<sup>13</sup>C of individual fatty acids) analyses. Our results confirmed previous observations of a southwestward Rhodanian imprint in the nearshore sediments, with 97% of terrigenous inputs of organic matter near the river mouth. Isotopic values of bulk organic carbon, as well as fatty acid biomarkers and compound-specific δ<sup>13</sup>C signatures of most fatty acids clearly indicate that the Rhône inputs consist of a mixture of organic matter (OM) from different origins with a strong contribution from terrestrial sources (soil and plant debris), and a smaller input from freshwater microalgae, mostly diatoms. The influence of the Rhône River was prominent within the first ten kilometers, but may still be observed on the outer shelf (~21 km) as indicated by the occurrence of long chain fatty acids, which are derived from vascular plants, and their δ<sup>13</sup>C signatures. In the proximal prodelta, bacteria-specific fatty acids were abundant (1.65 mg g<sup>−1</sup> OC at the mouth site) and were relatively depleted in δ<sup>13</sup>C confirming that bacteria mostly utilize land-derived OM. In the shelf area, the inputs of marine OM and its predominant utilization by the bacteria was confirmed, but the coupling between the pelagic and the benthic compartments appeared limited at this period of the year. <br><br> Overall, degradation indexes based on amino acids (Dauwe's degradation index) and pigments (ratio of intact chlorophyll-<I>a</I> to the sum of chlorophyll-<I>a</I> + phaeopigment-<I>a</I>), as well as isotopic enrichment of source-specific fatty acids reveal an offshore gradient of OM decay reflecting the rapid deposition of the terrestrial material in the prodelta, the low mixing with OM deriving from marine sources and the efficient degradation of the OM. The OM delivered by the Rhône is relatively labile based on the intermediary value of Dauwe's degradation index, the high proportion of bio-available nitrogen and the occurrence of polyunsaturated fatty acids. Deltaic sediments off the Rhône River should thus be of sufficiently high nutritional quality to sustain dense macrofaunal communities