Maximal subsemigroups of the semigroup of all mappings on an infinite set

In this paper we classify the maximal subsemigroups of the \emph{full transformation semigroup} $\Omega^\Omega$, which consists of all mappings on the infinite set $\Omega$, containing certain subgroups of the symmetric group \sym(\Omega) on $\Omega$. In 1965 Gavrilov showed that there are five maximal subsemigroups of $\Omega^\Omega$ containing \sym(\Omega) when $\Omega$ is countable and in 2005 Pinsker extended Gavrilov's result to sets of arbitrary cardinality. We classify the maximal subsemigroups of $\Omega^\Omega$ on a set $\Omega$ of arbitrary infinite cardinality containing one of the following subgroups of \sym(\Omega): the pointwise stabiliser of a non-empty finite subset of $\Omega$, the stabiliser of an ultrafilter on $\Omega$, or the stabiliser of a partition of $\Omega$ into finitely many subsets of equal cardinality. If $G$ is any of these subgroups, then we deduce a characterisation of the mappings $f,g\in \Omega^\Omega$ such that the semigroup generated by $G\cup \{f,g\}$ equals $\Omega^\Omega$.Comment: Revised according to comments by the referee, 29 pages, 11 figures, to appear in Trans. American Mathematical Societ

Parametric down-conversion from a wave-equations approach: geometry and absolute brightness

Using the approach of coupled wave equations, we consider spontaneous parametric down-conversion (SPDC) in the narrow-band regime and its relationship to classical nonlinear processes such as sum-frequency generation. We find simple expressions in terms of mode overlap integrals for the absolute pair production rate into single spatial modes, and simple relationships between the efficiencies of the classical and quantum processes. The results, obtained with Green function techniques, are not specific to any geometry or nonlinear crystal. The theory is applied to both degenerate and non-degenerate SPDC. We also find a time-domain expression for the correlation function between filtered signal and idler fields.Comment: 10 pages, no figure

Dispersion strengthening in vanadium microalloyed steels processed by simulated thin slab casting and direct charging: Part I - Processing parameters, mechanical properties and microstructure

A study simulating thin slab continuous casting followed by direct charging into an equalisation furnace has been undertaken based on six low carbon (0.06wt-%) vanadium microalloyed steels. Mechanical and impact test data showed properties were similar or better than those obtained from similar microalloyed conventional thick cast as rolled slabs. The dispersion plus dislocation strengthening was estimated to be in the range 80-250MPa.A detailed TEM/EELS analysis of the dispersion sized sub-15nm particles showed that in all the steels, they were essentially nitrides with little crystalline carbon detected. In the Steels V-Nb, V-Ti and V-Nb-Ti, mixed transition metal nitrides were present. Modelling of equilibrium precipitates in these steels, based on a modified version of ChemSage, predicted that only vanadium rich nitrides would precipitate in austenite but that the C/N ratio would increase through the two phase field and in ferrite. The experimental analytical data clearly points to the thin slab direct charging process, which has substantially higher cooling rates than conventional casting, nucleating non-equilibrium particles in ferrite which are close to stoichiometric nitrides. These did not coarsen during the final stages of processing, but retained their highly stable average size of ~7nm resulting in substantial dispersion strengthening. The results are considered in conjunction with pertinent published literature

Mifepristone Antagonization With Progesterone to Prevent Medical Abortion: A Randomized Controlled Trial.

ObjectiveTo estimate the efficacy and safety of mifepristone antagonization with high-dose oral progesterone.MethodsWe planned to enroll 40 patients in a double-blind, placebo-controlled, randomized trial. We enrolled patients at 44-63 days of gestation with ultrasound-confirmed gestational cardiac activity who were planning surgical abortion. Participants ingested mifepristone 200 mg and initiated oral progesterone 400 mg or placebo 24 hours later twice daily for 3 days, then once daily until their planned surgical abortion 14-16 days after enrollment. Follow-up visits were scheduled 3±1, 7±1, and 15±1 days after mifepristone intake with ultrasonography and blood testing for human chorionic gonadotropin and progesterone. Participants exited from the study when they had their surgical abortion or earlier for gestational cardiac activity absence, gestational sac expulsion, or medically indicated suction aspiration. We assessed the primary outcome of continued gestational cardiac activity at approximately 2 weeks (15±1 day), side effects after drug ingestion, and safety outcomes including hemorrhage and emergent treatment.ResultsWe enrolled participants from February to July 2019 and stopped enrollment after 12 patients for safety concerns. Mean gestational age was 52.5 days. Two (one per group) voluntarily discontinued 3 days after mifepristone ingestion for subjective symptoms (nausea and vomiting, bleeding). Among the remaining 10 patients (five per group), gestational cardiac activity continued for 2 weeks in four in the progesterone group and two in the placebo group. One patient in the placebo group had no gestational cardiac activity 3 days after mifepristone use. Severe hemorrhage requiring ambulance transport to hospital occurred in three patients; one received progesterone (complete expulsion, no aspiration) and two received placebo (aspiration for both, one required transfusion). We halted enrollment after the third hemorrhage. No other significant side effects were reported.ConclusionWe could not estimate the efficacy of progesterone for mifepristone antagonization due to safety concerns when mifepristone is administered without subsequent prostaglandin analogue treatment. Patients in early pregnancy who use only mifepristone may be at high risk of significant hemorrhage.Clinical trial registrationClinicalTrials.gov, NCT03774745

Gabapentin for pain management after osmotic dilator insertion and prior to dilation and evacuation: A randomized controlled trial.

ObjectiveTo evaluate if gabapentin 600 mg reduces pain after osmotic dilator placement the day before a dilation and evacuation (D&E) procedure.Study designWe conducted a double-blind, placebo-controlled, randomized (stratified by vaginal parity) trial among women undergoing osmotic dilator placement before D&E at 15-23 5/7 weeks gestation. Subjects received gabapentin 600 mg or placebo 30 min before dilator placement, with re-dosing 8 h later. We assessed pain after dilator placement using a numeric rating scale (NRS; scale 0-10) at 5 min, 2, 4, and 8 h, and at presentation for D&E. The primary outcome was median NRS pain score change from baseline to 8 h after dilator placement. Secondary outcomes included gabapentin-related side effects and analgesic use.ResultsOf 121 randomized women, we excluded three subjects (allergic reaction [placebo], randomization error, no NRS data), leaving 60 gabapentin and 58 placebo subjects. Of 110 (93%) women who provided 8-hour data, median pain score changes from baseline did not differ between gabapentin and placebo groups overall (2 vs. 2.5, p = 0.52), in vaginally nulliparous women (2 vs. 4, p = 0.10) or in parous women (2 vs. 1.5, p = 0.37). We found no statistically significant differences in median pain score change from baseline to any timepoint overall or when stratified by parity. Beginning at 2 h after dilator placement, more gabapentin than placebo users experienced dizziness (29/53[55%] vs. 11/53[21%], p = 0.001) and tiredness (34/54[63%] vs. 17/54[31%], p = 0.002). The proportion of women using narcotics did not differ between gabapentin (35/60[58%]) or placebo (40/58[69%]) users (p = 0.26).ConclusionsGabapentin does not reduce pain with overnight osmotic dilator placement prior to D&E and causes drug-related side effects.Implications statementWomen experience pain, mostly mild to moderate, with overnight cervical dilator placement at 15-23 5/7 weeks gestation. About 2/3 of women will use a limited quantity of narcotics if provided. Gabapentin does not decrease the pain with or following dilator placement and does not decrease narcotic use

Compact Brillouin devices through hybrid integration on Silicon

A range of unique capabilities in optical and microwave signal processing have been demonstrated using stimulated Brillouin scattering. The desire to harness Brillouin scattering in mass manufacturable integrated circuits has led to a focus on silicon-based material platforms. Remarkable progress in silicon-based Brillouin waveguides has been made, but results have been hindered by nonlinear losses present at telecommunications wavelengths. Here, we report a new approach to surpass this issue through the integration of a high Brillouin gain material, As2S3, onto a silicon chip. We fabricated a compact spiral device, within a silicon circuit, achieving an order of magnitude improvement in Brillouin amplification. To establish the flexibility of this approach, we fabricated a ring resonator with free spectral range precisely matched to the Brillouin shift, enabling the first demonstration of Brillouin lasing in a silicon integrated circuit. Combining active photonic components with the SBS devices shown here will enable the creation of compact, mass manufacturable optical circuits with enhanced functionality

Optimisation of ITER Nb3Sn CICCs for coupling loss, transverse electromagnetic load and axial thermal contraction

The ITER cable-in-conduit conductors (CICCs) are built up from sub-cable bundles, wound in different stages, which are twisted to counter coupling loss caused by time-changing external magnet fields. The selection of the twist pitch lengths has major implications for the performance of the cable in the case of strain sensitive superconductors, i.e. Nb3Sn, as the electromagnetic and thermal contraction loads are large but also for the heat load from the AC coupling loss. Reduction of the transverse load and warm-up cool-down degradation can be reached by applying longer twist pitches in a particular sequence for the sub-stages, offering a large cable transverse stiffness, adequate axial flexibility and maximum allowed lateral strand support. Analysis of short sample (TF conductor) data reveals that increasing the twist pitch can lead to a gain of the effective axial compressive strain of more than 0.3 % with practically no degradation from bending. For reduction of the coupling loss, specific choices of the cabling twist sequence are needed with the aim to minimize the area of linked strands and bundles that are coupled and form loops with the applied changing magnetic field, instead of simply avoiding longer pitches. In addition we recommend increasing the wrap coverage of the CS conductor from 50 % to at least 70 %. The models predict significant improvement against strain sensitivity and substantial decrease of the AC coupling loss in Nb3Sn CICCs, but also for NbTi CICCs minimization of the coupling loss can be achieved. Although the success of long pitches to transverse load degradation was already demonstrated, the prediction of the combination with low coupling loss needs to be validated by a short sample test.Comment: to be published in Supercond Sci Techno

Quasiparticle-like peaks, kinks, and electron-phonon coupling at the (π\pi,0) regions in the CMR oxide La2−2x_{2-2x}Sr1+2x_{1+2x}Mn2_{2}O7_{7}

Using Angle-Resolved Photoemission (ARPES), we present the first observation of sharp quasiparticle-like peaks in a CMR manganite. We focus on the ($\pi$,0) regions of k-space and study their electronic scattering rates and dispersion kinks, uncovering the critical energy scales, momentum scales, and strengths of the interactions that renormalize the electrons. To identify these bosons we measured phonon dispersions in the energy range of the kink by inelastic neutron scattering (INS), finding a good match in both energy and momentum to the oxygen bond-stretching phonons

Evolution of constrained layer damping using a cellular automaton algorithm

Constrained layer damping (CLD) is a highly effective passive vibration control strategy if optimized adequately. Factors controlling CLD performance are well documented for the flexural modes of beams but not for more complicated mode shapes or structures. The current paper introduces an approach that is suitable for locating CLD on any type of structure. It follows the cellular automaton (CA) principle and relies on the use of finite element models to describe the vibration properties of the structure. The ability of the algorithm to reach the best solution is demonstrated by applying it to the bending and torsion modes of a plate. Configurations that give the most weight-efficient coverage for each type of mode are first obtained by adapting the existing 'optimum length' principle used for treated beams. Next, a CA algorithm is developed, which grows CLD patches one at a time on the surface of the plate according to a simple set of rules. The effectiveness of the algorithm is then assessed by comparing the generated configurations with the known optimum ones