Approximating the maximum ergodic average via periodic orbits

Let sigma: Sigma(A) -> Sigma(A) be a subshift of finite type, let M-sigma be the set of all sigma-invariant Borel probability measures on Sigma(A), and let f : Sigma(A) -> R be a Holder continuous observable. There exists at least one or-invariant measure A which maximizes integral f d mu. The following question was asked by B. R. Hunt, E. Ott and G. Yuan: how quickly can the maximum of the integrals integral f d mu be approximated by averages along periodic orbits of period less than p? We give an example of a Holder observable f for which this rate of approximation is slower than stretched-exponential in p

Characterization of the complications associated with plasma exchange for thrombotic thrombocytopaenic purpura and related thrombotic microangiopathic anaemias: a single institution experience.

Plasma exchange (PEX) is a life-saving therapeutic procedure in patients with thrombotic thrombocytopaenic purpura (TTP) and other thrombotic microangiopathic anaemias (TMAs). However, it may be associated with significant complications, exacerbating the morbidity and mortality in this patient group

Biomass estimates of Pacific herring, Clupea pallasi, in California from the 1991-92 spawning-ground surveys

The spawning biomass of Pacific herring, Clupea pallasi, estimated from spawning-ground surveys in San Francisco Bay declined to 41,000 tons this season. This was the second consecutive year that the San Francisco Bay herring population estimate has declined. In Tomales Bay, the 1991-92 season spawning biomass estimate, including the catch of 24 tons from Bodega Bay, was 1,238 tons. This was the third consecutive season that the Tomales-Bodega area herring population has increased. The 1991-92 Humboldt Bay herring spawning biomass estimate of 225 tons, was nearly half of last season's estimate of 400 tons. December and January were the peak months of spawning activity in all areas surveyed. In San Francisco Bay, the first major spawn since the 1981-82 season occurred in the Sausalito area, and the Oakland-Alameda area accounted for 50% of all spawning activity. A total of 3.5 million m2 of eelgrass, Zostera marina, was measured in Tomales Bay this season. The eelgrass density declined in most beds this season. (46p.

SM 601 Supervised Ministry

• This SUPERVISED MINISTRY HANDBOOK is your working guide and textbook for two semesters of field education. It serves for SM 601, SM 602, and SM 603. Therefore, it is recommended that you keep it in a separate three-ring binder, since it is not a book-bound. STUDENT PASTORS who are enrolled in SM 601C will not use this handbook but will use the handbook titled, STUDENT PASTOR HANDBOOK. • An addendum of this handbook is the EXTENDED CASE GUIDELINES LOCATED AT THE BACK OF THE STUDENT HANDBOOK . The self- referent case study based on our EXTENDED CASE GUIDELINES format is the basic learning instrument for courses in supervised ministries. This addendum provides you with the model format and instruction for good case writing. • SM 601, 602 The text Lay Leadership for Ministry Training is required for Courses SM 601 and 602 (not Student Pastors). This text is needed for the Pastor and Local Church Lay Committee members of the local church where you serve. Request free copies via e-mail from the S.Min. office in Wilmore via e-mail to Claire Williams or you can download the material from the Intranet. • The text Field Supervisors Handbook: Local Church should be distributed to your supervising pastor to familiarize him/her with the role of supervising and mentoring pastor. (Student Pastors are exempt from having a Field Supervisor.) Copies are available from the S.Min. office or may be downloaded by clicking on “Intranet, Students, Class Syllabi, 2003-2004, Wilmore, Fall 2003, Smin 601, 602 FS Handbook.” • SM 603 The text Field Supervisors Handbook: Institutional should be distributed to your supervisor to familiarize him/her with the role of supervising and mentoring.https://place.asburyseminary.edu/syllabi/2884/thumbnail.jp

Towards the synthesis of fluoro-thromboxane A₂ analogues

Firstly, the biosynthesis and physiological role of thromboxanes and the potential for a thromboxane A₂ antagonist in cardiovascular therapy are discussed. Secondly, the importance of fluorine in drug design is outlined and the syntheses of a series of thromboxane A₂ structural analogues are reviewed. This is concluded by proposing how fluorine substitution should allow synthesis of a stable structural analogue of thromboxane A₂ which may have antagonistic properties. Finally, the synthetic conversion of a carbohydrate precursor, levoglucosan, into a suitable precursor to 10-α-flurothromboxane A₂ is discussed in detail

The history and evolution of young and distant radio sources

We study two classes of object to gain a better understanding of the evolution of Active Galactic Nuclei (AGN): Infrared-Faint Radio Sources (IFRSs) and Gigahertz Peaked Spectrum (GPS) / Compact Steep Spectrum (CSS) sources. IFRSs are a recently discovered rare class of object, which were found to be strong in the radio but undetectable in extremely sensitive infrared observations from the Spitzer Space Telescope, even in stacked images with σ 3. Therefore, IFRSs may significantly increase the number of known high-redshift galaxies. However, their non-detections in the optical and infrared prevented confirmation of their nature. Previous studies of IFRSs focused on very sensitive observations of a few small regions of the sky, and the largest sample consisted of 55 IFRSs. However, we follow the strategy of combining radio data with IR and optical data for a large region of the sky. Using these data, we discover a population of >1300 brighter IFRSs which are, for the first time, reliably detected in the infrared and optical. We present the first spectroscopic redshifts of IFRSs and show that the brightest IFRSs are at z > 2. Furthermore, we rule out that IFRSs are Star Forming Galaxies, hotspots, lobes or misidentifications. We find the first X-ray counterparts of IFRSs, and increase the number of known polarised IFRSs five-fold. We present an analysis of their radio spectra and show that IFRSs consist of GPS, CSS and ultra-steep-spectrum sources. We follow up >50 of these using VLBI observations, and confirm the AGN status of IFRSs. We conclude that IFRSs represent a new population of high-redshift radio galaxies, which, for the faintest IFRSs, may have redshifts as high as z = 7 and consist of a few hundred thousand objects across the μJy sky. GPS and CSS sources are compact radio sources with a convex radio spectrum. They are widely thought to represent young and evolving radio galaxies that have recently launched their jets. However, good evidence exists in individual cases that GPS and CSS sources are one of the following: 1) frustrated by interactions with dense gas and dust in their environment; 2) prematurely dying radio sources; 3) recurrent radio galaxies. Their convex spectrum is generally thought to be caused by Synchrotron Self Absorption (SSA), an internal process in which the same population of electrons is responsible for the synchrotron emission and self-absorption. However, recent studies have shown that the convex spectrum may be caused by Free-Free Absorption (FFA), an external process in which an inhomogeneous screen absorbs the synchrotron emission. The majority of GPS and CSS samples consist of Jy-level and therefore, high-luminosity sources. VLBI images show that GPS and CSS sources typically have double-lobed, edge-brightened morphologies on mas scales, appearing as scaled down versions of Fanaroff-Riley Class II (FR II) galaxies. Recently, two low-luminosity GPS sources were found to have jet-brightened morphologies, which appeared as scaled down versions of Fanaroff-Riley Class I (FR I) galaxies. From this, it was proposed that there exists a morphology-luminosity break analogous to the FR I/II break and that low-luminosity GPS and CSS sources are the compact counterparts of FR I galaxies. However, this hypothesis remains unconfirmed, since very few samples of low-luminosity GPS and CSS sources exist. We have observed the faintest population of GPS and CSS sources to date, consisting ⇠150 sources, many of which are low-luminosity. We use high-resolution radio observations to determine their linear size, resolve their jets and observe their small-scale morphology. We combine these data with a large number of radio observations at other frequencies to model their radio spectra using SSA and FFA models. In particular, we use very low frequency observations that have only recently become available to constrain their spectral peaks. We follow up eight of the most compact sources with VLBI and detect six of them. We find that our GPS and CSS sources are well modelled by an inhomogeneous FFA model (hereafter ‘FFA’). Furthermore, we find a number of very compact GPS and CSS sources that are inconsistent with SSA theory. We show that a single inhomogeneous SSA model fits poorly to the majority of radio spectra, predicting far too steep a slope below the peak. We resolve all of the sources with VLBI and derive their kinematic ages based on the jet sizes. Even when assuming more complex SSA models, we derive magnetic field strengths several orders of magnitude too high for one source. A few sources are well modelled by an FFA model in which the inhomogeneous absorption is dominated by clouds of high density, consistent with the frustration hypothesis. However, the majority of sources are well modelled by FFA models with low-density clouds. These models suggest that an inhomogeneous and clumpy medium surrounds the sources, implying they may undergo recurrent activity. Furthermore, the spectral model of one CSS source suggests it is a prematurely dying radio galaxy whose jets have been switched off for ∽600 years. However, we find no evidence of restarted radio galaxies within our high resolution observations. The kinematic and spectral ages we derive are consistent with the hypothesis that GPS and CSS sources are young and evolving. We find tentative evidence that at mJy-levels, the fraction of CSS sources is smaller than the fraction estimated for Jy-level sources. This may be accounted for as a selection effect or if a smaller fraction of mJy-level GPS sources evolve into CSS sources as compared to the Jy-level GPS sources. We find a few GPS sources with low luminosities, which we will follow up with VLBI to test whether they are the compact counterparts of FR I galaxies. We conclude that, despite being historically favoured, single inhomogeneous SSA is not the dominant form of absorption amongst a large fraction of GPS and CSS sources. We find that FFA provides a good model for the majority of the spectra with observable turnovers, suggesting an inhomogeneous and clumpy ambient medium. Furthermore, we conclude that the majority of our GPS and CSS sources are young and evolving and may undergo recurrent activity over small time scales. We conclude that a very small fraction of GPS and CSS sources consists of frustrated, dying or restarted radio galaxies