Rotating flow past an elliptic-cylindrical bump of large aspect ratio

Summary Very slow flow of a rapidly rotating fluid past a right cylindrical obstacle of heightd on one of two co-rotating parallel planes, separated by a distanceh, is studied. The elliptic boundaryvalue problem for the geostrophic flow is formulated quite generally, and solutions are given for an infinitely-long ridge and an elliptic cylinder. A modified Ekman number,E _*v/d ², where is the inverse aspect ratio of the cylinder, characterizes the latter solution. ForE _*<1, the fluid flows around a stagnant Taylor column over the elliptic cylinder; forE _*1, the fluid flows over the cylinder as though it were an infinitely-long ridge;E _*=O(1) shows part of the fluid flowing over, and part around, the cylinder. The drag increases from orderE ^–1/4 to orderE ^–1 asE _* increases from small to large values.

---

Zusammenfassung In dieser Arbeit wird die sehr langsame Strömung in einem rasch rotierenden Fluid untersucht um einen zylindrischen Körper, dessen Höhed die viel kleiner ist als die Distanzh der zwei unendlich ausgedehnten mitrotierenden parallelen Platten, welche das Fluid begrenzen; der Körper sitzt auf der unteren Platte. Eine allgemeine Formulierung des elliptischen Randwertproblems wurde für die geostrophische Strömung angegeben. Lösungen wurden für ein unendlich langes Wehr und einen elliptischen Zylinder gefunden. Eine modifizierte Ekman-Zahl,E _*=v/d ² E, in welcher das reziproke Verhältnis von Länge zu Durchmesser darstellt, charakterisiert die Lösung für den elliptischen Zylinder. WennE _*1, umgeht die Flüssigkeit die stagnierende Taylorsäule, die auf dem elliptischen Zylinder ruht; wennE _*1, geht die Flüssigkeit über den Zylinder, als ob er ein unendlich langes Wehr wäre; wennE _*=0(1), geht ein Teil der Flüssigkeit über den Zylinder und ein anderer um ihn herum. Der Reibungswiderstand erhöht sich von 0(E ^–1/4) zu 0(E ^–1), wennE _* von kleinen zu grossen Werten ansteigt.

     

Synthesis and characterization of Pd(II) complexes of 2‐ and 3‐thiophenecarbaldehyde immobilized on silica obtained from sepiolite

Silica obtained by acid treatment of sepiolite was used as a support for catalysts consisting of palladium complexes of 2‐ and 3‐thiophenecarbaldehyde. The support and the catalysts were characterized by X‐ray diffraction, and solid‐state ²⁹Si and ¹³C nuclear magnetic resonance spectroscopies. The supported palladium catalysts were used in the Suzuki reaction of bromobenzene with phenylboronic acid. Copyright © 2013 John Wiley & Sons, Ltd.     

Structural Characterization of the Condensation Polymer of Dipyridine Manganese II Dichloride with 1,3-Di-4-piperidy I propane

The synthesis of polymers derived from the condensation of dipyridine manganese II dichloride with 1,3-di-4-piperidylpro-pane is described. Structural analysis of the polyamines is detailed utilizing results based on infrared, thermal, elemental and solution analyses.     

Unexpected reactivity of pyridinium salts toward alkynyl Fischer complexes to produce oxo‐heterocycles

The unprecedented reaction of ketone‐containing aromatic pyridinium salts 3a ‐ e and alkynyl Fischer complexes 1a ‐ f proceeds via a mild domino process to provide 4,6‐disubstituted pyran‐2‐ones 5a ‐ k and 2,3,5‐trisubstituted furans 6a ‐ h (45‐97%). According of the results of isotopic labeling experiments, a mechanism involving an initial Michael addition appears to be the key step, obtaining a mesomeric structure responsible for the formation of both products.     

Montecrinanes A–C: Triterpenes with an Unprecedented Rearranged Tetracyclic Skeleton from Celastrus vulcanicola. Insights into Triterpenoid Biosynthesis Based on DFT Calculations

Three new triterpenoids with an unprecedented 6/6/6/6‐fused tetracyclic carbon skeleton, montecrinanes A–C ( 1 – 3 ), were isolated from the root bark of Celastrus vulcanicola, along with known D:B‐friedobaccharanes ( 4 – 6 ), and lupane‐type triterpenes ( 7 – 12 ). The stereostructures of the new metabolites were elucidated based on spectroscopic (1D and 2D NMR) and spectrometric (HR‐EIMS and HR‐ESIMS) techniques. Their absolute configurations were determined by both NMR spectroscopy, with (R)‐(?)‐α‐methoxyphenylacetic acid as a chiral derivatizing agent, and biogenetic considerations. Biogenetic pathways for montecrinane and D:B‐friedobaccharane skeletons were proposed and studied by DFT methods. The theoretical results support the energetic feasibility of the putative biogenetic pathways, in which the 1,2‐methyl shift from the secondary baccharenyl cation represents a novel and key reaction step for a new montecrinane skeleton.     

Pedagogical challenges in making mathematics relevant for Indigenous Australians

After the invasion and occupation of their land by Europeans, Indigenous Australians were expected to benefit from a Western education system based on that of the dominant Europeans. Gradually educators realized that Aboriginal children learn differently and that Indigenous culture and pedagogy has validity and strength. Of course, educators also need to be acutely aware of the diversity of Indigenous cultures in Australia and that there is not a monolithic sense of Aboriginal identity or Aboriginal pedagogy. Dispossession and alienation, poor health and few employment opportunities must also affect educational interest, attendance, application and performance. In this paper the characteristics of Indigenous learners are examined and pedagogical strategies to assist in both students' learning and teachers' delivery are explored. The message conveyed in this paper has particular relevance for teaching mathematics to Aboriginal learners. It is also of considerable value in teaching mathematics to nonAboriginal students, in Australia and elsewhere.     

Wide binaries as a critical test of classical gravity

Modified gravity scenarios where a change of regime appears at acceleration scales a<a ₀ have been proposed. Since for 1M _⊙ systems the acceleration drops below a ₀ at scales of around 7000 AU, a statistical survey of wide binaries with relative velocities and separations reaching 10⁴ AU and beyond should prove useful to the above debate. We apply the proposed test to the best currently available data. Results show a constant upper limit to the relative velocities in wide binaries which is independent of separation for over three orders of magnitude, in analogy with galactic flat rotation curves in the same a<a ₀ acceleration regime. Our results are suggestive of a breakdown of Kepler’s third law beyond a≈a ₀ scales, in accordance with generic predictions of modified gravity theories designed not to require any dark matter at galactic scales and beyond.     

One-Step Generalized Estimating Equations With Large Cluster Sizes

Medical studies increasingly involve a large sample of independent clusters, where the cluster sizes are also large. Our motivating example from the 2010 Nationwide Inpatient Sample (NIS) has 8,001,068 patients and 1049 clusters, with average cluster size of 7627. Consistent parameter estimates can be obtained naively assuming independence, which are inefficient when the intra-cluster correlation (ICC) is high. Efficient generalized estimating equations (GEE) incorporate the ICC and sum all pairs of observations within a cluster when estimating the ICC. For the 2010 NIS, there are 92.6 billion pairs of observations, making summation of pairs computationally prohibitive. We propose a one-step GEE estimator that (1) matches the asymptotic efficiency of the fully iterated GEE; (2) uses a simpler formula to estimate the ICC that avoids summing over all pairs; and (3) completely avoids matrix multiplications and inversions. These three features make the proposed estimator much less computationally intensive, especially with large cluster sizes. A unique contribution of this article is that it expresses the GEE estimating equations incorporating the ICC as a simple sum of vectors and scalars.     

Optimisation of sensor positions in random linear arrays based on statistical relations between geometry and performance

Due to the widespread use of acoustic arrays, optimisation techniques for array design, focused on improving array performance, have been widely published. This paper exploits the statistical relation between different measures of sidelobe levels and the spacing of elements in random linear arrays made up of a small number of sensors. This paper defines the methodology to obtain maximum probability functions, associating array geometry and performance. These maximum probability functions allow a pre-selection of those array geometries that are more likely to be associated to specified sidelobe level values. This pre-selection results in a significantly reduced computational burden.     

Simplified model for mass diffusivity estimation based on dynamic pendant drop volume analysis

We present a simplified correlation for calculating the dissolved gas moles in a pendant drop during the diffusion time, for several drop shapes. After this correlation is determined, the Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) dynamic pendant drop volume analysis (DPDVA) method for calculation of mass diffusivity from the pendant drop volume variation against time can be used. We solved the differential equation in cylindrical coordinates for the mass transfer model of the gas diffusion into the liquid inside the pendant drop, using a different characteristic length (L_C), instead of the outer radius of the syringe needle (r_n) used in Yang and Gu (Ind Eng Chem Res 44:4474–4483, 2005) for defining the dimensionless variables. L_C is the relationship between the pendant drop volume and its mass transfer surface area at the initial conditions. The generalized correlation saves time, simplifies the method application and the deviations in the diffusion coefficient calculation respect to the complete Yang and Gu model are below 6%.