Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. I. The One-Dimensional Case

We give an algorithm for testing the extremality of minimal valid functions for Gomory and Johnson's infinite group problem that are piecewise linear (possibly discontinuous) with rational breakpoints. This is the first set of necessary and sufficient conditions that can be tested algorithmically for deciding extremality in this important class of minimal valid functions. We also present an extreme function that is a piecewise linear function with some irrational breakpoints, whose extremality follows from a new principle.Comment: 38 pages, 10 figure

The family "Thelypteridaceae" in Europe

Thelypteridaceae are mainly tropical ferns, the total number of species is about one thousand. The five European species represent five different groups, each of which has recently been accorded generic status. Thelypteris palustris Schott (including three varieties) extends throughout north temperate regions, with a closely allied species south of the equator; chromosome number n=35. Phaegopteris connectilis (Michx) Watt (triploid with base number 30) and Oreopteris limbosperma (All.) Holub (n=34) are members of small genera confined to north temperate regions. Stegnogramma pozoi (Lag.) K. Iwats. (n=36) represents a genus of 12-15 species, mainly in Africa and Asia, with one in Mexico. Christella dentata (Forsk.) Brownsey & Jermy is a wide-ranging and variable tetraploid species of a pantropic genus (c. 60 spp) the centre of distribution of wich appears to be Burma-Assam (base number 36).The genus Cyclosurus (s. str.) comprises a small pantropic group of species with grow (like Thelypteris) in open permanently swampy ground; I belive Cyclosorus and Thelypteris to be closely related genera. Stegnogramma is related to Sphaerostephanos which (in arrangement of Holttum) is the most diversified genus in the Old World with c. 140 spp. in Malesia . Christella is probably also related to Sphaerostephanos though less nearly than Stegnogramma.Las Thelypteridaceae son helechos principalmente tropicales, comprende aproximadamente mil especies. Las cinco especies europeas representan cinco grupos diferentes cada uno de los cuales ha recibido recientemente un estatus genérico. Thelypteris palustris Schott (incluyendo tres variedades) se extiende por las regiones templadas del norte, con un conjunto de especies próximas al sur del ecuador; el número cromosómico es n=35. Phegopteris connectilis (Michx) Watt (triploide con número básico 30) y Oreopteris limbosperma (All.) Holub (n=34), son miembros de pequeños géneros confinados a las regiones templadas del norte.Stegnogramma pozoi (Lag.) K. Iwats. (n=36) representa un género de 12-15 especies principalmente de Africa y Asia con una en Méjico. Christe lla dentata (Forsk.) Brownsey & Jermy es una variable especie tetraploide de amplia distribución cuyo género pantropical (cerca de 60 especies) parece tener su centro de distribución en Burma-Assam (número básico 36).El género Cyclosorus (s. str.) comprende un pequeño grupo de especies pantropicales que viven en llanuras permanentemente pantanosas. Creemos que Cyclosorus y Thelypteris son géneros muy emparentados. Stegnogramma está relacionado con Sphaerostephanos, el cual (en la ordenación de Holttum) es el género más diversificado en el viejo mundo con cerca de 140 especies en Malasia Christella esta tambien relacionada,probablemente, con Sphaerostephanos aunque su proximidad es menor que la mantenida con Stegnogramma

Clinical measurement of the thoracic kyphosis : A study of the intra-rater reliability in subjects with and without shoulder pain

Copyright © Lewis and Valentine; licensee BioMed Central Ltd. 2010. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Abstract. Background. Clinical sagittal plane assessment of the thoracic kyphosis angle is considered an essential component of the postural examination of patients presenting with upper body pain syndromes. Cervical headaches and conditions involving the shoulder, such as subacromial pain syndrome, have all been associated with an increase in the thoracic kyphosis. Concomitantly a decrease in the thoracic kyphosis as a result of a stretching and strengthening rehabilitation programme is believed to be associated with a reduction in symptoms and pain and improvement in function. Clinicians generally measure the sagittal plane kyphosis angle visually. There is no certainty that this method is reliable or is capable of measuring angular changes over time or in response to intervention. As such a simple and reliable clinical method of measuring the thoracic kyphosis would enable clinicians to record this information. The aim of this investigation was to determine the intra-tester reliability of measuring the thoracic kyphosis angle using a clinical method. Methods. Measurements were made in 45 subjects with and 45 subjects without upper body symptoms. Measurements were made with the subjects in relaxed standing. Two gravity dependent inclinometers were used to measure the kyphosis. The first was placed over the region of the 1 and 2 thoracic spinous processes. The other, over the region of the 12 thoracic and 1 lumbar spinous processes. The angle produced by each inclinometer was measured 3 times in succession. Each set of 3 measurements was made on two occasions (separated by a minimum of 30 minutes and additional data collection involving 46 further measurements of posture and movement on the same and an additional subject before the thoracic kyphosis measurements were re-measured) by one rater. The reliability of the measurements was analyzed using 2-way ANOVA intraclass correlation coefficients (ICC), 95% confidence intervals (CI) and standard error of measurement (SEM) for precision, for a single measurement [ICC(single)] and the average of 3 measures [ICC(average)]. The assessor remained 'blinded' to data input and the measurements were staggered to reduce examiner bias. Results. The measurement of the thoracic kyphosis as used in this investigation was found to have excellent intra-rater reliability for both subjects with and without symptoms. The ICC(single) results for the subjects without symptoms were, .95; (95% CI .91-.97). The corresponding ICC(average) results were; .97; (95% CI .95-.99). The results for the subjects with symptoms were; 93; (95% CI .88-.96), for ICC(single) and for ICC(average); .97; (95% CI .94-.98). The SEM results for subjects without and with symptoms were 1.0° and 1.7°, respectively. Conclusions. The findings of this immediate test-retest reliability study suggest that the clinical measurement of the thoracic kyphosis using gravity dependent inclinometers demonstrates excellent intra-rater reliability. Additional research is required to determine the inter-rater reliability of this method. Trial registration. National Research Register: N0060148286.Peer reviewe

On the type of triangle groups

We prove a conjecture of R. Schwartz about the type of some complex hyperbolic triangle groups.Comment: 10 pages, 3 figure

Predicting the wake structure of the HART II rotor using the vorticity transport model

Brown’s Vorticity Transport Model has been used to predict the wake structure and resultant blade loading of the rotor that was studied during the HART II experimental programme. The descending flight condition of the experiment yields significant high-frequency content to the blade loading due to the presence of blade-vortex interactions. PIV images of the wake structure were compared against numerical predictions of the detailed geometry of the rotor wake using three different computational resolutions of the flow. This was done to investigate the origin of inaccuracies exposed in an earlier study of the system in capturing the effects of blade vortex interactions on the loading on the rotor. The predicted positions of the vortex cores agree with measured data to within a fraction of the blade chord, and the strength of the vortices is preserved to well downstream of the rotor, essentially independently of the resolution of the calculation. Nevertheless the amplitude of the loading impulses induced on the blade by vortex interaction are strongly influenced by the resolution of the calculation through the effect of cell density on the minimum vortex core size that can be supported. It would appear thus that the inaccuracies in predicting the high-frequency loading on the rotor are not due to any inherent deficiency in the representation of the wake, although viscous effects may need to be considered in future in order to decouple the vortex core size from the cell size, but rather due to the inherent deficiencies of the lifting line approach used to model the blade aerodynamics

Aerodynamic Response of a Hovering Rotor to Ramp Changes in Pitch Input

Under transient conditions, a helicopter rotor generates a complex, time-dependent pattern of shed and trailed vorticity in its wake that has profound eects on its loading. To examine these eects, the response of a two-bladed hovering rotor to a ramp change in collective pitch is investigated using three dierent computational approaches. Solutions obtained using a Compressible Reynolds Averaged Navier{Stokes ap- proach are compared to results obtained from lifting-line theory coupled to an Eulerian Vorticity Transport Model, and from a simple single-state dynamic in ow model. The dierent numerical approaches yield very similar predictions of the thrust response of the rotor to ramp changes in collective pitch, as long as the ramp rates are small. This suggests that the basic underlying ow physics is properly represented by all the approaches. For more rapid ramp rates, an additional delay in the aerodynamic response of the rotor, that is related to the nite extent of the wake during its early history, is predicted by the Navier{Stokes and Vorticity Transport approaches. Even though the evolution of the wake of the rotor is strongly three dimensional and highly unsteady, the predictions of the Navier{Stokes and lifting-line models agree very closely as long as the blades of the rotor do not stall. In the pre-stall regime, a quasi two-dimensional representation of the blade aerodynamics thus appears adequate for predicting the performance of such systems even under highly transient conditions. When ow separation occurs, the resulting three dimen- sionality of the blade aerodynamics forces the predictions of the Navier{Stokes and lifting-line approaches to diverge, however. The characterization of the wake interactions and stall propagation mechanisms that are presented in this study oers some insight into the fundamental uid dynamic mechanisms that govern the transient aerodynamic response of a rotor to control inputs, and provides some quantication of the limits of applicability of some popular current approaches to rotor aerodynamic analysis

Preliminary Observations on spawning potential in the striped bass (Roccus saxatilis Walbaum)

This study was initiated during the summer of 1940 with the following objectives: (1) To determine at what age sexual maturity begins in striped bass of the Chesapeake Bay. (2) To determine whether the potential of reproduction declines with increasing age in Chesapeake Bay fish. (3) To determine whether striped bass in northern waters have a spawning cycle similar to that found in the Chesapeake Bay fish

Main rotor-tail rotor intraction and its implications for helicopter directional control

Aerodynamic interference between the main and tail rotor can have a strong negative influence on the flight mechanics of a conventional helicopter. Significant unsteadiness in the tail rotor loading is encountered under certain flight conditions, but the character of the unsteadiness can depend on the direction of rotation of the tail rotor. Numerical simulations, using Brown's vorticity transport model, of the aerodynamic interaction between the main and tail rotors of a helicopter are presented for a range of forward and lateral flight trajectories. Distinct differences are predicted in the behavior of the system in left and right sideward flight that are consistent with flight experience that the greatest fluctuations in loading or control input are required in left sideways flight (for a counterclockwise rotating main rotor). These fluctuations are generally more extreme for a system with tail rotor rotating top-forward than top-aft. Differences are also exposed in the character of the lateral excitation of the system as forward flight speed is varied. The observed behavior appears to originate in the disruption of the tail rotor wake that is induced by its entrainment into the wake of the main rotor. The extent of the disruption is dependent on flight condition, and the unsteadiness of the process depends on the direction of rotation of the tail rotor. In intermediate-speed forward flight and right sideward flight, the free stream delays the entrainment of the tail rotor wake far enough downstream for the perturbations to the rotor loading to be slight. Conversely, in left sideward and quartering flight, the free stream confines the entrainment process close to the rotors, where it causes significant unsteadiness in the loads produced by the system