A Classification of Minimal Sets of Torus Homeomorphisms

We provide a classification of minimal sets of homeomorphisms of the two-torus, in terms of the structure of their complement. We show that this structure is exactly one of the following types: (1) a disjoint union of topological disks, or (2) a disjoint union of essential annuli and topological disks, or (3) a disjoint union of one doubly essential component and bounded topological disks. Periodic bounded disks can only occur in type 3. This result provides a framework for more detailed investigations, and additional information on the torus homeomorphism allows to draw further conclusions. In the non-wandering case, the classification can be significantly strengthened and we obtain that a minimal set other than the whole torus is either a periodic orbit, or the orbit of a periodic circloid, or the extension of a Cantor set. Further special cases are given by torus homeomorphisms homotopic to an Anosov, in which types 1 and 2 cannot occur, and the same holds for homeomorphisms homotopic to the identity with a rotation set which has non-empty interior. If a non-wandering torus homeomorphism has a unique and totally irrational rotation vector, then any minimal set other than the whole torus has to be the extension of a Cantor set.Comment: Published in Mathematische Zeitschrift, June 2013, Volume 274, Issue 1-2, pp 405-42

Measured and predicted shock shapes for AFE configuration at Mach 6 in air and in CF4

Shock shapes and stand-off distances were obtained for the Aeroassist Flight Experiment configuration from Mach 6 tests in air and in CF4. Results were plotted for an angle-of attack range from -10 to 10 degrees and comparisons were made at selected angles with inviscid-flow predictions. Tests were performed in the Langley Research Center (LaRC) 20 inch Mach 6 Tunnel (air) at unit free-stream Reynolds numbers (N sub Re, infinity) of 2 million/ft and 0.6 million/ft and in the LaRC Hypersonic CF4 Tunnel at N sub Re, infinity = 0.5 million/ft and 0.3 million/ft. Within the range of these tests, N sub Re, infinity did not affect the shock shape or stand off distance, and the predictions were in good agreement with the measurements. The shock stand-off distance in CF4 was approximately half of that in air. This effect resulted from the differences in density ratio across the normal shock, which was approximately 12 in CF4 and 5 in air. In both test gases, the shock lay progressively closer to the body as angle of attack decreased

Airline Liability for Loss, Damage or Delay of Passenger Baggage

The article discusses remedies and methods of enforcing airline liability for loss, damage or delay of passenger baggage. The article includes a discussion of the law as it relates both to domestic flights and to international flights where passenger luggage is lost, damaged or delayed. The article includes a discussion of the Warsaw Convention as it relates to international flights and of the Federal Aviation Regulations applicable in the case of domestic flights

Efficient algorithms for tensor scaling, quantum marginals and moment polytopes

We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our algorithm provides an efficient weak membership oracle for the associated moment polytopes, an important family of implicitly-defined convex polytopes with exponentially many facets and a wide range of applications. These include the entanglement polytopes from quantum information theory (in particular, we obtain an efficient solution to the notorious one-body quantum marginal problem) and the Kronecker polytopes from representation theory (which capture the asymptotic support of Kronecker coefficients). Our algorithm can be applied to succinct descriptions of the input tensor whenever the marginals can be efficiently computed, as in the important case of matrix product states or tensor-train decompositions, widely used in computational physics and numerical mathematics. We strengthen and generalize the alternating minimization approach of previous papers by introducing the theory of highest weight vectors from representation theory into the numerical optimization framework. We show that highest weight vectors are natural potential functions for scaling algorithms and prove new bounds on their evaluations to obtain polynomial-time convergence. Our techniques are general and we believe that they will be instrumental to obtain efficient algorithms for moment polytopes beyond the ones consider here, and more broadly, for other optimization problems possessing natural symmetries

Cluster-variation approximation for a network-forming lattice-fluid model

We consider a 3-dimensional lattice model of a network-forming fluid, which has been recently investigated by Girardi and coworkers by means of Monte Carlo simulations [J. Chem. Phys. \textbf{126}, 064503 (2007)], with the aim of describing water anomalies. We develop an approximate semi-analytical calculation, based on a cluster-variation technique, which turns out to reproduce almost quantitatively different thermodynamic properties and phase transitions determined by the Monte Carlo method. Nevertheless, our calculation points out the existence of two different phases characterized by long-range orientational order, and of critical transitions between them and to a high-temperature orientationally-disordered phase. Also, the existence of such critical lines allows us to explain certain ``kinks'' in the isotherms and isobars determined by the Monte Carlo analysis. The picture of the phase diagram becomes much more complex and richer, though unfortunately less suitable to describe real water.Comment: 10 pages, 9 figures, submitted to J. Chem. Phy

A toral diffeomorphism with a non-polygonal rotation set

We construct a diffeomorphism of the two-dimensional torus which is isotopic to the identity and whose rotation set is not a polygon

Hyperphosphorylation amplifies UPF1 activity to resolve stalls in nonsense-mediated mRNA decay.

Many gene expression factors contain repetitive phosphorylation sites for single kinases, but the functional significance is poorly understood. Here we present evidence for hyperphosphorylation as a mechanism allowing UPF1, the central factor in nonsense-mediated decay (NMD), to increasingly attract downstream machinery with time of residence on target mRNAs. Indeed, slowing NMD by inhibiting late-acting factors triggers UPF1 hyperphosphorylation, which in turn enhances affinity for factors linking UPF1 to decay machinery. Mutational analyses reveal multiple phosphorylation sites contributing to different extents to UPF1 activity with no single site being essential. Moreover, the ability of UPF1 to undergo hyperphosphorylation becomes increasingly important for NMD when downstream factors are depleted. This hyperphosphorylation-dependent feedback mechanism may serve as a molecular clock ensuring timely degradation of target mRNAs while preventing degradation of non-targets, which, given the prevalence of repetitive phosphorylation among central gene regulatory factors, may represent an important general principle in gene expression

The impact of space and space-related activities on a local economy. a case study of boulder, colorado. part ii- the income-product accounts

Total impact of space and space related activities on local economy of Boulder, Colorado - income-product account

Four layer bandage compared with short stretch bandage for venous leg ulcers: systematic review and meta-analysis of randomised controlled trials with data from individual patients

<p><b>Objective:</b> To compare the effectiveness of two types of compression treatment (four layer bandage and short stretch bandage) in people with venous leg ulceration.</p> <p><b>Design:</b> Systematic review and meta-analysis of patient level data.</p> <p><b>Data:</b> sources Electronic databases (the Cochrane Central Register of Controlled Trials, the Cochrane Wounds Group Specialised Register, Medline, Embase, CINAHL, and National Research Register) and reference lists of retrieved articles searched to identify relevant trials and primary investigators. Primary investigators of eligible trials were invited to contribute raw data for re-analysis.</p> <p><b>Review:</b> methods Randomised controlled trials of four layer bandage compared with short stretch bandage in people with venous leg ulceration were eligible for inclusion. The primary outcome for the meta-analysis was time to healing. Cox proportional hazards models were run to compare the methods in terms of time to healing with adjustment for independent predictors of healing. Secondary outcomes included incidence and number of adverse events per patient.</p> <p><b>Results:</b> Seven eligible trials were identified (887 patients), and patient level data were retrieved for five (797 patients, 90% of known randomised patients). The four layer bandage was associated with significantly shorter time to healing: hazard ratio (95% confidence interval) from multifactorial model based on five trials was 1.31 (1.09 to 1.58), P=0.005. Larger ulcer area at baseline, more chronic ulceration, and previous ulceration were all independent predictors of delayed healing. Data from two trials showed no evidence of a difference in adverse event profiles between the two bandage types.</p> <p><b>Conclusions:</b> Venous leg ulcers in patients treated with four layer bandages heal faster, on average, than those of people treated with the short stretch bandage. Benefits were consistent across patients with differing prognostic profiles.</p&gt