Periodic solutions of systems with asymptotically even nonlinearities

New conditions of solvability based on a general theorem on the calculation of the index at infinity for vector fields that have degenerate principal linear part as well as degenerate ... next order ... terms are obtained for the 2 Pi-periodic problem for the scalar equation x'' +n2x=g(|x|)+f(t,x)+b(t) with bounded g(u) and f(t,x) -> 0 as |x| -> 0. The result is also applied to the solvability of a two-point boundary value problem and to resonant problems for equations arising in control theory. AMS subject classifications: 47Hll, 47H30

Learning styles, personalisation and adaptable e-learning

Common Learning Management Systems (for example Moodle [1] and Blackboard [2]) are limited in the amount of personalisation that they can offer the learner. They are used widely and do offer a number of tools for instructors to enable them to create and manage courses, however, they do not allow for the learner to have a unique personalised learning experience. The e-Learning platform iLearn offers personalisation for the learner in a number of ways and one way is to offer the specific learning material to the learner based on the learner's learning style. Learning styles and how we learn is a vast research area. Brusilovsky and Millan [3] state that learning styles are typically defined as the way people prefer to learn. Examples of commonly used learning styles are Kolb Learning Styles Theory [4], Felder and Silverman Index of Learning Styles [5], VARK [6] and Honey and Mumford Index of Learning Styles [7] and many research projects (SMILE [8], INSPIRE [9], iWeaver [10] amonst others) attempt to incorporate these learning styles into adaptive e-Learning systems. This paper describes how learning styles are currently being used within the area of adaptive e-Learning. The paper then gives an overview of the iLearn project and also how iLearn is using the VARK learning style to enhance the platform's personalisation and adaptability for the learner. This research also describes the system's design and how the learning style is incorporated into the system design and semantic framework within the learner's profile

The California Red Sea Urchin, Strongylocentrotus franciscanus, Fishery: Catch, Effort, and Management Trends

California's red sea urchin, Strongylocentrotus franciscanus, catch peaked at 23,577 metric tons (t) in 1988. Since then, catches and CPUE have trended downward at different rates in northern and southern California, with 10,086 t landed statewide in 1995. West coast sea urchin catches and CPUE from British Columbia, Can., to Baja California, Mex., have generally declined during this period which followed a decade of rapid fishery expansion. This expansion was in response to increasing demand from Japan fueled by rising prices based largely on a more favorable export currency exchange rate. West coast stock assessment methods have been based on integrating a combination of fisheries dependent data and population surveys into models at various levels of complexity. California management policy has centered on technical measures such as size limits and seasonal closures and has been largely ineffective in stabilizing declining catches

Robust option replication for a Black-Scholes model extended with nondeterministic trends

Statistical analysis on various stocks reveals long range dependence behavior of the stock prices that is not consistent with the classical Black and Scholes model. This memory or nondeterministic trend behavior is often seen as a reflection of market sentiments and causes that the historical volatility estimator becomes unreliable in practice. We propose an extension of the Black and Scholes model by adding a term to the original Wiener term involving a smoother process which accounts for these effects. The problem of arbitrage will be discussed. Using a generalized stochastic integration theory [8], we show that it is possible to construct a self financing replicating portfolio for a European option without any further knowledge of the extension and that, as a consequence, the classical concept of volatility needs to be re-interpreted. AMS subject classifications: 60H05, 60H10, 90A09

Intermediate Palomar Transient Factory: Realtime Image Subtraction Pipeline

A fast-turnaround pipeline for realtime data reduction plays an essential role in discovering and permitting follow-up observations to young supernovae and fast-evolving transients in modern time-domain surveys. In this paper, we present the realtime image subtraction pipeline in the intermediate Palomar Transient Factory. By using high-performance computing, efficient database, and machine learning algorithms, this pipeline manages to reliably deliver transient candidates within ten minutes of images being taken. Our experience in using high performance computing resources to process big data in astronomy serves as a trailblazer to dealing with data from large-scale time-domain facilities in near future.Comment: 18 pages, 6 figures, accepted for publication in PAS

QCD Splitting/Joining Functions at Finite Temperature in the Deep LPM Regime

There exist full leading-order-in-alpha_s numerical calculations of the rates for massless quarks and gluons to split and join in the background of a quark-gluon plasma through hard, nearly collinear bremsstrahlung and inverse bremsstrahlung. In the limit of partons with very high energy E, where the physics is dominated by the Landau-Pomeranchuk-Migdal (LPM) effect, there are also analytic leading-log calculations of these rates, where the logarithm is ln(E/T). We extend those analytic calculations to next-to-leading-log order. We find agreement with the full result to within roughly 20% for E(less) >~ 10 T, where E(less) is the energy of the least energetic parton in the splitting/joining process. We also discuss how to account for the running of the coupling constant in the case that E/T is very large. Our results are also applicable to isotropic non-equilibrium plasmas if the plasma does not change significantly over the formation time associated with particle splitting.Comment: 20 pages, 6 figures. Changes from v3: Typos fixed in the subscripts of various Casimir factor