Somos Sequence Near-Addition Formulas and Modular Theta Functions

We have discovered conjectural near-addition formulas for Somos sequences. We have preliminary evidence suggesting the existence of modular theta functions.Comment: 31 page

Leading the evaluation of institutional online learning environments for quality enhancement in times of change

This paper reports on findings from a nationally funded project which aims to design and implement a quality management framework for online learning environments (OLEs). Evaluation is a key component of any quality management system and it is this aspect of the framework that is the focus of this paper. In developing the framework initial focus groups were conducted at the five participating institutions. These revealed that, although regarded as important, there did not appear to be a shared understanding of the nature and purpose of evaluation. A second series of focus groups revealed there were multiple perspectives arising from those with a vested interest in online learning. These perspectives will be outlined. Overall, how evaluation was undertaken was highly variable within and across the five institutions reflecting where they were at in relation to the development of their OLE

Somos Sequence Near-Addition Formulas and Modular Theta Functions

We have discovered conjectural near-addition formulas for Somos sequences. We have preliminary evidence suggesting the existence of modular theta functions

Asymptotic Properties of Difference Equations for Isotropic Loop Quantum Cosmology

In loop quantum cosmology, a difference equation for the wave function describes the evolution of a universe model. This is different from the differential equations that arise in Wheeler-DeWitt quantizations, and some aspects of general properties of solutions can appear differently. Properties of particular interest are boundedness and the presence of small-scale oscillations. Continued fraction techniques are used to show in different matter models the presence of special initial conditions leading to bounded solutions, and an explicit expression for these initial values is derived.Comment: 27 pages, 2 figure

Management of plant invasions mediated by frugivore interactions

1. Some of the most damaging invasive plants are dispersed by frugivores and this is an area of emerging importance in weed management. It highlights the need for practical information on how frugivores affect weed population dynamics and spread, how frugivore populations are affected by weeds and what management recommendations are available. 2. Fruit traits influence frugivore choice. Fruit size, the presence of an inedible peel, defensive chemistry, crop size and phenology may all be useful traits for consideration in screening and eradication programmes. By considering the effect of these traits on the probability, quality and quantity of seed dispersal, it may be possible to rank invasive species by their desirability to frugivores. Fruit traits can also be manipulated with biocontrol agents. 3. Functional groups of frugivores can be assembled according to broad species groupings, and further refined according to size, gape size, pre- and post-ingestion processing techniques and movement patterns, to predict dispersal and establishment patterns for plant introductions. 4. Landscape fragmentation can increase frugivore dispersal of invasives, as many invasive plants and dispersers readily use disturbed matrix environments and fragment edges. Dispersal to particular landscape features, such as perches and edges, can be manipulated to function as seed sinks if control measures are concentrated in these areas. 5.Where invasive plants comprise part of the diet of native frugivores, there may be a conservation conflict between control of the invasive and maintaining populations of the native frugivore, especially where other threats such as habitat destruction have reduced populations of native fruit species. 6. Synthesis and applications. Development of functional groups of frugivore-dispersed invasive plants and dispersers will enable us to develop predictions for novel dispersal interactions at both population and community scales. Increasingly sophisticated mechanistic seed dispersal models combined with spatially explicit simulations show much promise for providing weed managers with the information they need to develop strategies for surveying, eradicating and managing plant invasions. Possible conservation conflicts mean that understanding the nature of the invasive plant-frugivore interaction is essential for determining appropriate management.Ctr Invas Bio

Simplifying Multiple Sums in Difference Fields

In this survey article we present difference field algorithms for symbolic summation. Special emphasize is put on new aspects in how the summation problems are rephrased in terms of difference fields, how the problems are solved there, and how the derived results in the given difference field can be reinterpreted as solutions of the input problem. The algorithms are illustrated with the Mathematica package \SigmaP\ by discovering and proving new harmonic number identities extending those from (Paule and Schneider, 2003). In addition, the newly developed package \texttt{EvaluateMultiSums} is introduced that combines the presented tools. In this way, large scale summation problems for the evaluation of Feynman diagrams in QCD (Quantum ChromoDynamics) can be solved completely automatically.Comment: Uses svmult.cls, to appear as contribution in the book "Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions" (www.Springer.com

University students’ self-regulated learning using digital technologies

Abstract Analysing the process by which students—whether at university or not—manage and facilitate their own learning has been a recurrent educational research problem. Recently, the question arises about how the development of strategies taking place during the aforementioned process could be made easier by using technologies. In an effort to know whether university students really use digital technologies to plan, organize and facilitate their own learning, we have proposed three research questions. Which technologies do university students use to self-regulate their learning? What self-regulated learning strategies do they develop using technologies? What profiles could be identified among students based on their use of self-regulation strategies with technology? To answer these questions, the “Survey of Self-regulated Learning with Technology at the University” was designed. Information from a sample group with 711 students from various universities located in the region of Andalusia (Spain) was collected with this survey. The results indicate that university students, even when they are frequent users of digital technology, they tend not to use these technologies to regulate their own learning process. Of all technologies analysed, Internet information search and instant communication tools are used continually. In turn, the most generalised self-regulation learning strategies are those relative to social support. Nevertheless, students differ from each other regarding their use and frequency. There are groups of students who make use of self-regulation strategies when learning with technologies. In this regard, two distinctive groups of students have been identified, who show differentiated self-regulated levels