A New Family of Multistep Methods with Improved Phase Lag Characteristics for the Integration of Orbital Problems

In this work we introduce a new family of ten-step linear multistep methods for the integration of orbital problems. The new methods are constructed by adopting a new methodology which improves the phase lag characteristics by vanishing both the phase lag function and its first derivatives at a specific frequency. The efficiency of the new family of methods is proved via error analysis and numerical applications.Comment: 21 pages, 3 figures, 1 tabl

Developing a conceptual learning enhancement framework for study abroad programmes: the role of action research in the participation of students

Studying abroad is frequently described as a life changing experience yet evidence suggests that more can be done to improve and add value to the student experience. This doctoral study purposes to present how learning can be enhanced for the student abroad through a broad spanning consideration of good education practice. With an emphasis on the student as a valuable resource, this study uses an action research approach to uncover evidence of high value learning experiences by engaging student participation in the development of a learning enhancement framework design to guide practice. The doctoral project takes place at a study abroad university in Athens. The methodological design consists of action research within a qualitative setting and is conducted through a series of guided focus groups over a systematic time frame. The diverse sample consists of 12 students who attend a US homeschool and share the same study abroad location during the study. Enriching this primary study, two additional data sources are used to support and compare findings: - Professional observations systematically considered and recorded over time include critical incidents and offer professional insight into the study context. - Introducing Experiential Education, a professional project designed and instructed by the researcher took place separately during the timeframe of this doctoral project, the outcomes of which are directly relevant to the broader topic of learning enhancement and to the questions posed by this study. Supported by the relevant literature, the primary study and 2 secondary studies are used in the synthesis of triangulated outcomes and claims. Taking an in depth, critical examination of the study, and developing an emerging framework from this analysis, the case is made for utilising student participation to implement improvements to educational practice. Drawing on the complete findings and outcomes, a series of mechanisms bridging the gap between learning experience and student are presented as mechanisms that can be used within the Learning Enhancement Model as drivers of good practice. Significant outcomes include the correlation between students’ engagement with the local culture, academic performance and student enjoyment of the experience abroad. The emerging conceptual framework for learning enhancement is presented as the primary contribution to knowledge in the study abroad field and identifies a system of professional good practice that could be adopted and adapted by learning instructors, administrators and study abroad providers. The presentation of the work offers the second contribution to knowledge by showcasing the role of action research in the participation of students and documenting the development of the study. The thesis concludes that study abroad currently provides the potential for a rich learning experience. Innovatively, the study determines that by considering the emerging indicators of enhanced learning and incorporating them into strategic and teaching levels, students and educators will benefit from a re-evaluated model of practice, through the emerging Learning Enhancement Framework is presented in the study

A Phase-Fitted Runge-Kutta-Nystr\"om method for the Numerical Solution of Initial Value Problems with Oscillating Solutions

A new Runge-Kutta-Nystr\"om method, with phase-lag of order infinity, for the integration of second-order periodic initial-value problems is developed in this paper. The new method is based on the Dormand and Prince Runge-Kutta-Nystr\"om method of algebraic order four\cite{pa}. Numerical illustrations indicate that the new method is much more efficient than the classical one.Comment: 10 page

Will gravitational waves confirm Einstein's General Relativity?

Even if Einstein's General Relativity achieved a great success and overcame lots of experimental tests, it also showed some shortcomings and flaws which today advise theorists to ask if it is the definitive theory of gravity. In this proceeding paper it is shown that, if advanced projects on the detection of Gravitational Waves (GWs) will improve their sensitivity, allowing to perform a GWs astronomy, accurate angular and frequency dependent response functions of interferometers for GWs arising from various Theories of Gravity, i.e. General Relativity and Extended Theories of Gravity, will be the ultimate test for General Relativity. This proceeding paper is also a short review of the Essay which won Honorable Mention at the 2009 Gravity Research Foundation Awards.Comment: To appear in Proceedings of the 7th International Conference of Numerical Analysis and Applied Mathematics, Rethymno, Crete (near to Chania), Greece, 18-22 September 200

Reducing Spatial Data Complexity for Classification Models

Intelligent data analytics gradually becomes a day-to-day reality of today's businesses. However, despite rapidly increasing storage and computational power current state-of-the-art predictive models still can not handle massive and noisy corporate data warehouses. What is more adaptive and real-time operational environment requires multiple models to be frequently retrained which fiirther hinders their use. Various data reduction techniques ranging from data sampling up to density retention models attempt to address this challenge by capturing a summarised data structure, yet they either do not account for labelled data or degrade the classification performance of the model trained on the condensed dataset. Our response is a proposition of a new general framework for reducing the complexity of labelled data by means of controlled spatial redistribution of class densities in the input space. On the example of Parzen Labelled Data Compressor (PLDC) we demonstrate a simulatory data condensation process directly inspired by the electrostatic field interaction where the data are moved and merged following the attracting and repelling interactions with the other labelled data. The process is controlled by the class density function built on the original data that acts as a class-sensitive potential field ensuring preservation of the original class density distributions, yet allowing data to rearrange and merge joining together their soft class partitions. As a result we achieved a model that reduces the labelled datasets much further than any competitive approaches yet with the maximum retention of the original class densities and hence the classification performance. PLDC leaves the reduced dataset with the soft accumulative class weights allowing for efficient online updates and as shown in a series of experiments if coupled with Parzen Density Classifier (PDC) significantly outperforms competitive data condensation methods in terms of classification performance at the comparable compression levels

Analytic Approach for Controlling Realistic Quantum Chaotic Systems

An analytic approach for controlling quantum states, which was originally applied to fully random matrix systems [T. Takami and H. Fujisaki, Phys. Rev. E 75, 036219 (2007)], is extended to deal with more realistic quantum systems with a banded random matrix (BRM). The validity of the new analytic field is confirmed by directly solving the Schroedinger equation with a BRM interaction. We find a threshold of the width of the BRM for the quantum control to be successful.Comment: 4 pages with 4 PostScript figures, to appear in the Proceedings of ICCMSE 2007 in a section of Symposium 8 "Quantum Control and Light-Matter Interactions: Recent Computational and Theoretical Results