Intersection local times of fractional Brownian motions with H∈(0,1)H\in(0,1) as generalized white noise functionals

In $\R^d$, for any dimension $d\geq 1$, expansions of self-intersection local times of fractional Brownian motions with arbitrary Hurst coefficients in $(0,1)$ are presented. The expansions are in terms of Wick powers of white noises (corresponding to multiple Wiener integrals), being well-defined in the sense of generalized white noise functionals.Comment: 17 page

Searching for Communities in Bipartite Networks

Bipartite networks are a useful tool for representing and investigating interaction networks. We consider methods for identifying communities in bipartite networks. Intuitive notions of network community groups are made explicit using Newman's modularity measure. A specialized version of the modularity, adapted to be appropriate for bipartite networks, is presented; a corresponding algorithm is described for identifying community groups through maximizing this measure. The algorithm is applied to networks derived from the EU Framework Programs on Research and Technological Development. Community groups identified are compared using information-theoretic methods.Comment: 12 pages, 4 figures, to appear in "Proceedings of the 5th Jagna International Workshop: Stochastic and Quantum Dynamics of Biomolecular Systems," C. C. Bernido and M. V. Carpio-Bernido, editors. A version with full-quality figures and larger file size is available at http://ccm.uma.pt/publications/Barber-Faria-Streit-Strogan-2008.pd

Mapping of non-central potentials under point canonical transformations

Motivated by the observation that all known exactly solvable shape invariant central potentials are inter-related via point canonical transformations, we develop an algebraic framework to show that a similar mapping procedure is also exist between a class of non-central potentials. As an illustrative example, we discuss the inter-relation between the generalized Coulomb and oscillator systems.Comment: 11 pages article in LaTEX (uses standard article.sty). Please check http://www1.gantep.edu.tr/~gonul for other studies of Nuclear Physics Group at University of Gaziante

GUIDED INQUIRY-BASED LEARNING OF TRIGONOMETRIC IDENTITIES

The implementation of K-12 basic education curriculum brought some concerns in the educational sector of the Philippines such as shortage in teaching and learning materials, and the required teaching-learning approach that would cater for the development of 21st century skills among learners. This study developed and validated guided inquiry-based learning materials in understanding the trigonometric identities in Grade 11 Pre-calculus to promote self-directed, independent, and inquiry-based learning, and to verify its effects in student learning. The guided inquiry-based learning materials underwent evaluation and validation, and were evaluated as Highly Acceptable to teachers and students. This study utilized the descriptive method using the 7-point scale. Quasi-experimental design was adopted to measure the effects of the validated learning materials and the use of inquiry-based learning in student’s performance. Results confirmed that students are equally able to develop cognitive skills in trigonometric identities through IBL and conventional learning modality. Thus, the validated guided inquiry-based materials developed and used in this study can be adopted in its original form to promote 11th graders’ self-directed, independent, and inquiry learning necessary for developing 21st century skills such as critical thinking.&nbsp

Path Integral Discussion for Smorodinsky-Winternitz Potentials: I.\ Two- and Three Dimensional Euclidean Space

Path integral formulations for the Smorodinsky-Winternitz potentials in two- and three-dimen\-sional Euclidean space are presented. We mention all coordinate systems which separate the Smorodinsky-Winternitz potentials and state the corresponding path integral formulations. Whereas in many coordinate systems an explicit path integral formulation is not possible, we list in all soluble cases the path integral evaluations explicitly in terms of the propagators and the spectral expansions into the wave-functions.Comment: LaTeX 60 pages, DESY 94-01

Polynomial Solution of Non-Central Potentials

We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov-Bohm potentials as special cases. The results are in exact agreement with other methods.Comment: 18 page

Describing the on-the-job training experiences of bachelor of science in management accounting students

This study aims to describe the on-the-job training experiences of BSMA students at Saint Columban College, Pagadian City. A single case study was most appropriate for the research’s proper conduct since this study wants to describe and understand the on-the-job training of BSMA students who experience this program. The findings led the researchers to the conclusion that the research participants described their on-the-job training as a journey of learning, growth, and application of their academic knowledge to the real-world context of accounting and management fields. They expressed a sense of practicality and hands-on learning, emphasizing the transition from theoretical concepts to practical applications. Their narratives show the importance of concrete experiences within their training, followed by reflective observations that allow them to derive meaningful insights. The development of abstract conceptualizations and stage of active experimentation highlights the value of these experiences in shaping their professional skills and development

The generalized MIC-Kepler system

This paper deals with dynamical system that generalizes the MIC-Kepler system. It is shown that the Schr\"{o}dinger equation for this generalized MIC-Kepler system can be separated in spherical and parabolic coordinates. The spectral problem in spherical and parabolic coordinates is solved.Comment: 8 page