Role of the Mean-field in Bloch Oscillations of a Bose-Einstein Condensate in an Optical Lattice and Harmonic Trap

Using the Crank-Nicholson method, we study the evolution of a Bose-Einstein condensate in an optical lattice and harmonic trap. The condensate is excited by displacing it from the center of the harmonic trap. The mean field plays an important role in the Bloch-like oscillations that occur after sufficiently large initial displacement. We find that a moderate mean field significantly suppresses the dispersion of the condensate in momentum space. When the mean field becomes large, soliton and vortex structures appear in the condensate wavefunction.Comment: BEC simulation, 7 figure

Development of a health care systems curriculum.

Background: There is currently no gold standard for delivery of systems-based practice in medical education, and it is challenging to incorporate into medical education. Health systems competence requires physicians to understand patient care within the broader health care system and is vital to improving the quality of care clinicians provide. We describe a health systems curriculum that utilizes problem-based learning across 4 years of systems-based practice medical education at a single institution. Methods: This case study describes the application of a problem-based learning approach to system-based practice medical education. A series of behavioral statements, called entrustable professional activities, was created to assess student health system competence. Student evaluation of course curriculum design, delivery, and assessment was provided through web-based surveys. Results: To meet competency standards for system-based practice, a health systems curriculum was developed and delivered across 4 years of medical school training. Each of the health system lectures and problem-based learning activities are described herein. The majority of first and second year medical students stated they gained working knowledge of health systems by engaging in these sessions. The majority of the 2016 graduating students (88.24%) felt that the course content, overall, prepared them for their career. Conclusion: A health systems curriculum in undergraduate medical education using a problem-based learning approach is feasible. The majority of students learning health systems curriculum through this format reported being prepared to improve individual patient care and optimize the health system\u27s value (better care and health for lower cost)

Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports

In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we are focused in the study of the asymptotic behaviour of such polynomials as well as in the distribution of their zeros. Some open problems as well as some new directions for a future research are formulated.Comment: Changed content; 34 pages, 41 reference

Splines and Wavelets on Geophysically Relevant Manifolds

Analysis on the unit sphere $\mathbb{S}^{2}$ found many applications in seismology, weather prediction, astrophysics, signal analysis, crystallography, computer vision, computerized tomography, neuroscience, and statistics. In the last two decades, the importance of these and other applications triggered the development of various tools such as splines and wavelet bases suitable for the unit spheres $\mathbb{S}^{2}$, $\>\>\mathbb{S}^{3}$ and the rotation group $SO(3)$. Present paper is a summary of some of results of the author and his collaborators on generalized (average) variational splines and localized frames (wavelets) on compact Riemannian manifolds. The results are illustrated by applications to Radon-type transforms on $\mathbb{S}^{d}$ and $SO(3)$.Comment: The final publication is available at http://www.springerlink.co

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials

Three cases of bone metastases in patients with gastrointestinal stromal tumors

Gastrointestinal stromal tumors (GISTs) are rare, but represent the most common mesenchymal neoplasms of the gastrointestinal tract. Tumor resection is the treatment of choice for localized disease. Tyrosine kinase inhibitors (imatinib, sunitinib) are the standard therapy for metastatic or unresectable GISTs. GISTs usually metastasize to the liver and peritoneum. Bone metastases are uncommon. We describe three cases of bone metastases in patients with advanced GISTs: two women (82 and 54 years of age), and one man (62 years of age). Bones metastases involved the spine, pelvis and ribs in one patient, multiple vertebral bodies and pelvis in one, and the spine and iliac wings in the third case. The lesions presented a lytic pattern in all cases. Two patients presented with multiple bone metastases at the time of initial diagnosis and one patient after seven years during the follow-up period. This report describes the diagnosis and treatment of the lesions and may help clinicians to manage bones metastases in GIST patients