Physical Sciences and Mathematics Commons^™

Vortices In Bose-Einstein Condensates: Some Recent Developments, Panos Kevrekidis, R. Carretero-Gonzalez, D. J. Frantzeskakis, I. G. Kevrekidis

Panos Kevrekidis

In this brief review we summarize a number of recent developments in the study of vortices in Bose-Einstein condensates, a topic of considerable theoretical and experimental interest in the past few years. We examine the generation of vortices by means of phase imprinting, as well as via dynamical instabilities. Their stability is subsequently examined in the presence of purely magnetic trapping, and in the combined presence of magnetic and optical trapping. We then study pairs of vortices and their interactions, illustrating a reduced description in terms of ordinary differential equations for the vortex centers. In the realm of two vortices …

The Topology, Geometry And Conformal Structure Of Properly Embedded Minimal Surfaces, Pascal Collin, Robert Kusner, William H. Meeks, Harold Rosenberg

Robert Kusner

This paper develops new tools for understanding surfaces with more than one end and infinite topology which are properly minimally embedded in Euclidean three-space. On such a surface, the set of ends forms a totally disconnected compact Hausdorff space, naturally ordered by the relative heights of the ends in space. One of our main results is that the middle ends of the surface have quadratic area growth, and are thus not limit ends. This implies that the surface can have at most two limit ends, which occur at the top and bottom of the ordering, and thus only a countable …

On A Theorem Of Peters On Automorphisms Of Kahler Surfaces, Weimin Chen Chen

Weimin Chen

For any K¨ahler surface which admits no nonzero holomorphic vectorfields, we consider the group of holomorphic automorphisms which induce identity on the second rational cohomology. Assuming the canonical linear system is without base points and fixed components, C.A.M. Peters [12] showed that this group is trivial except when the K¨ahler surface is of general type and either c21 = 2c2 or c21 = 3c2 holds. Moreover, this group is a 2-group in the former case, and is a 3-group in the latter. The purpose of this note is to give further information about this group. In particular, we show that …

Measurement Of The Generalized Forward Spin Polarizabilities Of The Neutron, M. Amarian, L. Auerbach, T. Averett, J. Berthot, P. Bertin, W. Bertozzi, T. Black, E. Brash, D. Brown, E. Burtin, J. Calarco, G. Cates, Z. Chai, J. P. Chen, Seonho Choi, E. Chudakov, E. Cisbani, C. W. De Jager, A. Deur, R. Disalvo, S. Dieterich, P. Djawotho, J. M. Finn, K. Fissum, H. Fonvieille, S. Frullani, H. Gao, J. Gao, F. Garibaldi, A. Gasparian, S. Gilad, R. Gilman, A. Glamazdin, C. Glashausser, E. Goldberg, J. Gomez, V. Gorbenko, J. O. Hansen, B. Hersman, R. Holmes, G. M. Huber, E. Hughes, B. Humensky, S. W. Korsch, K. Kramer, K. Kumar, G. Kumbartzki, M. Kuss, Enkeleida K. Lakuriqi, G. Laveissiere, J. Lerose, M. Liang, N. Liyanage, G. Lolos, S. Malov, J. Marroncle, K. Mccormick, R. Mckeown, Z. E. Meziani, R. Michaels, J. Mitchell, Z. Papandreou, T. Pavlin, G. G. Petratos, D. Pripstein, D. Prout, R. Ransome, Y. Roblin, D. Rowntree, M. Rvachev, F. Sabatie, A. Saha, K. Slifer, P. Souder, T. Saito, S. Strauch, R. Suleiman, K. Takahashi, S. Teijiro, L. Todor, H. Tsubota, H. Ueno, G. Urciuoli, R. Van Der Meer, P. Vernin, H. Voskanian, B. Wojtsekhowski, F. Xiong, W. Xu, J. C. Yang, B. Zhang, P. A. Zolnierczuk

Enkeleida K. Lakuriqi

The generalized forward spin polarizabilities γ0 and δLT f the neutron have been extracted for the first time in a Q2 range from 0.1 to 0.9 GeV2. Since γ0 is sensitive to nucleon resonances and δLT is insensitive to the Δ resonance, it is expected that the pair of forward spin polarizabilities should provide benchmark tests of the current understanding of the chiral dynamics of QCD. The new results on δLT how significant disagreement with chiral perturbation theory calculations, while the data for γ0 at low Q2 re in good agreement with a next-to-leading-order …

Wavelet Estimation Of Partially Linear Models, Xiao-Wen Chang, Leming Qu

Leming Qu

A wavelet approach is presented for estimating a partially linear model (PLM). We find an estimator of the PLM by minimizing the square of the l₂ norm of the residual vector while penalizing the l₁ norm of the wavelet coefficients of the nonparametric component. This approach, an extension of the wavelet approach for nonparametric regression problems, avoids the restrictive smoothness requirements for the nonparametric function of the traditional smoothing approaches for PLM, such as smoothing spline, kernel and piecewise polynomial methods. To solve the optimization problem, an efficient descent algorithm with an exact line search is presented. Simulation …

Group Actions In Number Theory, Tyler J. Evans

Tyler Evans

Bounding The Firing Synchronization Problem On A Ring, André Berthiaume, Todd Bittner, Ljubomir Perković, Amber Settle, Janos Simon

Amber Settle

Orbifold Adjunction Formula And Sympletic Corbordisms Between Lens Spaces, Weimin Chen Chen

Weimin Chen

Each lens space has a canonical contact structure which lifts to the distribution of complex lines on the three-sphere. In this paper, we show that a symplectic homology cobordism between two lens spaces, which is given with the canonical contact structure on the boundary, must be diffeomorphic to the product of a lens space with the unit interval. As one of the main ingredients in the proof, we also derive in this paper the adjunction and intersection formulae for pseudoholomorphic curves in an almost complex 4–orbifold, extending the relevant work of Gromov and McDuff in the manifold setting.

Application Of A Mickens Finite-Difference Scheme To The Cylindrical Bratu-Gelfand Problem, Ron Buckmire

Ron Buckmire

No abstract provided.

Self-Similarity And Symmetries Of Pascal’S Triangles And Simplices Mod P, Richard P. Kubelka

Richard P. Kubelka

No abstract provided.

An Informal Introduction To Computing With Chern Classes, Zach Teitler

Zach Teitler

Some time ago, Dr. Teitler began work on a short expository set of notes on Chern classes in algebraic geometry, particularly in the context of enumerative problems. The notes are not polished. Some day he hopes to finish them; in the meantime, here is a draft, in PDF format (21 pages).

Miniaturen. Studien Zu Kalkül Und Kreativität 1998-2002, Rudolf Kaehr

Rudolf Kaehr

Informatik, künstlerische Praktik und Kunsttheorie der digitalen Bildtechnologien NULL&NICHTS; weder leer, noch nicht – oder Kraut und Rüben Gedanken zu einer autonomen Medienwissenschaft Das Menschenbild aus der Sicht einer polykontexturalen Systemtheorie Thesen zum trans-klassischen Menschenbild Gebaute Phantasien, unkontrollierbare Schwankungen Kreativität und Kalkül Ver_Endungen in/der Programmierbarkeit Diagrammatik: Denken a la Carte Zur Verstörung des (H)ortes der Zerstörung Zur Kenogrammatik der Medientheorie

Dynamic Semantic Web, Rudolf Kaehr

Rudolf Kaehr

Dynamic Semantic Web (DSW) is based at first on the techniques, methods and paradigms of the emerging Semantic Web movement and its applications. DSW is advancing one fundamental step further from a static to a dynamic concept of the Semantic Web with extended flexibility in the navigation between ontologies and more profound transparency of the informational system. Web Services are now redefinded by Semantic Web. To proof the advantages of DSW, it is the main aim of this project to develop the tools and methods necessary to develop a DSW based Web Service (DSW business application). The existing framework of …

Multi-Scale Analysis Of Seed Dispersal Contributes Tothe Resolution Of Reid’S Paradox, James A. Powell, N. E. Zimmermann

James A. Powell

‘‘Reid’s paradox’’ is the mismatch between theoretical estimates of invasion rates for plants and ‘‘observed’’ rates of plant migration, particularly in the Holocene postglacial migration northwards. While Reid couched his paradox in terms of the migration of oaks in Great Britain, observers have documented the same problem in a wide variety of species. In almost all cases, these authors suggest that occasional, long-distance events, probably mitigated by active dispersal factors (ants, birds, rodents) are responsible. Clark and co-workers have shown that order statistics can bridge the gap between theory and predictions, essentially using ‘‘fat-tailed’’ dispersal kernels raised to high powers …

Uniqueness Theorems In Bioluminescence Tomography, Ge Wang, Yi Li, Ming Jiang

Yi Li

Motivated by bioluminescent imaging needs for studies on gene therapy and other applications in the mouse models, a bioluminescence tomography (BLT) system is being developed in the University of Iowa. While the forward imaging model is described by the well-known diffusion equation, the inverse problem is to recover an internal bioluminescent source distribution subject to Cauchy data. Our primary goal in this paper is to establish the solution uniqueness for BLT under practical constraints despite the ill-posedness of the inverse problem in the general case. After a review on the inverse source literature, we demonstrate that in the general case …

On The Edge Set Of Graphs Of Lattice Paths, Lara Pudwell, Steven Klee, Rick Gillman

Lara K. Pudwell

No abstract provided.

On Cross Numbers Of Minimal Zero Sequences In Certain Cyclic Groups, Lara Pudwell, Scott Chapman, Paul Baginski, Kathryn Mcdonald

Lara K. Pudwell

No abstract provided.

Hands-On Geometry, S. Sportsman, Shannon Driskell

Shannon O.S. Driskell

Sportsman, S. (Co-PI), & Driskell, S. (Co-PI), Improving Teacher Quality State Grants Program, Ohio Board of Regents, $90,246

Fixed Point Theorems, Karen Saxe, Karine Moe

Karen Saxe

No abstract provided.

Biorthogonal Spline Type Wavelets, Tian-Xiao He

Tian-Xiao He

Let ¢ be an orthonormal scaling function with approximation degree p - 1, and let Bn be the B-spline of order n. Then, spline type scaling functions defined by fn = f * Bn (n = 1, 2, ... ) possess higher approximation order, p+n-1, and compact support. The corresponding biorthogonal wavelet functions are also constructed. This technique is extended to the case of biorthogonal scaling function system. As an application of the method supplied in this paper, one can easily construct a sequence of pairs of biorthogonal spline type scaling functions from one pair of biorthogonal scaling functions or …

Students’ Problem-Solving Strategies With Fractions, Shannon Driskell

Shannon O.S. Driskell

Driskell, S. (PI), University of Dayton Research Council Seed Grant, $4,000

Pseudospectral Iterated Method For Differential Equations With Delay Terms, Jodi Mead, Barbara Zubik-Kowal

Jodi Mead

New efficient numerical methods for hyperbolic and parabolic partial differential equations with delay terms are investigated. These equations model a development of cancer cells in human bodies. Our goal is to study numerical methods which can be applied in a parallel computing environment. We apply our new numerical method to the delay partial differential equations and analyse the error of the method. Numerical experiments confirm our theoretical results.

Almost Alternating Harmonic Series, Ramin Naimi, Curtis Fesit

Ramin Naimi

No abstract provided.

Inverse Eigenproblems And Associated Approximation Problems For Matrices With Generalized Symmetry Or Skew Symmetry, William F. Trench

William F. Trench

No abstract provided.

Hermitian, Hermitian R-Symmetric, And Hermitian R-Skew Symmetric Procrustes Problems, William F. Trench

William F. Trench

No abstract provided.

Minimization Problems For (R,S)-Symmetric And (R,S)-Skew Symmetric Matrices, William F. Trench

William F. Trench

No abstract provided.

Simplification And Strengthening Of Weyl's Definition Of Asymptotic Equal Distribution Of Two Families Of Finite Sets, William F. Trench

William F. Trench

No abstract provided.

An Elementary Note On Asymptotic Properties Of Toeplitz And Multilevel Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.

On Multivariate Abel-Gontscharoff Interpolation, Tian-Xiao He

Tian-Xiao He

By using Gould's annihilation coefficients, we obtain an explicit fundamental polynomials of Multivariate Abel-Gontscharoff Interpolation and its remainder expression.

Using Dynamic Information In The Supply Network, Jeffrey Barker

Jeffrey Barker

No abstract provided.