A Numerical Method for Singular Two Point Boundary Value Problems

The numerical solution of boundary value problems for linear systems of first order equations with a regular singular point at one endpoint is considered. The standard procedure of expanding about the singularity to get a nonsingular problem over a reduced interval is justified in some detail. Quite general boundary conditions are included which permit unbounded solutions. Error estimates are given and some numerical calculations are presented to check the theory

Arc-Length Continuation and Multigrid Techniques for Nonlinear Elliptic Eigenvalue Problems

We investigate multi-grid methods for solving linear systems arising from arc-length continuation techniques applied to nonlinear elliptic eigenvalue problems. We find that the usual multi-grid methods diverge in the neighborhood of singular points of the solution branches. As a result, the continuation method is unable to continue past a limit point in the Bratu problem. This divergence is analyzed and a modified multi-grid algorithm has been devised based on this analysis. In principle, this new multi-grid algorithm converges for elliptic systems, arbitrarily close to singularity and has been used successfully in conjunction with arc-length continuation procedures on the model problem. In the worst situation, both the storage and the computational work are only about a factor of two more than the unmodified multi-grid methods

Quantum Cluster Variables via Serre Polynomials

For skew-symmetric acyclic quantum cluster algebras, we express the quantum $F$-polynomials and the quantum cluster monomials in terms of Serre polynomials of quiver Grassmannians of rigid modules. As byproducts, we obtain the existence of counting polynomials for these varieties and the positivity conjecture with respect to acyclic seeds. These results complete previous work by Caldero and Reineke and confirm a recent conjecture by Rupel.Comment: minor corrections, reference added, example 4.3 added, 38 page

Convergence Rates for Newton’s Method at Singular Points

If Newton’s method is employed to find a root of a map from a Banach space into itself and the derivative is singular at that root, the convergence of the Newton iterates to the root is linear rather than quadratic. In this paper we give a detailed analysis of the linear convergence rates for several types of singular problems. For some of these problems we describe modifications of Newton’s method which will restore quadratic convergence

SkyMapper and the Southern Sky Survey - a resource for the southern sky

SkyMapper is amongst the first of a new generation of dedicated, wide-field survey telescopes. The 1.3m SkyMapper telescope features a 5.7 square degree field-of-view Cassegrain imager and will see first light in late 2007. The primary goal of the facility is to conduct the Southern Sky Survey a six colour, six epoch survey of the southern sky. The survey will provide photometry for objects between 8th and 23rd magnitude with global photometric accuracy of 0.03 magnitudes and astrometry to 50 mas. This will represent a valuable scientific resource for the southern sky and in addition provide a basis for photometric and astrometric calibration of imaging data.Comment: 6 pages, 4 figures, proceedings of ESO Calibration Workshop 200

Homotopy Method for the Large, Sparse, Real Nonsymmetric Eigenvalue Problem

A homotopy method to compute the eigenpairs, i.e., the eigenvectors and eigenvalues, of a given real matrix A1 is presented. From the eigenpairs of some real matrix A0, the eigenpairs of A(t) ≡ (1 − t)A0 + tA1 are followed at successive "times" from t = 0 to t = 1 using continuation. At t = 1, the eigenpairs of the desired matrix A1 are found. The following phenomena are present when following the eigenpairs of a general nonsymmetric matrix: • bifurcation, • ill conditioning due to nonorthogonal eigenvectors, • jumping of eigenpaths. These can present considerable computational difficulties. Since each eigenpair can be followed independently, this algorithm is ideal for concurrent computers. The homotopy method has the potential to compete with other algorithms for computing a few eigenvalues of large, sparse matrices. It may be a useful tool for determining the stability of a solution of a PDE. Some numerical results will be presented

The Stability of One-Step Schemes for First-Order Two-Point Boundary Value Problems

The stability of a finite difference scheme is related explicitly to the stability of the continuous problem being solved. At times, this gives materially better estimates for the stability constant than those obtained by the standard process of appealing to the stability of the numerical scheme for the associated initial value problem

His story/her story: A dialogue about including men and masculinities in the women’s studies curriculum

The article discusses the issue of inclusion of men and masculinities in the Women\u27s Studies curriculum. Women\u27s Studies programs were started to compensate for the male domination in the academics. Women\u27s Studies presented a platform where scholarship for women was produced and taken seriously, female students and faculty could find their say or voice, and theoretical investigations required for the advancement of the aims of the women\u27s movement could take place. If the academy as a whole does not sufficiently integrate Women\u27s Studies into the curriculum, integrating Men\u27s Studies into Women\u27s Studies might end up further marginalizing Women\u27s Studies by decreasing the number of classroom hours students spend engaging women\u27s lives and feminist scholarship. Such an integration would presents an another form of male privilege, with men manipulating their way into the only branch of scholarship that has consistently focused on women. On a ground level, feminist scholars are apprehensive that a move from a Women\u27s Studies program to a Gender Studies program will reduce the political aspect of women\u27s programs

A magnetic lens for cold atoms controlled by a rf field

We report on a new type of magnetic lens that focuses atomic clouds using a static inhomogeneous magnetic field in combination with a radio-frequency field. The experimental study is performed with a cloud of cold cesium atoms. The rf field adiabatically deforms the magnetic potential of a coil and therefore changes its focusing properties. The focal length can be tuned precisely by changing the rf frequency value. Depending on the rf antenna position relative to the DC magnetic profile, the focal length of the atomic lens can be either decreased or increased by the rf field