We present a new nonlinear optimization procedure for the computation of generalized Gaussian quadratures for a broad class of functions. While some of the components of this algorithm have been previously published, we present a simple and robust scheme for the determination of a sparse solution to an underdetermined nonlinear optimization problem which replaces the continuation scheme of the previously published works. The performance of the resulting procedure is illustrated with several numerical examples.

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We describe the operational in-orbit calibration of the Geostationary Operational Environmental Satellite (GOES)-8 and-9 imagers and sounders. In the infrared channels the calibration is based on observations of space and an onboard blackbody. The calibration equation expresses radiance as a quadratic in instrument output. To suppress noise in the blackbody sequences, we filter the calibration slopes. The calibration equation also accounts for an unwanted variation of the reflectances of the instruments' scan mirrors with east-west scan position, which was not discovered until the instruments were in orbit. The visible channels are not calibrated, but the observations are provided relative to the level of space and are normalized to minimize east-west striping in the images. Users receive scaled radiances in a GOES variable format (GVAR) data stream. We describe the procedure users can apply to transform GVAR counts into radiances, temperatures, and mode-A counts.

We describe an approach to the numerical solution of the integral equations of scattering theory on planar curves with corners. It is rather comprehensive in that it applies to a wide variety of boundary value problems; here, we treat the Neumann and Dirichlet problems as well as the boundary value problem arising from acoustic scattering at the interface of two fluids. It achieves high accuracy, is applicable to largescale problems and, perhaps most importantly, does not require asymptotic estimates for solutions. Instead, the singularities of solutions are resolved numerically. The approach is efficient, however, only in the lowand mid-frequency regimes. Once the scatterer becomes more than several hundred wavelengths in size, the performance of the algorithm of this paper deteriorates significantly. We illustrate our method with several numerical experiments, including the solution of a Neumann problem for the Helmholtz equation given on a domain with nearly 10000 corner points.

The Nyström method can produce ill-conditioned systems of linear equations and inaccurate results when applied to integral equations on domains with corners. This defect can already be seen in the simple case of the integral equations arising from the Neumann problem for Laplace's equation. We explain the origin of this instability and show that a straightforward modification to the Nyström scheme, which renders it mathematically equivalent to Galerkin discretization, corrects the difficulty without incurring the computational penalty associated with Galerkin methods. We also present the results of numerical experiments showing that highly accurate solutions of integral equations on domains with corners can be obtained, irrespective of whether their solutions exhibit bounded or unbounded singularities, assuming that proper discretizations are used.On the Nyström discretization of integral equations on planar curves with corners ON THE NYSTRÖM DISCRETIZATION OF INTEGRAL EQUATIONS ON PLANAR CURVES WITH CORNERS JAMES BREMERAbstract. The Nyström method can produce ill-conditioned systems of linear equations and inaccurate results when applied to integral equations on domains with corners. This defect can already be seen in the simple case of the integral equations arising from the Neumann problem for Laplace's equation. We explain the origin of this instability and show that a straightforward modification to the Nyström scheme, which renders it mathematically equivalent to Galerkin discretization, corrects the difficulty without incurring the computational penalty associated with Galerkin methods. We also present the results of numerical experiments showing that highly accurate solutions of integral equations on domains with corners can be obtained, irrespective of whether their solutions exhibit bounded or unbounded singularities, assuming that proper discretizations are used.

Abstract. We describe a numerical procedure for the construction of quadrature formulae suitable for the efficient discretization of boundary integral equations over very general curve segments. While the procedure has applications to the solution of boundary value problems on a wide class of complicated domains, we concentrate in this paper on a particularly simple case: the rapid solution of boundary value problems for Laplace's equation on two-dimensional polygonal domains. We view this work as the first step toward the efficient solution of boundary value problems on very general singular domains in both two and three dimensions. The performance of the method is illustrated with several numerical examples.

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION / AVAILABILITY STATEMENTApproved for Public Release; Distribution Unlimited SUPPLEMENTARY NOTES ABSTRACTA mouse model of breast cancer with human breast cancer cell lines MCF7 (wild type) or MCF7-doxorubicin resistant (MCF7-R) cells was used evaluate the efficacy of low molecular weight heparins (LMWH) either alone or in combination with doxorubicin to prevent tumor growth. Tumor volume measurements were performed at intervals throughout the course of treatment. LMWH compounds (Enoxaparin or non-anticoagulant heparin NACH) given together with chemotherapeutic agent doxorubicin decreased tumor growth rate and prolong survival in animals bearing MCF7 wild-type tumors. These agents appeared to be less effective in animals bearing doxorubicin-resistant tumors. Bleeding times determined on animals in all treatment groups showed that there were no statistically significant differences among the groups. However, animals in ENOX groups showed increased bruising at the sites of injection. These studies will be repeated, and studies with alpha v beta 3-targeted nanoparticle formulations will be performed to compare the efficacies of non-targeted and targeted therapies. SUBJECT TERMS

Abstract. In a previous work, the authors introduced a scheme for the numerical evaluation of the singular integrals which arise in the discretization of certain weakly singular integral operators of acoustic and electromagnetic scattering. That scheme is designed to achieve high-order algebraic convergence and high-accuracy when applied to operators given on smoothly parameterized surfaces. This paper generalizes the approach to a wider class of integral operators including many defined via the Cauchy principal value. Operators of this type frequently occur in the course of solving scattering problems involving boundary conditions on tangential derivatives. The resulting scheme achieves high-order algebraic convergence and approximately 12 digits of accuracy.One of the principal observations of integral operator theory is that certain linear elliptic boundary value problems can be reformulated as systems of integral equations whose constituent operators act on spaces of square integrable functions [7,20]. This observation plays a particularly important role in scattering theory, where such reformulations are standard [14,11,15,13,12,7,8]. Not surprisingly, it also figures prominently in the numerical treatment of scattering problems [16,17,1,10]. But while the integral equation approach to scattering theory is a venerable and well-developed subject, the corresponding numerical analysis -that is, the study of the integral equations of scattering theory using computers and finite precision arithmetic -is rather newer and considerably less developed. As a result, many fundamental problems in numerical scattering theory are as yet unresolved. Examples of this phenomenon can be found in recent contributions like [9] and [2], which offer new integral formulations of certain boundary value problems for Maxwell's equations that, unlike classical formulations, are amenable to numerical treatment.This article concerns another unresolved problem: the evaluation of the singular integrals of scattering theory. A key difficulty in the discretization of those integral operators which arise from the reformulation of linear elliptic boundary value problems is the efficient and accurate evaluation of integrals of the formwhere Σ is a surface, q is a point in Σ, B (q) denotes the ball of radius centered at the point q, K is singular kernel and f a smooth function. The technique used to evaluate such integrals depends on the representation of the surface Σ which is employed. Certain schemes are designed for triangulated surfaces [6], while others operate on the assumption that a smooth partition of unity given on Σ is available [22]. The setting for this article is a parameterized piecewise smooth surface whose parameterization domain has been triangulated. More specifically, it is assumed that the surface Σ is specified via a finite collection of smooth mappingsgiven on the standard simplex ∆ 1 = (s, t) ∈ R 2 : 0 ≤ s ≤ 1, 0 ≤ t ≤ 1 − s such that the sets ρ 1