We discuss the numerical integration of polynomials times exponential weighting functions arising from multiscale finite element computations. The new rules are more accurate than standard quadratures and are better suited to existing codes than formulas computed by symbolic integration. We test our approach in a multiscale finite element method for the 2D reaction-diffusion equation. Standard ...

tex Sat Dec 05 13:37:58 2015 1 Two notable advances in numerical methods were supported by this grant. First, a fast algorithm was derived, analyzed, and tested for the Fourier transform of pi ecewise polynomials given on d-dimensional simplices in D-dimensional Euclidean space. T hese transforms play a key role in computational problems ranging from medical imaging to partial differential equa...

There are many situations for which a feasible nonholonomic motion plan must be generated immediately based on real-time perceptual information. Parametric trajectory representations limit computation because they reduce the search space for solutions (at the cost of potentially introducing suboptimality). The use of any parametric trajectory model converts the optimal control formulation into ...

we study the notion of bounded approximate connes-amenability for‎ ‎dual banach algebras and characterize this type of algebras in terms‎ ‎of approximate diagonals‎. ‎we show that bounded approximate‎ ‎connes-amenability of dual banach algebras forces them to be unital‎. ‎for a separable dual banach algebra‎, ‎we prove that bounded‎ ‎approximate connes-amenability implies sequential approximate...

A phase-sensitive four-wave mixing (FWM) scheme enabling the simultaneous conversion of the two orthogonal quadratures of an optical signal to different wavelengths is demonstrated for the first time under dynamic operation using a highly nonlinear optical fiber (HNLF) as the nonlinear medium. The scheme is first optimized with respect to the power levels and phases of the four phase-coherent p...

We consider states leading to the equality sign in the uncertainty inequalities associated with correlations in open quantum systems which have been recently derived by Ponomarenko and Wolf @Phys. Rev. A 63, 062106 ~2001!#. The new inequalities involve fluctuations defined in terms of the square of the density operator that characterizes mixed states. We find the minimum-correlation states asso...

Integrable models of dilaton gravity coupled to electromagnetic and scalar matter fields in dimensions 1+1 and 0+1 are reviewed. The 1+1 dimensional integrable models are either solved in terms of explicit quadratures or reduced to the classically integrable Liouville equation. The 0+1 dimensional integrable models emerge as sectors in generally non integrable 1+1 dimensional models and can be ...