Results 51 to 60 of about 70,750 (232)

Quadrature formulas for monotone functions [PDF]

Proceedings of the American Mathematical Society, 1992
We prove that adaptive quadrature formulas for the class of monotone functions are much better than nonadaptive ones if the average error is considered. Up to now it was only known that adaptive methods are not better in the worst case (for this and many other classes of functions) or in various average case settings.
openaire   +2 more sources

Pulse Generation by On‐Chip Dispersion Compensation at 8 µm Wavelength

Laser &Photonics Reviews, EarlyView.
This work demonstrates on‐chip pulse generation at 8 μm$\mathrm{\mu}\mathrm{m}$ using chirped Bragg gratings in SiGe graded‐index photonic circuits to compensate the quadratic phase of quantum cascade laser frequency combs. With this approach pulses as short as 1.39 ps were produced, close to the transform limit, representing a key step toward compact,
Annabelle Bricout, Mathieu Bertrand, Philipp Täschler, Barbara Schneider, Victor Turpaud, Stefano Calcaterra, Davide Impelluso, Marco Faverzani, David Bouville, Jean‐René Coudevylle, Samson Edmond, Etienne Herth, Carlos Alonso‐Ramos, Laurent Vivien, Jacopo Frigerio, Giovanni Isella, Jérôme Faist, Delphine Marris‐Morini   +17 more
wiley   +1 more source

Cubic scaling algorithms for RPA correlation using interpolative separable density fitting

, 2017
We present a new cubic scaling algorithm for the calculation of the RPA correlation energy. Our scheme splits up the dependence between the occupied and virtual orbitals in $\chi^0$ by use of Cauchy's integral formula.
Lu, Jianfeng, Thicke, Kyle
core   +2 more sources

A highly accurate numerical method for solving boundary value problem of generalized Bagley‐Torvik equation

Mathematical Methods in the Applied Sciences, EarlyView.
A highly accurate numerical method is given for the solution of boundary value problem of generalized Bagley‐Torvik (BgT) equation with Caputo derivative of order 0<β<2$$ 0<\beta <2 $$ by using the collocation‐shooting method (C‐SM). The collocation solution is constructed in the space Sm+1(1)$$ {S}_{m+1}^{(1)} $$ as piecewise polynomials of degree at ...
Suzan Cival Buranay, Mtema James Chin, Nazim I. Mahmudov   +2 more
wiley   +1 more source

Spectral/quadrature duality: Picard-Vessiot theory and finite-gap potentials

, 2012
In the framework of differential Galois theory we treat the classical spectral problem $\Psi"-u(x)\Psi=\lambda\Psi$ and its finite-gap potentials as exactly solvable in quadratures by Picard--Vessiot without involving special functions; the ideology goes
Brezhnev, Yurii V.
core   +1 more source

Quadrature Formulas for Infinite Integrals [PDF]

Mathematics of Computation, 1962
have become increasingly important. The only quadrature generally available for the case b = - a = oo is the Hermite-Gauss formula although the LaguerreGauss formula can also be used if f(x) is an even function of x. The latter would, however, require computation of twice the number of ordinates for a corresponding degree of precision and would ...
openaire   +2 more sources

Absolute Quantification of Brain Deuterium Metabolic Imaging in Healthy Volunteers and Glioblastoma Patients at 7T

Magnetic Resonance in Medicine, EarlyView.
ABSTRACT Purpose We present a method for absolute quantification of deuterated metabolites in vivo at 7T. We describe acquisition protocols and an analysis pipeline compatible with 7T Terra MRIs. We apply them using a 2H/1H receive array in healthy volunteers and glioblastoma patients.
Jabrane Karkouri, Masha Novoselova, Sarah Miller, Minghao Zhang, Alexandra Constantinou, Carina Graf, Özlem Ipek, Daniel Atkinson, Brandon Tramm, Scott Schillak, Richard Mair, Kevin Brindle, Christopher T. Rodgers   +12 more
wiley   +1 more source

An iterative method based on the average quadrature formula [PDF]

Computational Algorithms and Numerical Dimensions
In our research, a new third-order iterative method has been introduced. This method involves the creation of a new quadrature formula by averaging Simpson's 1/3 rd and Trapezoidal rules.
Tusar Singh, Dwiti Behera, Shno Othman Ahmed, Rostam Saeed   +3 more
doaj   +1 more source

Bending Analysis of Thickness‐ and Shear‐Deformable Materially Imperfect Composite Shells With von Kármán‐Type Geometric Nonlinearities

International Journal of Mechanical System Dynamics, EarlyView.
ABSTRACT Geometrically nonlinear static analysis of materially imperfect composite doubly curved shells is investigated via the generalised differential quadrature method. The effects of both shear and thickness deformation are considered through a thickness‐ and shear‐deformable third‐order theory formulated in curvilinear coordinates, while the ...
Behrouz Karami, Mergen H. Ghayesh, Shahid Hussain, Marco Amabili   +3 more
wiley   +1 more source

Soil Nail Design Optimization Through Adaptive Slope Stability Analysis Using Improved Limit Equilibrium Method

International Journal for Numerical and Analytical Methods in Geomechanics, EarlyView.
ABSTRACT Design optimization for automatically generating optimal design results is a promising technique for enhancing the efficiency of design processes and outcomes. However, its development for soil nail reinforced slopes is limited since the traditional slope stability analysis using the limit equilibrium method (LEM) becomes relatively time ...
Weihang Ouyang, Kai Liu, Si‐Wei Liu
wiley   +1 more source