In this paper, we consider a two-term time-fractional diffusion-wave equation which involves the fractional orders α ∈ (1, 2) and β (0, 1), respectively. By using piecewise linear Galerkin finite element method in space convolution quadrature based on second-order backward difference time, obtain robust fully discrete scheme. Error estimates for semidiscrete schemes are established with respect...

This paper presents fast and accurate algorithms for computing the prices of discretely sampled lookback options. Under the Black-Scholes framework, the pricing of a discrete lookback option can be reduced to a series of convolutions of a function with the Gaussian distribution. Using this fact, an efficient algorithm, which computes these convolutions by a combination of the double-exponential...

This paper presents a new and efficient approach for optimization and implementation of filter banks e.g. velocity channels, orientation channels and scale spaces. The multi layered structure of a filter network enable a powerful decomposition of complex filters into simple filter components and the intermediary results may contribute to several output nodes. Compared to a direct implementation...

Contents: 1. A bit of history and results 2. Basic automorphic forms 3. Summation formulas 4. Convolution sums 5. Point to integral mean-values of Dirichlet's series 6. Evaluation of A(T) 7. Approximate functional equation 8. Evaluation of ℓ(s) on average 9. Estimation of x(s) on average 10. Applications The group of ideal classes Cℓ(K) of an imaginary quadratic field K = Q(√ −q) is the most fa...

Multiresolution representations are very effective for analyzing the information content of images. We study the properties of the operator which approximates a signal at a given resolution. We show that the difference of information between the approximation of a signal at the resolutions 2’ + ’ and 2jcan be extracted by decomposing this signal on a wavelet orthonormal basis of L*(R”). In LL(R...

Aims. Accurate measurement of gravitational shear from images of distant galaxies is one of the most direct ways of studying the distribution of mass in the universe. We describe an implementation of a technique that is based on the shapelets formalism. Methods. The shapelets technique describes PSF and observed images in terms of Gauss-Hermite expansions (Gaussians times polynomials). It allow...

Many important physical applications are governed by the wave equation. The formulation as time domain boundary integral equations involves retarded potentials. For the numerical solution of this problem we employ the convolution quadrature method for the discretization in time and the Galerkin boundary element method for the space discretization. We introduce a simple a-priori cutoff strategy ...

Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of interfacial phenomena, as well as problems in adsorption, colloidal science and phase transitions in fluids. Typical DFT equations are highly non-linear, stiff and co...

The Feynman-Kac equation governs the distribution of statistical observable — functional, having wide applications in almost all disciplines. After overcoming some challenges from time-space coupled nonlocal operator and possible low regularity this paper develops high-order fully discrete scheme for backward fractional by using difference formulas (BDF) convolution quadrature time, finite elem...

Maxwell’s equations are considered with transparent boundary conditions, with initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The proposed computational scheme only involves the interior domain and its boundary. The transparent boundary conditions are imposed via a time-dependent boundary integ...