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The nonlinear problem is an important and interesting topic in many research fields. For example, the nonlinear optics model can more accurately describe the light propagation at very high intensities...
The rapid growth of data starts to inflict a major impact in many fields such as computational mathematics, optimization, statistics, computer science, etc. Big data analysis is a new and exciting dir...
This paper introduces a novel approach for rapidly computing a very large number of geodesics on a smooth surface.The idea is to apply the recently developed phase flow method [L. Ying, E.J. Cande `s,...
This paper is concerned with the fast computation of Fourier integral operators of the general form Rd e2πıΦ(x,k)f(k)dk, where k is a frequency variable, Φ(x, k) is a phase function obeying a st...
This paper is concerned with the evaluation of the partial Fourier transform ux =|k|in one and two dimensions. The motivating application is the wave extrapolation procedure in ...
We introduce a general purpose algorithm for rapidly computing certain types of oscillatory integrals which frequently arise in problems connected to wave propagation, general hyperbolic equations, an...
The boundary integral method is an efficient approach for solving time-harmonic acoustic obstacle scattering problems. The main computational task is the evaluation of an oscillatory boundary integral...
Computation of Lyapunov exponents for dynamical system with impact.
A perturbation procedure for the modes and cut-off frequencies of cylindrical acoustic waveguides of arbitrary cross-section with a small temperature gradient along the walls was presented in [1, 2]. ...
Frequency dimension is used to characterize fractals that come as distinct individual objects which are spread over a range of space. In this paper, the number and area frequency dimensions of mount...
Efficient and fast solutions to the problem of computing the Hausdorff metric between two arbitrary grey-scale, digitised images are considered. The more efficient of the techniques proposed here cons...
A two-dimensional free surface potential flow of a liquid poured from a container is calculated when the liquid runs along the underside of the spout. The effect of surface tension is taken into consi...
We derive a lattice approximation for a class of equilibrium quantum statistics describing the behaviour of any combination and number of bosonic and fermionic particles with any sufficiently binding...

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