The numerical approximation of the solution of the time-harmonic Maxwell equations by a least-squares nite element discretization is discussed in this paper. Our emphasis lies in the eecient solution of the system of linear algebraic equations arising from the discretization. Additive multilevel preconditioning is analyzed theoretically and by computational experiments for a simple two-dimensio...

The influence of additive noise, multiplicative noise, and higher-order effects on exploding solitons in the framework of the prototype complex cubic-quintic Ginzburg-Landau equation is studied. Transitions from explosions to filling-in to the noisy spatially homogeneous finite amplitude solution, collapse (zero solution), and periodic exploding dissipative solitons are reported.

We show that the Cauchy Problem for a randomly forced, periodic multi-dimensional scalar first-order conservation law with additive or multiplicative noise is well-posed: it admits a unique solution, characterized by a kinetic formulation of the problem, which is the limit of the solution of the stochastic parabolic approximation.

Under suitable assumptions of regularity and non-degeneracy on the covariance of the driving additive noise, any Markov solution to the stochastic NavierStokes equations has an associated generator of the diffusion and is the unique solution to the corresponding martingale problem. Some elementary examples are discussed to interpret these results.

The problem of inference of an additive tree from an incomplete dissimilarity matrix is known to be very delicate. As a solution to this problem, it has been suggested either to estimate the missing entries of a given partial dissimilarity matrix prior to tree reconstruction (De Soete, 1984 and Landry et al., 1997) or directly reconstruct an additive tree from incomplete data (Makarenkov and Le...

In this paper the training of Least Squares Support Vector Machines (LS-SVMs) for classification and regression and the determination of its regularization constants is reformulated in terms of additive regularization. In contrast with the classical Tikhonov scheme, a major advantage of this additive regularization mechanism is that it enables to achieve computational fusion of the training and...

Necessary and sufficient conditions are given for the existence of a countably additive extension of a given finite measure in the case of any finite or disjoint countable perturbation of its -algebra. It provides a complete description of all countably additive extensions of finite measures in such cases. In particular, simple characterizations are obtained for the existence of some extremal c...

Up to now, researchers have proposed several synthesis methods for the preparation of β-nickel(II) hydroxide nanostructures. Most of these approaches contain harsh synthetic conditions such as multi-step processes, high temperatures and long reaction time. In this work, a novel, facile and low cost method is introduced to produce of β-Ni(OH)2 nanostructures using the gas-solution precipitation ...

Digital images are mostly corrupted by mixed noise from several sources. It is a challenging problem to remove mixed noise in color images. Generally, some image denoising filters can reduce either additive or impulse noise, but it fails to remove both impulsive noise and additive noise. This paper presents modified bilateral filtering method, which can simultaneously remove both impulsive and ...

The modularity is the best known and widely used quality function for community detection in graphs. We investigate approximability of maximization problem some related problems. first design a polynomial-time 0.4209-additive approximation algorithm problem, which improves current additive error 0.4672. Our theoretical analysis also demonstrates that proposed obtains nearly-optimal solution any...