Exponential Stability of Interval Dynamical Systems with Quadratic Nonlinearity

This article proposes an approach for investigating the exponential stability of a nonlinear interval dynamical system with the nonlinearity of a quadratic type on the basis of the Lyapunov’s direct method. It also constructs an inner estimate of the attraction domain to the origin for the system under consideration.     

The schnittaxiom and unions of fuzzy subgroups

A necessary and sufficient condition for the union of an arbitrary family of fuzzy subgroups of a group to be a fuzzy group has been proposed. The criterion which gives a cut of the unit interval is called the Schnittaxiom. It has been applied successfully to investigate fuzzy subgroupness of arbitrary unions of homomorphic images and preimages.     

Precipitation behavior of σ phase in fusion zone of dissimilar stainless steel welds during multi-pass GTAW process

The purpose of this study is to investigate the precipitation characteristics of σ phase in the fusion zone of stainless steel welds at various welding passes during a tungsten are welding (GTAW) process. The morphology, quantity, and chemical composition of the δ-ferrite and σ phase were analyzed using optical microscopy (OM), a ferritscope (FS), a X-ray diffractometer (XRD), scanning electron microscopy (SEM), an electron probe micro-analyzer (EPMA), and a wavelength dispersive spectrometer (WDS), respectively. Massive δ-ferrite was observed in the fusion zone of the first pass welds during welding of dissimilar stainless steels. The σ phase precipitated at the inner δ-ferrite particles and decreased δ-ferrite content during the third pass welding. The σ and δ phases can be stabilized by Si element, which promoted the phase transformation of σ→ϱ+λ₂ in the fusion zone of the third pass welds. It was found that the σ phase was a Fe−Cr−Si intermetallic compound found in the fusion zone of the third pass welds during multi-pass welding.     

Wavelet domain-based video noise reduction using temporal discrete cosine transform and hierarchically adapted thresholding

A novel spatio-temporal filter for video denoising, which operates entirely in the wavelet domain, is proposed. For effective noise reduction, the spatial and temporal redundancies that exist in the wavelet domain representation of a video signal are exploited. First, a 2D discrete wavelet transform is applied to the input noisy frames. This is followed by a discrete cosine transform (DCT), which is applied to the temporal subband coefficients to minimise the redundancy among the consecutive frames. The DCT transformed, noise-free coefficients in the different wavelet domain subbands for the original image sequence are modelled using a prior having a generalised Gaussian distribution. On the basis of this prior, filtering of the noisy wavelet coefficients in each subband is carried out using a new, low-complexity wavelet shrinkage method, which utilises the correlation that exists between subsequent resolution levels. Experimental results show that the proposed scheme outperforms several state-of-the-art spatio-temporal filters in terms of both the peak signal-to-noise ratio and the visual quality     

A Survey on the Numerics and Computations for the Landau-Lifshitz Equation of Micromagnetism

The Landau-Lifshitz (LL)equation of micromagnetism governs rich variety of the evolution of magnetization patterns in ferromagnetic media. This is due to the complexity of physical quantities appearing in the LL equation. This complexity causes also an interesting mathematical properties of the LL equation: nonlocal character for some quantities,nonconvex side-constraints, strongly nonlinear terms. These effects influence also the numerical approximations. In this work, recent developments on the approximation of weak solutions, together with the overview of well-known methods for strong solutions,are addressed. Author is supported by the Fund for Scientific Research - Flanders FWO (Belgium).