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.     

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.     

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).     

Fivefold symmetry in real and reciprocal spaces

Tetrahedrally close-packed structures with juxtaposed pentagonal antiprisms, such as the μ, C14 Laves and the newly found C phases, were studied by means of HREM and SAD. It was found that each bright spot in the structural image corresponds to an antiprism. Differently oriented domains of these phases intergrow frequently with a fairly good match at the interphase boundary. All diffraction patterns of these phases show a fivefold distribution of spot-pairs, and it is shown that this fivefold symmetry comes from the pentagons and spot-pairs from two pentagonal prisms superposed in antisymmetrical positions.     

鄱阳湖湖底沉积物放射性水平

本文报道了1985年鄱阳湖湖底沉积物放射性水平的调查结果。沉积物中 U、Th、~(226)Ra、~(40)(?)和~(137)Cs 的比活度分别为64.8、67.9,58.9、676.1和3.5Bq/kg;用~(137)Cs 测龄方法作了沉积物泥芯垂直深度的年代定位,由此得知1985—1958年对应深度沉积物中 U、Th、~(226)Ra 和~(40)K 的比活度与1957—1930年对应深度沉积物比较无显著性差异;U、Th 和~(226)Ra 的浓集因予分别为5.2×10~413.9×10~4和4.8×10~4L/kg。     

Feature Reduction via Generalized Uncorrelated Linear Discriminant Analysis

High-dimensional data appear in many applications of data mining, machine learning, and bioinformatics. Feature reduction is commonly applied as a preprocessing step to overcome the curse of dimensionality. Uncorrelated Linear Discriminant Analysis (ULDA) was recently proposed for feature reduction. The extracted features via ULDA were shown to be statistically uncorrelated, which is desirable for many applications. In this paper, an algorithm called ULDA/QR is proposed to simplify the previous implementation of ULDA. Then, the ULDA/GSVD algorithm is proposed, based on a novel optimization criterion, to address the singularity problem which occurs in undersampled problems, where the data dimension is larger than the sample size. The criterion used is the regularized version of the one in ULDA/QR. Surprisingly, our theoretical result shows that the solution to ULDA/GSVD is independent of the value of the regularization parameter. Experimental results on various types of data sets are reported to show the effectiveness of the proposed algorithm and to compare it with other commonly used feature reduction algorithms.