Dynamics of the periodic type-K competitive Kolmogorov systems

For time-periodic dissipative and irreducible type-K competitive Kolmogorov systems, it is proved that there is a canonically defined countable family F of unordered, disjoint invariant sets with the property that, for every persistent trajectory whose ω-limit set is not a cycle, there exists a unique trajectory in some element of F such that these two trajectories are asymptotic and the corresponding points in these two trajectories are K-related.     

时滞种群模型的正周期解对所有正解的吸引性

建立了对数种群模型Ｎ′（ｔ）＝Ｎ（ｔ）｛ｒ（ｔ）－ａ１（ｔ）ｌｎ［Ｎ（ｔ）］－ａ２（ｔ）ｌｎ［Ｎ（ｔ－τ（ｔ））］｝的周期正解的存在性，并得到了正周期解对所有正解的吸引性．     

Estimating the Scale Parameter of a Lévy-stable Distribution via the Extreme Value Approach

The characteristic exponent α of a Lévy-stable law S _α (σ, β, μ) was thoroughly studied as the extreme value index of a heavy tailed distribution. For 1 < α < 2, Peng (Statist. Probab. Lett. 52: 255–264, 2001) has proposed, via the extreme value approach, an asymptotically normal estimator for the location parameter μ. In this paper, we derive by the same approach, an estimator for the scale parameter σ and we discuss its limiting behavior.      

Asymptotic stability, ergodicity and other asymptotic properties of the nonlinear filter

In this work we study connections between various asymptotic properties of the nonlinear filter. It is assumed that the signal has a unique invariant probability measure. The key property of interest is expressed in terms of a relationship between the observation σ field and the tail σ field of the signal, in the stationary filtering problem. This property can be viewed as the permissibility of the interchange of the order of the operations of maximum and countable intersection for certain σ-fields. Under suitable conditions, it is shown that the above property is equivalent to various desirable properties of the filter such as

(a) uniqueness of invariant measure for the signal,

(b) uniqueness of invariant measure for the pair (signal, filter),

(c) a finite memory property of the filter,

(d) a property of finite time dependence between the signal and observation σ fields and

(e) asymptotic stability of the filter.

Previous works on the asymptotic stability of the filter for a variety of filtering models then identify a rich class of filtering problems for which the above equivalent properties hold.     

沉积铁钝化膜的傅立叶变换表面增强拉曼光谱

利用恒电流沉积技术、傅立叶变换表面增强拉曼散射技术现场研究了0 1mol/LNaOH溶液中铁金属电极在不同电位下的表面氧化物的组成。结果表明,在电极预钝化区,表面首先生成的Fe(OH)2可由拉曼谱图中出现的550cm-1表征,证实了以往的研究结果。进入钝化区,表面二价氧化物逐步转化为高价氧化物Fe3O4及α 、δ 和γ FeOOH。在电位回扫的过程中,各氧化产物的还原以及铁表面SERS活性的逐渐消失导致谱峰强度降低。     

An invariance of geometric mean with respect to Lagrangian means

The invariance of the geometric mean G with respect to the Lagrangian mean-type mapping (Lf,Lg), i.e. the equation G○(Lf,Lg)=G, is considered. We show that the functions f and g must be of high class regularity. This fact allows to reduce the problem to a differential equation and determine the second derivatives of the generators f and g.     

Feature Selection using Fuzzy Support Vector Machines

The feature selection consists of obtaining a subset of these features to optimally realize the task without the irrelevant ones. Since it can provide faster and cost-effective learning machines and also improve the prediction performance of the predictors, it is a crucial step in machine learning. The feature selection methods using support machines have obtained satisfactory results, but the noises and outliers often reduce the performance. In this paper, we propose a feature selection approach using fuzzy support vector machines and compare it with the previous work, the results of experiments on the UCI data sets show that feature selection using fuzzy SVM obtains better results than using SVM.     

Scale invariance rule in electromagnetic scattering

The volume integral equation formalism is used to prove the scale invariance rule for an arbitrarily sized scatterer with an arbitrary shape, morphology, and orientation. The only assumptions are that the scatterer is made of optically isotropic linear materials and is embedded in a homogeneous, linear, isotropic, and nonabsorbing infinite medium.     

Equivariant mappings: a new approach in stochastic simulations

Stochastic simulations on manifolds usually are traced back to ⁿ via charts. If a group G is acting on a manifold M and if the respective distribution v is invariant under this group action then in many cases of practical interest there exists a more convenient approach which uses equivariant mappings. The concept of equivariant mappings will be discussed intensively at the instance of the Grassman manifold in which case G equals the orthogonal group. Further advantages of this concept will be demonstrated by applying it to a probabilistic problem from the field of combinatorial geometry.