This paper deals with the oscillatory properties of a class of nonlinear advanced difference equations. Sufficient criteria in the form of infinite sum for the equation to be oscillatory are obtained. In the linear cases, our results coincide with those in the literature.
The separation of anomalies from geochemical background is an important part of data analysis because lack of such identifications might have profound influence on or even distort the final analysis results. In this article, 1 672 geochemical analytical data of 11 elements, including Cu, Mo, Ag, Sn, and others, from a region within Tibet, South China, are used as one example. Together with the traditional anomaly recognition method of using the iterative mean ±2σ local multifractality theory has been utilized to delineate the ranges of geochemical anomalies of the elements. To different degrees, on the basis of original data mapping, C-A fractal analysis and singularity exponents, Sn differs from the other 10 elements. Moreover, geochemical mapping results based on values of the multifractal asymmetry index for all elements delineate the highly anomalous area. Similar to other 10 elements, the anomalous areas of Sn delineated by the asymmetry index distribute along the main structure orientations. According to the asymmetry indexes, the 11 elements could be classified into 3 groups： （1） Ag and Au, （2） As-Sb-Cu-Pb-Zn-Mo, and （3） Sn-Bi-W. This parageneflc association of elements can be used to interpret possible origins of mineralization, which is in agreement with petrological analysis and field survey results.
Sphalerite banding is a common texture in Jinding （金顶） Pb-Zn deposit, Yunnan （云南）, southwestern China. The frequency distribution and irregularity of sphalerite grains observed in the bandings are characterized quantitatively by fractal models. Fractal dimensions calculated by several fractal models including box-counting model, perimeter-area （P-A） model, and number-area （N-A） model show the gradual change from outer banding to inner banding, indicating a decrease in area percentage, in irregularity, in shape and in grain size, and an increase in the numbers of grains. These results may imply an inward growth of sphalerite during mineralization, and self-organization properties are involved in the nonlinear process of mineralization.
In this paper, oscillatory properties for solutions of certain nonlinear impulsive parabolic equation are investigated and a series of new sufficient conditions is established.
This paper deals with the oscillatory properties of a class of nonlinear difference equations with several delays. Sufficient criteria in the form of infinite sum for the equations to be oscillatory are obtained.
Wang Xiaomei Liu Anping Liu Keying Liu Jing ( School of Math, and Physics, China University of Geosciences, Wuhan 430074
