The Application of Continuous Spatial Scaling Model of NDVI in Validation and Its Sensibility Analysis to Various Image Characteristics

Based on the fractal theory, this study establishes a Continuous Spatial Scaling Model （CSSM） of the Normalized Difference Vegetation Index （NDVI） to address issues arising with spatial up-scaling in quantitative remote sensing. This model is able to quantitatively describe transformation relationships of the NDVI on continuous scales. Then the following experiments are accomplished： （1） the validation of ETM＋ NDVI imagery is implemented based on the GEOEYE-1 image and its NDVI CSSM, and the following conclusion is obtained： because of bad stripes in the ETM＋ image and the limited effect of destriping, the ETM＋ NDVI image had a rather large error, and the error for the entire experimental imagery is about 25%, so the ETM＋ NDVI product is not suitable for direct practical application; （2） Shatian Byland （Beihai City, China） is taken as the experimental area, and four images （two ETM＋ images with wider and smaller coverage, respectively, a GEOEYE-1 image, and an HJ-1B CCD1 image） are studied. The most suitable scale levels are computed and compared for the four images, and a better understanding is obtained of the impact of various image characteristics （area of coverage, spatial resolution, and imaging quality） on determining the scale level for the NDVI CSSM.

Fractal dynamics in the ionization of helium Rydberg atoms

We study the ionization of helium Rydberg atoms in an electric field above the classical ionization threshold within the semiclassical theory.By introducing a fractal approach to describe the chaotic dynamical behavior of the ionization,we identify the fractal self-similarity structure of the escape time versus the distribution of the initial launch angles of electrons,and find that the self-similarity region shifts toward larger initial launch angles with a decrease in the scaled energy.We connect the fractal structure of the escape time plot to the escape dynamics of ionized electrons.Of particular note is that the fractal dimensions are sensitively controlled by the scaled energy and magnetic field,and exhibit excellent agreement with the chaotic extent of the ionization systems for both helium and hydrogen Rydberg atoms.It is shown that,besides the electric and magnetic fields,core scattering is a primary factor in the fractal dynamics.

Self-assembling metal–organic coordinated fractal crystals

Fractals are essentially characterized by their self-similarity at different scales and non-integer Hausdorff dimensions[1],while crystals always show certain symmetries and discrete diffraction diagrams[2].Thus,a fractal crystal by definition must be identical at all scales with a compatible symmetry with crystals.Although fractals,e.g.snowflakes,trees,coastlines and blood-vascular systems,

Krein regularization of λφ~3 theory

In this paper, the one-loop self energy of λφ3 theory is calculated by using Krein regularization in four and six dimensions and the result, which is finite, is compared with the conventional result of λφ3 theory in Hilbert space. The self energy is calculated in the one-loop approximation and the result is automatically regularized as a result of “Krein Regularization”.