An analytical process of spatial autocorrelation functions based on Moran’s index

A number of spatial statistic measurements such as Moran’s I and Geary’s C can be used for spatial autocorrelation analysis. Spatial autocorrelation modeling proceeded from the 1-dimension autocorrelation of time series analysis, with time lag replaced by spatial weights so that the autocorrelation functions degenerated to autocorrelation coefficients. This paper develops 2-dimensional spatial autocorrelation functions based on the Moran index using the relative staircase function as a weight function to yield a spatial weight matrix with a displacement parameter. The displacement bears analogy with the time lag in time series analysis. Based on the spatial displacement parameter, two types of spatial autocorrelation functions are constructed for 2-dimensional spatial analysis. Then the partial spatial autocorrelation functions are derived by using the Yule-Walker recursive equation. The spatial autocorrelation functions are generalized to the autocorrelation functions based on Geary’s coefficient and Getis’ index. As an example, the new analytical framework was applied to the spatial autocorrelation modeling of Chinese cities. A conclusion can be reached that it is an effective method to build an autocorrelation function based on the relative step function. The spatial autocorrelation functions can be employed to reveal deep geographical information and perform spatial dynamic analysis, and lay the foundation for the scaling analysis of spatial correlation.

Introduction, generation and entanglement of entangled displaced even and odd squeezed states

In this paper, first, we introduce special types of entangled quantum states named “entangled displaced even and odd squeezed states” by using displaced even and odd squeezed states which are constructed via the action of displacement operator on the even and odd squeezed states, respectively. Next, we present a theoretical scheme to generate the introduced entangled states. This scheme is based on the interaction between a [Formula: see text]-type three-level atom and a two-mode quantized field in the presence of two strong classical fields. In the continuation, we consider the entanglement feature of the introduced entangled states by evaluating concurrence. Moreover, we study the influence of the displacement parameter on the entanglement degree of the introduced entangled states and compare the results. It will be observed that the concurrence of the “entangled displaced odd squeezed states” has less decrement with respect to the “entangled displaced even squeezed states” by increasing the displacement parameter.

Source Parameter Estimation Method for Assessment of Structural Resiliencies

Assessing structural integrity and sustainability during natural hazards, for instance, strong earthquakes, is an effective way to reduce or even avoid large losses of life and property damage. With the established vulnerability relationships between source parameter and building damage, the seismic resilience of structures can be obtained after the source parameter is estimated in the early stage of an earthquake. For this purpose, we propose a method that employs the P wave displacement parameter to estimate earthquake magnitude in real time to quick assess the structural resiliencies. By selecting period and amplitude parameter as comparisons, the magnitude estimation formulas are derived, respectively, where the proposed P wave displacement parameter method is of the highest precision. Through the evolutionary estimation of the P wave displacement parameter as a function of the time window used, we show that the existing regression relationships can be extended to the large earthquake. Therefore, this paper provides a quick earthquake magnitude estimation method for the establishment of a more reasonable and accurate resilience assessment system for structures.

The atomic anisotropic displacement tensor – completing the picture

A simplified approach for calculating the equivalent isotropic displacement parameter is presented and the transformation property of the tensor representationUto point-group operations is analysed. Complete tables have been compiled for the restrictions imposed upon the tensor owing to the site symmetry associated with all special positions as listed in Hahn [(2011),International Tables for Crystallography, Vol. A,Space-group Symmetry, 5th revised ed. Chichester: John Wiley and Sons, Ltd].

CRYSTALSenhancements: asymmetric restraints

The traditional Waser distance restraint, the rigid-bond restraint and atomic displacement parameter (ADP) similarity restraints have an equal influence on both atoms involved in the restraint. This may be inappropriate in cases where it can reasonably be expected that the precision of the determination of the positional parameters and ADPs is not equal,e.g.towards the extremities of a librating structure or where one atom is a significantly stronger scatterer than the other. In these cases, the traditional restraint feeds information from the poorly defined atom to the better defined atom, with the possibility that its characteristics become degraded. The modified restraint described here feeds information from the better defined atom to the more poorly defined atom with minimal feedback.