CHAIN RECURRENT POINTS AND TOPOLOGICAL ENTROPY OF A TREE MAP

Let f be a tree map,P(f) the set of periodic points of f and CR(f) the set of chain recurrent points of f. In this paper,the notion of division for invariant closed subsets of a tree map is introduced.It is proved that: (1) f has zero topological entropy if and only if for any x∈CR(f)-P(f) and each natural number s the orbit of x under f s has a division; (2) If f has zero topological entropy,then for any x∈CR(f)-P(f) the ω-limit set of x is an infinite minimal set.

Equivalence of Network-Solution and PPP-Solution

The technique of precise point positioning (PPP) is gradually becoming a popular method in GPS data-processing. In GPS observation equation, the unknown parameters can be separated into two parts: global parameters and local parameters. The global parameters include orbit, satellite clock and geodynamic parameters. The local parameters are site-occupation-specific, such as position, tropospheric delay, etc. The formulas of local parameters are firstly derived under the network-solution and the PPP-solution conditions respectively. If the weight matrix of global parameters in PPP-solution is small enough, the cofactor matrices of local parameters are the same as that in network-solution. Then, 16 daily solutions are obtained in both PPP mode and network mode. Three sites are selected to compare the solutions. The experimental results demonstrated that the difference between two solutions in coordinates and tropospheric delays are only few millimeters. This level of difference can be neglected so that the solutions from both PPP mode and network mode can be taken as the same in the actual application.

Method of Estimation of Chemical Compounds of a Solution by Analysis of Video Images of Titration from a Semi-Automatic Approach

To titrate or measure a chemical species in a solution is to estimate its quantity of matter or its molar concentration in a given solution. Several methods of estimating molar concentrations of chemical species exist, the main ones being Colorimetric titration, Conductimetric titration, pH metric titration. In practice, all these methods present approximative results because the operator repeats the experiment to ensure the reliability of the results. As a consequence, we have a prolonged time of the experiment which involves a cost in reagents. Given the repetitions of the same experiment, the final result is the average of the results of each experiment. The aim of this paper is to correct this subjectivity by implementing a semi-automatic approach based on colorimetric titration. At the end of the implementation of our approach, we compared our results to those of existing techniques. These results show the reliability of the calculation by the semi-automatic method. This method of estimating the volume at equivalence is fast because it is not manual and does not involve the use of geometric measuring instruments to find the volume at equivalence. This method improves the manual calculation of the volume at equivalence used in the laboratories in school and student environment.

Numerical simulation of scattering wave imaging in a goaf

Goafs are threats to safe mining.Their imaging effects or those of other complex geological bodies are often poor in conventional reflected wave images.Hence,accurate detection of goafs has become an important problem,to be solved with a sense of urgency.Based on scattering theory,we used an equivalent offset method to extract Common Scattering Point gathers,in order to analyze different scattering wave characteristics between Common Scattering Point and Common Mid Point gathers and to compare stack and migration imaging effects.Our research results show that the scattering wave imaging method is more efficient than the conventional imaging method and is therefore a more effective imaging method for detecting goafs and other complex geological bodies.It has important implications for safe mining procedures and infrastructures.

The simulation of ultrasonic beams with a Gaussian beam equivalent point source model

Point Sources and Gaussian beams are used frequently as fundamental building blocks for developing ultrasonic beam models. Both these models have different weaknesses that limit their effectiveness. Here, we will show that one can develop a Gaussian Beam Equivalent Point Source （GBEPS） model that removes those weaknesses and combines the accuracy and versatility of the point source models with much of the speed and well-behaved nature of Gaussian beam models. We will demonstrate the efficiency and versatility of this new GBEPS model in simulating the beams generated from ultrasonic phased arrays, using as few as one Gaussian beam per element of the array. A single element GBEPS model will be shown to be as accurate as a point source model even when substantial beam focusing or steering is present in the array or where the array beam is transmitted through an interface. At the same time the GBEPS model will be shown to be several orders of magnitude faster than the point source model.