A modified method of discontinuity trace mapping using three-dimensional point clouds of rock mass surfaces

This paper presents an automated method for discontinuity trace mapping using three-dimensional point clouds of rock mass surfaces.Specifically,the method consists of five steps:(1)detection of trace feature points by normal tensor voting theory,(2)co ntraction of trace feature points,(3)connection of trace feature points,(4)linearization of trace segments,and(5)connection of trace segments.A sensitivity analysis was then conducted to identify the optimal parameters of the proposed method.Three field cases,a natural rock mass outcrop and two excavated rock tunnel surfaces,were analyzed using the proposed method to evaluate its validity and efficiency.The results show that the proposed method is more efficient and accurate than the traditional trace mapping method,and the efficiency enhancement is more robust as the number of feature points increases.

WEYL TRANSFORMATIONS ON MANIFOLDS Ⅱ. Generalized Trace and Inverse Mapping Formula

The two gate formula for a diffusion X_t in R^n is considered.The formula gives an expressionof the density function of X_t in terms of the path integral of the Brownian bridge starting from xand ending on y at time t.

Proterozoic to Phanerozoic case studies of laser ablation microanalysis for microbial carbonate U–Pb geochronology

Some of the earliest bio-sedimentary records of life on Earth are represented by microbial carbonates,which are also critical geochemical archives of ancient seawater chemistry and the environmental circumstances in which they precipitated.Reconstructing paleo-microbial environments on Earth and potentially other planets requires precise determination of the depositional ages of these materials.The(abiogenic)carbonate geochemistry communities can now use developments in in-situ laser ablation U-Pb dating using inductively coupled plasma mass spectrometry(LA-ICP-MS).Due to the effects of impurity mixing and diagenesis,microbial carbonates have received little geochronological study despite their broad relevance for understanding ancient seawater’s environmental conditions and geochemical compositions.This study demonstrates using time-of-flight mass spectrometry(TOF-MS)to perform quick,quantitative elemental mapping before U-Pb spot dating to improve experiment success rates and data reliability and offers four practical application examples.

On Reed-Solomon Codes

The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory.The main problem is to compute the error distance of a received word.Using the Weil bound for character sum estimate,Li and Wan showed that the error distance can be determined when the degree of the received word as a polynomial is small.In the first part,the result of Li and Wan is improved.On the other hand,one of the important parameters of an error-correcting code is the dimension.In most cases,one can only get bounds for the dimension.In the second part,a formula for the dimension of the generalized trace Reed-Solomon codes in some cases is obtained.