This study utilizes a semantic-level computer vision-based detection to characterize fracture traces of hard rock pillars in underground space.The trace images captured by photogrammetry are used to establish the data...This study utilizes a semantic-level computer vision-based detection to characterize fracture traces of hard rock pillars in underground space.The trace images captured by photogrammetry are used to establish the database for training two convolutional neural network(CNN)-based models,i.e.,U-Net(University of Freiburg,Germany)and DeepLabV3+(Google,USA)models.Chain code technology,polyline approximation algorithm,and the circular window scanning approach are combined to quantify the main characteristics of fracture traces on flat and uneven surfaces,including trace length,dip angle,density,and intensity.The extraction results indicate that the CNN-based models have better performances than the edge detection methods-based Canny and Sobel operators for extracting the trace and reducing noise,especially the DeepLabV3+model.Furthermore,the quantization results further prove the reliability of extracting the fracture trace.As a result,a case study with two types of traces(i.e.,on flat and uneven surfaces)demonstrates that the applied semantic-level computer vision detection is an accurate and efficient approach for characterizing the fracture trace of hard rock pillars.展开更多
This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset ...This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil＇s formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L^2 （G / H, μ）.展开更多
In this paper,we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline cases.We first give a full characterization of the existence of trace spac...In this paper,we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline cases.We first give a full characterization of the existence of trace spaces for these weighted Sobolev spaces,and then study the trace parts and the extension parts between the weighted Sobolev spaces and a new kind of Besov-type spaces(on hyperplanes)which are defined by using integral averages over selected layers of dyadic cubes.展开更多
Let A be a unital C-algebra, n ∈ N ∪ {∞}. It is proved that the isomorphism △n : is isometric for some suitable distances. Asan application, the author has the split exact sequence with iA contractive (and isometr...Let A be a unital C-algebra, n ∈ N ∪ {∞}. It is proved that the isomorphism △n : is isometric for some suitable distances. Asan application, the author has the split exact sequence with iA contractive (and isometric if n = ∞) under certain condition of A.展开更多
A program of proving the Riemann hypothesis by using the Fourier analysis on global fields is given by Connes(1999). The difficulty for realizing the program lies in proving the validity of Connes' global trace fo...A program of proving the Riemann hypothesis by using the Fourier analysis on global fields is given by Connes(1999). The difficulty for realizing the program lies in proving the validity of Connes' global trace formula on an L2-space. In this paper, a new global trace formula is obtained on a Fr′echet space which gives the Weil distribution △(h).展开更多
基金This research is partially supported by the National Natural Science Foundation Project of China(Grant No.42177164)the Outstanding Youth Project of Hunan Provincial Department of Education(Grant No.23B0008)the Distinguished Youth Science Foundation of Hunan Province of China(2022JJ10073).
文摘This study utilizes a semantic-level computer vision-based detection to characterize fracture traces of hard rock pillars in underground space.The trace images captured by photogrammetry are used to establish the database for training two convolutional neural network(CNN)-based models,i.e.,U-Net(University of Freiburg,Germany)and DeepLabV3+(Google,USA)models.Chain code technology,polyline approximation algorithm,and the circular window scanning approach are combined to quantify the main characteristics of fracture traces on flat and uneven surfaces,including trace length,dip angle,density,and intensity.The extraction results indicate that the CNN-based models have better performances than the edge detection methods-based Canny and Sobel operators for extracting the trace and reducing noise,especially the DeepLabV3+model.Furthermore,the quantization results further prove the reliability of extracting the fracture trace.As a result,a case study with two types of traces(i.e.,on flat and uneven surfaces)demonstrates that the applied semantic-level computer vision detection is an accurate and efficient approach for characterizing the fracture trace of hard rock pillars.
文摘This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G and μ be the normalized G-invariant measure on G/H associated to the Weil＇s formula. Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L^2 （G / H, μ）.
基金partly supported by NNSF of China(Grant No.11822105)partly supported by NNSF of China(Grant Nos.12071121 and 11720101003)supported by NNSF of China(Grant No.12101226)。
文摘In this paper,we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline cases.We first give a full characterization of the existence of trace spaces for these weighted Sobolev spaces,and then study the trace parts and the extension parts between the weighted Sobolev spaces and a new kind of Besov-type spaces(on hyperplanes)which are defined by using integral averages over selected layers of dyadic cubes.
基金Project supported by the National Natural Science Foundation of China (No.10271090).
文摘Let A be a unital C-algebra, n ∈ N ∪ {∞}. It is proved that the isomorphism △n : is isometric for some suitable distances. Asan application, the author has the split exact sequence with iA contractive (and isometric if n = ∞) under certain condition of A.
文摘A program of proving the Riemann hypothesis by using the Fourier analysis on global fields is given by Connes(1999). The difficulty for realizing the program lies in proving the validity of Connes' global trace formula on an L2-space. In this paper, a new global trace formula is obtained on a Fr′echet space which gives the Weil distribution △(h).
