Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D G...Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.展开更多
To fully extract and mine the multi-scale features of reservoirs and geologic structures in time/depth and space dimensions, a new 3D multi-scale volumetric curvature （MSVC） methodology is presented in this paper. W...To fully extract and mine the multi-scale features of reservoirs and geologic structures in time/depth and space dimensions, a new 3D multi-scale volumetric curvature （MSVC） methodology is presented in this paper. We also propose a fast algorithm for computing 3D volumetric curvature. In comparison to conventional volumetric curvature attributes, its main improvements and key algorithms introduce multi-frequency components expansion in time-frequency domain and the corresponding multi-scale adaptive differential operator in the wavenumber domain, into the volumetric curvature calculation. This methodology can simultaneously depict seismic multi-scale features in both time and space. Additionally, we use data fusion of volumetric curvatures at various scales to take full advantage of the geologic features and anomalies extracted by curvature measurements at different scales. The 3D MSVC can highlight geologic anomalies and reduce noise at the same time. Thus, it improves the interpretation efficiency of curvature attributes analysis. The 3D MSVC is applied to both land and marine 3D seismic data. The results demonstrate that it can indicate the spatial distribution of reservoirs, detect faults and fracture zones, and identify their multi-scale properties.展开更多
One of the methods of mathematical analysis in many cases makes it possible to reduce the study of differential operators, pseudo-differential operators and certain types of integral operators and the solution of equa...One of the methods of mathematical analysis in many cases makes it possible to reduce the study of differential operators, pseudo-differential operators and certain types of integral operators and the solution of equations containing them, to an examination of simpler algebraic problems. The development and systematic use of operational calculus began with the work of O. Heaviside (1892), who proposed formal rules for dealing with the differentiation operator d/dt and solved a number of applied problems. However, he did not give operational calculus a mathematical basis;this was done with the aid of the Laplace transform;J. Mikusi<span style="white-space:nowrap;">ń</span>ski (1953) put operational calculus into algebraic form, using the concept of a function ring <a href="#ref1">[1]</a>. Thereupon I’m suggesting here the use of the integration operator dt to make an extension for the systematic use of operational calculus. Throughout designing and analyzing a control system, we need to treat the functionality of the system with respect to time. The reaction of the system instructs us how to stable it by amplifiers and feedbacks <a href="#ref2">[2]</a>, thereafter the Differential Transform is a good tool for doing this, and it’s a technique to frustrate difficulties we may bump into, also it has the methods to find the immediate reaction of the system with respect to infinitesimal (tiny) time which spares us from the hard work in finding the time dependent function, this could be done by producing finite series.展开更多
The partial differential equation(PDE)solution of the telegrapher is a promising fault location method among time-domain and model-based techniques.Recent research works have shown that the leap-frog process is superi...The partial differential equation(PDE)solution of the telegrapher is a promising fault location method among time-domain and model-based techniques.Recent research works have shown that the leap-frog process is superior to other explicit methods for the PDE solution.However,its implementation is challenged by determining the initial conditions in time and the boundary conditions in space.This letter proposes two implicit solution methods for determining the initial conditions and an analytical way to obtain the boundary conditions founded on the signal decomposition.The results show that the proposal gives fault location accuracy superior to the existing leap-frog scheme,particularly in the presence of harmonics.展开更多
Recent advances in high-throughput chromosome conformation capture(Hi-C)techniques have allowed us to map genome-wide chromatin interactions and uncover higher-order chromatin structures,thereby shedding light on the ...Recent advances in high-throughput chromosome conformation capture(Hi-C)techniques have allowed us to map genome-wide chromatin interactions and uncover higher-order chromatin structures,thereby shedding light on the principles of genome architecture and functions.However,statistical methods for detecting changes in large-scale chromatin organization such as topologically associating domains(TADs)are still lacking.Here,we proposed a new statistical method,DiffGR,for detecting differentially interacting genomic regions at the TAD level between Hi-C contact maps.We utilized the stratum-adjusted correlation coefficient to measure similarity of local TAD regions.We then developed a nonparametric approach to identify statistically significant changes of genomic interacting regions.Through simulation studies,we demonstrated that DiffGR can robustly and effectively discover differential genomic regions under various conditions.Furthermore,we successfully revealed cell type-specific changes in genomic interacting regions in both human and mouse Hi-C datasets,and illustrated that DiffGR yielded consistent and advantageous results compared with state-of-the-art differential TAD detection methods.The DiffGR R package is published under the GNU General Public License(GPL)≥2 license and is publicly available at https://github.com/wmalab/DiffGR.展开更多
Applying the Riemann-Roch theorem,we calculate the dimension of a kind of mero- morphicλ-differentials’ space on compact Riemann surfaces.And we also construct a basis of theλ-differentials’ space.As the main resu...Applying the Riemann-Roch theorem,we calculate the dimension of a kind of mero- morphicλ-differentials’ space on compact Riemann surfaces.And we also construct a basis of theλ-differentials’ space.As the main result,the Cauchy type of integral formula on compact Riemann surfaces is established.展开更多
基金The paper was financially supported by the National Natural Science Foundation of China (No. 19802008)Excellent Doctoral Dissertation Grant of the Ministry of Education of China (No. 199927)
文摘Based on the Laplace transform, a direct derivation of the ordinary differential equations for the three-dimensional transient free-surface Green function in marine hydrodynamics is presented. The results for the 3D Green function and all its spatial derivatives are a set of fourth-order ordinary differential equations, which are identical with that of Clement (1998). All of these results may be used to accelerate numerical computation for the time-domain boundary element method in marine hydrodynamics.
基金supported by the National Natural Science Foundation of China (No. 41004054) Research Fund for the Doctoral Program of Higher Education of China (No. 20105122120002)Natural Science Key Project, Sichuan Provincial Department of Education (No. 092A011)
文摘To fully extract and mine the multi-scale features of reservoirs and geologic structures in time/depth and space dimensions, a new 3D multi-scale volumetric curvature （MSVC） methodology is presented in this paper. We also propose a fast algorithm for computing 3D volumetric curvature. In comparison to conventional volumetric curvature attributes, its main improvements and key algorithms introduce multi-frequency components expansion in time-frequency domain and the corresponding multi-scale adaptive differential operator in the wavenumber domain, into the volumetric curvature calculation. This methodology can simultaneously depict seismic multi-scale features in both time and space. Additionally, we use data fusion of volumetric curvatures at various scales to take full advantage of the geologic features and anomalies extracted by curvature measurements at different scales. The 3D MSVC can highlight geologic anomalies and reduce noise at the same time. Thus, it improves the interpretation efficiency of curvature attributes analysis. The 3D MSVC is applied to both land and marine 3D seismic data. The results demonstrate that it can indicate the spatial distribution of reservoirs, detect faults and fracture zones, and identify their multi-scale properties.
文摘One of the methods of mathematical analysis in many cases makes it possible to reduce the study of differential operators, pseudo-differential operators and certain types of integral operators and the solution of equations containing them, to an examination of simpler algebraic problems. The development and systematic use of operational calculus began with the work of O. Heaviside (1892), who proposed formal rules for dealing with the differentiation operator d/dt and solved a number of applied problems. However, he did not give operational calculus a mathematical basis;this was done with the aid of the Laplace transform;J. Mikusi<span style="white-space:nowrap;">ń</span>ski (1953) put operational calculus into algebraic form, using the concept of a function ring <a href="#ref1">[1]</a>. Thereupon I’m suggesting here the use of the integration operator dt to make an extension for the systematic use of operational calculus. Throughout designing and analyzing a control system, we need to treat the functionality of the system with respect to time. The reaction of the system instructs us how to stable it by amplifiers and feedbacks <a href="#ref2">[2]</a>, thereafter the Differential Transform is a good tool for doing this, and it’s a technique to frustrate difficulties we may bump into, also it has the methods to find the immediate reaction of the system with respect to infinitesimal (tiny) time which spares us from the hard work in finding the time dependent function, this could be done by producing finite series.
基金Izudin Dzafic was supported by the Federal Ministry of Education and ScienceBosniathrough funding
文摘The partial differential equation(PDE)solution of the telegrapher is a promising fault location method among time-domain and model-based techniques.Recent research works have shown that the leap-frog process is superior to other explicit methods for the PDE solution.However,its implementation is challenged by determining the initial conditions in time and the boundary conditions in space.This letter proposes two implicit solution methods for determining the initial conditions and an analytical way to obtain the boundary conditions founded on the signal decomposition.The results show that the proposal gives fault location accuracy superior to the existing leap-frog scheme,particularly in the presence of harmonics.
基金supported by the National Science Foundation,USA(Grant No.DBI-1751317)the National Institute of Health,USA(Grant No.R35GM133678).
文摘Recent advances in high-throughput chromosome conformation capture(Hi-C)techniques have allowed us to map genome-wide chromatin interactions and uncover higher-order chromatin structures,thereby shedding light on the principles of genome architecture and functions.However,statistical methods for detecting changes in large-scale chromatin organization such as topologically associating domains(TADs)are still lacking.Here,we proposed a new statistical method,DiffGR,for detecting differentially interacting genomic regions at the TAD level between Hi-C contact maps.We utilized the stratum-adjusted correlation coefficient to measure similarity of local TAD regions.We then developed a nonparametric approach to identify statistically significant changes of genomic interacting regions.Through simulation studies,we demonstrated that DiffGR can robustly and effectively discover differential genomic regions under various conditions.Furthermore,we successfully revealed cell type-specific changes in genomic interacting regions in both human and mouse Hi-C datasets,and illustrated that DiffGR yielded consistent and advantageous results compared with state-of-the-art differential TAD detection methods.The DiffGR R package is published under the GNU General Public License(GPL)≥2 license and is publicly available at https://github.com/wmalab/DiffGR.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10626054,10701077)the Knowledge Innovation Project of Chinese Academy of Sciences(Grant No.KJCX3-SYW-S03)the National Key Basic Research Project of China(Grant No.2004CB31800,2006CB805905)
文摘Applying the Riemann-Roch theorem,we calculate the dimension of a kind of mero- morphicλ-differentials’ space on compact Riemann surfaces.And we also construct a basis of theλ-differentials’ space.As the main result,the Cauchy type of integral formula on compact Riemann surfaces is established.
