The main aim of this paper is to derive some new summation theorems for terminating and truncated Clausen’s hypergeometric series with unit argument,when one numerator parameter and one denominator parameter are nega...The main aim of this paper is to derive some new summation theorems for terminating and truncated Clausen’s hypergeometric series with unit argument,when one numerator parameter and one denominator parameter are negative integers.Further,using our truncated summation theorems,we obtain the Mellin transforms of the product of exponential function and Goursat’s truncated hypergeometric function.展开更多
In nD differential geometry, basic geometric structures and properties are described locally by differentiable functions and equations with indices that obey Einstein summation convention. Although symbolic manipulati...In nD differential geometry, basic geometric structures and properties are described locally by differentiable functions and equations with indices that obey Einstein summation convention. Although symbolic manipulation of such indexed functions is one of the oldest research topics in computer algebra, so far there exists no normal form reduction algorithm to judge whether two indexed polynomials involving indices of different coordinate systems are equal or not. It is a challenging task in computer algebra. In this paper, for a typical framework—the partial derivatives in coordinate transformation matrix involved are of order no more than two (such as local computations of ordinary curvatures and tor-sion), we put forward two algorithms, one on elimination of all redundant dummy indices of indexed polynomials, the other on normalization of such indexed polynomials, by which we can judge whether two indexed polynomials are equal or not. We implement the algorithms with Maple V.10 and use them to solve tensor verification problems in differential geometry, and to derive automatically the transformation rules of locally defined indexed functions under the change of local coordinates.展开更多
The geological conditions for coal mining in China are complex,with various structural issues such as faults and collapsed columns seriously compromising the safety of coal mine production.In-seam wave exploration is ...The geological conditions for coal mining in China are complex,with various structural issues such as faults and collapsed columns seriously compromising the safety of coal mine production.In-seam wave exploration is an effective technique for acquiring detailed information on geological structures in coal seam working faces.However,the existing reflected in-seam wave imaging technique can no longer meet the exploration precision requirements,making it imperative to develop a new reflected in-seam wave imaging technique.This study applies the Gaussian beam summation(GBS)migration method to imaging coal seams'reflected in-seam wave data.Firstly,with regard to the characteristics of the reflected in-seam wave data,methods such as wavefield removal and enveloped superposition are employed for the corresponding wavefield separation,wave train compression and other processing of reflected in-seam waves.Thereafter,imaging is performed using the GBS migration technique.The feasibility and effectiveness of the proposed method for reflected in-seam wave imaging are validated by conducting GBS migration tests on 3D coal-seam fault models with different dip angles and throws.By applying the method to reflected in-seam wave data for an actual coal seam working face,accurate imaging of a fault structure is obtained,thereby validating its practicality.展开更多
To investigate the distribution and velocity attributes of gas hydrates in the northern continental slope of South China Sea, Guangzhou Marine Geological Survey conducted four-component （4C） ocean-bottom seismometer...To investigate the distribution and velocity attributes of gas hydrates in the northern continental slope of South China Sea, Guangzhou Marine Geological Survey conducted four-component （4C） ocean-bottom seismometer （OBS） surveys. A case study is presented to show the results of acquiring and processing OBS data for detecting gas hydrates. Key processing steps such as repositioning, reorientation, PZ summation, and mirror imaging are discussed. Repositioning and reorientation find the correct location and direction of nodes. PZ summation matches P- and Z-components and sums them to separate upgoing and downgoing waves. Upgoing waves are used in conventional imaging, whereas downgoing waves are used in mirror imaging. Mirror imaging uses the energy of the receiver ghost reflection to improve the illumination of shallow structures, where gas hydrates and the associated bottom-simulating reflections （BSRs） are located. We developed a new method of velocity analysis using mirror imaging. The proposed method is based on velocity scanning and iterative prestack time migration. The final imaging results are promising. When combined with the derived velocity field, we can characterize the BSR and shallow structures; hence, we conclude that using 4C OBS can reveal the distribution and velocity attributes of gas hydrates.展开更多
The phase summation effect in sum-frequency mixing process is utilized to avoid a nonlinearity obstacle in the power scaling of single-frequency visible or ultraviolet lasers.Two single-frequency fundamental lasers ar...The phase summation effect in sum-frequency mixing process is utilized to avoid a nonlinearity obstacle in the power scaling of single-frequency visible or ultraviolet lasers.Two single-frequency fundamental lasers are spectrally broadened by phase modulation to suppress stimulated Brillouin scattering in fiber amplifier and achieve higher power.After sum-frequency mixing in a nonlinear optical crystal,the upconverted laser returns to single frequency due to phase summation,when the phase modulations on two fundamental lasers have a similar amplitude but opposite sign.The method was experimentally proved in a Raman fiber amplifier-based laser system,which generated a power-scalable sideband-free single-frequency 590 nm laser.The proposal manifests the importance of phase operation in wave-mixing processes for precision laser technology.展开更多
Instrumental and environmental disturbances do affect FG5 absolute gravimeter observations and the estimated gravity values, sometimes to the degree that entire measurement campaigns are discarded. We propose a method...Instrumental and environmental disturbances do affect FG5 absolute gravimeter observations and the estimated gravity values, sometimes to the degree that entire measurement campaigns are discarded. We propose a method which moves towards the re-assessment of previously discarded observations. Once an estimate of the frequency and amplitude of a disturbance in a FG5 data set exists, the proposed method can estimate its impact on the estimated gravity value. This is performed through a Gaussian Bell Summation approach of the functional relationship between disturbance frequency and standard deviation of gravity. The filtering of the identified disturbance is realized through a modification of the functional model of the equation of motion in the least squares adjustment of FG5 observations. The results reveal that the Gaussian Bell Summation approximates the frequency—gravity impact relationship sufficiently well with negligible uncertainties, while the accuracy of the detected disturbance frequency defines a limiting factor for the gravity impact estimation. A realistic disturbance of 15 Hz with an amplitude of 1.5 nm had an impact of ≈48 [μGal] on the gravity estimate. The proposed filter approach reduced the impact to ≈12 [μGal], with the remaining effect being almost entirely associated to the uncertainty in disturbance frequency detection.展开更多
目的研究一个包含伪Smarandache无平方因子函数Zω(n)的极限问题。方法利用初等及解析方法。结果证明了该极限存在且其值为1。结论解决了Felice Russo在文献A set of new Smarandache functions,sequences and conjectures in number th...目的研究一个包含伪Smarandache无平方因子函数Zω(n)的极限问题。方法利用初等及解析方法。结果证明了该极限存在且其值为1。结论解决了Felice Russo在文献A set of new Smarandache functions,sequences and conjectures in number theory中提出的一个极限问题。展开更多
文摘The main aim of this paper is to derive some new summation theorems for terminating and truncated Clausen’s hypergeometric series with unit argument,when one numerator parameter and one denominator parameter are negative integers.Further,using our truncated summation theorems,we obtain the Mellin transforms of the product of exponential function and Goursat’s truncated hypergeometric function.
基金supported by Major State Basic Research Development Program of China (Grant No.2004CB318001)Leading Academic Disciplines Program of Shanghai (Grant No. S30501)
文摘In nD differential geometry, basic geometric structures and properties are described locally by differentiable functions and equations with indices that obey Einstein summation convention. Although symbolic manipulation of such indexed functions is one of the oldest research topics in computer algebra, so far there exists no normal form reduction algorithm to judge whether two indexed polynomials involving indices of different coordinate systems are equal or not. It is a challenging task in computer algebra. In this paper, for a typical framework—the partial derivatives in coordinate transformation matrix involved are of order no more than two (such as local computations of ordinary curvatures and tor-sion), we put forward two algorithms, one on elimination of all redundant dummy indices of indexed polynomials, the other on normalization of such indexed polynomials, by which we can judge whether two indexed polynomials are equal or not. We implement the algorithms with Maple V.10 and use them to solve tensor verification problems in differential geometry, and to derive automatically the transformation rules of locally defined indexed functions under the change of local coordinates.
基金supported by the National Natural Science Foundation of China(Grant No.42174157)the CAGS Research Fund(Grant No.JKY202216)the Chinese Geological Survey Project(Grant Nos.DD20230008,DD20233002).
文摘The geological conditions for coal mining in China are complex,with various structural issues such as faults and collapsed columns seriously compromising the safety of coal mine production.In-seam wave exploration is an effective technique for acquiring detailed information on geological structures in coal seam working faces.However,the existing reflected in-seam wave imaging technique can no longer meet the exploration precision requirements,making it imperative to develop a new reflected in-seam wave imaging technique.This study applies the Gaussian beam summation(GBS)migration method to imaging coal seams'reflected in-seam wave data.Firstly,with regard to the characteristics of the reflected in-seam wave data,methods such as wavefield removal and enveloped superposition are employed for the corresponding wavefield separation,wave train compression and other processing of reflected in-seam waves.Thereafter,imaging is performed using the GBS migration technique.The feasibility and effectiveness of the proposed method for reflected in-seam wave imaging are validated by conducting GBS migration tests on 3D coal-seam fault models with different dip angles and throws.By applying the method to reflected in-seam wave data for an actual coal seam working face,accurate imaging of a fault structure is obtained,thereby validating its practicality.
基金supported by the National Hi-tech Research and Development Program of China(863 Program)(Grant No.2013AA092501)the China Geological Survey Projects(Grant Nos.GZH201100303 and GZH201100305)
文摘To investigate the distribution and velocity attributes of gas hydrates in the northern continental slope of South China Sea, Guangzhou Marine Geological Survey conducted four-component （4C） ocean-bottom seismometer （OBS） surveys. A case study is presented to show the results of acquiring and processing OBS data for detecting gas hydrates. Key processing steps such as repositioning, reorientation, PZ summation, and mirror imaging are discussed. Repositioning and reorientation find the correct location and direction of nodes. PZ summation matches P- and Z-components and sums them to separate upgoing and downgoing waves. Upgoing waves are used in conventional imaging, whereas downgoing waves are used in mirror imaging. Mirror imaging uses the energy of the receiver ghost reflection to improve the illumination of shallow structures, where gas hydrates and the associated bottom-simulating reflections （BSRs） are located. We developed a new method of velocity analysis using mirror imaging. The proposed method is based on velocity scanning and iterative prestack time migration. The final imaging results are promising. When combined with the derived velocity field, we can characterize the BSR and shallow structures; hence, we conclude that using 4C OBS can reveal the distribution and velocity attributes of gas hydrates.
基金The work was partly supported by the National Natural Science Foundation of China(No.62075226).
文摘The phase summation effect in sum-frequency mixing process is utilized to avoid a nonlinearity obstacle in the power scaling of single-frequency visible or ultraviolet lasers.Two single-frequency fundamental lasers are spectrally broadened by phase modulation to suppress stimulated Brillouin scattering in fiber amplifier and achieve higher power.After sum-frequency mixing in a nonlinear optical crystal,the upconverted laser returns to single frequency due to phase summation,when the phase modulations on two fundamental lasers have a similar amplitude but opposite sign.The method was experimentally proved in a Raman fiber amplifier-based laser system,which generated a power-scalable sideband-free single-frequency 590 nm laser.The proposal manifests the importance of phase operation in wave-mixing processes for precision laser technology.
文摘Instrumental and environmental disturbances do affect FG5 absolute gravimeter observations and the estimated gravity values, sometimes to the degree that entire measurement campaigns are discarded. We propose a method which moves towards the re-assessment of previously discarded observations. Once an estimate of the frequency and amplitude of a disturbance in a FG5 data set exists, the proposed method can estimate its impact on the estimated gravity value. This is performed through a Gaussian Bell Summation approach of the functional relationship between disturbance frequency and standard deviation of gravity. The filtering of the identified disturbance is realized through a modification of the functional model of the equation of motion in the least squares adjustment of FG5 observations. The results reveal that the Gaussian Bell Summation approximates the frequency—gravity impact relationship sufficiently well with negligible uncertainties, while the accuracy of the detected disturbance frequency defines a limiting factor for the gravity impact estimation. A realistic disturbance of 15 Hz with an amplitude of 1.5 nm had an impact of ≈48 [μGal] on the gravity estimate. The proposed filter approach reduced the impact to ≈12 [μGal], with the remaining effect being almost entirely associated to the uncertainty in disturbance frequency detection.
文摘目的研究一个包含伪Smarandache无平方因子函数Zω(n)的极限问题。方法利用初等及解析方法。结果证明了该极限存在且其值为1。结论解决了Felice Russo在文献A set of new Smarandache functions,sequences and conjectures in number theory中提出的一个极限问题。
