A new modification of false position method for solving nonlinear equations is presented by applying homotopy analysis method （HAM）. Some numerical illustrations are given to show the efficiency of algorithm.
NLLoc is a nonlinear search positioning method.In this study,we use simulated arrival time data to quantitatively evaluate the NLLoc method from three aspects:arrival time picking accuracy,station distribution,and vel...NLLoc is a nonlinear search positioning method.In this study,we use simulated arrival time data to quantitatively evaluate the NLLoc method from three aspects:arrival time picking accuracy,station distribution,and velocity model.The results show that the NLLoc method exhibits high positioning accuracy and stability in terms of arrival time picking accuracy and station distribution;however,it is sensitive to the velocity model.The positioning accuracy is higher when the velocity model is smaller than the true velocity.We combined absolute and relative positioning methods.First,we use the NLLoc method for absolute positioning of seismic data and then the double difference positioning method for relative positioning to obtain a more accurate relocation result.Furthermore,we used the combined method to locate the earthquake sequence after collecting dense seismic array data on the Luanzhou M_(S)4.3 earthquake that occurred on April 16,2021,in Hebei Province.By fitting the fault plane with the relocated earthquake sequences,the results show that the strike and dip angles of the seismogenic fault of the Luanzhou M_(S)4.3 earthquake are 208.5°and 85.6°,respectively.This indicates a high-dip angle fault with North-North-East strike and North-West dip directions.Furthermore,we infer that the seismogenic fault of the Luanzhou M_(S)4.3 earthquake is the Lulong fault.展开更多
Optimization calculations of 209 polychlorinated biphenyls （PCBs） were carried out at the B3LYP/6-31G^＊ level. It was found that there is significant correlation between the Cl substitution position and some struct...Optimization calculations of 209 polychlorinated biphenyls （PCBs） were carried out at the B3LYP/6-31G^＊ level. It was found that there is significant correlation between the Cl substitution position and some structural parameters. Consequently, Cl substitution positions were taken as theoretical descriptors to establish a novel QSPR model for predicting –lgSw of all PCB congeners. The model achieved in this work contains four variables, of which r^2 = 0.9527, q^2 = 0.9490 and SD = 0.25 with large t values. In addition, the variation inflation factors （VIFs） of variables in this model are all less than 5.0, suggesting high accuracy of the –lgSw predicting model. And the results of cross-validation test and method validation also show that the model exhibits optimum stability and better predictive capability than that from the AM1 method.展开更多
Optimized calculations of 75 PCDDs and their parent DD were carded out at the B3LYP/6-31G＊ level by density functional theory （DFT） method. The structural parameters were obtained and significant correlation betwee...Optimized calculations of 75 PCDDs and their parent DD were carded out at the B3LYP/6-31G＊ level by density functional theory （DFT） method. The structural parameters were obtained and significant correlation between the C1 substitution position and some structural parameters was found. Consequently, the number of C1 substitution positions was taken as theoretical descriptors to establish two novel QSPR models for predicting lgKow and -lgSw of all PCDD congeners. The two models achieved in this work contain two variables （Na and Nβ）, of which r = 0.9312, 0.9965 and SD = 0.27, 0.12 respectively, and t values are all large. The variation inflation factors （VIF） of variables in the two models herein are both less than 5.0, suggesting high accuracy of the lgKow and -lgSw predicting models, and the results of cross-validation test also show that the two models exhibit optimum stability and good predictive power. By comparison, the correlation and predictive ability of the present work are more advantageous than those obtained using semi-empirical AM1 and GC-RI methods.展开更多
The sound ray tracing method can achieve higher accuracy in determining depths and plan positions with multibeam echo sounding system.In data processing,actual sound speed profile must be used in the method.However,th...The sound ray tracing method can achieve higher accuracy in determining depths and plan positions with multibeam echo sounding system.In data processing,actual sound speed profile must be used in the method.However,the method is too complicated.In order to overcome the shortcoming,this paper presents a new method,the position correction method.Two situations are considered in the new method,namely,change of sound velocity keeps constant gradient in whole water column(including N layers)or in different water layer.展开更多
Gas holdup is one of the key parameters in flotation process. Gas holdup as measured by a differential pressure method was investigated and the relative errors compared to the average gas holdup from the volume expans...Gas holdup is one of the key parameters in flotation process. Gas holdup as measured by a differential pressure method was investigated and the relative errors compared to the average gas holdup from the volume expansion method. The errors were used to establish optimum measurement positions. The results show that the measurement position should be in the middle of the column and in the region half way from the center to the wall (the half-radius). The gas holdup along the axial direction is lower at the bottom and higher at the top of the floatation column. The gas holdup along the radial direction is lower near the wall and higher near the center of the flotation column. The average gas holdup measure- ment can be replaced by regional gas holdup values.展开更多
Yang Hui was one of the most important authors of mathematical works during the thirteenth century.Mathematical Methods Explaining in Detail The Nine Chapters(Xiangjie jiuzhang suanfa詳解九章算法,1261 CE)is the earlie...Yang Hui was one of the most important authors of mathematical works during the thirteenth century.Mathematical Methods Explaining in Detail The Nine Chapters(Xiangjie jiuzhang suanfa詳解九章算法,1261 CE)is the earliest extant work attributed to Yang Hui.From the thirteenth to the fifteenth century,this work played a crucial role in the circulation and popularization of The Nine Chapters on Mathematical Procedures(Jiuzhang suanshu九章算术).However,the only surviving printed edition of Mathematical Methods is incomplete and contains many mistakes obstructing contemporary researchers'understanding of this work.The "Fangcheng" chapter of The Nine Chapters deals with problems related to solving what today are known as simultaneous sets of linear equations.However,interpreting the text in this chapter of Mathematical Methods and recovering the mathematical practices relating to fangcheng are difficult.Through detailed textual and mathematical analyses,the author of this paper explains Yang Hufs understanding and practice relating to〃the fangcheng method"and"the method of the positive and the negative".This paper includes an appendix that provides a detailed translation of the ambiguous text relating to"the method of the positive and the negative"and gives reasons supporting the interpretation provided here.Yang Hufs understanding of the concepts of"positive"and"negative"and his practice relating to these two concepts may easily be confused with their apparent counterparts in modem mathematics.Also,careful analysis of the mathematical methods in this work reveal that the order of problems in Yang Hufs Reclassifications of Mathematical Methods Explaining in Detail The Nine Chapters([Xiangjie jiuzhang suanfa zuanlei詳解九章算法纂類],namely,the last section of Mathematical Methods)were rearranged according to commentaries to specific methods that appear in Mathematical Methods.Some textual clues referring to the zzprevious question"(qianwen前問)in certain commentaries of Mathematical Methods indeed reflect the order of problems in Reclassifications.Yang Hui made especially detailed commentaries on the problems that he arranged in a sequence that differs with respect to the original order of problems as they appear in the ancient classic work,The Nine Chapters.All these discoveries reveal and serve to prove a close relationship between Yang Hufs Mathematical Methods and his Reclassifications.展开更多
Magneto-electro-elastic(MEE)materials are a specific class of advanced smart materials that simultaneouslymanifest the coupling behavior under electric,magnetic,and mechanical loads.This unique combination ofpropertie...Magneto-electro-elastic(MEE)materials are a specific class of advanced smart materials that simultaneouslymanifest the coupling behavior under electric,magnetic,and mechanical loads.This unique combination ofproperties allows MEE materials to respond to mechanical,electric,and magnetic stimuli,making them versatile forvarious applications.This paper investigates the static and time-harmonic field solutions induced by the surface loadin a three-dimensional(3D)multilayered transversally isotropic(TI)linear MEE layered solid.Green’s functionscorresponding to the applied uniform load(in both horizontal and vertical directions)are derived using the Fourier-Bessel series(FBS)system of vector functions.By virtue of this FBS method,two sets of first-order ordinarydifferential equations(i.e.,N-type and LM-type)are obtained,with the expansion coefficients being Love numbers.It is noted that the LM-type system corresponds to the MEE-coupled P-,SV-,and Rayleigh waves,while the N-typecorresponds to the purely elastic SH-and Love waves.By applying the continuity conditions across interfaces,the solutions for each layer of the structure(from the bottom to the top)are derived using the dual-variable andposition(DVP)method.This method(i.e.,DVP)is unconditionally stable when propagating solutions throughdifferent layers.Numerical examples illustrate the impact of load types,layering,and frequency on the response ofthe structure,as well as the accuracy and convergence of the proposed approach.The numerical results are usefulin designing smart devices made of MEE solids,which are applicable to engineering fields like renewable energy.展开更多
OBJECTIVE: The characteristics of lip-mouth region including the soft and hard tissues in smiling position with frontal fixed position photographic computer-aided analysis were studied. METHODS: The subjects were 80 p...OBJECTIVE: The characteristics of lip-mouth region including the soft and hard tissues in smiling position with frontal fixed position photographic computer-aided analysis were studied. METHODS: The subjects were 80 persons (40 male and 40 females, age range: 17 to approximately 25 years) with acceptable faces and individual normal occlusions. The subjects were asked to take maximum smiling position to accept photographic measurement with computer-aided analysis. RESULTS: The maximum smile line could be divided into 3 categories: low smile line (16.25%), average smile line (68.75%), and high smile line (15%). CONCLUSION: The method adopting maximum smiling position to study the lip-month region is reproducible and comparable. This study would be helpful to provide a quantitative reference for clinical investigation, diagnosis, treatment and efficacy appraisal.展开更多
The conventional technique for positioning seafloor geophones in ocean bottom seismic exploration encounters several challenges,including the significant impact of outliers on positioning results,underutilization of h...The conventional technique for positioning seafloor geophones in ocean bottom seismic exploration encounters several challenges,including the significant impact of outliers on positioning results,underutilization of high-precision observations,and low efficiency in real-time data processing.These issues inevitably affect the quality of seismic exploration outcomes.To address these challenges and enhance the accuracy of geophone positioning,this paper proposes a rigorous real-time acoustic positioning method for geophones based on sequential adjustment and Baarda's outlier detection approach.The proposed method comprises three key steps:grouping the original acoustic observations,constructing the intra-group acoustic positioning model,and synthesizing the positioning results across the different groups.The validity and practicality of this approach are confirmed through a simulation experiment as well as the field experiment conducted in the Bohai Sea,China.The results demonstrate that the proposed method effectively eliminates outliers in the original observations and maximizes the utilization of high-quality observations.Compared to traditional acoustic positioning methods,it significantly reduces positioning errors from meters to decimeters,and in some cases can achieve centimeter-level precision.When the sound velocity profile in the operating sea area is measured,the method can attain the posterior standard deviation at the millimeter level and positioning errors within 10 cm.When the sound velocity profile is unknown,the method can achieve the posterior standard deviation at centimeter-level and positioning errors of approximately 20 cm.展开更多
The double pulse sources （DPS） method is presented for linear track estimation in this work. In the field of noise identification of underwater moving target, the Doppler will distort the frequency and amplitude of ...The double pulse sources （DPS） method is presented for linear track estimation in this work. In the field of noise identification of underwater moving target, the Doppler will distort the frequency and amplitude of the radiated noise. To eliminate this, the track estimation is necessary. In the DPS method, we first estimate bearings of two sinusoidal pulse sources installed in the moving target through baseline positioning method. Meanwhile, the emitted and recorded time of each pulse are also acquired. Then the linear track parameters will be achieved based on the geometry pattern with the help of double sources spacing. The simulated results confirm that the DPS improves the performance of the previous double source spacing method. The simulated experiments were carried out using a moving battery car to further evaluate its performance. When the target is 40-60m away, the experiment results show that biases of track azimuth and abeam distance of DPS are under 0.6° and 3.4m, respectively. And the average deviation of estimated velocity is around 0.25m/s.展开更多
文摘A new modification of false position method for solving nonlinear equations is presented by applying homotopy analysis method （HAM）. Some numerical illustrations are given to show the efficiency of algorithm.
基金Supported by the Foundation:This research project is jointly supported by Hebei Provincial Science and Technology Program(No.22375406D)The Earthquake Science and Technology Program of Hebei Province(No.DZ2023120500009,DZ2024120500001).
文摘NLLoc is a nonlinear search positioning method.In this study,we use simulated arrival time data to quantitatively evaluate the NLLoc method from three aspects:arrival time picking accuracy,station distribution,and velocity model.The results show that the NLLoc method exhibits high positioning accuracy and stability in terms of arrival time picking accuracy and station distribution;however,it is sensitive to the velocity model.The positioning accuracy is higher when the velocity model is smaller than the true velocity.We combined absolute and relative positioning methods.First,we use the NLLoc method for absolute positioning of seismic data and then the double difference positioning method for relative positioning to obtain a more accurate relocation result.Furthermore,we used the combined method to locate the earthquake sequence after collecting dense seismic array data on the Luanzhou M_(S)4.3 earthquake that occurred on April 16,2021,in Hebei Province.By fitting the fault plane with the relocated earthquake sequences,the results show that the strike and dip angles of the seismogenic fault of the Luanzhou M_(S)4.3 earthquake are 208.5°and 85.6°,respectively.This indicates a high-dip angle fault with North-North-East strike and North-West dip directions.Furthermore,we infer that the seismogenic fault of the Luanzhou M_(S)4.3 earthquake is the Lulong fault.
基金This work was supported by the 973 National Basic Research Program of China (2003CB415002)the China Postdoctoral Science Foundation (No. 2003033486)
文摘Optimization calculations of 209 polychlorinated biphenyls （PCBs） were carried out at the B3LYP/6-31G^＊ level. It was found that there is significant correlation between the Cl substitution position and some structural parameters. Consequently, Cl substitution positions were taken as theoretical descriptors to establish a novel QSPR model for predicting –lgSw of all PCB congeners. The model achieved in this work contains four variables, of which r^2 = 0.9527, q^2 = 0.9490 and SD = 0.25 with large t values. In addition, the variation inflation factors （VIFs） of variables in this model are all less than 5.0, suggesting high accuracy of the –lgSw predicting model. And the results of cross-validation test and method validation also show that the model exhibits optimum stability and better predictive capability than that from the AM1 method.
基金This work was supported by the National Natural Science Foundation of China (No. 20737001)(2003CB415002)China Postdoctoral Science Foundation (No. 2003033486)
文摘Optimized calculations of 75 PCDDs and their parent DD were carded out at the B3LYP/6-31G＊ level by density functional theory （DFT） method. The structural parameters were obtained and significant correlation between the C1 substitution position and some structural parameters was found. Consequently, the number of C1 substitution positions was taken as theoretical descriptors to establish two novel QSPR models for predicting lgKow and -lgSw of all PCDD congeners. The two models achieved in this work contain two variables （Na and Nβ）, of which r = 0.9312, 0.9965 and SD = 0.27, 0.12 respectively, and t values are all large. The variation inflation factors （VIF） of variables in the two models herein are both less than 5.0, suggesting high accuracy of the lgKow and -lgSw predicting models, and the results of cross-validation test also show that the two models exhibit optimum stability and good predictive power. By comparison, the correlation and predictive ability of the present work are more advantageous than those obtained using semi-empirical AM1 and GC-RI methods.
文摘The sound ray tracing method can achieve higher accuracy in determining depths and plan positions with multibeam echo sounding system.In data processing,actual sound speed profile must be used in the method.However,the method is too complicated.In order to overcome the shortcoming,this paper presents a new method,the position correction method.Two situations are considered in the new method,namely,change of sound velocity keeps constant gradient in whole water column(including N layers)or in different water layer.
基金supports for this work provided by the NationalKey Technology R&D Program in the 11th Five-Year Plan of China(No. 2008BAB31B03)
文摘Gas holdup is one of the key parameters in flotation process. Gas holdup as measured by a differential pressure method was investigated and the relative errors compared to the average gas holdup from the volume expansion method. The errors were used to establish optimum measurement positions. The results show that the measurement position should be in the middle of the column and in the region half way from the center to the wall (the half-radius). The gas holdup along the axial direction is lower at the bottom and higher at the top of the floatation column. The gas holdup along the radial direction is lower near the wall and higher near the center of the flotation column. The average gas holdup measure- ment can be replaced by regional gas holdup values.
基金research projects“Elements of Continuity between Mathematical Writings from the Thirteenth to the Fifteenth Century in China(十三至十五世纪中国数学著作连续性Y950051)”“Transmission of the Knowledge of Science and Technology along the Silk Road(丝绸之路科技知识传播Y921011012,Director:Guo Yuanyuan郭园园)”of the Institute for the History of Natural Sciences,Chinese Academy of Sciences.The paper has been copyedited by John Moffett。
文摘Yang Hui was one of the most important authors of mathematical works during the thirteenth century.Mathematical Methods Explaining in Detail The Nine Chapters(Xiangjie jiuzhang suanfa詳解九章算法,1261 CE)is the earliest extant work attributed to Yang Hui.From the thirteenth to the fifteenth century,this work played a crucial role in the circulation and popularization of The Nine Chapters on Mathematical Procedures(Jiuzhang suanshu九章算术).However,the only surviving printed edition of Mathematical Methods is incomplete and contains many mistakes obstructing contemporary researchers'understanding of this work.The "Fangcheng" chapter of The Nine Chapters deals with problems related to solving what today are known as simultaneous sets of linear equations.However,interpreting the text in this chapter of Mathematical Methods and recovering the mathematical practices relating to fangcheng are difficult.Through detailed textual and mathematical analyses,the author of this paper explains Yang Hufs understanding and practice relating to〃the fangcheng method"and"the method of the positive and the negative".This paper includes an appendix that provides a detailed translation of the ambiguous text relating to"the method of the positive and the negative"and gives reasons supporting the interpretation provided here.Yang Hufs understanding of the concepts of"positive"and"negative"and his practice relating to these two concepts may easily be confused with their apparent counterparts in modem mathematics.Also,careful analysis of the mathematical methods in this work reveal that the order of problems in Yang Hufs Reclassifications of Mathematical Methods Explaining in Detail The Nine Chapters([Xiangjie jiuzhang suanfa zuanlei詳解九章算法纂類],namely,the last section of Mathematical Methods)were rearranged according to commentaries to specific methods that appear in Mathematical Methods.Some textual clues referring to the zzprevious question"(qianwen前問)in certain commentaries of Mathematical Methods indeed reflect the order of problems in Reclassifications.Yang Hui made especially detailed commentaries on the problems that he arranged in a sequence that differs with respect to the original order of problems as they appear in the ancient classic work,The Nine Chapters.All these discoveries reveal and serve to prove a close relationship between Yang Hufs Mathematical Methods and his Reclassifications.
基金The National Science and Technology Council of Taiwan(Grant No.NSTC 111-2811-E-516 A49-534)provided financial support for this study。
文摘Magneto-electro-elastic(MEE)materials are a specific class of advanced smart materials that simultaneouslymanifest the coupling behavior under electric,magnetic,and mechanical loads.This unique combination ofproperties allows MEE materials to respond to mechanical,electric,and magnetic stimuli,making them versatile forvarious applications.This paper investigates the static and time-harmonic field solutions induced by the surface loadin a three-dimensional(3D)multilayered transversally isotropic(TI)linear MEE layered solid.Green’s functionscorresponding to the applied uniform load(in both horizontal and vertical directions)are derived using the Fourier-Bessel series(FBS)system of vector functions.By virtue of this FBS method,two sets of first-order ordinarydifferential equations(i.e.,N-type and LM-type)are obtained,with the expansion coefficients being Love numbers.It is noted that the LM-type system corresponds to the MEE-coupled P-,SV-,and Rayleigh waves,while the N-typecorresponds to the purely elastic SH-and Love waves.By applying the continuity conditions across interfaces,the solutions for each layer of the structure(from the bottom to the top)are derived using the dual-variable andposition(DVP)method.This method(i.e.,DVP)is unconditionally stable when propagating solutions throughdifferent layers.Numerical examples illustrate the impact of load types,layering,and frequency on the response ofthe structure,as well as the accuracy and convergence of the proposed approach.The numerical results are usefulin designing smart devices made of MEE solids,which are applicable to engineering fields like renewable energy.
文摘OBJECTIVE: The characteristics of lip-mouth region including the soft and hard tissues in smiling position with frontal fixed position photographic computer-aided analysis were studied. METHODS: The subjects were 80 persons (40 male and 40 females, age range: 17 to approximately 25 years) with acceptable faces and individual normal occlusions. The subjects were asked to take maximum smiling position to accept photographic measurement with computer-aided analysis. RESULTS: The maximum smile line could be divided into 3 categories: low smile line (16.25%), average smile line (68.75%), and high smile line (15%). CONCLUSION: The method adopting maximum smiling position to study the lip-month region is reproducible and comparable. This study would be helpful to provide a quantitative reference for clinical investigation, diagnosis, treatment and efficacy appraisal.
基金supported by the National Key R&D Program of China(Grant No.:2016YFB0501703)Science and Technology Innovation Project(Grant No.:LSKJ202205102)Funded by Laoshan Laboratory.
文摘The conventional technique for positioning seafloor geophones in ocean bottom seismic exploration encounters several challenges,including the significant impact of outliers on positioning results,underutilization of high-precision observations,and low efficiency in real-time data processing.These issues inevitably affect the quality of seismic exploration outcomes.To address these challenges and enhance the accuracy of geophone positioning,this paper proposes a rigorous real-time acoustic positioning method for geophones based on sequential adjustment and Baarda's outlier detection approach.The proposed method comprises three key steps:grouping the original acoustic observations,constructing the intra-group acoustic positioning model,and synthesizing the positioning results across the different groups.The validity and practicality of this approach are confirmed through a simulation experiment as well as the field experiment conducted in the Bohai Sea,China.The results demonstrate that the proposed method effectively eliminates outliers in the original observations and maximizes the utilization of high-quality observations.Compared to traditional acoustic positioning methods,it significantly reduces positioning errors from meters to decimeters,and in some cases can achieve centimeter-level precision.When the sound velocity profile in the operating sea area is measured,the method can attain the posterior standard deviation at the millimeter level and positioning errors within 10 cm.When the sound velocity profile is unknown,the method can achieve the posterior standard deviation at centimeter-level and positioning errors of approximately 20 cm.
文摘The double pulse sources （DPS） method is presented for linear track estimation in this work. In the field of noise identification of underwater moving target, the Doppler will distort the frequency and amplitude of the radiated noise. To eliminate this, the track estimation is necessary. In the DPS method, we first estimate bearings of two sinusoidal pulse sources installed in the moving target through baseline positioning method. Meanwhile, the emitted and recorded time of each pulse are also acquired. Then the linear track parameters will be achieved based on the geometry pattern with the help of double sources spacing. The simulated results confirm that the DPS improves the performance of the previous double source spacing method. The simulated experiments were carried out using a moving battery car to further evaluate its performance. When the target is 40-60m away, the experiment results show that biases of track azimuth and abeam distance of DPS are under 0.6° and 3.4m, respectively. And the average deviation of estimated velocity is around 0.25m/s.
