The traditional spheroidal kernel results in the spectrum leakage,and the utilization rate of the removed degrees of the measured data is low.Hence,a kind of spheroidal kernel whose high-and low-degrees are both modif...The traditional spheroidal kernel results in the spectrum leakage,and the utilization rate of the removed degrees of the measured data is low.Hence,a kind of spheroidal kernel whose high-and low-degrees are both modified is introduced in this research,which is exampled by the Hotine kernel.In addition,the low-degree modified spheroidal kernel is proposed.Either cosine or linear modification factors can be utilized.The modified kernel functions can effectively control the spectrum leakage compared with the traditional spheroidal kernel.Furthermore,the modified kernel augments the contribution rate of the measured data to height anomaly in the modified frequency domain.The experimental results show that the accuracy of the quasi-geoid by the cosine or linear low-degree modified kernel is higher than that by the traditional spheroidal kernel.And the accuracy equals the accuracy of the quasi-geoid using the spheroidal kernel with high-and low-degrees modified approximately when the low-degree modification bandwidths of these two kinds of kernels are the same.Since the computational efficiency of the low-degree modified kernel is much higher,the low-degree modified kernel behaves better in constructing the(quasi-)geoid based on Stokes-Helmert or Hotine-Helmert boundary-value theory.展开更多
Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with rand...Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.展开更多
Introduction: Although the Brief Psychiatric Rating Scale (BPRS) is widely used for evaluating patients with schizophrenia, the meaning of the weights of the individual symptoms is ambiguous. The aims of the study wer...Introduction: Although the Brief Psychiatric Rating Scale (BPRS) is widely used for evaluating patients with schizophrenia, the meaning of the weights of the individual symptoms is ambiguous. The aims of the study were 1) to investigate whether the modification of relative weights of items of the BPRS is able to enhance its correlation with the Clinical Global Impression-Schizophrenia scale (CGI-SCH) and 2) to construct a potential modified BPRS. Methods: We evaluated 200 schizophrenia patients using the BPRS and the CGI-SCH and drew the scatter plot distributions of the two scales. Next, univariate regression for the CGI-SCH using individual symptoms of the BPRS was performed. Multivariate regression utilizing the ‘logistic function’ was then conducted to allocate marks to each item and Pearson’s r correlation coefficient and r-squared between the two scales were assessed. After that, we constructed an example of a potential modified BPRS. Results: With the scatter plot for the two scales, a logarithmic curve was obtained;this was described by [CGI-SCH] = 3.2248 × ln[18-item BPRS] – 7.2044 (p i” that could express the relative weights of individual symptoms. Subsequently, modification of point allocations according to “Pi” yielded a Pearson’s r of 0.8491 and an r-squared of 0.7718 (not changed) (both p < 0.001). An example of a potential modified BPRS was constructed. Conclusions: Within the limits of our data, the weightings of items of the BPRS improved the correlation of the BPRS with the CGI-SCH for evaluating schizophrenia.展开更多
We present calculations and improvement inspired by the work of Lorenzo Zaninetti, published in 2020, it concerns a problem whose origin dates back 1911 with so called Maxwell-Jüttner distribution these lies on t...We present calculations and improvement inspired by the work of Lorenzo Zaninetti, published in 2020, it concerns a problem whose origin dates back 1911 with so called Maxwell-Jüttner distribution these lies on the Lorentz factor , with . This work uses powerful modern software for a reconstruction of Zaninetti work, which computes with special functions, these are included in the Mathematica software, as by instance Bessel and Meijer G-functions ready to manipulate. A progress is made, it is possible to perform an integral that is not computed in Zaninetti paper. This author connects the correct relativistic probability law: the Maxwell-Jüttner to the synchrotron emissivity with a magnetic B field, this work generalize these results, using the linear Stark effect and deals with an electric field E.展开更多
Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical fiber. In th...Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical fiber. In this paper, we first study the existence and uniqueness of eigenvalues, and then investigate three numerical algorithms, namely Picard iteration, nonlinear Rayleigh quotient iteration and successive linear approximation method （SLAM）. The global convergence of the SLAM is proven under some mild assumptions. Numerical examples illustrate that the SLAM is the most robust method.展开更多
基金National Natural Science Foundation of China(Nos.41674025,41674082)Open Research Foundation of State Key Laboratory of Geo-information Engineering(Nos.SKLGIE2016-M-1-5,SKLGIE2018-ZZ-10)。
文摘The traditional spheroidal kernel results in the spectrum leakage,and the utilization rate of the removed degrees of the measured data is low.Hence,a kind of spheroidal kernel whose high-and low-degrees are both modified is introduced in this research,which is exampled by the Hotine kernel.In addition,the low-degree modified spheroidal kernel is proposed.Either cosine or linear modification factors can be utilized.The modified kernel functions can effectively control the spectrum leakage compared with the traditional spheroidal kernel.Furthermore,the modified kernel augments the contribution rate of the measured data to height anomaly in the modified frequency domain.The experimental results show that the accuracy of the quasi-geoid by the cosine or linear low-degree modified kernel is higher than that by the traditional spheroidal kernel.And the accuracy equals the accuracy of the quasi-geoid using the spheroidal kernel with high-and low-degrees modified approximately when the low-degree modification bandwidths of these two kinds of kernels are the same.Since the computational efficiency of the low-degree modified kernel is much higher,the low-degree modified kernel behaves better in constructing the(quasi-)geoid based on Stokes-Helmert or Hotine-Helmert boundary-value theory.
基金the financial support of the National Natural Science Foundation of China(Grant No.42074016,42104025,42274057and 41704007)Hunan Provincial Natural Science Foundation of China(Grant No.2021JJ30244)Scientific Research Fund of Hunan Provincial Education Department(Grant No.22B0496)。
文摘Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.
文摘Introduction: Although the Brief Psychiatric Rating Scale (BPRS) is widely used for evaluating patients with schizophrenia, the meaning of the weights of the individual symptoms is ambiguous. The aims of the study were 1) to investigate whether the modification of relative weights of items of the BPRS is able to enhance its correlation with the Clinical Global Impression-Schizophrenia scale (CGI-SCH) and 2) to construct a potential modified BPRS. Methods: We evaluated 200 schizophrenia patients using the BPRS and the CGI-SCH and drew the scatter plot distributions of the two scales. Next, univariate regression for the CGI-SCH using individual symptoms of the BPRS was performed. Multivariate regression utilizing the ‘logistic function’ was then conducted to allocate marks to each item and Pearson’s r correlation coefficient and r-squared between the two scales were assessed. After that, we constructed an example of a potential modified BPRS. Results: With the scatter plot for the two scales, a logarithmic curve was obtained;this was described by [CGI-SCH] = 3.2248 × ln[18-item BPRS] – 7.2044 (p i” that could express the relative weights of individual symptoms. Subsequently, modification of point allocations according to “Pi” yielded a Pearson’s r of 0.8491 and an r-squared of 0.7718 (not changed) (both p < 0.001). An example of a potential modified BPRS was constructed. Conclusions: Within the limits of our data, the weightings of items of the BPRS improved the correlation of the BPRS with the CGI-SCH for evaluating schizophrenia.
文摘We present calculations and improvement inspired by the work of Lorenzo Zaninetti, published in 2020, it concerns a problem whose origin dates back 1911 with so called Maxwell-Jüttner distribution these lies on the Lorentz factor , with . This work uses powerful modern software for a reconstruction of Zaninetti work, which computes with special functions, these are included in the Mathematica software, as by instance Bessel and Meijer G-functions ready to manipulate. A progress is made, it is possible to perform an integral that is not computed in Zaninetti paper. This author connects the correct relativistic probability law: the Maxwell-Jüttner to the synchrotron emissivity with a magnetic B field, this work generalize these results, using the linear Stark effect and deals with an electric field E.
基金supported in part by NSF grants DMS-0611548 and OCI-0749217 and DOE grant DE-FC02-06ER25794supported in part by NSF of China under the contract number 10871049 and Shanghai Down project 200601.
文摘Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical fiber. In this paper, we first study the existence and uniqueness of eigenvalues, and then investigate three numerical algorithms, namely Picard iteration, nonlinear Rayleigh quotient iteration and successive linear approximation method （SLAM）. The global convergence of the SLAM is proven under some mild assumptions. Numerical examples illustrate that the SLAM is the most robust method.
