In this paper,we find some mistakes in the paper “Several Inequalities of Matrix Traces” which was published in Chinese Quarterly Journal of Mathematics,Vol.10,No.2.
The trace of a Wishart matrix, either central or non-central, has important roles in various multi-variate statistical questions. We review several expressions of its distribution given in the literature, establish so...The trace of a Wishart matrix, either central or non-central, has important roles in various multi-variate statistical questions. We review several expressions of its distribution given in the literature, establish some new results and provide a discussion on computing methods on the distribution of the ratio: the largest eigenvalue to trace.展开更多
Dehghan and Hajarian, [4], investigated the matrix equations A^TXB＋B^TX^TA = C and A^TXB ＋ B^TXA = C providing inequalities for the determinant of the solutions of these equations. In the same paper, the authors pre...Dehghan and Hajarian, [4], investigated the matrix equations A^TXB＋B^TX^TA = C and A^TXB ＋ B^TXA = C providing inequalities for the determinant of the solutions of these equations. In the same paper, the authors presented a lower bound for the product of the eigenvalues of the solutions to these matrix equations. Inspired by their work, we give some generalizations of Dehghan and Hajarian results. Using the theory of the numerical ranges, we present an inequality involving the trace of C when A, B, X are normal matrices satisfying A^T B = BA^T.展开更多
A An analytical method using high resolution inductively coupled plasma mass spectrometry （HR-ICP-MS） for rapid simultaneous determination of 24 elements （Be, Mg, A1, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Ga, Ge, As, Se, ...A An analytical method using high resolution inductively coupled plasma mass spectrometry （HR-ICP-MS） for rapid simultaneous determination of 24 elements （Be, Mg, A1, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Ga, Ge, As, Se, Mo, Ag, Cd, Sn Sb, Ba, Pt, Au, and Pb） in high purity cobalt was described. Sample digestions were performed in closed microwave vessels using HNO3 and HCI. The matrix effects because of the presence of excess HCI and Co were evaluated. The usefulness of high mass resolution for overcoming some spectral interference was demonstrated. The optimum conditions for the determination were tested and discussed. The standard addition method was employed for quantitative analysis. The detection limits were 0.016-1.50 ].tg·g^-1, the recovery ratios were 92.2%-111.2%, and the RSD was less than 3.6%. The method was accurate, quick, and convenient. It was applied to the determination of trace impurities in high purity cobalt with satisfactory results.展开更多
An analytical method using high resolution inductively coupled plasma mass spectrometry （HR-ICP-MS） for rapid simultaneous determination of Be, Mg, Al, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Ga, Ge, As, Se, Mo, Ag, Cd, Sn, ...An analytical method using high resolution inductively coupled plasma mass spectrometry （HR-ICP-MS） for rapid simultaneous determination of Be, Mg, Al, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Ga, Ge, As, Se, Mo, Ag, Cd, Sn, Sb, Ba, Pt, Au and Pb in high purity cobalt was described. Sample digestions were performed in closed microwave vessels using HNO3 and HCl. The matrix effects due to the presence of excess HCl and Co were evaluated. The usefulness of high mass resolution for overcoming some spectral interference was demonstrated. The optimum conditions for the determination was tested and discussed. Correction for matrix effects, Sc, Rh and Bi were used as internal standards. The detection limits is 0.003-0.57 μg/g, the recovery ratio is 92.2%-111.2%, and the RSD is less than 3.6%. The method is accurate, quick and convenient. It has been applied to the determination of trace impurities in high purity cobalt with satisfactory results.展开更多
Purpose： To comprehensively evaluate the overall performance of a group or an individual in both bibliometrics and patentometrics. Design/methodology/approach： Trace metrics were applied to the top 30 universities i...Purpose： To comprehensively evaluate the overall performance of a group or an individual in both bibliometrics and patentometrics. Design/methodology/approach： Trace metrics were applied to the top 30 universities in the2014 Academic Ranking of World Universities（ARWU） — computer sciences, the top 30 ESI highly cited papers in the computer sciences field in 2014, as well as the top 30 assignees and the top 30 most cited patents in the National Bureau of Economic Research（NBER） computer hardware and software category.Findings： We found that, by applying trace metrics, the research or marketing impact efficiency, at both group and individual levels, was clearly observed. Furthermore, trace metrics were more sensitive to the different publication-citation distributions than the average citation and h-index were.Research limitations： Trace metrics considered publications with zero citations as negative contributions. One should clarify how he/she evaluates a zero-citation paper or patent before applying trace metrics.Practical implications： Decision makers could regularly examinine the performance of their university/company by applying trace metrics and adjust their policies accordingly.Originality/value： Trace metrics could be applied both in bibliometrics and patentometrics and provide a comprehensive view. Moreover, the high sensitivity and unique impact efficiency view provided by trace metrics can facilitate decision makers in examining and adjusting their policies.展开更多
The purpose of this paper is to discuss the theorems for the trace of any positive integer power of 2 × 2 real matrix. We obtain a new formula to compute trace of any positive integer power of 2 × 2 real mat...The purpose of this paper is to discuss the theorems for the trace of any positive integer power of 2 × 2 real matrix. We obtain a new formula to compute trace of any positive integer power of 2 × 2 real matrix A, in the terms of Trace of A (TrA) and Determinant of A (DetA), which are based on definition of trace of matrix and multiplication of the matrixn times, where n is positive integer and this formula gives some corollary for TrAn when TrA or DetA are zero.展开更多
Starting from the wave normal tracing treatment in the Savart polariscope that relates the Jones matrix to its transmission performance, this paper establishes a simple and effective model for the Jones matrix at an a...Starting from the wave normal tracing treatment in the Savart polariscope that relates the Jones matrix to its transmission performance, this paper establishes a simple and effective model for the Jones matrix at an arbitrary incidence in the spatial domain. Analytical expressions of all the matrix components are determined with the consideration of all the main impact factors. This model needs only a few parameters hence it is convenient to be employed to evaluate the propagation performance of any birefringent optical system. The simulated results obtained with it demonstrate that this model gives a precise representation of the characteristic of light propagation in the Savart polariscope. This would provide useful suggestions for the design, calibration, and performance improvement of any other birefringent polarisation element and optical system.展开更多
Singular spectrum analysis is widely used in geodetic time series analysis.However,when extracting time-varying periodic signals from a large number of Global Navigation Satellite System(GNSS)time series,the selection...Singular spectrum analysis is widely used in geodetic time series analysis.However,when extracting time-varying periodic signals from a large number of Global Navigation Satellite System(GNSS)time series,the selection of appropriate embedding window size and principal components makes this method cumbersome and inefficient.To improve the efficiency and accuracy of singular spectrum analysis,this paper proposes an adaptive singular spectrum analysis method by combining spectrum analysis with a new trace matrix.The running time and correlation analysis indicate that the proposed method can adaptively set the embedding window size to extract the time-varying periodic signals from GNSS time series,and the extraction efficiency of a single time series is six times that of singular spectrum analysis.The method is also accurate and more suitable for time-varying periodic signal analysis of global GNSS sites.展开更多
文摘In this paper,we find some mistakes in the paper “Several Inequalities of Matrix Traces” which was published in Chinese Quarterly Journal of Mathematics,Vol.10,No.2.
文摘The trace of a Wishart matrix, either central or non-central, has important roles in various multi-variate statistical questions. We review several expressions of its distribution given in the literature, establish some new results and provide a discussion on computing methods on the distribution of the ratio: the largest eigenvalue to trace.
基金partially supported by FCT(Portugal)with national funds through Centro de Matemática da Universidade de Trás-os-Montes e Alto Douro(PEst-OE/MAT/UI4080/2014)
文摘Dehghan and Hajarian, [4], investigated the matrix equations A^TXB＋B^TX^TA = C and A^TXB ＋ B^TXA = C providing inequalities for the determinant of the solutions of these equations. In the same paper, the authors presented a lower bound for the product of the eigenvalues of the solutions to these matrix equations. Inspired by their work, we give some generalizations of Dehghan and Hajarian results. Using the theory of the numerical ranges, we present an inequality involving the trace of C when A, B, X are normal matrices satisfying A^T B = BA^T.
基金the Natural Science Foundation of Hunan Province, China (No. 05JJ40017).
文摘A An analytical method using high resolution inductively coupled plasma mass spectrometry （HR-ICP-MS） for rapid simultaneous determination of 24 elements （Be, Mg, A1, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Ga, Ge, As, Se, Mo, Ag, Cd, Sn Sb, Ba, Pt, Au, and Pb） in high purity cobalt was described. Sample digestions were performed in closed microwave vessels using HNO3 and HCI. The matrix effects because of the presence of excess HCI and Co were evaluated. The usefulness of high mass resolution for overcoming some spectral interference was demonstrated. The optimum conditions for the determination were tested and discussed. The standard addition method was employed for quantitative analysis. The detection limits were 0.016-1.50 ].tg·g^-1, the recovery ratios were 92.2%-111.2%, and the RSD was less than 3.6%. The method was accurate, quick, and convenient. It was applied to the determination of trace impurities in high purity cobalt with satisfactory results.
基金supported by the Natural Science Foundation of Hunan Province(No.05JJ40017)Education Department of Hunan Province(No.05B064).
文摘An analytical method using high resolution inductively coupled plasma mass spectrometry （HR-ICP-MS） for rapid simultaneous determination of Be, Mg, Al, Ti, V, Cr, Mn, Fe, Ni, Cu, Zn, Ga, Ge, As, Se, Mo, Ag, Cd, Sn, Sb, Ba, Pt, Au and Pb in high purity cobalt was described. Sample digestions were performed in closed microwave vessels using HNO3 and HCl. The matrix effects due to the presence of excess HCl and Co were evaluated. The usefulness of high mass resolution for overcoming some spectral interference was demonstrated. The optimum conditions for the determination was tested and discussed. Correction for matrix effects, Sc, Rh and Bi were used as internal standards. The detection limits is 0.003-0.57 μg/g, the recovery ratio is 92.2%-111.2%, and the RSD is less than 3.6%. The method is accurate, quick and convenient. It has been applied to the determination of trace impurities in high purity cobalt with satisfactory results.
基金the National Natural Science Foundation of China (Grant No.: 71173187)Jiangsu Key Laboratory Fund for financial support
文摘Purpose： To comprehensively evaluate the overall performance of a group or an individual in both bibliometrics and patentometrics. Design/methodology/approach： Trace metrics were applied to the top 30 universities in the2014 Academic Ranking of World Universities（ARWU） — computer sciences, the top 30 ESI highly cited papers in the computer sciences field in 2014, as well as the top 30 assignees and the top 30 most cited patents in the National Bureau of Economic Research（NBER） computer hardware and software category.Findings： We found that, by applying trace metrics, the research or marketing impact efficiency, at both group and individual levels, was clearly observed. Furthermore, trace metrics were more sensitive to the different publication-citation distributions than the average citation and h-index were.Research limitations： Trace metrics considered publications with zero citations as negative contributions. One should clarify how he/she evaluates a zero-citation paper or patent before applying trace metrics.Practical implications： Decision makers could regularly examinine the performance of their university/company by applying trace metrics and adjust their policies accordingly.Originality/value： Trace metrics could be applied both in bibliometrics and patentometrics and provide a comprehensive view. Moreover, the high sensitivity and unique impact efficiency view provided by trace metrics can facilitate decision makers in examining and adjusting their policies.
文摘The purpose of this paper is to discuss the theorems for the trace of any positive integer power of 2 × 2 real matrix. We obtain a new formula to compute trace of any positive integer power of 2 × 2 real matrix A, in the terms of Trace of A (TrA) and Determinant of A (DetA), which are based on definition of trace of matrix and multiplication of the matrixn times, where n is positive integer and this formula gives some corollary for TrAn when TrA or DetA are zero.
基金Project supported by the State Key Program of National Natural Science Foundation of China (Grant No. 40537031)the National Natural Science Foundation of China (Grant No. 40875013)+1 种基金the National Defense Basic Scientific Research Project,China (Grant No. A1420080187)the National High Technology Research and Development Program of China (Grant No. 2006AA12Z152)
文摘Starting from the wave normal tracing treatment in the Savart polariscope that relates the Jones matrix to its transmission performance, this paper establishes a simple and effective model for the Jones matrix at an arbitrary incidence in the spatial domain. Analytical expressions of all the matrix components are determined with the consideration of all the main impact factors. This model needs only a few parameters hence it is convenient to be employed to evaluate the propagation performance of any birefringent optical system. The simulated results obtained with it demonstrate that this model gives a precise representation of the characteristic of light propagation in the Savart polariscope. This would provide useful suggestions for the design, calibration, and performance improvement of any other birefringent polarisation element and optical system.
基金supported by the National Natural Science Foundation of China(Grants:42204006,42274053,42030105,and 41504031)the Open Research Fund Program of the Key Laboratory of Geospace Environment and Geodesy,Ministry of Education,China(Grants:20-01-03 and 21-01-04)。
文摘Singular spectrum analysis is widely used in geodetic time series analysis.However,when extracting time-varying periodic signals from a large number of Global Navigation Satellite System(GNSS)time series,the selection of appropriate embedding window size and principal components makes this method cumbersome and inefficient.To improve the efficiency and accuracy of singular spectrum analysis,this paper proposes an adaptive singular spectrum analysis method by combining spectrum analysis with a new trace matrix.The running time and correlation analysis indicate that the proposed method can adaptively set the embedding window size to extract the time-varying periodic signals from GNSS time series,and the extraction efficiency of a single time series is six times that of singular spectrum analysis.The method is also accurate and more suitable for time-varying periodic signal analysis of global GNSS sites.
