As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initiall...As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.展开更多
[Objective] The aim was to evaluate the uncertainty of determining aspartame in beverage by high performance liquid chromatography （ HPLC）. [Method] The content of aspartame in beverage was determined by HPLC, then ...[Objective] The aim was to evaluate the uncertainty of determining aspartame in beverage by high performance liquid chromatography （ HPLC）. [Method] The content of aspartame in beverage was determined by HPLC, then the source of uncertainty in the whole determination process was analyzed, and each component of uncertainty was evaluated and combined. [ Result] Through 6 repeated determinations by the method in GB/T 22254-2008 ＂Determination of Aspartame in Food＂, the average content of aspartame in beverage was （0.806 ±0.038） g/kg, and k =2. The main sources of uncertainty to affect the process were the sample weighting process, the preparation process of standard solution introduced by sample constant volume and the uncertainty introduced by fitting standard curve. ①The uncertainty of standard work-solution. The combined uncertainty of standard work-solution was 0.013 9, among them the uncertainty introduced by standard sample purity was 0.005 8, the standard uncertainty introduced by standard material weighting was 1.49 ×10^4, the relative uncertainty introduced by glass apparatus calibration in the preparation process of aspartame standard reserving solution was 0. 007 88, and the uncertainty introduced by glass apparatus calibration in the preparation process of standard work-solution was 0. 009 9. ②The uncertainty introduced by the preparation process of sample specimen. Among them the relative standard uncertainty introduced by sample weighting process was 0. 009, and the uncertainty introduced by sample constant volume was 0.000 78. ③The uncertainty introduced by the fitting process of standard curve. Among them the relative uncertainty of curve fitting was 0.002 46, the uncertainty introduced by the determined results of aspartame was 0.017 0, the total combined standard uncertainty was 0.023 9, and the expanded standard uncertainty was 0.019. [ Conclusion] The uncertainty components of standard solution, standard curve and repeatability are the main sources of uncertainty, while those of sample weighting and sample constant volume account for little proportion.展开更多
A new algorithm for iterative reconstruction is suggested.It is named simple self-correlative algebraic reconstruction technique (SSART).With numerical simulation experiments,SSART was applied in reconstructing a non-...A new algorithm for iterative reconstruction is suggested.It is named simple self-correlative algebraic reconstruction technique (SSART).With numerical simulation experiments,SSART was applied in reconstructing a non-ideal-bordered field in order to test its reconstructive effect.For contrast,three current representative algebraic reconstruction(ARTs) including basic ART,simultaneous ART (SART) and modified SART (MSART) were simulated simultaneously.The calculated results and reconstructive accuracy are discussed with three kinds of error indexes,namely mean-square error (MSE),absolute value error (AVE) and peak error (PE).As the results,the indexes of reconstructive accuracy are much improved by the proposed SSART.The MSE and PE have been decreased by 63.6% on the order of magnitude 10-4 and 88.9% on the order of magnitude 0-2,respectively,compared to that of ART.It is concluded that SSART is one of the most super iterative reconstructing techniques.展开更多
Using the glucose and L-glutamic-acid to prepare the standard substance according to the ratio of 1：1, and the artificial seawater and the standard substance to prepare a series of standard solutions, the distributio...Using the glucose and L-glutamic-acid to prepare the standard substance according to the ratio of 1：1, and the artificial seawater and the standard substance to prepare a series of standard solutions, the distribution pattern of uncertainty in measurement of seawater COD is obtained based on the measured results of the series of standard solutions by the potassium iodide-alkaline potassium permanganate determination method. The distribution pattern is as follows： Uncertainty in measurement is big and not constant at the high end, but small and constant at the low end.展开更多
It is necessary for precise measurement to estimate the uncertainty of measurement result. When measuring flatness error in close way by pitch, usually the uncertainty of measurement result is independently estimated ...It is necessary for precise measurement to estimate the uncertainty of measurement result. When measuring flatness error in close way by pitch, usually the uncertainty of measurement result is independently estimated according to pitch points. By analyzing a concrete example, this paper proposed that the uncertainty should be evaluated by the correlation calculating method. This approach greatly improved the deficiencies of the assessment method according to independent measurement and enhanced measurement precision. It provides a reference value for uncertainty assessment in leveling a flat.展开更多
基金supported by the National Natural Science Foundation of China (No.72071202)the Key Laboratory of Mathematics and Engineering ApplicationsMinistry of Education。
文摘As a generalization of the two-term conjugate gradient method(CGM),the spectral CGM is one of the effective methods for solving unconstrained optimization.In this paper,we enhance the JJSL conjugate parameter,initially proposed by Jiang et al.(Computational and Applied Mathematics,2021,40:174),through the utilization of a convex combination technique.And this improvement allows for an adaptive search direction by integrating a newly constructed spectral gradient-type restart strategy.Then,we develop a new spectral CGM by employing an inexact line search to determine the step size.With the application of the weak Wolfe line search,we establish the sufficient descent property of the proposed search direction.Moreover,under general assumptions,including the employment of the strong Wolfe line search for step size calculation,we demonstrate the global convergence of our new algorithm.Finally,the given unconstrained optimization test results show that the new algorithm is effective.
基金Supported by the Key Project of Science and Technology of Anhui Province(08010302216)~~
文摘[Objective] The aim was to evaluate the uncertainty of determining aspartame in beverage by high performance liquid chromatography （ HPLC）. [Method] The content of aspartame in beverage was determined by HPLC, then the source of uncertainty in the whole determination process was analyzed, and each component of uncertainty was evaluated and combined. [ Result] Through 6 repeated determinations by the method in GB/T 22254-2008 ＂Determination of Aspartame in Food＂, the average content of aspartame in beverage was （0.806 ±0.038） g/kg, and k =2. The main sources of uncertainty to affect the process were the sample weighting process, the preparation process of standard solution introduced by sample constant volume and the uncertainty introduced by fitting standard curve. ①The uncertainty of standard work-solution. The combined uncertainty of standard work-solution was 0.013 9, among them the uncertainty introduced by standard sample purity was 0.005 8, the standard uncertainty introduced by standard material weighting was 1.49 ×10^4, the relative uncertainty introduced by glass apparatus calibration in the preparation process of aspartame standard reserving solution was 0. 007 88, and the uncertainty introduced by glass apparatus calibration in the preparation process of standard work-solution was 0. 009 9. ②The uncertainty introduced by the preparation process of sample specimen. Among them the relative standard uncertainty introduced by sample weighting process was 0. 009, and the uncertainty introduced by sample constant volume was 0.000 78. ③The uncertainty introduced by the fitting process of standard curve. Among them the relative uncertainty of curve fitting was 0.002 46, the uncertainty introduced by the determined results of aspartame was 0.017 0, the total combined standard uncertainty was 0.023 9, and the expanded standard uncertainty was 0.019. [ Conclusion] The uncertainty components of standard solution, standard curve and repeatability are the main sources of uncertainty, while those of sample weighting and sample constant volume account for little proportion.
基金This project was supported by China Postdoctoral Science Foun-dation(2004036121) the National Natural Science Foundation ofChina(10404022) Education Bureau of Shandong province(J04A63)
文摘A new algorithm for iterative reconstruction is suggested.It is named simple self-correlative algebraic reconstruction technique (SSART).With numerical simulation experiments,SSART was applied in reconstructing a non-ideal-bordered field in order to test its reconstructive effect.For contrast,three current representative algebraic reconstruction(ARTs) including basic ART,simultaneous ART (SART) and modified SART (MSART) were simulated simultaneously.The calculated results and reconstructive accuracy are discussed with three kinds of error indexes,namely mean-square error (MSE),absolute value error (AVE) and peak error (PE).As the results,the indexes of reconstructive accuracy are much improved by the proposed SSART.The MSE and PE have been decreased by 63.6% on the order of magnitude 10-4 and 88.9% on the order of magnitude 0-2,respectively,compared to that of ART.It is concluded that SSART is one of the most super iterative reconstructing techniques.
文摘Using the glucose and L-glutamic-acid to prepare the standard substance according to the ratio of 1：1, and the artificial seawater and the standard substance to prepare a series of standard solutions, the distribution pattern of uncertainty in measurement of seawater COD is obtained based on the measured results of the series of standard solutions by the potassium iodide-alkaline potassium permanganate determination method. The distribution pattern is as follows： Uncertainty in measurement is big and not constant at the high end, but small and constant at the low end.
文摘It is necessary for precise measurement to estimate the uncertainty of measurement result. When measuring flatness error in close way by pitch, usually the uncertainty of measurement result is independently estimated according to pitch points. By analyzing a concrete example, this paper proposed that the uncertainty should be evaluated by the correlation calculating method. This approach greatly improved the deficiencies of the assessment method according to independent measurement and enhanced measurement precision. It provides a reference value for uncertainty assessment in leveling a flat.
