Under the optimum experimental conditions (i. e., pH=1.6, c KI=10.6 mmol/L, =5.4 mmol/L, =1.30 mmol/L) derived from simplex operations, trace molybdenum(VI) was determined through the agency of its catalytic effect ...Under the optimum experimental conditions (i. e., pH=1.6, c KI=10.6 mmol/L, =5.4 mmol/L, =1.30 mmol/L) derived from simplex operations, trace molybdenum(VI) was determined through the agency of its catalytic effect on the reaction of H2O2 with I? in acid medium. The detection limit and linear calibration range of molybdenum were obtained as 0.5×10?6 mol/L and 0.5×10?6～120×10?6mol/L respectively. This method was applied to the examination of the industrial waste water, and the recovery ratios were found to be in the range of 101% and 107%. Key words oscillographic potentiometry - catalyzing kinetic analysis - simplex optimization - molybdenum Supported by the National Natural Science Foundation of China (Grant No. 20175013) and the Higher Education Development Foundation of Shanghai in China (Grant No. 01A17)展开更多
Formulation of the simplex matrix referred to n-D space, is presented in terms of the scalar product of vectors, known from elementary algebra. The principles of a simplex optimization procedure are presented on a sim...Formulation of the simplex matrix referred to n-D space, is presented in terms of the scalar product of vectors, known from elementary algebra. The principles of a simplex optimization procedure are presented on a simple example, with use of a target function taken as a criterion of optimization, where accuracy and precision are treated equally in searching optimal conditions of a gravimetric analysis.展开更多
An advanced earthquake location technique presented by Prugger and Gendzwill (1988) was introduced in this paper. Its characteristics are: 1) adopting the difference between the mean value by observed arrival times an...An advanced earthquake location technique presented by Prugger and Gendzwill (1988) was introduced in this paper. Its characteristics are: 1) adopting the difference between the mean value by observed arrival times and the mean value by calculated travel times as the original reference time of event to calculate the traveltime residuals, thus resulting in the 'true' minimum of travel-time residuals; 2) choosing the L1 norm statistic of the residuals that is more suitable to earthquake location; 3) using a simplex optimized algorithm to search for the minimum residual value directly and iteratively, thus it does not require derivative calculations and avoids matrix inversions, it can be used for any velocity structures and different network systems and can solve out hypocentral parameters (λ, ,h) rapidly and exactly; 4) original time is further derived alone, so the trade-off between focal depth and original time is avoided. All these prominent features make us obtain more accurate Tibetan earthquake locations in the rare network condition by using this method. In this paper, we examined these schemes for our mobile and permanent networks in Tibet with artificial data sets,then using these methods, we determined the hypocentral parameters of partial events observed in the field work period of this project from July 1991 to September 1991 and the seven problematic earthquakes during 1989 - 1990. The hypocentral location errors may be estimated to be less than 3. 6 km approximately. The events with focal depth more than 40 km seem to be distributed in parallel to Qinghai-Sichuan-Yunnan arc structural zone.展开更多
We consider the problem of minimizing a fixed-degree polynomial over the standard simplex.This problem is well known to be NP-hard,since it contains the maximum stable set problem in combinatorial optimization as a sp...We consider the problem of minimizing a fixed-degree polynomial over the standard simplex.This problem is well known to be NP-hard,since it contains the maximum stable set problem in combinatorial optimization as a special case.In this paper,we revisit a known upper bound obtained by taking the minimum value on a regular grid,and a known lower bound based on Pólya’s representation theorem.More precisely,we consider the difference between these two bounds and we provide upper bounds for this difference in terms of the range of function values.Our results refine the known upper bounds in the quadratic and cubic cases,and they asymptotically refine the known upper bound in the general case.展开更多
Static var compensators （SVCs） are used for voltage and reactive power control in power systems. In this paper, we will consider the structure of SVCs that mainly consists of Y-connection of mechanically-switched ca...Static var compensators （SVCs） are used for voltage and reactive power control in power systems. In this paper, we will consider the structure of SVCs that mainly consists of Y-connection of mechanically-switched capacitor （MSC） and delta connection of thyrister-controlled reactor （TCR）. First, the control model of SVC was established in this paper. Then, a novel optimal nonlinear voltage controller for SVCs is proposed. The proposed SVC voltage controller consists of a nonlinear function and a conventional PI controller. The improved simplex method （SPX） is presented to adjust and optimize the parameters of the nonlinear PI controller in real-time, and to make transient state response procedure of SVC optimum. The integration of time multiplied absolute error （ITAE） is adopted as the optimized objective function of SPX. Simulation and engineering application results show that the proposed voltage control method is able to track reference voltage value of SVC immediately. It also demonstrates that the whole SVC control System can synthetically compensate reactive power.展开更多
文摘Under the optimum experimental conditions (i. e., pH=1.6, c KI=10.6 mmol/L, =5.4 mmol/L, =1.30 mmol/L) derived from simplex operations, trace molybdenum(VI) was determined through the agency of its catalytic effect on the reaction of H2O2 with I? in acid medium. The detection limit and linear calibration range of molybdenum were obtained as 0.5×10?6 mol/L and 0.5×10?6～120×10?6mol/L respectively. This method was applied to the examination of the industrial waste water, and the recovery ratios were found to be in the range of 101% and 107%. Key words oscillographic potentiometry - catalyzing kinetic analysis - simplex optimization - molybdenum Supported by the National Natural Science Foundation of China (Grant No. 20175013) and the Higher Education Development Foundation of Shanghai in China (Grant No. 01A17)
文摘Formulation of the simplex matrix referred to n-D space, is presented in terms of the scalar product of vectors, known from elementary algebra. The principles of a simplex optimization procedure are presented on a simple example, with use of a target function taken as a criterion of optimization, where accuracy and precision are treated equally in searching optimal conditions of a gravimetric analysis.
文摘An advanced earthquake location technique presented by Prugger and Gendzwill (1988) was introduced in this paper. Its characteristics are: 1) adopting the difference between the mean value by observed arrival times and the mean value by calculated travel times as the original reference time of event to calculate the traveltime residuals, thus resulting in the 'true' minimum of travel-time residuals; 2) choosing the L1 norm statistic of the residuals that is more suitable to earthquake location; 3) using a simplex optimized algorithm to search for the minimum residual value directly and iteratively, thus it does not require derivative calculations and avoids matrix inversions, it can be used for any velocity structures and different network systems and can solve out hypocentral parameters (λ, ,h) rapidly and exactly; 4) original time is further derived alone, so the trade-off between focal depth and original time is avoided. All these prominent features make us obtain more accurate Tibetan earthquake locations in the rare network condition by using this method. In this paper, we examined these schemes for our mobile and permanent networks in Tibet with artificial data sets,then using these methods, we determined the hypocentral parameters of partial events observed in the field work period of this project from July 1991 to September 1991 and the seven problematic earthquakes during 1989 - 1990. The hypocentral location errors may be estimated to be less than 3. 6 km approximately. The events with focal depth more than 40 km seem to be distributed in parallel to Qinghai-Sichuan-Yunnan arc structural zone.
文摘We consider the problem of minimizing a fixed-degree polynomial over the standard simplex.This problem is well known to be NP-hard,since it contains the maximum stable set problem in combinatorial optimization as a special case.In this paper,we revisit a known upper bound obtained by taking the minimum value on a regular grid,and a known lower bound based on Pólya’s representation theorem.More precisely,we consider the difference between these two bounds and we provide upper bounds for this difference in terms of the range of function values.Our results refine the known upper bounds in the quadratic and cubic cases,and they asymptotically refine the known upper bound in the general case.
基金supported by the National Basic Research Program of China (973 Program) (No. 2009CB219706)the Scientific Research Plan of Hunan Provincial Science and Technology Department of China (Nos. 2009FJ3036, 2011FJ3035)
文摘Static var compensators （SVCs） are used for voltage and reactive power control in power systems. In this paper, we will consider the structure of SVCs that mainly consists of Y-connection of mechanically-switched capacitor （MSC） and delta connection of thyrister-controlled reactor （TCR）. First, the control model of SVC was established in this paper. Then, a novel optimal nonlinear voltage controller for SVCs is proposed. The proposed SVC voltage controller consists of a nonlinear function and a conventional PI controller. The improved simplex method （SPX） is presented to adjust and optimize the parameters of the nonlinear PI controller in real-time, and to make transient state response procedure of SVC optimum. The integration of time multiplied absolute error （ITAE） is adopted as the optimized objective function of SPX. Simulation and engineering application results show that the proposed voltage control method is able to track reference voltage value of SVC immediately. It also demonstrates that the whole SVC control System can synthetically compensate reactive power.
