This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solve...This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.展开更多
The paper＇s aim is how to forecast data with variations involving at times series data to get the best forecasting model. When researchers are going to forecast data with variations involving at times series data （i...The paper＇s aim is how to forecast data with variations involving at times series data to get the best forecasting model. When researchers are going to forecast data with variations involving at times series data （i.e., secular trends, cyclical variations, seasonal effects, and stochastic variations）, they believe the best forecasting model is the one which realistically considers the underlying causal factors in a situational relationship and therefore has the best ＂track records＂ in generating data. Paper＇s models can be adjusted for variations in related a time series which processes a great deal of randomness, to improve the accuracy of the financial forecasts. Because of Na＇fve forecasting models are based on an extrapolation of past values for future. These models may be adjusted for seasonal, secular, and cyclical trends in related data. When a data series processes a great deal of randomness, smoothing techniques, such as moving averages and exponential smoothing, may improve the accuracy of the financial forecasts. But neither Na＇fve models nor smoothing techniques are capable of identifying major future changes in the direction of a situational data series. Hereby, nonlinear techniques, like direct and sequential search approaches, overcome those shortcomings can be used. The methodology which we have used is based on inferential analysis. To build the models to identify the major future changes in the direction of a situational data series, a comparative model building is applied. Hereby, the paper suggests using some of the nonlinear techniques, like direct and sequential search approaches, to reduce the technical shortcomings. The final result of the paper is to manipulate, to prepare, and to integrate heuristic non-linear searching methods to serve calculating adjusted factors to produce the best forecast data.展开更多
To provide an energy-efficient and slab-demand-compliant rolling delay strategy,the simulation software is utilized to calculate the rolling delay process of the reheating furnace.Based on energy consumption evaluatio...To provide an energy-efficient and slab-demand-compliant rolling delay strategy,the simulation software is utilized to calculate the rolling delay process of the reheating furnace.Based on energy consumption evaluation,two optimization methods were employed.The bisection approach uses the needs of the slab to estimate the rolling delay temperature,and the golden section search method uses the energy consumption analysis of the slab to determine the high-temperature insulation duration.Generally,the slab closest to the discharge position in the control zone is selected as the optimization target.The optimized slab does not show a significant temperature rise after the end of the rolling delay process.When comparing the optimized rolling delay strategies with the traditional ones,the optimized rolling delay strategies not only meet the output requirements for slabs but also offer significant advantages in terms of energy efficiency,and this advantage increases with rolling delay time.展开更多
Abstract：ools. The effective strain rate for for determining the total pressure developed during forging of a rectangular bar forging with bulging was expressed in terms of four-dimensional strain rate vector. The in...Abstract：ools. The effective strain rate for for determining the total pressure developed during forging of a rectangular bar forging with bulging was expressed in terms of four-dimensional strain rate vector. The inner-product of the vector was termwise integrated and summed. The integral mean value theorem was applied to determining the ratio of the strain rate components and the values of direction cosine of the vector and then an analytical solution of stress effective factor was obtained. The compression experiments of pure lead bar were performed to test the accuracy of the solution. The optimized results of total pressure by golden section search were compared with those of the indicator readings of the testing machine. It indicates that the optimized total pressures are 2.60%-10.14% higher than those measured. The solution is available and still an upper-bound solution.展开更多
In this paper, proportional fairness(PF)-based energy-efficient power allocation is studied for multiple-input multiple-output(MIMO) non-orthogonal multiple access(NOMA) systems. In our schemes, statistical channel st...In this paper, proportional fairness(PF)-based energy-efficient power allocation is studied for multiple-input multiple-output(MIMO) non-orthogonal multiple access(NOMA) systems. In our schemes, statistical channel state information(CSI) is utilized for perfect CSI is impossible to achieve in practice. PF is used to balance the transmission efficiency and user fairness. Energy efficiency(EE) is formulated under basic data rate requirements and maximum transmitting power constraints. Due to the non-convex nature of EE, a two-step algorithm is proposed to obtain sub-optimal solution with a low complexity. Firstly, power allocation is determined by golden section search for fixed power. Secondly total transmitting power is determined by fractional programming method in the feasible regions. Compared to the performance of MIMO-NOMA without PF constraint, fairness is obtained at expense of decreasing of EE.展开更多
The steepest descent(or ascent)search is employed for finding optimum diffusion coefficients in T42L9G model,with a view to improving the model's computational stability or prediction accuracy.The method of the st...The steepest descent(or ascent)search is employed for finding optimum diffusion coefficients in T42L9G model,with a view to improving the model's computational stability or prediction accuracy.The method of the steepest descent search is first described,in which the golden section search is chosen as the fundamental one- dimensional search used in the multi-dimentional steepest descent search,and then the optimization of the dif- fusion coefficients is described.展开更多
In his classical article[3], J. Kiefer introduced the Fibonacci search as a direct optimal method. The optimality was proved under the restriction: the total number of tests is given in advance and fixed. To avoid thi...In his classical article[3], J. Kiefer introduced the Fibonacci search as a direct optimal method. The optimality was proved under the restriction: the total number of tests is given in advance and fixed. To avoid this restriction, some different concepts of optimality were proposed and some corresponding optimal methods were obtained in [1], [2], [5] and [6]. In particular, the even-block search was treated in [1]. This paper deals with the odd-block search. The main result is Theorem 1.15.展开更多
基金the National Science and Tech-nology Council,Taiwan for their financial support(Grant Number NSTC 111-2221-E-019-048).
文摘This study sets up two new merit functions,which are minimized for the detection of real eigenvalue and complex eigenvalue to address nonlinear eigenvalue problems.For each eigen-parameter the vector variable is solved from a nonhomogeneous linear system obtained by reducing the number of eigen-equation one less,where one of the nonzero components of the eigenvector is normalized to the unit and moves the column containing that component to the right-hand side as a nonzero input vector.1D and 2D golden section search algorithms are employed to minimize the merit functions to locate real and complex eigenvalues.Simultaneously,the real and complex eigenvectors can be computed very accurately.A simpler approach to the nonlinear eigenvalue problems is proposed,which implements a normalization condition for the uniqueness of the eigenvector into the eigenequation directly.The real eigenvalues can be computed by the fictitious time integration method(FTIM),which saves computational costs compared to the one-dimensional golden section search algorithm(1D GSSA).The simpler method is also combined with the Newton iterationmethod,which is convergent very fast.All the proposed methods are easily programmed to compute the eigenvalue and eigenvector with high accuracy and efficiency.
文摘The paper＇s aim is how to forecast data with variations involving at times series data to get the best forecasting model. When researchers are going to forecast data with variations involving at times series data （i.e., secular trends, cyclical variations, seasonal effects, and stochastic variations）, they believe the best forecasting model is the one which realistically considers the underlying causal factors in a situational relationship and therefore has the best ＂track records＂ in generating data. Paper＇s models can be adjusted for variations in related a time series which processes a great deal of randomness, to improve the accuracy of the financial forecasts. Because of Na＇fve forecasting models are based on an extrapolation of past values for future. These models may be adjusted for seasonal, secular, and cyclical trends in related data. When a data series processes a great deal of randomness, smoothing techniques, such as moving averages and exponential smoothing, may improve the accuracy of the financial forecasts. But neither Na＇fve models nor smoothing techniques are capable of identifying major future changes in the direction of a situational data series. Hereby, nonlinear techniques, like direct and sequential search approaches, overcome those shortcomings can be used. The methodology which we have used is based on inferential analysis. To build the models to identify the major future changes in the direction of a situational data series, a comparative model building is applied. Hereby, the paper suggests using some of the nonlinear techniques, like direct and sequential search approaches, to reduce the technical shortcomings. The final result of the paper is to manipulate, to prepare, and to integrate heuristic non-linear searching methods to serve calculating adjusted factors to produce the best forecast data.
文摘To provide an energy-efficient and slab-demand-compliant rolling delay strategy,the simulation software is utilized to calculate the rolling delay process of the reheating furnace.Based on energy consumption evaluation,two optimization methods were employed.The bisection approach uses the needs of the slab to estimate the rolling delay temperature,and the golden section search method uses the energy consumption analysis of the slab to determine the high-temperature insulation duration.Generally,the slab closest to the discharge position in the control zone is selected as the optimization target.The optimized slab does not show a significant temperature rise after the end of the rolling delay process.When comparing the optimized rolling delay strategies with the traditional ones,the optimized rolling delay strategies not only meet the output requirements for slabs but also offer significant advantages in terms of energy efficiency,and this advantage increases with rolling delay time.
基金Project(51074052)supported by the National Natural Science Foundation of ChinaProject(20100470676)supported by the China Postdoctoral Science Foundation
文摘Abstract：ools. The effective strain rate for for determining the total pressure developed during forging of a rectangular bar forging with bulging was expressed in terms of four-dimensional strain rate vector. The inner-product of the vector was termwise integrated and summed. The integral mean value theorem was applied to determining the ratio of the strain rate components and the values of direction cosine of the vector and then an analytical solution of stress effective factor was obtained. The compression experiments of pure lead bar were performed to test the accuracy of the solution. The optimized results of total pressure by golden section search were compared with those of the indicator readings of the testing machine. It indicates that the optimized total pressures are 2.60%-10.14% higher than those measured. The solution is available and still an upper-bound solution.
基金supported by the National Natural Science Foundation of China (No. 61671252)
文摘In this paper, proportional fairness(PF)-based energy-efficient power allocation is studied for multiple-input multiple-output(MIMO) non-orthogonal multiple access(NOMA) systems. In our schemes, statistical channel state information(CSI) is utilized for perfect CSI is impossible to achieve in practice. PF is used to balance the transmission efficiency and user fairness. Energy efficiency(EE) is formulated under basic data rate requirements and maximum transmitting power constraints. Due to the non-convex nature of EE, a two-step algorithm is proposed to obtain sub-optimal solution with a low complexity. Firstly, power allocation is determined by golden section search for fixed power. Secondly total transmitting power is determined by fractional programming method in the feasible regions. Compared to the performance of MIMO-NOMA without PF constraint, fairness is obtained at expense of decreasing of EE.
文摘The steepest descent(or ascent)search is employed for finding optimum diffusion coefficients in T42L9G model,with a view to improving the model's computational stability or prediction accuracy.The method of the steepest descent search is first described,in which the golden section search is chosen as the fundamental one- dimensional search used in the multi-dimentional steepest descent search,and then the optimization of the dif- fusion coefficients is described.
文摘In his classical article[3], J. Kiefer introduced the Fibonacci search as a direct optimal method. The optimality was proved under the restriction: the total number of tests is given in advance and fixed. To avoid this restriction, some different concepts of optimality were proposed and some corresponding optimal methods were obtained in [1], [2], [5] and [6]. In particular, the even-block search was treated in [1]. This paper deals with the odd-block search. The main result is Theorem 1.15.
