In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on comp...In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.展开更多
In this paper we investigate simultaneous approximation for arbitrary system of nodes on smooth domain in complex plane. Some results which are better than those of known theorems are obtained.
In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth...In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in DR = {z ∈ C; ｜z｜ 〈 R}. Also, the exact order of approximation is found. The method used allows to construct complex Szasz-type and Baskakov-type approximation operators without involving the values on [0,∞）.展开更多
This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ab...This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ability, and adaptability greatly in learning processes of networks. The simulation results have been shown that the method can be applied to the modeling and identification of complex dynamic control systems.展开更多
High-speed magnitude approximation algorithms for complex vectors are discussed intensively. The performance and the convergence speed of these approximation algorithms are analyzed. For the polygon fitting algorithms...High-speed magnitude approximation algorithms for complex vectors are discussed intensively. The performance and the convergence speed of these approximation algorithms are analyzed. For the polygon fitting algorithms, the approximation formula under the least mean square error criterion is derived. For the iterative algorithms, a modified CORDIC (coordinate rotation digital computer) algorithm is developed. This modified CORDIC algorithm is proved to be with a maximum relative error about one half that of the original CORDIC algorithm. Finally, the effects of the finite register length on these algorithms are also concerned, which shows that 9 to 12-bit coefficients are sufficient for practical applications.展开更多
In the present article, we deal with the so-called overconvergence phenomenon in C of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real...In the present article, we deal with the so-called overconvergence phenomenon in C of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real axis in the complex plane.In this sense, error estimates in approximation and a quantitative Voronovskaya-type asymptotic formula are established.展开更多
Brain systems engage in what are generally considered to be among the most complex forms of information processing. In the present study, we investigated the functional complexity of anuran auditory processing using t...Brain systems engage in what are generally considered to be among the most complex forms of information processing. In the present study, we investigated the functional complexity of anuran auditory processing using the approximate entropy（Ap En） protocol for electroencephalogram（EEG） recordings from the forebrain and midbrain while male and female music frogs（Babina daunchina） listened to acoustic stimuli whose biological significance varied. The stimuli used were synthesized white noise（reflecting a novel signal）, conspecific male advertisement calls with either high or low sexual attractiveness（reflecting sexual selection） and silence（reflecting a baseline）. The results showed that 1） Ap En evoked by conspecific calls exceeded Ap En evoked by synthesized white noise in the left mesencephalon indicating this structure plays a critical role in processing acoustic signals with biological significance; 2） Ap En in the mesencephalon was significantly higher than for the telencephalon, consistent with the fact that the anuran midbrain contains a large well-organized auditory nucleus（torus semicircularis） while the forebrain does not; 3） for females Ap En in the mesencephalon was significantly different than that of males, suggesting that males and females process biological stimuli related to mate choice differently.展开更多
In this article, we discuss the approximate method of solving the Riemann-Hilbert boundary value problem for nonlinear uniformly elliptic complex equation of first order (0.1) with the boundary conditions (0.2) in a m...In this article, we discuss the approximate method of solving the Riemann-Hilbert boundary value problem for nonlinear uniformly elliptic complex equation of first order (0.1) with the boundary conditions (0.2) in a multiply connected unbounded domain D, the above boundary value problem will be called Problem A. If the complex Equation (0.1) satisfies the conditions similar to Condition C of (1.1), and the boundary condition (0.2) satisfies the conditions similar to (1.5), then we can obtain approximate solutions of the boundary value problems (0.1) and (0.2). Moreover the error estimates of approximate solutions for the boundary value problem is also given. The boundary value problem possesses many applications in mechanics and physics etc., for instance from (5.114) and (5.115), Chapter VI, [1], we see that Problem A of (0.1) possesses the important application to the shell and elasticity.展开更多
This paper presents a high efficiency spread spectrum scheme using approximate orthogonal complex (AOC) sequences. In this scheme, the 64 AOC sequences picked up from 84 complex sequences space are employed for spread...This paper presents a high efficiency spread spectrum scheme using approximate orthogonal complex (AOC) sequences. In this scheme, the 64 AOC sequences picked up from 84 complex sequences space are employed for spreading spectrum. In modulation, 6 input bits is used to select one AOC sequence, and the selected sequence is then phase-rotated by another 2 input bits. In demodulator, a complex correlator detects the transmitted AOC sequence. Simulation results show that the proposed scheme has better BER performance than the existing complementary code keying (CCK) modulation scheme. For AOC, additional processing gain of 1.79dB can be obtained when the sequence length is 8.展开更多
An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the rea...An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the real model superposition approximation method to the seismic response calculation of industrial buildings.The analysis using lumped mass-and-shear spring models indicates that for the equipment-to-structure frequency ratiosγf>1.1 orγf<0.9,the non-classical damping effect is limited,and the real mode superposition approximation method provides accurate estimates.For 0.9<γf<1.1,the system may have a pair of closely spaced frequency modes,and the non-zero off-diagonal damping terms have a non-negligible effect on the damping ratios and mode shape vectors of these modes.For 0.9<γf<1.1 and the equipment-to-structure mass ratiosγm<0.07,the real mode superposition approximation method results in large errors,while the approximation method can provide an accurate estimation for 0.9<γf<1.1 andγm>0.07.Furthermore,extensive parametric analyses are conducted,where both steel structures and reinforced concrete structures with equipment with various damping ratios are considered.Finally,the finite element analysis of a five-story industrial building is adopted to validate the proposed range of applicability.展开更多
In this paper, two different methods are used to study the cyclic structure solution and the optimal approximation of the quaternion Stein equation AXB - X = F . Firstly, the matrix equation equivalent to the ta...In this paper, two different methods are used to study the cyclic structure solution and the optimal approximation of the quaternion Stein equation AXB - X = F . Firstly, the matrix equation equivalent to the target structure matrix is constructed by using the complex decomposition of the quaternion matrix, to obtain the necessary and sufficient conditions for the existence of the cyclic solution of the equation and the expression of the general solution. Secondly, the Stein equation is converted into the Sylvester equation by adding the necessary parameters, and the condition for the existence of a cyclic solution and the expression of the equation’s solution are then obtained by using the real decomposition of the quaternion matrix and the Kronecker product of the matrix. At the same time, under the condition that the solution set is non-empty, the optimal approximation solution to the given quaternion circulant matrix is obtained by using the property of Frobenius norm property. Numerical examples are given to verify the correctness of the theoretical results and the feasibility of the proposed method. .展开更多
稳健性是信号处理中的一个重要考虑因素,特别是对独立成分分析(ICA)的分离性能有显著影响。因此,提出一种基于最大负熵的复值信号稳健近似多项式,用于改善复值ICA的稳健性。在实际信号处理领域中,使用ICA分离复值信号是信号处理中常见...稳健性是信号处理中的一个重要考虑因素,特别是对独立成分分析(ICA)的分离性能有显著影响。因此,提出一种基于最大负熵的复值信号稳健近似多项式,用于改善复值ICA的稳健性。在实际信号处理领域中,使用ICA分离复值信号是信号处理中常见的技术;相应地,利用负熵度量非高斯性是ICA中的一种常用方法。然而,负熵的估计性能极易受观测信号中的异常值影响。采用稳健估计理论和多项式展开方法,提出的函数可以在观测值受到异常值污染时,负熵仍然保持稳健的估计性能(Amari指数小于-10)。此外,结合所研究的近似方法,复值ICA算法在源信号与异常值混合的情况下仍能保持良好的分离性能(10 log I A<-10),证明了该方法的有效性。展开更多
In this paper, the improved complex variable moving least-squares （ICVMLS） approximation is presented. The ICVMLS approximation has an explicit physics meaning. Compared with the complex variable moving least-squar...In this paper, the improved complex variable moving least-squares （ICVMLS） approximation is presented. The ICVMLS approximation has an explicit physics meaning. Compared with the complex variable moving least-squares （CVMLS） approximations presented by Cheng and Ren, the ICVMLS approximation has a great computational precision and efficiency. Based on the element-free Galerkin （EFG） method and the ICVMLS approximation, the improved complex variable element-free Galerkin （ICVEFG） method is presented for two-dimensional elasticity problems, and the corresponding formulae are obtained. Compared with the conventional EFC method, the ICVEFG method has a great computational accuracy and efficiency. For the purpose of demonstration, three selected numerical examples are solved using the ICVEFG method.展开更多
文摘In the present paper, we deal with the complex Szasz-Durrmeyer operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth on compact disks. Also, the exact order of approximation is found.
文摘In this paper we investigate simultaneous approximation for arbitrary system of nodes on smooth domain in complex plane. Some results which are better than those of known theorems are obtained.
文摘In this paper, we deal with the complex Baskakov-Szasz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in DR = {z ∈ C; ｜z｜ 〈 R}. Also, the exact order of approximation is found. The method used allows to construct complex Szasz-type and Baskakov-type approximation operators without involving the values on [0,∞）.
文摘This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ability, and adaptability greatly in learning processes of networks. The simulation results have been shown that the method can be applied to the modeling and identification of complex dynamic control systems.
基金This project was supported by the Natural Science Foundation of Shaanxi Province.
文摘High-speed magnitude approximation algorithms for complex vectors are discussed intensively. The performance and the convergence speed of these approximation algorithms are analyzed. For the polygon fitting algorithms, the approximation formula under the least mean square error criterion is derived. For the iterative algorithms, a modified CORDIC (coordinate rotation digital computer) algorithm is developed. This modified CORDIC algorithm is proved to be with a maximum relative error about one half that of the original CORDIC algorithm. Finally, the effects of the finite register length on these algorithms are also concerned, which shows that 9 to 12-bit coefficients are sufficient for practical applications.
文摘In the present article, we deal with the so-called overconvergence phenomenon in C of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real axis in the complex plane.In this sense, error estimates in approximation and a quantitative Voronovskaya-type asymptotic formula are established.
基金supported by the grants from the National Natural Science Foundation of China (No. 31372217 and No. 31672305) to Guangzhan Fang
文摘Brain systems engage in what are generally considered to be among the most complex forms of information processing. In the present study, we investigated the functional complexity of anuran auditory processing using the approximate entropy（Ap En） protocol for electroencephalogram（EEG） recordings from the forebrain and midbrain while male and female music frogs（Babina daunchina） listened to acoustic stimuli whose biological significance varied. The stimuli used were synthesized white noise（reflecting a novel signal）, conspecific male advertisement calls with either high or low sexual attractiveness（reflecting sexual selection） and silence（reflecting a baseline）. The results showed that 1） Ap En evoked by conspecific calls exceeded Ap En evoked by synthesized white noise in the left mesencephalon indicating this structure plays a critical role in processing acoustic signals with biological significance; 2） Ap En in the mesencephalon was significantly higher than for the telencephalon, consistent with the fact that the anuran midbrain contains a large well-organized auditory nucleus（torus semicircularis） while the forebrain does not; 3） for females Ap En in the mesencephalon was significantly different than that of males, suggesting that males and females process biological stimuli related to mate choice differently.
文摘In this article, we discuss the approximate method of solving the Riemann-Hilbert boundary value problem for nonlinear uniformly elliptic complex equation of first order (0.1) with the boundary conditions (0.2) in a multiply connected unbounded domain D, the above boundary value problem will be called Problem A. If the complex Equation (0.1) satisfies the conditions similar to Condition C of (1.1), and the boundary condition (0.2) satisfies the conditions similar to (1.5), then we can obtain approximate solutions of the boundary value problems (0.1) and (0.2). Moreover the error estimates of approximate solutions for the boundary value problem is also given. The boundary value problem possesses many applications in mechanics and physics etc., for instance from (5.114) and (5.115), Chapter VI, [1], we see that Problem A of (0.1) possesses the important application to the shell and elasticity.
文摘This paper presents a high efficiency spread spectrum scheme using approximate orthogonal complex (AOC) sequences. In this scheme, the 64 AOC sequences picked up from 84 complex sequences space are employed for spreading spectrum. In modulation, 6 input bits is used to select one AOC sequence, and the selected sequence is then phase-rotated by another 2 input bits. In demodulator, a complex correlator detects the transmitted AOC sequence. Simulation results show that the proposed scheme has better BER performance than the existing complementary code keying (CCK) modulation scheme. For AOC, additional processing gain of 1.79dB can be obtained when the sequence length is 8.
基金Fund of China National Industrial Building Diagnosis and Reconstruction Engineering Technology Research Center under Grant No.YZA2017Ky03the Beijing Natural Science Foundation under Grant No.JQ18029the National Natural Science Foundation of China under Grant No.52078277。
文摘An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment.The objective of this paper is to quantify the range of applicability of the real model superposition approximation method to the seismic response calculation of industrial buildings.The analysis using lumped mass-and-shear spring models indicates that for the equipment-to-structure frequency ratiosγf>1.1 orγf<0.9,the non-classical damping effect is limited,and the real mode superposition approximation method provides accurate estimates.For 0.9<γf<1.1,the system may have a pair of closely spaced frequency modes,and the non-zero off-diagonal damping terms have a non-negligible effect on the damping ratios and mode shape vectors of these modes.For 0.9<γf<1.1 and the equipment-to-structure mass ratiosγm<0.07,the real mode superposition approximation method results in large errors,while the approximation method can provide an accurate estimation for 0.9<γf<1.1 andγm>0.07.Furthermore,extensive parametric analyses are conducted,where both steel structures and reinforced concrete structures with equipment with various damping ratios are considered.Finally,the finite element analysis of a five-story industrial building is adopted to validate the proposed range of applicability.
文摘In this paper, two different methods are used to study the cyclic structure solution and the optimal approximation of the quaternion Stein equation AXB - X = F . Firstly, the matrix equation equivalent to the target structure matrix is constructed by using the complex decomposition of the quaternion matrix, to obtain the necessary and sufficient conditions for the existence of the cyclic solution of the equation and the expression of the general solution. Secondly, the Stein equation is converted into the Sylvester equation by adding the necessary parameters, and the condition for the existence of a cyclic solution and the expression of the equation’s solution are then obtained by using the real decomposition of the quaternion matrix and the Kronecker product of the matrix. At the same time, under the condition that the solution set is non-empty, the optimal approximation solution to the given quaternion circulant matrix is obtained by using the property of Frobenius norm property. Numerical examples are given to verify the correctness of the theoretical results and the feasibility of the proposed method. .
文摘稳健性是信号处理中的一个重要考虑因素,特别是对独立成分分析(ICA)的分离性能有显著影响。因此,提出一种基于最大负熵的复值信号稳健近似多项式,用于改善复值ICA的稳健性。在实际信号处理领域中,使用ICA分离复值信号是信号处理中常见的技术;相应地,利用负熵度量非高斯性是ICA中的一种常用方法。然而,负熵的估计性能极易受观测信号中的异常值影响。采用稳健估计理论和多项式展开方法,提出的函数可以在观测值受到异常值污染时,负熵仍然保持稳健的估计性能(Amari指数小于-10)。此外,结合所研究的近似方法,复值ICA算法在源信号与异常值混合的情况下仍能保持良好的分离性能(10 log I A<-10),证明了该方法的有效性。
基金supported by the National Natural Science Foundation of China (Grant No.11026223)the Shanghai Leading Academic Discipline Project,China (Grant No.S30106)the Innovation Fund Project for Graduate Student of Shanghai University,China (Grant No.SHUCX112359)
文摘In this paper, the improved complex variable moving least-squares （ICVMLS） approximation is presented. The ICVMLS approximation has an explicit physics meaning. Compared with the complex variable moving least-squares （CVMLS） approximations presented by Cheng and Ren, the ICVMLS approximation has a great computational precision and efficiency. Based on the element-free Galerkin （EFG） method and the ICVMLS approximation, the improved complex variable element-free Galerkin （ICVEFG） method is presented for two-dimensional elasticity problems, and the corresponding formulae are obtained. Compared with the conventional EFC method, the ICVEFG method has a great computational accuracy and efficiency. For the purpose of demonstration, three selected numerical examples are solved using the ICVEFG method.
