The primary goal of this work is to characterize the impact of weighting selection strategy and multistatic geometry on the multistatic radar performance. With the relationship between the multistatic ambiguity functi...The primary goal of this work is to characterize the impact of weighting selection strategy and multistatic geometry on the multistatic radar performance. With the relationship between the multistatic ambiguity function （AF） and the multistatie Cram6r-Rao lower bound （CRLB）, the problem of calculating the multistatic AF and the multistatic CRLB as a performance metric for multistatic radar system is studied. Exactly, based on the proper selection of the system parameters, the multistatic radar performance can be significantly improved. The simulation results illustrate that the multistatic AF and the multistatic CRLB can serve as guidelines for future multistatic fusion rule development and multistatic radars deployment.展开更多
Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|x...Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.展开更多
The lower bounds for the blow-up time of blow-up solutions to the nonlinear nolocal porous equation ut=△u^m＋u^p∫Ωu^qdxwith either null Dirichlet boundary condition or homogeneous Neumann boundary condi- tion is g...The lower bounds for the blow-up time of blow-up solutions to the nonlinear nolocal porous equation ut=△u^m＋u^p∫Ωu^qdxwith either null Dirichlet boundary condition or homogeneous Neumann boundary condi- tion is given in this article by using a differential inequality technique.展开更多
The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee ...The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee discrepancy of fractional factorial designs with two and three mixed levels. Our new lower bound is sharper and more valid than other existing lower bounds in literature, which is a useful complement to the lower bound theory of discrepancies.展开更多
Li et al. in [3] obtained blow-up results for a system of Petrovskey equations in some different cases. In this article we obtain lower bounds for the blow up time under some considerations on initial data.
In this paper, the k-partitioning problem with partition matroid constraint is considered. LPT algorithm is modified to fit the problem and its worst-ease performance is analyzed. The lower bounds of optimal solution ...In this paper, the k-partitioning problem with partition matroid constraint is considered. LPT algorithm is modified to fit the problem and its worst-ease performance is analyzed. The lower bounds of optimal solution for the min-max problem are given.展开更多
In this note,we give a new proof to the energy conservation for the weak solutions of the incompressible 3D MHD equations.Moreover,we give the lower bounds for possible singular solutions to the incompressible 3D MHD ...In this note,we give a new proof to the energy conservation for the weak solutions of the incompressible 3D MHD equations.Moreover,we give the lower bounds for possible singular solutions to the incompressible 3D MHD equations.展开更多
The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regressi...The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regression(GPR)model based on Conditional Likelihood Lower Bound Search(CLLBS)to optimize the design of the generator,which can filter the noise in the data and search for global optimization by combining the Conditional Likelihood Lower Bound Search method.Taking the efficiency optimization of 15 kW Permanent Magnet Synchronous Motor as an example.Firstly,this method uses the elementary effect analysis to choose the sensitive variables,combining the evolutionary algorithm to design the super Latin cube sampling plan;Then the generator-converter system is simulated by establishing a co-simulation platform to obtain data.A Gaussian process regression model combing the method of the conditional likelihood lower bound search is established,which combined the chi-square test to optimize the accuracy of the model globally.Secondly,after the model reaches the accuracy,the Pareto frontier is obtained through the NSGA-II algorithm by considering the maximum output torque as a constraint.Last,the constrained optimization is transformed into an unconstrained optimizing problem by introducing maximum constrained improvement expectation(CEI)optimization method based on the re-interpolation model,which cross-validated the optimization results of the Gaussian process regression model.The above method increase the efficiency of generator by 0.76%and 0.5%respectively;And this method can be used for rapid modeling and multi-objective optimization of generator systems.展开更多
In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for th...In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for the system under either homogeneous Dirichlet or nonhomogeneous Neumann boundary conditions are obtained.展开更多
The mobile channel is slow fading and time selective, thus the multiplicative and additive noise of the channel will smear the spectral line, or arouse Doppler spread. This spread will make the parameters estimation a...The mobile channel is slow fading and time selective, thus the multiplicative and additive noise of the channel will smear the spectral line, or arouse Doppler spread. This spread will make the parameters estimation accuracy degrade. The goal of this paper is to analytically assess this degradation when Carrier Frequency Offset (CFO) and Doppler shift exist jointly. Then the finite-sample Cramer-Rao Lower Bound (CRLB) is derived and close-form asymptotical expression is given for large-sample CRLB. These expressions give insights into the performance room for frequency estimation. Also the variance of Doppler shift estimator is simulated to illustrate the theoretical results.展开更多
Most currently existing investigations on the observability of passive guidance systems can only provide a qualitative result. In this paper, a quantitative method, which utilizes Cramér-Rao lower bound in the es...Most currently existing investigations on the observability of passive guidance systems can only provide a qualitative result. In this paper, a quantitative method, which utilizes Cramér-Rao lower bound in the estimability analysis of closed-loop guidance systems with bearings-only measurements, is proposed. The new method provides an intuitive result for observability of the guidance system through graphical analysis. As a demonstration, a numerical example is presented, in which the degrees of observability of the guidance systems under two commonly used guidance laws are compared by using the new approach.展开更多
This paper will correct some gaps existing in the proof of a theorem written in an earlier paper by the author on the lower bounds for sums of BDH type published in 1993. Some improvements upon the previous version of...This paper will correct some gaps existing in the proof of a theorem written in an earlier paper by the author on the lower bounds for sums of BDH type published in 1993. Some improvements upon the previous version of that theorem will be obtained.展开更多
In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.
In this paper, estimations of the lower solution bounds for the discrete algebraic Lyapunov Equation (the DALE) are addressed. By utilizing linear algebraic techniques, several new lower solution bounds of the DALE ar...In this paper, estimations of the lower solution bounds for the discrete algebraic Lyapunov Equation (the DALE) are addressed. By utilizing linear algebraic techniques, several new lower solution bounds of the DALE are presented. We also propose numerical algorithms to develop sharper solution bounds. The obtained bounds can give a supplement to those appeared in the literature. 展开更多
In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizi...In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies .展开更多
The lower bounds on the maximum genus of loopless graphs are obtained according to the connectivity of these graphs. This not only answers a question of Chen, Archdeacon and Gross, but also generalizes the previous kn...The lower bounds on the maximum genus of loopless graphs are obtained according to the connectivity of these graphs. This not only answers a question of Chen, Archdeacon and Gross, but also generalizes the previous known results. Thus, a picture of the lower bounds on the maximum genus of loopless multigraphs is presented.展开更多
Abstract In this paper, by using the explicit expression of the kernel of the cubic spline interpolation, the optimal error bounds for the cubic spline interpolation of lower soomth functions are obtained.
Since the features of low energy consumption and limited power supply are very impor- tant for wireless sensor networks （WSNs）, the problems of distributed state estimation with quan- tized innovations are investiga...Since the features of low energy consumption and limited power supply are very impor- tant for wireless sensor networks （WSNs）, the problems of distributed state estimation with quan- tized innovations are investigated in this paper. In the first place, the assumptions of prior and posterior probability density function （PDF） with quantized innovations in the previous papers are analyzed. After that, an innovative Gaussian mixture estimator is proposed. On this basis, this paper presents a Gaussian mixture state estimation algorithm based on quantized innovations for WSNs. In order to evaluate and compare the performance of this kind of state estimation algo- rithms for WSNs, the posterior Cram6r-Rao lower bound （CRLB） with quantized innovations is put forward. Performance analysis and simulations show that the proposed Gaussian mixture state estimation algorithm is efficient than the others under the same number of quantization levels and the performance of these algorithms can be benchmarked by the theoretical lower bound.展开更多
The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower b...The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate （BER） for maximal ratio combining （MRC） with Gaussian distributed weighting errors on independent and identically distributed （i. i. d） fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.展开更多
The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize th...The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize the Carleman＇s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna＇s representation for harmonic functions in the half sphere by using HSrmander＇s theorem.展开更多
基金Project(61271441)supported by the National Natural Science Foundation of ChinaProject(NCET-10-0895)supported by the Program for New Century Excellent Talents in Universities of China
文摘The primary goal of this work is to characterize the impact of weighting selection strategy and multistatic geometry on the multistatic radar performance. With the relationship between the multistatic ambiguity function （AF） and the multistatie Cram6r-Rao lower bound （CRLB）, the problem of calculating the multistatic AF and the multistatic CRLB as a performance metric for multistatic radar system is studied. Exactly, based on the proper selection of the system parameters, the multistatic radar performance can be significantly improved. The simulation results illustrate that the multistatic AF and the multistatic CRLB can serve as guidelines for future multistatic fusion rule development and multistatic radars deployment.
文摘Let p be a prime with p≡3(mod 4). In this paper,by using some results relate the representation of integers by primitive binary quadratic forms,we prove that if x,y,z are positive integers satisfying x^p+y^p=z^p, p|xyz, x<y<z, then y>p^(6p-2)/2.
基金supported by the Fundamental Research Funds for the Central Universities (CDJXS 11 10 00 19)Mu Chunlai is supported by NSF of China(11071266)
文摘The lower bounds for the blow-up time of blow-up solutions to the nonlinear nolocal porous equation ut=△u^m＋u^p∫Ωu^qdxwith either null Dirichlet boundary condition or homogeneous Neumann boundary condi- tion is given in this article by using a differential inequality technique.
基金supported by the National Natural Science Foundation of China(11301546).supported by the National Natural Science Foundation of China(11271147,11471136)
文摘The objective of this paper is to study the issue of uniformity on asymmetrical designs with two and three mixed levels in terms of Lee discrepancy. Based on the known formulation, we present a new lower bound of Lee discrepancy of fractional factorial designs with two and three mixed levels. Our new lower bound is sharper and more valid than other existing lower bounds in literature, which is a useful complement to the lower bound theory of discrepancies.
文摘Li et al. in [3] obtained blow-up results for a system of Petrovskey equations in some different cases. In this article we obtain lower bounds for the blow up time under some considerations on initial data.
基金Supported by the National Natural Science Foundation of China(10671177)
文摘In this paper, the k-partitioning problem with partition matroid constraint is considered. LPT algorithm is modified to fit the problem and its worst-ease performance is analyzed. The lower bounds of optimal solution for the min-max problem are given.
基金supported by a Research Grant of Andong National University NRF-2015R1A5A1009350 and NRF-2016R1D1A1B03930422。
文摘In this note,we give a new proof to the energy conservation for the weak solutions of the incompressible 3D MHD equations.Moreover,we give the lower bounds for possible singular solutions to the incompressible 3D MHD equations.
基金supported in part by the National Key Research and Development Program of China(2019YFB1503700)the Hunan Natural Science Foundation-Science and Education Joint Project(2019JJ70063)。
文摘The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regression(GPR)model based on Conditional Likelihood Lower Bound Search(CLLBS)to optimize the design of the generator,which can filter the noise in the data and search for global optimization by combining the Conditional Likelihood Lower Bound Search method.Taking the efficiency optimization of 15 kW Permanent Magnet Synchronous Motor as an example.Firstly,this method uses the elementary effect analysis to choose the sensitive variables,combining the evolutionary algorithm to design the super Latin cube sampling plan;Then the generator-converter system is simulated by establishing a co-simulation platform to obtain data.A Gaussian process regression model combing the method of the conditional likelihood lower bound search is established,which combined the chi-square test to optimize the accuracy of the model globally.Secondly,after the model reaches the accuracy,the Pareto frontier is obtained through the NSGA-II algorithm by considering the maximum output torque as a constraint.Last,the constrained optimization is transformed into an unconstrained optimizing problem by introducing maximum constrained improvement expectation(CEI)optimization method based on the re-interpolation model,which cross-validated the optimization results of the Gaussian process regression model.The above method increase the efficiency of generator by 0.76%and 0.5%respectively;And this method can be used for rapid modeling and multi-objective optimization of generator systems.
基金Supported by the Natural Science Foundation of Shaanxi Province(2019JM-534)the Youth Innovation Team of Shaanxi Universities+7 种基金the 14th Five Year Plan for Educational Science in Shaanxi Province(SGH21Y0308)Key Topic of China Higher Education Association(21DFD04)Higher Education Teaching Reform Project of Xi’an International University(2023B03)2022 Annual Planning Project of China Association of Private Education(School Development)(CANFZG22222)Project of Department of Education of Shaanxi Provincethe 2022 Annual Topic of the"14th Five-Year Plan"of Shaanxi Provincial Educational Science(SGH22Y1885)Project of Qi Fang Education Research Institute of Xi’an International University(23mjy10)Special Project of the Shaanxi Provincial Social Science Found in 2023(2023SJ12,2023LS04)。
文摘In this paper,a class of slow reaction-diffusion equations with nonlocal source and inner absorption terms are studied.By using the technique of improved differential inequality,the lower bounds of blow up time for the system under either homogeneous Dirichlet or nonhomogeneous Neumann boundary conditions are obtained.
文摘The mobile channel is slow fading and time selective, thus the multiplicative and additive noise of the channel will smear the spectral line, or arouse Doppler spread. This spread will make the parameters estimation accuracy degrade. The goal of this paper is to analytically assess this degradation when Carrier Frequency Offset (CFO) and Doppler shift exist jointly. Then the finite-sample Cramer-Rao Lower Bound (CRLB) is derived and close-form asymptotical expression is given for large-sample CRLB. These expressions give insights into the performance room for frequency estimation. Also the variance of Doppler shift estimator is simulated to illustrate the theoretical results.
基金the National Natural Science Foundation of China (Grant No. 60104003 and 60374024).
文摘Most currently existing investigations on the observability of passive guidance systems can only provide a qualitative result. In this paper, a quantitative method, which utilizes Cramér-Rao lower bound in the estimability analysis of closed-loop guidance systems with bearings-only measurements, is proposed. The new method provides an intuitive result for observability of the guidance system through graphical analysis. As a demonstration, a numerical example is presented, in which the degrees of observability of the guidance systems under two commonly used guidance laws are compared by using the new approach.
文摘This paper will correct some gaps existing in the proof of a theorem written in an earlier paper by the author on the lower bounds for sums of BDH type published in 1993. Some improvements upon the previous version of that theorem will be obtained.
文摘In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.
文摘In this paper, estimations of the lower solution bounds for the discrete algebraic Lyapunov Equation (the DALE) are addressed. By utilizing linear algebraic techniques, several new lower solution bounds of the DALE are presented. We also propose numerical algorithms to develop sharper solution bounds. The obtained bounds can give a supplement to those appeared in the literature.
文摘In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies .
文摘The lower bounds on the maximum genus of loopless graphs are obtained according to the connectivity of these graphs. This not only answers a question of Chen, Archdeacon and Gross, but also generalizes the previous known results. Thus, a picture of the lower bounds on the maximum genus of loopless multigraphs is presented.
文摘Abstract In this paper, by using the explicit expression of the kernel of the cubic spline interpolation, the optimal error bounds for the cubic spline interpolation of lower soomth functions are obtained.
基金jointly supported by the National Natural Science Foundation of China(No.61175008)State Key Laboratory of Complex Electromagnetic Environment Effects on Electronics and Information System of China(No.CEMEE2014K0301A)the Natural Science Foundation of Jiangsu Province of China(No.BK20140896)
文摘Since the features of low energy consumption and limited power supply are very impor- tant for wireless sensor networks （WSNs）, the problems of distributed state estimation with quan- tized innovations are investigated in this paper. In the first place, the assumptions of prior and posterior probability density function （PDF） with quantized innovations in the previous papers are analyzed. After that, an innovative Gaussian mixture estimator is proposed. On this basis, this paper presents a Gaussian mixture state estimation algorithm based on quantized innovations for WSNs. In order to evaluate and compare the performance of this kind of state estimation algo- rithms for WSNs, the posterior Cram6r-Rao lower bound （CRLB） with quantized innovations is put forward. Performance analysis and simulations show that the proposed Gaussian mixture state estimation algorithm is efficient than the others under the same number of quantization levels and the performance of these algorithms can be benchmarked by the theoretical lower bound.
文摘The theoretical lower bounds on mean squared channel estimation errors for typical fading channels are presented by the infinite-length and non-causal Wiener filter and the exact closed-form expressions of the lower bounds for different channel Doppler spectra are derived. Based on the obtained lower bounds on mean squared channel estimation errors, the limits on bit error rate （BER） for maximal ratio combining （MRC） with Gaussian distributed weighting errors on independent and identically distributed （i. i. d） fading channels are presented. Numerical results show that the BER performances of ideal MRC are the lower bounds on the BER performances of non-ideal MRC and deteriorate as the maximum Doppler frequency increases or the SNR of channel estimate decreases.
基金Project supported by the Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality (IHLB201008257)Scientific Research Common Program of Beijing Municipal Commission of Education (KM200810011005)+1 种基金PHR (IHLB 201102)research grant of University of Macao MYRG142(Y1-L2)-FST111-KKI
文摘The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n 〉 2. To this end, we first generalize the Carleman＇s formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna＇s representation for harmonic functions in the half sphere by using HSrmander＇s theorem.
