给出了一种简易的控制系统设计方法——标准特征多项式设计方法,多回路控制系统采用这种方法将使控制系统设计的工作量大为简化。在此基础上,采用NCD工具箱,用标准特征多项式方法得到的参数值作为NCD(nonlinear control design)模块的...给出了一种简易的控制系统设计方法——标准特征多项式设计方法,多回路控制系统采用这种方法将使控制系统设计的工作量大为简化。在此基础上,采用NCD工具箱,用标准特征多项式方法得到的参数值作为NCD(nonlinear control design)模块的初始化值对控制系统的参数进一步进行优化,并与任意选择的6组参数值作为NCD模块初始化值而得到的优化效果进行了比较。还对飞行控制的多回路控制系统的鲁棒性进行了研究。结果证明,用标准特征多项式和NCD优化方法,设计方便,并且系统有很好的鲁棒性。展开更多
A Schrodinger eigenvalue problem is solved for the 219 quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two comp...A Schrodinger eigenvalue problem is solved for the 219 quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, （i） an application of the Kelly error estimator, and （ii） a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver.展开更多
Focused on the seed region selection and homogeneity criterion in Seeded Region Growing (SRG), an unsupervised seed region selection and a polynomial fitting homogeneity criterion for SRG are proposed in this paper. F...Focused on the seed region selection and homogeneity criterion in Seeded Region Growing (SRG), an unsupervised seed region selection and a polynomial fitting homogeneity criterion for SRG are proposed in this paper. First of all, making use of Peer Group Filtering (PGF) techniques, an unsupervised seed region selection algorithm is presented to construct a seed region. Then based on the constructed seed region a polynomial fitting homogeneity criterion is applied to solve the concrete problem of doorplate segmentation appearing in the robot navigation along a corridor. At last, experiments are performed and the results demonstrate the effectiveness of the proposed algorithm.展开更多
Let Hn be the set of real algebraic polynomials of degree n, whose zeros all lie in the interval [-1,1]. The well known Turán type inequalities tell us that forf（x）∈Hn, it holds ‖f＇‖≥C√n‖f‖. This note d...Let Hn be the set of real algebraic polynomials of degree n, whose zeros all lie in the interval [-1,1]. The well known Turán type inequalities tell us that forf（x）∈Hn, it holds ‖f＇‖≥C√n‖f‖. This note deals with the weighted Turán type inequalities with the weights having inner singularities under L^p norm for 0〈p≤∞. Our results essentially extend the result of Wang and Zhou （2002）, and the method used in this paper is simpler and more direct than that of Wang and Zhou （2002）. The results and methods have their own values in approximation theory and computation.展开更多
Determining deep holes is an important open problem in decoding Reed-Solomon codes. It is well known that the received word is trivially a deep hole if the degree of its Lagrange interpolation polynomial equals the di...Determining deep holes is an important open problem in decoding Reed-Solomon codes. It is well known that the received word is trivially a deep hole if the degree of its Lagrange interpolation polynomial equals the dimension of the Reed-Solomon code. For the standard Reed-Solomon codes [p-1, k]p with p a prime, Cheng and Murray conjectured in 2007 that there is no other deep holes except the trivial ones. In this paper, we show that this conjecture is not true. In fact, we find a new class of deep holes for standard Reed-Solomon codes [q-1, k]q with q a power of the prime p. Let q≥4 and 2≤k≤q-2. We show that the received word u is a deep hole if its Lagrange interpolation polynomial is the sum of monomial of degree q-2 and a polynomial of degree at most k-1. So there are at least 2(q-1)qk deep holes if k q-3.展开更多
The m-th order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion onto the subspace spanned by polynomials of degree up to m. We obtain the Karhunen-Loeve ex...The m-th order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion onto the subspace spanned by polynomials of degree up to m. We obtain the Karhunen-Loeve expansion for the process and establish a connection with the generalized （m-th order） Brownian bridge developed by MacNeill （1978） in the study of distributions of polynomial regression. The resulting distribution identity is also verified by a stochastic Fubini approach. As applications, large and small deviation asymptotic behaviors for the L2 norm are given.展开更多
Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are ...Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all {D-2i}D i=0. Suppose that denotes the tetrahedron algebra. In this paper, the authors display an action of ■ on the standard module V of H(D, 2). To describe this action, the authors define six matrices in Mat X(C), called A, A*, B, B*, K, K*.Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ■ on V.展开更多
. Let S = k[x1,..., xn] be a non-standard polynomial ring over a field k and let M be a finitely generated graded S-module. In this paper, we investigate the behaviour of Hilbert function of M and its relations with l.... Let S = k[x1,..., xn] be a non-standard polynomial ring over a field k and let M be a finitely generated graded S-module. In this paper, we investigate the behaviour of Hilbert function of M and its relations with lattice point counting. More precisely, by using combinatorial tools, we prove that there exists a polytope such that the image of Hilbert function in some degree is equal to the number of lattice points of this polytope.展开更多
文摘给出了一种简易的控制系统设计方法——标准特征多项式设计方法,多回路控制系统采用这种方法将使控制系统设计的工作量大为简化。在此基础上,采用NCD工具箱,用标准特征多项式方法得到的参数值作为NCD(nonlinear control design)模块的初始化值对控制系统的参数进一步进行优化,并与任意选择的6组参数值作为NCD模块初始化值而得到的优化效果进行了比较。还对飞行控制的多回路控制系统的鲁棒性进行了研究。结果证明,用标准特征多项式和NCD优化方法,设计方便,并且系统有很好的鲁棒性。
基金Developed under the Auspices of the Development Projects N N519 402837 and R15 012 03Founded by the Polish Ministry of Science and Higher Education
文摘A Schrodinger eigenvalue problem is solved for the 219 quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, （i） an application of the Kelly error estimator, and （ii） a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver.
基金Supported by the National Hi-Tech R&D Program of China (No.2002AA423160)the Na-tional Natural Science Foundation of China (No.60205004)the Henan Natural Science Foundation (No.0411013700).
文摘Focused on the seed region selection and homogeneity criterion in Seeded Region Growing (SRG), an unsupervised seed region selection and a polynomial fitting homogeneity criterion for SRG are proposed in this paper. First of all, making use of Peer Group Filtering (PGF) techniques, an unsupervised seed region selection algorithm is presented to construct a seed region. Then based on the constructed seed region a polynomial fitting homogeneity criterion is applied to solve the concrete problem of doorplate segmentation appearing in the robot navigation along a corridor. At last, experiments are performed and the results demonstrate the effectiveness of the proposed algorithm.
文摘Let Hn be the set of real algebraic polynomials of degree n, whose zeros all lie in the interval [-1,1]. The well known Turán type inequalities tell us that forf（x）∈Hn, it holds ‖f＇‖≥C√n‖f‖. This note deals with the weighted Turán type inequalities with the weights having inner singularities under L^p norm for 0〈p≤∞. Our results essentially extend the result of Wang and Zhou （2002）, and the method used in this paper is simpler and more direct than that of Wang and Zhou （2002）. The results and methods have their own values in approximation theory and computation.
基金the National Natural Science Foundation of China (10371036)the Natural Science Foundation of Beijing (1042001)the Fundamental Research Foundation of Beijing University of Technology (KZ0601200382)
文摘This paper deals with Δ-good filtration dimensions of a standardly stratified algebra and Δ[x]-good titration dimensions of its polynomial algebra.
基金supported by National Natural Science Foundation of China (Grant No.10971145)by the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20100181110073)
文摘Determining deep holes is an important open problem in decoding Reed-Solomon codes. It is well known that the received word is trivially a deep hole if the degree of its Lagrange interpolation polynomial equals the dimension of the Reed-Solomon code. For the standard Reed-Solomon codes [p-1, k]p with p a prime, Cheng and Murray conjectured in 2007 that there is no other deep holes except the trivial ones. In this paper, we show that this conjecture is not true. In fact, we find a new class of deep holes for standard Reed-Solomon codes [q-1, k]q with q a power of the prime p. Let q≥4 and 2≤k≤q-2. We show that the received word u is a deep hole if its Lagrange interpolation polynomial is the sum of monomial of degree q-2 and a polynomial of degree at most k-1. So there are at least 2(q-1)qk deep holes if k q-3.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.DL13BBX10)
文摘The m-th order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion onto the subspace spanned by polynomials of degree up to m. We obtain the Karhunen-Loeve expansion for the process and establish a connection with the generalized （m-th order） Brownian bridge developed by MacNeill （1978） in the study of distributions of polynomial regression. The resulting distribution identity is also verified by a stochastic Fubini approach. As applications, large and small deviation asymptotic behaviors for the L2 norm are given.
基金supported by the National Natural Science Foundation of China(Nos.11471097,11271257)the Specialized Research Fund for the Doctoral Program of Higher Education of China(No.20121303110005)+1 种基金the Natural Science Foundation of Hebei Province(No.A2013205021)the Key Fund Project of Hebei Normal University(No.L2012Z01)
文摘Let D be an integer at least 3 and let H(D, 2) denote the hypercube. It is known that H(D, 2) is a Q-polynomial distance-regular graph with diameter D, and its eigenvalue sequence and its dual eigenvalue sequence are all {D-2i}D i=0. Suppose that denotes the tetrahedron algebra. In this paper, the authors display an action of ■ on the standard module V of H(D, 2). To describe this action, the authors define six matrices in Mat X(C), called A, A*, B, B*, K, K*.Moreover, for each matrix above, the authors compute the transpose and then compute the transpose of each generator of ■ on V.
文摘. Let S = k[x1,..., xn] be a non-standard polynomial ring over a field k and let M be a finitely generated graded S-module. In this paper, we investigate the behaviour of Hilbert function of M and its relations with lattice point counting. More precisely, by using combinatorial tools, we prove that there exists a polytope such that the image of Hilbert function in some degree is equal to the number of lattice points of this polytope.
