Suppose that the outer mapping function of domain D has its second continuous derivatives. In this paper, the order proximation by (0,1,…,q) Hermite-Fejer interpolating polynomials at nearly Fejer's points of fun...Suppose that the outer mapping function of domain D has its second continuous derivatives. In this paper, the order proximation by (0,1,…,q) Hermite-Fejer interpolating polynomials at nearly Fejer's points of function of class A(D) are presented. Moreover in general the order of approximation is sharp.展开更多
Value distributions of the general differential monomials is discussed.The following theorem is obtained:Let f be a transcendental meromorphic function in the plane,F=f n 0 (f (i) ) n i …(f (k) ) ...Value distributions of the general differential monomials is discussed.The following theorem is obtained:Let f be a transcendental meromorphic function in the plane,F=f n 0 (f (i) ) n i …(f (k) ) n k -c,n i≥1,c≠0 be a constant then (n 0-2)T(r,f)≤(r,1F)+S(r,f) when n 0】2;T(r,f)≤7(i+1)i( i) (r,1f)+(r,1F))+S(r,f) when n 0=1;T(r,f)≤7(N(r,1f)+(r,1F))+S(r,f) when n 0=0.展开更多
In is paper, a necessary and sufficient condition of regularity of (0,2)_interpolation on the zeros of the Lascenov Polynomials R (α,β) n(x)(α,β>-1) in a manageable form is estabished. Meanwhile, the exp...In is paper, a necessary and sufficient condition of regularity of (0,2)_interpolation on the zeros of the Lascenov Polynomials R (α,β) n(x)(α,β>-1) in a manageable form is estabished. Meanwhile, the explicit representation of the fundamental polynomials, when they exist, is given.展开更多
In this paper,a new third type S.N.Bernstein interpolation polynomial H n(f;x,r) with zeros of the Chebyshev ploynomial of the second kind is constructed. H n(f;x,r) converge uniformly on [-1,1] for any continuous fun...In this paper,a new third type S.N.Bernstein interpolation polynomial H n(f;x,r) with zeros of the Chebyshev ploynomial of the second kind is constructed. H n(f;x,r) converge uniformly on [-1,1] for any continuous function f(x) . The convergence order is the best order if \{f(x)∈C j[-1,1],\}0jr, where r is an odd natural number.展开更多
Let f（z） be a meromorphic function and ψ be the differential polynomial of f which satisfies the condition of -↑N（r, f）＋-↑N （r, 1/f） = S（r, f）. We obtain several results about the zero point of the ψ and ...Let f（z） be a meromorphic function and ψ be the differential polynomial of f which satisfies the condition of -↑N（r, f）＋-↑N （r, 1/f） = S（r, f）. We obtain several results about the zero point of the ψ and those results extend and improve the results of Yang and Yi in this paper.展开更多
This paper discover that when disturbance occurs on Chebyshev knot, so long as the disturbance amount does not exceed , then the course of the quasi Hemite-Fejer interpolation on the disturbed Chebyshev knot still ke...This paper discover that when disturbance occurs on Chebyshev knot, so long as the disturbance amount does not exceed , then the course of the quasi Hemite-Fejer interpolation on the disturbed Chebyshev knot still keeps the converge uniformly properlies for any continuous function on . Besides,the paper estimates the convergance rate.展开更多
The correct answer of Pal's interpolation polynomial problem has been given in this paper ,especially, the explict form of this polynomial has been obtained.
Some properties of characteristic polynomials, eigenvalues, and eigenvectors of the Wilkinson matrices W2n＋1 and W2n＋1 are presented. It is proved that the eigenvalues of W2n＋1 just are the eigenvalues of its leadi...Some properties of characteristic polynomials, eigenvalues, and eigenvectors of the Wilkinson matrices W2n＋1 and W2n＋1 are presented. It is proved that the eigenvalues of W2n＋1 just are the eigenvalues of its leading principal submatrix Vn and a bordered matrix of Vn. Recurrence formula are given for the characteristic polynomial of W2＋n＋1 . The eigenvectors of W2＋n＋1 are proved to be symmetric or skew symmetric. For W2n＋1 , it is found that its eigenvalues are zero and the square roots of the eigenvalues of a bordered matrix of Vn2. And the eigenvectors of W2n＋1 , which the corresponding eigenvahies are opposite in pairs, have close relationship.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
In this paper an error in[4]is pointed out and a method for constructingsurface interpolating scattered data points is presented.The main feature of the methodin this paper is that the surface so constructed is polyno...In this paper an error in[4]is pointed out and a method for constructingsurface interpolating scattered data points is presented.The main feature of the methodin this paper is that the surface so constructed is polynomial,which makes the construction simple and the calculation easy.展开更多
Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cu...Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Chebyshev weight functions and associated interpolation polynomials on [-1,1]^2, as well as new results on [-1, 1]^3. In particular, compact formulas for the fundamental interpolation polynomials are derived, based on n3/4 ＋ O（n^2） nodes of a cubature formula on [-1,1]^3.展开更多
The conventional ring signature schemes cannot address the scenario where the rank of members of the ring needs to be distinguished, for example, in electronically commerce application. To solve this problem, we prese...The conventional ring signature schemes cannot address the scenario where the rank of members of the ring needs to be distinguished, for example, in electronically commerce application. To solve this problem, we presented a Trusted Platform Module （TPM）-based threshold ring signature schen. Employing a reliable secret Share Distribution Center （SDC）, the proposed approach can authenticate the TPM-based identity rank of members of the ring but not track a specific member＇s identity. A subset including t members with the same identity rank is built. With the signing cooperation of t members of the subset, the ring signature based on Chinese remainder theorem is generated. We proved the anonymity and unforgeability of the proposed scheme and compared it with the threshold ring signature based on Lagrange interpolation polynomial. Our scheme is relatively simpler to calculate.展开更多
The general interpolation mentioned in this a rticle provides an effective way for reducing the amount of calculation of direc t optimal exploration. It has been testified by real case calculations that the interpolat...The general interpolation mentioned in this a rticle provides an effective way for reducing the amount of calculation of direc t optimal exploration. It has been testified by real case calculations that the interpolation is not only reliable but also can save the amount of calculation by nearly 36%. Large amount of calculation and lacking strict theoretical bas is has been th e two disadvantage of direct method by new. If this defect is not overcome, they will not only s eriously affect the application of this method, but also hinder its further rese arch. Based on sufficient calculation practice, this article has made a primary discussion about the theory and method of reducing the amount of calculation, an d has achieved some satisfactory results.展开更多
In this paper, we study the quantic Diophantine equation （1） with elementary geometry method, therefore all positive integer solutions of the equation （1） are obtained, and existence of Heron triangle whose median...In this paper, we study the quantic Diophantine equation （1） with elementary geometry method, therefore all positive integer solutions of the equation （1） are obtained, and existence of Heron triangle whose median lengths are all positive integer are discussed here.展开更多
The motion＇s generation consists in finding an analytic expression of a motion according to time. A Map road type planner or Cell decomposition provide to the motion generator some possible free crossing points of co...The motion＇s generation consists in finding an analytic expression of a motion according to time. A Map road type planner or Cell decomposition provide to the motion generator some possible free crossing points of collision. The global trajectory＇s interpolation by a polynomial is generally not possible, because the degree of the polynomial increases with the number of crossing points which can generate vibrations or loops of the. trajectory. The solution consists in using polynomials in an inferior degree and to build the motion in pieces. The theoretical developments concern the motion＇s generation, the modeling of the vehicle, then the management of its redundancy steam-power. All these methods contribute to improve the robot precision （accuracy）. The authors are presenting the motion＇s generator which constructs into lines a continuous trajectory C2 while enabling the transformation of the crossing points into lines. The generator presented here as part of omnidirectional robot is adaptable to any kind of vehicle.展开更多
文摘Suppose that the outer mapping function of domain D has its second continuous derivatives. In this paper, the order proximation by (0,1,…,q) Hermite-Fejer interpolating polynomials at nearly Fejer's points of function of class A(D) are presented. Moreover in general the order of approximation is sharp.
文摘Value distributions of the general differential monomials is discussed.The following theorem is obtained:Let f be a transcendental meromorphic function in the plane,F=f n 0 (f (i) ) n i …(f (k) ) n k -c,n i≥1,c≠0 be a constant then (n 0-2)T(r,f)≤(r,1F)+S(r,f) when n 0】2;T(r,f)≤7(i+1)i( i) (r,1f)+(r,1F))+S(r,f) when n 0=1;T(r,f)≤7(N(r,1f)+(r,1F))+S(r,f) when n 0=0.
文摘In is paper, a necessary and sufficient condition of regularity of (0,2)_interpolation on the zeros of the Lascenov Polynomials R (α,β) n(x)(α,β>-1) in a manageable form is estabished. Meanwhile, the explicit representation of the fundamental polynomials, when they exist, is given.
文摘In this paper,a new third type S.N.Bernstein interpolation polynomial H n(f;x,r) with zeros of the Chebyshev ploynomial of the second kind is constructed. H n(f;x,r) converge uniformly on [-1,1] for any continuous function f(x) . The convergence order is the best order if \{f(x)∈C j[-1,1],\}0jr, where r is an odd natural number.
基金Supported by the Natural Science Fundation of Henan Proivince(0211050200)
文摘Let f（z） be a meromorphic function and ψ be the differential polynomial of f which satisfies the condition of -↑N（r, f）＋-↑N （r, 1/f） = S（r, f）. We obtain several results about the zero point of the ψ and those results extend and improve the results of Yang and Yi in this paper.
文摘This paper discover that when disturbance occurs on Chebyshev knot, so long as the disturbance amount does not exceed , then the course of the quasi Hemite-Fejer interpolation on the disturbed Chebyshev knot still keeps the converge uniformly properlies for any continuous function on . Besides,the paper estimates the convergance rate.
文摘The correct answer of Pal's interpolation polynomial problem has been given in this paper ,especially, the explict form of this polynomial has been obtained.
基金The Fundamental Research Funds for the Central Universities, China (No.10D10908)
文摘Some properties of characteristic polynomials, eigenvalues, and eigenvectors of the Wilkinson matrices W2n＋1 and W2n＋1 are presented. It is proved that the eigenvalues of W2n＋1 just are the eigenvalues of its leading principal submatrix Vn and a bordered matrix of Vn. Recurrence formula are given for the characteristic polynomial of W2＋n＋1 . The eigenvectors of W2＋n＋1 are proved to be symmetric or skew symmetric. For W2n＋1 , it is found that its eigenvalues are zero and the square roots of the eigenvalues of a bordered matrix of Vn2. And the eigenvectors of W2n＋1 , which the corresponding eigenvahies are opposite in pairs, have close relationship.
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In this paper an error in[4]is pointed out and a method for constructingsurface interpolating scattered data points is presented.The main feature of the methodin this paper is that the surface so constructed is polynomial,which makes the construction simple and the calculation easy.
基金supported by NSFC Grants 10601056,10431050 and 60573023supported by National Basic Research Program grant 2005CB321702supported by NSF Grant DMS-0604056.
文摘Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Chebyshev weight functions and associated interpolation polynomials on [-1,1]^2, as well as new results on [-1, 1]^3. In particular, compact formulas for the fundamental interpolation polynomials are derived, based on n3/4 ＋ O（n^2） nodes of a cubature formula on [-1,1]^3.
基金Acknowledgements This work was supported by the National Basic Research Program of China under Crant No. 2007CB311100, Core Electronic Devices, High-end General Purpose Chips and Basic Software Products in China under Oant No. 2010ZX01037-001-001 Ph.D. Start-up Fund of Beijing University of Technology under Grants No. X0007211201101 and No. X00700054R1764, National Soft Science Research Program under Crant No. 2010GXQ5D317 and the National Natural Science Foundation of China underGrant No. 91018008 ,Opening Project of Key Lab of Information Network Security, Ministry of Public Security under Crant No. C11610, Opening Project of State Key Laboratory of Information Security （Institute of Sottware, Chinese Academy of Sciences） under Cxant No. 04-04-1.
文摘The conventional ring signature schemes cannot address the scenario where the rank of members of the ring needs to be distinguished, for example, in electronically commerce application. To solve this problem, we presented a Trusted Platform Module （TPM）-based threshold ring signature schen. Employing a reliable secret Share Distribution Center （SDC）, the proposed approach can authenticate the TPM-based identity rank of members of the ring but not track a specific member＇s identity. A subset including t members with the same identity rank is built. With the signing cooperation of t members of the subset, the ring signature based on Chinese remainder theorem is generated. We proved the anonymity and unforgeability of the proposed scheme and compared it with the threshold ring signature based on Lagrange interpolation polynomial. Our scheme is relatively simpler to calculate.
文摘The general interpolation mentioned in this a rticle provides an effective way for reducing the amount of calculation of direc t optimal exploration. It has been testified by real case calculations that the interpolation is not only reliable but also can save the amount of calculation by nearly 36%. Large amount of calculation and lacking strict theoretical bas is has been th e two disadvantage of direct method by new. If this defect is not overcome, they will not only s eriously affect the application of this method, but also hinder its further rese arch. Based on sufficient calculation practice, this article has made a primary discussion about the theory and method of reducing the amount of calculation, an d has achieved some satisfactory results.
基金Foundation item: Supported by the Natural Science Foundation of China(10271104)Supported by the Natural Science Foundation of Education Department of Sichuan Province(2004B25)
文摘In this paper, we study the quantic Diophantine equation （1） with elementary geometry method, therefore all positive integer solutions of the equation （1） are obtained, and existence of Heron triangle whose median lengths are all positive integer are discussed here.
文摘The motion＇s generation consists in finding an analytic expression of a motion according to time. A Map road type planner or Cell decomposition provide to the motion generator some possible free crossing points of collision. The global trajectory＇s interpolation by a polynomial is generally not possible, because the degree of the polynomial increases with the number of crossing points which can generate vibrations or loops of the. trajectory. The solution consists in using polynomials in an inferior degree and to build the motion in pieces. The theoretical developments concern the motion＇s generation, the modeling of the vehicle, then the management of its redundancy steam-power. All these methods contribute to improve the robot precision （accuracy）. The authors are presenting the motion＇s generator which constructs into lines a continuous trajectory C2 while enabling the transformation of the crossing points into lines. The generator presented here as part of omnidirectional robot is adaptable to any kind of vehicle.
