Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax i...Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.展开更多
The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9（t） ～ t^γ, 0 ≤ γ 〈...The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9（t） ～ t^γ, 0 ≤ γ 〈 2, and the probability density function ω（t） of a particle＇s waiting time t follows a power law form for large t： ω（t） ～t^-（1＋α）, 0 〈 α 〈 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent 7 and the long-tailed index α of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.展开更多
A sufficient condition for the order of approximation of a continuous 2π periodic function with a given majorant for the modulus of continuity by the [F, d_n] means of its Fourier serier to be of Jackson order is obt...A sufficient condition for the order of approximation of a continuous 2π periodic function with a given majorant for the modulus of continuity by the [F, d_n] means of its Fourier serier to be of Jackson order is obtained. This sufficient condition is shown to be not enough for the order of approximation by partial sums of their Fourier series to be of Jackson order. The error estimate is shown to be the best possible.展开更多
This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability ...This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of their infinitesimal generators w.r.t.parameters imply the differentiability of the C 0 semigroups.The results are applied to the differentiability of the solution of a linear delay differential equation w.r.t.its delays.展开更多
This paper presents a new subband adaptive filter(SAF)algorithm for system identification scenario under impulsive interference,named generalized continuous mixed p-norm SAF(GCMPN-SAF)algorithm.The proposed algorithm ...This paper presents a new subband adaptive filter(SAF)algorithm for system identification scenario under impulsive interference,named generalized continuous mixed p-norm SAF(GCMPN-SAF)algorithm.The proposed algorithm uses a GCMPN cost function to combat the impul-sive interference.To further accelerate the convergence rate in the sparse and the block-sparse system identification processes,the proportionate versions of the proposed algorithm,the L0-norm GCMPN-SAF(L0-GCMPN-SAF)and the block-sparse GCMPN-SAF(BSGCMPN-SAF)algorithms are also developed.Moreover,the convergence analysis of the proposed algorithm is provided.Simulation results show that the proposed algorithms have a better performance than some other state-of-the-art algorithms in the literature with respect to the convergence rate and the tracking capability.展开更多
Knot insertion algorithm is one of the most important technologies of B-spline method. By inserting a knot the local prop- erties of B-spline curve and the control flexibility of its shape can be fiu＇ther improved, a...Knot insertion algorithm is one of the most important technologies of B-spline method. By inserting a knot the local prop- erties of B-spline curve and the control flexibility of its shape can be fiu＇ther improved, also the segmentation of the curve can be rea- lized. ECT spline curve is drew by the multi-knots spline curve with associated matrix in ECT spline space; Muehlbach G and Tang Y and many others have deduced the existence and uniqueness of the ECT spline function and developed many of its important properties .This paper mainly focuses on the knot insertion algorithm of ECT B-spline curve.It is the widest popularization of B-spline Behm algorithm and theory. Inspired by the Behm algorithm, in the ECT spline space, structure of generalized P61ya poly- nomials and generalized de Boor Fix dual functional, expressing new control points which are inserted after the knot by linear com- bination of original control vertex the single knot, and there are two cases, one is the single knot, the other is the double knot. Then finally comes the insertion algorithm of ECT spline curve knot. By application of the knot insertion algorithm, this paper also gives out the knot insertion algorithm of four order geometric continuous piecewise polynomial B-spline and algebraic trigonometric spline B-spline, which is consistent with previous results.展开更多
We study Jackson＇s inequality between the best approximation of a function f∈ L2（R^3） by entire functions of exponential spherical type and its generalized modulus of continuity. We prove Jackson＇s inequality wit...We study Jackson＇s inequality between the best approximation of a function f∈ L2（R^3） by entire functions of exponential spherical type and its generalized modulus of continuity. We prove Jackson＇s inequality with the exact constant and the optimal argument in the modulus of continuity. In particular, Jackson＇s inequality with the optimal parameters is obtained for classical modulus of continuity of order r and Thue-Morse modulus of continuity of order r∈ N. These results are based on the solution of the generalized Logan problem for entire functions of exponential type. For it we construct a new quadrature formulas for entire functions of exponential type.展开更多
In this paper,we study mulit-dimensional oblique reflected backward stochastic differential equations(RBSDEs)in a more general framework over finite or infinite time horizon,corresponding to the pricing problem for a ...In this paper,we study mulit-dimensional oblique reflected backward stochastic differential equations(RBSDEs)in a more general framework over finite or infinite time horizon,corresponding to the pricing problem for a type of real option.We prove that the equation can be solved uniquely in L^(p)(1<p≤2)-space,when the generators are uniformly continuous but each component taking values independently.Furthermore,if the generator of this equation fulfills the infinite time version of Lipschitzian continuity,we can also conclude that the solution to the oblique RBSDE exists and is unique,despite the fact that the values of some generator components may affect one another.展开更多
The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual o...The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual of P is generalized completely continuous;(3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11126346)
文摘Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11605003 and 11547231
文摘The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9（t） ～ t^γ, 0 ≤ γ 〈 2, and the probability density function ω（t） of a particle＇s waiting time t follows a power law form for large t： ω（t） ～t^-（1＋α）, 0 〈 α 〈 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent 7 and the long-tailed index α of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.
文摘A sufficient condition for the order of approximation of a continuous 2π periodic function with a given majorant for the modulus of continuity by the [F, d_n] means of its Fourier serier to be of Jackson order is obtained. This sufficient condition is shown to be not enough for the order of approximation by partial sums of their Fourier series to be of Jackson order. The error estimate is shown to be the best possible.
文摘This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of their infinitesimal generators w.r.t.parameters imply the differentiability of the C 0 semigroups.The results are applied to the differentiability of the solution of a linear delay differential equation w.r.t.its delays.
文摘This paper presents a new subband adaptive filter(SAF)algorithm for system identification scenario under impulsive interference,named generalized continuous mixed p-norm SAF(GCMPN-SAF)algorithm.The proposed algorithm uses a GCMPN cost function to combat the impul-sive interference.To further accelerate the convergence rate in the sparse and the block-sparse system identification processes,the proportionate versions of the proposed algorithm,the L0-norm GCMPN-SAF(L0-GCMPN-SAF)and the block-sparse GCMPN-SAF(BSGCMPN-SAF)algorithms are also developed.Moreover,the convergence analysis of the proposed algorithm is provided.Simulation results show that the proposed algorithms have a better performance than some other state-of-the-art algorithms in the literature with respect to the convergence rate and the tracking capability.
基金Supported by Financially Supported by the NUAA Fundamental Research Funds(No.NZ2013201)
文摘Knot insertion algorithm is one of the most important technologies of B-spline method. By inserting a knot the local prop- erties of B-spline curve and the control flexibility of its shape can be fiu＇ther improved, also the segmentation of the curve can be rea- lized. ECT spline curve is drew by the multi-knots spline curve with associated matrix in ECT spline space; Muehlbach G and Tang Y and many others have deduced the existence and uniqueness of the ECT spline function and developed many of its important properties .This paper mainly focuses on the knot insertion algorithm of ECT B-spline curve.It is the widest popularization of B-spline Behm algorithm and theory. Inspired by the Behm algorithm, in the ECT spline space, structure of generalized P61ya poly- nomials and generalized de Boor Fix dual functional, expressing new control points which are inserted after the knot by linear com- bination of original control vertex the single knot, and there are two cases, one is the single knot, the other is the double knot. Then finally comes the insertion algorithm of ECT spline curve knot. By application of the knot insertion algorithm, this paper also gives out the knot insertion algorithm of four order geometric continuous piecewise polynomial B-spline and algebraic trigonometric spline B-spline, which is consistent with previous results.
基金Supported by the Russian Foundation for Basic Research(Grant No.16-01-00308)
文摘We study Jackson＇s inequality between the best approximation of a function f∈ L2（R^3） by entire functions of exponential spherical type and its generalized modulus of continuity. We prove Jackson＇s inequality with the exact constant and the optimal argument in the modulus of continuity. In particular, Jackson＇s inequality with the optimal parameters is obtained for classical modulus of continuity of order r and Thue-Morse modulus of continuity of order r∈ N. These results are based on the solution of the generalized Logan problem for entire functions of exponential type. For it we construct a new quadrature formulas for entire functions of exponential type.
基金supported by the Natural Science Foundation of Shandong Province(Grant Nos.ZR2022MA079 and ZR2021MG049)the National Social Science Funding of China(Grant No.21CJY027)the TianYuan Special Funds of the National Natural Science Foundation of China(Grant No.11626146)。
文摘In this paper,we study mulit-dimensional oblique reflected backward stochastic differential equations(RBSDEs)in a more general framework over finite or infinite time horizon,corresponding to the pricing problem for a type of real option.We prove that the equation can be solved uniquely in L^(p)(1<p≤2)-space,when the generators are uniformly continuous but each component taking values independently.Furthermore,if the generator of this equation fulfills the infinite time version of Lipschitzian continuity,we can also conclude that the solution to the oblique RBSDE exists and is unique,despite the fact that the values of some generator components may affect one another.
基金supported by the National Natural Science Foundation of China(Nos.10861007,11161023)the National Excellent Doctoral Dissertation of China(No.2007B14)+1 种基金the Ganpo 555 Programme for Leading Talents of Jiangxi Province,the Natural Science Foundation of Jiangxi Province(No.20114BAB201008)the Fund of Education Department of Jiangxi Province(No.GJJ12657)
文摘The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent:(1) P is hypercontinuous;(2) the dual of P is generalized completely continuous;(3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained.
