This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a gen...This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set.In the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random inputs.This allows for avoiding repeated computations of invariant substructures while generating the input-output data set.Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy.Consequently,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs.The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.展开更多
Let(X,T)be a weakly mixing minimal system,p_(1),...,p_(d) be integer-valued generalized polynomials and(p_(1),p_(2),...,p_(d))be non-degenerate.Then there exists a residual subset X_(0) of X such that for all x∈X0,{(...Let(X,T)be a weakly mixing minimal system,p_(1),...,p_(d) be integer-valued generalized polynomials and(p_(1),p_(2),...,p_(d))be non-degenerate.Then there exists a residual subset X_(0) of X such that for all x∈X0,{(T^(p1(n))x,...,T^(pd(n))x):n∈Z}is dense in X^(d).展开更多
This paper is concerned with the application of generalized polynomial chaos (gPC) method to nonlinear random pantograph equations. An error estimation of gPC method is derived. The global error analysis is given fo...This paper is concerned with the application of generalized polynomial chaos (gPC) method to nonlinear random pantograph equations. An error estimation of gPC method is derived. The global error analysis is given for the error arising from finite-dimensional noise (FDN) assumption, projection error, aliasing error and discretization error. In the end, with several numerical experiments, the theoretical results are further illustrated.展开更多
Let the set of generalized polynomials having bounded coeffiicients be K={p=sum from j=1 to n α_j g_j α_j≤α_j≤β,j=1, 2,…, n}, where g_1, g_2,…, g_n are linearly independent continuous functions defined on thei...Let the set of generalized polynomials having bounded coeffiicients be K={p=sum from j=1 to n α_j g_j α_j≤α_j≤β,j=1, 2,…, n}, where g_1, g_2,…, g_n are linearly independent continuous functions defined on theinterval [a,b], α_j β_j are extended real numbers satisfying α_j<+∞, β_j>? andα_j≤β_j. Assumethat f is a continuous function defined on a compact set X [a, b]. This paper gives the characterizationtheorem for p being the best uniform approximation to f from K, and points out that the characteri-zation theorem can be applied in calculating the approximate solution of best approximation to f fromK.展开更多
In the present paper, we give the explicit formula of the principal part of ∑k=0^n({k}q-[n]qx)^sxk ∏m=0^n-k-1(1-q^mx) with respect to [n]q for any integer s and q ∈ (0, 1]. And, using the expressions, we obtai...In the present paper, we give the explicit formula of the principal part of ∑k=0^n({k}q-[n]qx)^sxk ∏m=0^n-k-1(1-q^mx) with respect to [n]q for any integer s and q ∈ (0, 1]. And, using the expressions, we obtain saturation theorems for Bn (f , qn,x) approximating to f(x) ∈ C[O, 1], 0 〈 qn ≤ 1, qn → 1.展开更多
This note establishes a pair of exponential generating functions for generalized Eulerian polynomials and Eulerian fractions, respectively. A kind of recurrence relation is obtained for the Eulerian fractions. Finally...This note establishes a pair of exponential generating functions for generalized Eulerian polynomials and Eulerian fractions, respectively. A kind of recurrence relation is obtained for the Eulerian fractions. Finally, a short proof of a certain summarion formula is given展开更多
We present a definition of general Sobolev spaces with respect to arbitrary measures, Wk,p(Ω,μ) for 1 .≤p≤∞.In [RARP] we proved that these spaces are complete under very light conditions. Now we prove that if we ...We present a definition of general Sobolev spaces with respect to arbitrary measures, Wk,p(Ω,μ) for 1 .≤p≤∞.In [RARP] we proved that these spaces are complete under very light conditions. Now we prove that if we consider certain general types of measures, then Cτ∞(R) is dense in these spaces. As an application to Sobolev orthogonal polynomials, toe study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.展开更多
In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the g...In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.展开更多
The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generali...The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .展开更多
In this article, we establish the Bessel polynomials with varying large negative parameters and discuss their orthogonality based on the generalized Bessel polynomials. By using the Riemann-Hilbert boundary value prob...In this article, we establish the Bessel polynomials with varying large negative parameters and discuss their orthogonality based on the generalized Bessel polynomials. By using the Riemann-Hilbert boundary value problem on the positive real axis, we get the Riemann-Hilbert characterization of the main Bessel polynomials with varying large negative parameters.展开更多
In this paper some novel integrals associated with the product of classical Hermite's polynomials ∫-∞+∞(x2)mexp(-x2){Hr(x)}2dx,∫0∞exp(-x2)H2k(x)H2s+1(x)dx,∫0∞exp(-x2)H2k(x)H2s(x)dx and ∫0...In this paper some novel integrals associated with the product of classical Hermite's polynomials ∫-∞+∞(x2)mexp(-x2){Hr(x)}2dx,∫0∞exp(-x2)H2k(x)H2s+1(x)dx,∫0∞exp(-x2)H2k(x)H2s(x)dx and ∫0∞exp(-x2)H2k+1(x)H2s+1(x)dx, are evaluated using hypergeometric approach and Laplace transform method, which is a different approach from the approaches given by the other authors in the field of spe- cial functions. Also the results may be of significant nature, and may yield numerous other interesting integrals involving the product of classical Hermite's polynomials by suitable simplifications of arbitrary parameters.展开更多
We investigate a generalized homogeneous Hahn polynomial in some detail. This polynomial includes as special cases the homogeneous Hahn polynomial and the homogeneous Rogers-Szeg o polynomial.A generating function, wh...We investigate a generalized homogeneous Hahn polynomial in some detail. This polynomial includes as special cases the homogeneous Hahn polynomial and the homogeneous Rogers-Szeg o polynomial.A generating function, which contains a known generating function as a special case, is given. We also give a finite series generating function. Some results on the asymptotic expansion for this polynomial are derived.Certain results on zeros are also obtained. We deduce several results on zeros of certain entire functions involving this generalized Hahn polynomial. As results, one of Zhang(2017)’s results as well as others is obtained. Finally,we derive several general results on q-congruences of the generalized q-Apéry polynomials, from which two qcongruences involving the generalized homogeneous Hahn polynomial are deduced.展开更多
Inverse synthetic aperture radar (ISAR) imaging of ship targets is very important in the national defense. For the high maneuverability of ship targets, the Doppler frequency shift of the received signal is time-var...Inverse synthetic aperture radar (ISAR) imaging of ship targets is very important in the national defense. For the high maneuverability of ship targets, the Doppler frequency shift of the received signal is time-varying, which will degrade the ISAR image quality for the traditional range-Doppler (RD) algorithm. In this paper, the received signal in a range bin is characterized as the multi-component polynomial phase signal (PPS) after the motion compensation, and a new approach of time-frequency represen- tation, generalized polynomial Wigner-Ville distribution (GPWVD), is proposed for the azimuth focusing. The GPWVD is based on the exponential matched-phase (EMP) principle. Compared with the conventional polynomial Wigner-Ville distribution (PWVD), the EMP principle transfers the non-integer lag coefficients of the PWVD to the position of the exponential of the signal, and the interpolation can be avoided completely. For the GPWVD, the cross-terms between multi-component signals can be reduced by decomposing the GPWVD into the convolution of Wigner-Ville distribution (WVD) and the spectrum of phase adjust functions. The GPWVD is used in the ISAR imaging of ship targets, and the high quality instantaneous ISAR images can be obtained. Simulation results and measurement data demonstrate the effectiveness of the proposed new method.展开更多
Let R be a 2-torsion free prime ring and L a noncommutative Lie ideal of R. Suppose that (d,σ) is a skew derivation of R such that xsd(x)xt = 0 for all x ∈ L, where s, t are fixed non-negative integers. Then d = 0.
Let R be a prime ring of characteristic different from 2, d and 9 two derivations of R at least one of which is nonzero, L a non-central Lie ideal of R, and a ∈ R. We prove that if a(d(u)u - ug(u)) = 0 for any...Let R be a prime ring of characteristic different from 2, d and 9 two derivations of R at least one of which is nonzero, L a non-central Lie ideal of R, and a ∈ R. We prove that if a(d(u)u - ug(u)) = 0 for any u ∈ L, then either a = O, or R is an sa-ring, d(x) = [p, x], and g(x) = -d(x) for some p in the Martindale quotient ring of R.展开更多
Let R be an associative ring not necessarily possessing an identity and (S,≤) a strictly totally ordered monoid which is also artinian and satisfies that 0≤s for any s∈S.Assume that M is a left R-module having pr...Let R be an associative ring not necessarily possessing an identity and (S,≤) a strictly totally ordered monoid which is also artinian and satisfies that 0≤s for any s∈S.Assume that M is a left R-module having property (F).It is shown that M is a co-Hopfian left R-module if and only if [M<sup>S,≤</sup>]is a co-Hopfan left [[R<sup>S,≤</sup>]]-module.展开更多
In this article, we develop a fully Discrete Galerkin(DG) method for solving ini- tial value fractional integro-differential equations(FIDEs). We consider Generalized Jacobi polynomials(CJPs) with indexes corres...In this article, we develop a fully Discrete Galerkin(DG) method for solving ini- tial value fractional integro-differential equations(FIDEs). We consider Generalized Jacobi polynomials(CJPs) with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. The fractional derivatives are used in the Caputo sense. The numerical solvability of algebraic system obtained from implementation of proposed method for a special case of FIDEs is investigated. We also provide a suitable convergence analysis to approximate solutions under a more general regularity assumption on the exact solution. Numerical results are presented to demonstrate the effectiveness of the proposed method.展开更多
This paper is motivated by S. Park [10] in which the injective cover of left R[x]- module M[x? ] of inverse polynomials over a left R-module M was discussed. The 1 author considers the ?-covers of modules and shows th...This paper is motivated by S. Park [10] in which the injective cover of left R[x]- module M[x? ] of inverse polynomials over a left R-module M was discussed. The 1 author considers the ?-covers of modules and shows that if η : P ?→ M is an ?- cover of M, then [ηS, ] : [PS, ] ?→ [MS, ] is an [?S, ]-cover of left [[RS, ]]-module ≤ ≤ ≤ ≤ ≤ [MS, ], where ? is a class of left R-modules and [MS, ] is the left [[RS, ]]-module of ≤ ≤ ≤ generalized inverse polynomials over a left R-module M. Also some properties of the injective cover of left [[RS, ]]-module [MS, ] are discussed. ≤展开更多
It is well-known that such non-conventional digital control schemes,such as generalized sampled-data hold functions,have clear advantages over the conventional single-rate digital control systems.However,they have the...It is well-known that such non-conventional digital control schemes,such as generalized sampled-data hold functions,have clear advantages over the conventional single-rate digital control systems.However,they have theoretical negative aspects that deviation of the input can lead to intersample oscillations or intersample ripples.This paper investigates the zero dynamics of sampleddata models,as the sampling period tends to zero,composed of a new generalized hold polynomial function,a nonlinear continuous-time plant and a sampler in cascade.For a new design of generalized hold circuit,the authors give the approximate expression of the resulting sampled-data systems as power series with respect to a sampling period up to the some order term on the basis of the normal form representation for the nonlinear continuous-time systems,and remarkable improvements in the stability properties of discrete system zero dynamics may be achieved by using proper adj us tment.Of particular interest are the stability conditions of sampling zero dynamics in the case of a new hold proposed.Also,an insightful interpretation of the obtained sampled-data models can be made in terms of minimal intersample ripple by design,where the ordinary multirate sampled systems have a poor intersample behavior.It has shown that the intersample behavior arising from the multirate input polynomial function can be localised by appropriately selecting the design parameters based on the stability condition of the sampling zero dynamics.The results presen ted here generalize the well-known notion of sampling zero dynamics from the linear case to nonlinear systems.展开更多
We construct a quadrature formula of the singular integral with the Chebyshev weight of the second kind by using Lagrange interpolation based on the rational system {1/(x?a 1), 1/(x?a 2), …}, and both the remainder a...We construct a quadrature formula of the singular integral with the Chebyshev weight of the second kind by using Lagrange interpolation based on the rational system {1/(x?a 1), 1/(x?a 2), …}, and both the remainder and convergence of the quadrature formula established here are discussed. Our results extend some classical ones.展开更多
基金Project supported by the National Research Foundation of Korea(Nos.NRF-2020R1C1C1011970 and NRF-2018R1A5A7023490)。
文摘This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random inputs.The method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data set.In the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random inputs.This allows for avoiding repeated computations of invariant substructures while generating the input-output data set.Combining substructuring with static condensation further improves the computational efficiency of the reanalysis without losing accuracy.Consequently,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional inputs.The numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.
基金Supported by NNSF of China(Grant Nos.11871188,12031019)。
文摘Let(X,T)be a weakly mixing minimal system,p_(1),...,p_(d) be integer-valued generalized polynomials and(p_(1),p_(2),...,p_(d))be non-degenerate.Then there exists a residual subset X_(0) of X such that for all x∈X0,{(T^(p1(n))x,...,T^(pd(n))x):n∈Z}is dense in X^(d).
基金Supported by the National Natural Science Foundation of China(No.11501427,11571128)
文摘This paper is concerned with the application of generalized polynomial chaos (gPC) method to nonlinear random pantograph equations. An error estimation of gPC method is derived. The global error analysis is given for the error arising from finite-dimensional noise (FDN) assumption, projection error, aliasing error and discretization error. In the end, with several numerical experiments, the theoretical results are further illustrated.
文摘Let the set of generalized polynomials having bounded coeffiicients be K={p=sum from j=1 to n α_j g_j α_j≤α_j≤β,j=1, 2,…, n}, where g_1, g_2,…, g_n are linearly independent continuous functions defined on theinterval [a,b], α_j β_j are extended real numbers satisfying α_j<+∞, β_j>? andα_j≤β_j. Assumethat f is a continuous function defined on a compact set X [a, b]. This paper gives the characterizationtheorem for p being the best uniform approximation to f from K, and points out that the characteri-zation theorem can be applied in calculating the approximate solution of best approximation to f fromK.
基金Supported by the National Natural Science Foundation (10601065)
文摘In the present paper, we give the explicit formula of the principal part of ∑k=0^n({k}q-[n]qx)^sxk ∏m=0^n-k-1(1-q^mx) with respect to [n]q for any integer s and q ∈ (0, 1]. And, using the expressions, we obtain saturation theorems for Bn (f , qn,x) approximating to f(x) ∈ C[O, 1], 0 〈 qn ≤ 1, qn → 1.
文摘This note establishes a pair of exponential generating functions for generalized Eulerian polynomials and Eulerian fractions, respectively. A kind of recurrence relation is obtained for the Eulerian fractions. Finally, a short proof of a certain summarion formula is given
基金Research Partially Supported by a Grant from DGES (MEC), Spain.
文摘We present a definition of general Sobolev spaces with respect to arbitrary measures, Wk,p(Ω,μ) for 1 .≤p≤∞.In [RARP] we proved that these spaces are complete under very light conditions. Now we prove that if we consider certain general types of measures, then Cτ∞(R) is dense in these spaces. As an application to Sobolev orthogonal polynomials, toe study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.
基金supported by the Simons Foundation:Collaboration Grantssupported by the AFOSR grant FA9550-18-1-0383.
文摘In this paper,we consider the high order method for solving the linear transport equations under diffusive scaling and with random inputs.To tackle the randomness in the problem,the stochastic Galerkin method of the generalized polynomial chaos approach has been employed.Besides,the high order implicit-explicit scheme under the micro-macro decomposition framework and the discontinuous Galerkin method have been employed.We provide several numerical experiments to validate the accuracy and the stochastic asymptotic-preserving property.
文摘The Fourier series of the 2π-periodic functions tg(x2)and 1sin(x)and some of their relatives (first of their integrals) are investigated and illustrated with respect to their convergence. These functions are Generalized functions and the convergence is weak convergence in the sense of the convergence of continuous linear functionals defining them. The figures show that the approximations of the Fourier series possess oscillations around the function which they represent in a broad band embedding them. This is some analogue to the Gibbs phenomenon. A modification of Fourier series by expansion in powers cosn(x)for the symmetric part of functions and sin(x)cosn−1(x)for the antisymmetric part (analogous to Taylor series) is discussed and illustrated by examples. The Fourier series and their convergence behavior are illustrated also for some 2π-periodic delta-function-like sequences connected with the Poisson theorem showing non-vanishing oscillations around the singularities similar to the Gibbs phenomenon in the neighborhood of discontinuities of functions. .
基金supported by NNSF of China(#11171260)RFDP of Higher Education of China(#20100141110054)
文摘In this article, we establish the Bessel polynomials with varying large negative parameters and discuss their orthogonality based on the generalized Bessel polynomials. By using the Riemann-Hilbert boundary value problem on the positive real axis, we get the Riemann-Hilbert characterization of the main Bessel polynomials with varying large negative parameters.
文摘In this paper some novel integrals associated with the product of classical Hermite's polynomials ∫-∞+∞(x2)mexp(-x2){Hr(x)}2dx,∫0∞exp(-x2)H2k(x)H2s+1(x)dx,∫0∞exp(-x2)H2k(x)H2s(x)dx and ∫0∞exp(-x2)H2k+1(x)H2s+1(x)dx, are evaluated using hypergeometric approach and Laplace transform method, which is a different approach from the approaches given by the other authors in the field of spe- cial functions. Also the results may be of significant nature, and may yield numerous other interesting integrals involving the product of classical Hermite's polynomials by suitable simplifications of arbitrary parameters.
基金supported by National Natural Science Foundation of China(Grant No.11801451)the Natural Science Foundation of Hunan Province(Grant No.2020JJ5682).
文摘We investigate a generalized homogeneous Hahn polynomial in some detail. This polynomial includes as special cases the homogeneous Hahn polynomial and the homogeneous Rogers-Szeg o polynomial.A generating function, which contains a known generating function as a special case, is given. We also give a finite series generating function. Some results on the asymptotic expansion for this polynomial are derived.Certain results on zeros are also obtained. We deduce several results on zeros of certain entire functions involving this generalized Hahn polynomial. As results, one of Zhang(2017)’s results as well as others is obtained. Finally,we derive several general results on q-congruences of the generalized q-Apéry polynomials, from which two qcongruences involving the generalized homogeneous Hahn polynomial are deduced.
基金supported by the National Natural Science Foundation of China (61001166)the Specialized Research Fund for the Doctoral Program of Higher Education (20092302120002)+3 种基金the Aerospace Support Fund (2011-HT-HGD-16)the Fundamental Research Funds for the Central Universities (HIT.BRETIII.201207)the Postdoctoral ScienceResearch Developmental Foundation of Heilongjiang Province (LBHQ11092)the Heilongjiang Postdoctoral Specialized Research Fund
文摘Inverse synthetic aperture radar (ISAR) imaging of ship targets is very important in the national defense. For the high maneuverability of ship targets, the Doppler frequency shift of the received signal is time-varying, which will degrade the ISAR image quality for the traditional range-Doppler (RD) algorithm. In this paper, the received signal in a range bin is characterized as the multi-component polynomial phase signal (PPS) after the motion compensation, and a new approach of time-frequency represen- tation, generalized polynomial Wigner-Ville distribution (GPWVD), is proposed for the azimuth focusing. The GPWVD is based on the exponential matched-phase (EMP) principle. Compared with the conventional polynomial Wigner-Ville distribution (PWVD), the EMP principle transfers the non-integer lag coefficients of the PWVD to the position of the exponential of the signal, and the interpolation can be avoided completely. For the GPWVD, the cross-terms between multi-component signals can be reduced by decomposing the GPWVD into the convolution of Wigner-Ville distribution (WVD) and the spectrum of phase adjust functions. The GPWVD is used in the ISAR imaging of ship targets, and the high quality instantaneous ISAR images can be obtained. Simulation results and measurement data demonstrate the effectiveness of the proposed new method.
基金The NSF(1408085QA08)of Anhui Provincialthe Key University Science Research Project(KJ2014A183)of Anhui Province of Chinathe Training Program(2014PY06)of Chuzhou University of China
文摘Let R be a 2-torsion free prime ring and L a noncommutative Lie ideal of R. Suppose that (d,σ) is a skew derivation of R such that xsd(x)xt = 0 for all x ∈ L, where s, t are fixed non-negative integers. Then d = 0.
文摘Let R be a prime ring of characteristic different from 2, d and 9 two derivations of R at least one of which is nonzero, L a non-central Lie ideal of R, and a ∈ R. We prove that if a(d(u)u - ug(u)) = 0 for any u ∈ L, then either a = O, or R is an sa-ring, d(x) = [p, x], and g(x) = -d(x) for some p in the Martindale quotient ring of R.
基金Research supported by National Natural Science Foundation of China,19671063
文摘Let R be an associative ring not necessarily possessing an identity and (S,≤) a strictly totally ordered monoid which is also artinian and satisfies that 0≤s for any s∈S.Assume that M is a left R-module having property (F).It is shown that M is a co-Hopfian left R-module if and only if [M<sup>S,≤</sup>]is a co-Hopfan left [[R<sup>S,≤</sup>]]-module.
文摘In this article, we develop a fully Discrete Galerkin(DG) method for solving ini- tial value fractional integro-differential equations(FIDEs). We consider Generalized Jacobi polynomials(CJPs) with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. The fractional derivatives are used in the Caputo sense. The numerical solvability of algebraic system obtained from implementation of proposed method for a special case of FIDEs is investigated. We also provide a suitable convergence analysis to approximate solutions under a more general regularity assumption on the exact solution. Numerical results are presented to demonstrate the effectiveness of the proposed method.
基金the National Natural Science Foundation of China (No.10171082) the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China and NWNU-KJCXGC212.
文摘This paper is motivated by S. Park [10] in which the injective cover of left R[x]- module M[x? ] of inverse polynomials over a left R-module M was discussed. The 1 author considers the ?-covers of modules and shows that if η : P ?→ M is an ?- cover of M, then [ηS, ] : [PS, ] ?→ [MS, ] is an [?S, ]-cover of left [[RS, ]]-module ≤ ≤ ≤ ≤ ≤ [MS, ], where ? is a class of left R-modules and [MS, ] is the left [[RS, ]]-module of ≤ ≤ ≤ generalized inverse polynomials over a left R-module M. Also some properties of the injective cover of left [[RS, ]]-module [MS, ] are discussed. ≤
基金supported by the National Natural Science Foundation of China under Grant No.61763004the Joint Funds of the Natural Science Foundation Project of Guizhou under Grant No.LH[2014]7362the Ph.D Launch Scientific Research Projects of Guizhou Institute Technology under Grant No.2014
文摘It is well-known that such non-conventional digital control schemes,such as generalized sampled-data hold functions,have clear advantages over the conventional single-rate digital control systems.However,they have theoretical negative aspects that deviation of the input can lead to intersample oscillations or intersample ripples.This paper investigates the zero dynamics of sampleddata models,as the sampling period tends to zero,composed of a new generalized hold polynomial function,a nonlinear continuous-time plant and a sampler in cascade.For a new design of generalized hold circuit,the authors give the approximate expression of the resulting sampled-data systems as power series with respect to a sampling period up to the some order term on the basis of the normal form representation for the nonlinear continuous-time systems,and remarkable improvements in the stability properties of discrete system zero dynamics may be achieved by using proper adj us tment.Of particular interest are the stability conditions of sampling zero dynamics in the case of a new hold proposed.Also,an insightful interpretation of the obtained sampled-data models can be made in terms of minimal intersample ripple by design,where the ordinary multirate sampled systems have a poor intersample behavior.It has shown that the intersample behavior arising from the multirate input polynomial function can be localised by appropriately selecting the design parameters based on the stability condition of the sampling zero dynamics.The results presen ted here generalize the well-known notion of sampling zero dynamics from the linear case to nonlinear systems.
文摘We construct a quadrature formula of the singular integral with the Chebyshev weight of the second kind by using Lagrange interpolation based on the rational system {1/(x?a 1), 1/(x?a 2), …}, and both the remainder and convergence of the quadrature formula established here are discussed. Our results extend some classical ones.