This paper considers to replace △_m(x)=(1-x^2)~2(1/2)/n +1/n^2 in the following result for simultaneous Lagrange interpolating approximation with (1-x^2)~2(1/2)/n: Let f∈C_(-1.1)~0 and r=[(q+2)/2],then |f^(k)(x)-P_^...This paper considers to replace △_m(x)=(1-x^2)~2(1/2)/n +1/n^2 in the following result for simultaneous Lagrange interpolating approximation with (1-x^2)~2(1/2)/n: Let f∈C_(-1.1)~0 and r=[(q+2)/2],then |f^(k)(x)-P_^(k)(f,x)|=O(1)△_(n)^(a-k)(x)ω(f^(a),△(x))(‖L_n-‖+‖L_n‖),0≤k≤q, where P_n( f ,x)is the Lagrange interpolating polynomial of degree n+ 2r-1 of f on the nodes X_n U Y_n(see the definition of the text), and thus give a problem raised in [XiZh] a complete answer.展开更多
This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of...This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next).展开更多
The multivariate splines which were first presented by deBooor as a complete theoretical system have intrigued many mathematicians who have devoted many works in this field which is still in the process of development...The multivariate splines which were first presented by deBooor as a complete theoretical system have intrigued many mathematicians who have devoted many works in this field which is still in the process of development.The author of this paper is interested in the area of inter- polation with special emphasis on the interpolation methods and their approximation orders. But such B-splines(both univariate and multivariate)do not interpolated directly,so I ap- proached this problem in another way which is to extend my interpolating spline of degree 2n-1 in univariate case(See[7])to multivariate case.I selected triangulated region which is inspired by other mathematicians'works(e.g.[2]and[3])and extend the interpolating polynomials from univariate to m-variate case(See[10])In this paper some results in the case m=2 are discussed and proved in more concrete details.Based on these polynomials,the interpolating splines(it is defined by me as piecewise polynomials in which the unknown par- tial derivatives are determined under certain continuous conditions)are also discussed.The approximation orders of interpolating polynomials and of cubic interpolating splines are inverstigated.We lunited our discussion on the rectangular domain which is partitioned into equal right triangles.As to the case in which the rectangular domain is partitioned into unequal right triangles as well as the case of more complicated domains,we will discuss in the next pa- per.展开更多
In this paper. a quantitative estimate for Hermite interpolant to function ψ(z)=(z^m-β~m)~l on the ze- ros of (z^n-α~n)~r is obtained Using this estimate. a rather wide exiension of the theorem of Walsh is proved a...In this paper. a quantitative estimate for Hermite interpolant to function ψ(z)=(z^m-β~m)~l on the ze- ros of (z^n-α~n)~r is obtained Using this estimate. a rather wide exiension of the theorem of Walsh is proved and five special cases of it are given.展开更多
In this paper,an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials.Based on this condition,two new local optim...In this paper,an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials.Based on this condition,two new local optimization methods are developed.The solution points obtained by the new local optimization methods can improve the Karush–Kuhn–Tucker(KKT)points in general.Two global optimization methods then are proposed by combining the two new local optimization methods with a filled function method.Some numerical examples are reported to show the effectiveness of the proposed methods.展开更多
In this paper we investigate simultaneous approximation for arbitrary system of nodes on smooth domain in complex plane. Some results which are better than those of known theorems are obtained.
In this paper, an interpolation polynomial operator F n(f; l,x) is constructed based on the zeros of a kind of Jacobi polynomials as the interpolation nodes. For any continuous function f(x)∈C b [-1,1] ...In this paper, an interpolation polynomial operator F n(f; l,x) is constructed based on the zeros of a kind of Jacobi polynomials as the interpolation nodes. For any continuous function f(x)∈C b [-1,1] (0≤b≤l) F n(f; l,x) converges to f(x) uniformly, where l is an odd number.展开更多
Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P&...Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P'n-1(x). By the theory of the inverse Pal-Type interpolation, for a function f(x) ∈ C[-1 1], there exists a unique polynomial Rn(x) of degree 2n - 2 (if n is even) satisfying conditions Rn(f,ξk) = f(∈ek)(1≤ k≤ n - 1) ;R'n(f,xk) = f'(xk)(1≤ k≤ n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation polynomial {Rn(f,x)} (n is even) and the main result of this paper is that if f ∈ C'[1,1], r≥2, n≥ + 2> and n is even thenholds uniformly for all x ∈ [- 1,1], where h(x) = 1 +展开更多
In this note, we seek for functions f which are approximated by the sequence of interpolation polynomials of f obtained by any prescribed system of nodes.
Here concerned and further investigated is a certain operator method for the computation of convolutions of polynomials.We provide a general formulation of the method with a refinement for certain old results,and also...Here concerned and further investigated is a certain operator method for the computation of convolutions of polynomials.We provide a general formulation of the method with a refinement for certain old results,and also give some new applications to convolved sums involving several noted special polynomials.The advantage of the method using operators is illustrated with concrete examples.Finally,also presented is a brief investigation on convolution polynomials having two types of summations.展开更多
The following theorem is proved Theorem 1.Let q be a polynomial of degree n(qP_n)with n distinct zeroes lying in the interval[-1,1] and △'_q={-1}∪{τ_i:q'(τ_i)=0,i=1,n-1}∪{1}. If polynomial pP_n satisfies ...The following theorem is proved Theorem 1.Let q be a polynomial of degree n(qP_n)with n distinct zeroes lying in the interval[-1,1] and △'_q={-1}∪{τ_i:q'(τ_i)=0,i=1,n-1}∪{1}. If polynomial pP_n satisfies the inequality then for each k=1,n and any x[-1,1]its k-th derivative satisfies the inequality 丨p^(k)(x)丨≤max{丨q^((k))(x)丨,丨1/k(x^2-1)q^(k+1)(x)+xq^((k))(x)丨}. This estimate leads to the Markov inequality for the higher order derivatives of polynomials if we set q=T_n,where Tn is Chebyshev polynomial least deviated from zero. Some other results are established which gives evidence to the conjecture that under the conditions of Theorem 1 the inequality ‖p^((k))‖≤‖q^(k)‖holds.展开更多
Gear flank modification is essential to reduce the noise generated in the gear meshing process,improve the gear transmission performance,and reduce the meshing impact.Aiming at the problem of solving the additional mo...Gear flank modification is essential to reduce the noise generated in the gear meshing process,improve the gear transmission performance,and reduce the meshing impact.Aiming at the problem of solving the additional motions of each axis in the higher-order topology modification technique and how to accurately add the different movements expressed in the form of higher-order polynomials to the corresponding motion axes of the machine tool,a flexible higher-order gear topology modification technique based on an electronic gearbox is proposed.Firstly,a two-parameter topology gear surface equation and a grinding model of wheel grinding gears are established,and the axial feed and tangential feed are expressed in a fifth-order polynomial formula.Secondly,the polynomial coefficients are solved according to the characteristics of the point contact when grinding gears.Finally,an improved electronic gearbox model is constructed by combining the polynomial interpolation function to achieve gear topology modification.The validity and feasibility of the modification method based on the electronic gearbox are verified by experimental examples,which is of great significance for the machining of modification gears based on the continuous generative grinding method of the worm grinding wheel.展开更多
This work’s aim is to participate in local materials (raw or fiber improved), which can be used in sustainable and accessible buildings to every Senegalese. To do this, studied materials are respectively collected fr...This work’s aim is to participate in local materials (raw or fiber improved), which can be used in sustainable and accessible buildings to every Senegalese. To do this, studied materials are respectively collected from a laterite clay pit in Ndouloumadjie Dembe (Matam, Northern Senegal) and another from a termite mound in Tattaguine (Fatick, Central Senegal). These samples are first subjected to Geotechnical identification tests. Mud bricks are then made with raw or sifted millet involucre improved to 1%, 2%, and 3% at 5 mm sieve samples. These briquettes are subjected to compression tests and thermal evaluations. Lagrange and Newton methods of numeric modelling are used to test the whole mixture points between 1% and 3% millet involucre for a better correlation between mechanical and thermal parameters. The results show that in Matam, as well as in Tattaguine, these muds, raw or improved, are of good thermomechanical quality when they are used in bricks making. And the thermomechanical coupling quality reaches a maximum situated at 2.125% for Ndouloumadjie and 2.05% for Tattaguine. These briquettes’ building quality depends on the mud content used in iron, aluminum, silica and clay. Thus, same natural materials can be used in the establishment of habitats according to their geotechnical, chemical, mechanical and thermal characteristics.展开更多
A novel suppression method of the phase noise is proposed to reduce the negative impacts of phase noise in coherent optical orthogonal frequency division multiplexing(CO-OFDM)systems.The method integrates the sub-symb...A novel suppression method of the phase noise is proposed to reduce the negative impacts of phase noise in coherent optical orthogonal frequency division multiplexing(CO-OFDM)systems.The method integrates the sub-symbol second-order polynomial interpolation(SSPI)with cubature Kalman filter(CKF)to improve the precision and effectiveness of the data processing through using a three-stage processing approach of phase noise.First of all,the phase noise values in OFDM symbols are calculated by using pilot symbols.Then,second-order Newton interpolation(SNI)is used in second-order interpolation to acquire precise noise estimation.Afterwards,every OFDM symbol is partitioned into several sub-symbols,and second-order polynomial interpolation(SPI)is utilized in the time domain to enhance suppression accuracy and time resolution.Ultimately,CKF is employed to suppress the residual phase noise.The simulation results show that this method significantly suppresses the impact of the phase noise on the system,and the error floors can be decreased at the condition of 16 quadrature amplitude modulation(16QAM)and 32QAM.The proposed method can greatly improve the CO-OFDM system's ability to tolerate the wider laser linewidth.This method,compared to the linear interpolation sub-symbol common phase error compensation(LI-SCPEC)and Lagrange interpolation and extended Kalman filter(LRI-EKF)algorithms,has superior suppression effect.展开更多
This paper shows that the sequence of Lagrange interpolation polynomials corresponding to the rune tion f（z） =｜x｜^α（1〈α〈2） on [-1,1] can diverge everywhere in the interval except at zero and the end-points.
The acoustic Doppler current profilers(ADCP)as a new type of flow measuring equipment,can measure the flow velocity of the channel section directly.ADCP has the advantages of short measuring time and wide measuring ra...The acoustic Doppler current profilers(ADCP)as a new type of flow measuring equipment,can measure the flow velocity of the channel section directly.ADCP has the advantages of short measuring time and wide measuring range.The traditional ADCP processing system uses analog method to realize demodulation and filtering,which will introduce extra errors.While digital processing system will greatly increase the computation and slow down the speed of data processing.To solve this problem,an efficient real-time broadband ADCP digital signal processing system is proposed based on the low computational cascade integrator comb(CIC)cascade and interpolated second-order polynomial(ISOP)filter banks.The digital in-phase and quadrature(IQ)demodulation,CIC filter banks,and complex autocorrelation operation steps are cascaded with a pipelined method in the system,which greatly improves the system operating speed while avoiding the high memory occupation of non-real-time systems.展开更多
Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this p...Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.展开更多
Subpixel accuracy for V-groove center in robot welding is researched and a software measure to increase the accuracy of seam tracking by laser is presented. LOG （ Laplacian of Gaussian ） operator is adopted to detec...Subpixel accuracy for V-groove center in robot welding is researched and a software measure to increase the accuracy of seam tracking by laser is presented. LOG （ Laplacian of Gaussian ） operator is adopted to detect image edge. Vgroove center is extracted by corner detection of extremum curvature. Subpixel position is obtained by Lagarange polynomial interpolation algorithm. Experiment results show that the method is brief and applied, and is sufficient for the real time of robot welding by laser sensors.展开更多
We study the optimal order of approximation for|x|α(0<α<1)by Lagrange interpolation polynomials based on Chebyshev nodes of the first kind.It is proved that the Jackson order of approximation is attained.
The Fourier p-element method is an improvement to the finite element method,and is particularly suitable for vibration analysis due to the well-behaved Fourier series.In this paper,an iteration procedure is presented ...The Fourier p-element method is an improvement to the finite element method,and is particularly suitable for vibration analysis due to the well-behaved Fourier series.In this paper,an iteration procedure is presented for solving the resulting nonlinear eigenvalue problem.Three types of Fourier version shape functions are constructed for analyzing the circular shaft torsional vibration,the plate in-plane vibration and annular plate flexural vibration modes,respectively. The numerical results show that this method can achieve higher accuracy and converge much faster than the FEM based on polynomial interpolation,especially for higher mode analysis.展开更多
文摘This paper considers to replace △_m(x)=(1-x^2)~2(1/2)/n +1/n^2 in the following result for simultaneous Lagrange interpolating approximation with (1-x^2)~2(1/2)/n: Let f∈C_(-1.1)~0 and r=[(q+2)/2],then |f^(k)(x)-P_^(k)(f,x)|=O(1)△_(n)^(a-k)(x)ω(f^(a),△(x))(‖L_n-‖+‖L_n‖),0≤k≤q, where P_n( f ,x)is the Lagrange interpolating polynomial of degree n+ 2r-1 of f on the nodes X_n U Y_n(see the definition of the text), and thus give a problem raised in [XiZh] a complete answer.
基金The second named author was supported in part by an NSERC Postdoctoral Fellowship,Canada and a CR F Grant,University of Alberta
文摘This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next).
文摘The multivariate splines which were first presented by deBooor as a complete theoretical system have intrigued many mathematicians who have devoted many works in this field which is still in the process of development.The author of this paper is interested in the area of inter- polation with special emphasis on the interpolation methods and their approximation orders. But such B-splines(both univariate and multivariate)do not interpolated directly,so I ap- proached this problem in another way which is to extend my interpolating spline of degree 2n-1 in univariate case(See[7])to multivariate case.I selected triangulated region which is inspired by other mathematicians'works(e.g.[2]and[3])and extend the interpolating polynomials from univariate to m-variate case(See[10])In this paper some results in the case m=2 are discussed and proved in more concrete details.Based on these polynomials,the interpolating splines(it is defined by me as piecewise polynomials in which the unknown par- tial derivatives are determined under certain continuous conditions)are also discussed.The approximation orders of interpolating polynomials and of cubic interpolating splines are inverstigated.We lunited our discussion on the rectangular domain which is partitioned into equal right triangles.As to the case in which the rectangular domain is partitioned into unequal right triangles as well as the case of more complicated domains,we will discuss in the next pa- per.
基金The Project is supported by National Natural Science Foundation of China.
文摘In this paper. a quantitative estimate for Hermite interpolant to function ψ(z)=(z^m-β~m)~l on the ze- ros of (z^n-α~n)~r is obtained Using this estimate. a rather wide exiension of the theorem of Walsh is proved and five special cases of it are given.
基金the National Natural Science Foundation of China(No.11471062).
文摘In this paper,an optimality condition for nonlinear programming problems with box constraints is given by using linear transformation and Lagrange interpolating polynomials.Based on this condition,two new local optimization methods are developed.The solution points obtained by the new local optimization methods can improve the Karush–Kuhn–Tucker(KKT)points in general.Two global optimization methods then are proposed by combining the two new local optimization methods with a filled function method.Some numerical examples are reported to show the effectiveness of the proposed methods.
文摘In this paper we investigate simultaneous approximation for arbitrary system of nodes on smooth domain in complex plane. Some results which are better than those of known theorems are obtained.
文摘In this paper, an interpolation polynomial operator F n(f; l,x) is constructed based on the zeros of a kind of Jacobi polynomials as the interpolation nodes. For any continuous function f(x)∈C b [-1,1] (0≤b≤l) F n(f; l,x) converges to f(x) uniformly, where l is an odd number.
文摘Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P'n-1(x). By the theory of the inverse Pal-Type interpolation, for a function f(x) ∈ C[-1 1], there exists a unique polynomial Rn(x) of degree 2n - 2 (if n is even) satisfying conditions Rn(f,ξk) = f(∈ek)(1≤ k≤ n - 1) ;R'n(f,xk) = f'(xk)(1≤ k≤ n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation polynomial {Rn(f,x)} (n is even) and the main result of this paper is that if f ∈ C'[1,1], r≥2, n≥ + 2> and n is even thenholds uniformly for all x ∈ [- 1,1], where h(x) = 1 +
文摘In this note, we seek for functions f which are approximated by the sequence of interpolation polynomials of f obtained by any prescribed system of nodes.
文摘Here concerned and further investigated is a certain operator method for the computation of convolutions of polynomials.We provide a general formulation of the method with a refinement for certain old results,and also give some new applications to convolved sums involving several noted special polynomials.The advantage of the method using operators is illustrated with concrete examples.Finally,also presented is a brief investigation on convolution polynomials having two types of summations.
文摘The following theorem is proved Theorem 1.Let q be a polynomial of degree n(qP_n)with n distinct zeroes lying in the interval[-1,1] and △'_q={-1}∪{τ_i:q'(τ_i)=0,i=1,n-1}∪{1}. If polynomial pP_n satisfies the inequality then for each k=1,n and any x[-1,1]its k-th derivative satisfies the inequality 丨p^(k)(x)丨≤max{丨q^((k))(x)丨,丨1/k(x^2-1)q^(k+1)(x)+xq^((k))(x)丨}. This estimate leads to the Markov inequality for the higher order derivatives of polynomials if we set q=T_n,where Tn is Chebyshev polynomial least deviated from zero. Some other results are established which gives evidence to the conjecture that under the conditions of Theorem 1 the inequality ‖p^((k))‖≤‖q^(k)‖holds.
基金Projects(52275483,52075142,U22B2084)supported by the National Natural Science Foundation of ChinaProject(JZ2023HGPA0292)supported by the Fundamental Research Funds for the Central Universities of China。
文摘Gear flank modification is essential to reduce the noise generated in the gear meshing process,improve the gear transmission performance,and reduce the meshing impact.Aiming at the problem of solving the additional motions of each axis in the higher-order topology modification technique and how to accurately add the different movements expressed in the form of higher-order polynomials to the corresponding motion axes of the machine tool,a flexible higher-order gear topology modification technique based on an electronic gearbox is proposed.Firstly,a two-parameter topology gear surface equation and a grinding model of wheel grinding gears are established,and the axial feed and tangential feed are expressed in a fifth-order polynomial formula.Secondly,the polynomial coefficients are solved according to the characteristics of the point contact when grinding gears.Finally,an improved electronic gearbox model is constructed by combining the polynomial interpolation function to achieve gear topology modification.The validity and feasibility of the modification method based on the electronic gearbox are verified by experimental examples,which is of great significance for the machining of modification gears based on the continuous generative grinding method of the worm grinding wheel.
文摘This work’s aim is to participate in local materials (raw or fiber improved), which can be used in sustainable and accessible buildings to every Senegalese. To do this, studied materials are respectively collected from a laterite clay pit in Ndouloumadjie Dembe (Matam, Northern Senegal) and another from a termite mound in Tattaguine (Fatick, Central Senegal). These samples are first subjected to Geotechnical identification tests. Mud bricks are then made with raw or sifted millet involucre improved to 1%, 2%, and 3% at 5 mm sieve samples. These briquettes are subjected to compression tests and thermal evaluations. Lagrange and Newton methods of numeric modelling are used to test the whole mixture points between 1% and 3% millet involucre for a better correlation between mechanical and thermal parameters. The results show that in Matam, as well as in Tattaguine, these muds, raw or improved, are of good thermomechanical quality when they are used in bricks making. And the thermomechanical coupling quality reaches a maximum situated at 2.125% for Ndouloumadjie and 2.05% for Tattaguine. These briquettes’ building quality depends on the mud content used in iron, aluminum, silica and clay. Thus, same natural materials can be used in the establishment of habitats according to their geotechnical, chemical, mechanical and thermal characteristics.
基金supported by the National Natural Science Foundation of China(Nos.U21A20447 and 61971079)。
文摘A novel suppression method of the phase noise is proposed to reduce the negative impacts of phase noise in coherent optical orthogonal frequency division multiplexing(CO-OFDM)systems.The method integrates the sub-symbol second-order polynomial interpolation(SSPI)with cubature Kalman filter(CKF)to improve the precision and effectiveness of the data processing through using a three-stage processing approach of phase noise.First of all,the phase noise values in OFDM symbols are calculated by using pilot symbols.Then,second-order Newton interpolation(SNI)is used in second-order interpolation to acquire precise noise estimation.Afterwards,every OFDM symbol is partitioned into several sub-symbols,and second-order polynomial interpolation(SPI)is utilized in the time domain to enhance suppression accuracy and time resolution.Ultimately,CKF is employed to suppress the residual phase noise.The simulation results show that this method significantly suppresses the impact of the phase noise on the system,and the error floors can be decreased at the condition of 16 quadrature amplitude modulation(16QAM)and 32QAM.The proposed method can greatly improve the CO-OFDM system's ability to tolerate the wider laser linewidth.This method,compared to the linear interpolation sub-symbol common phase error compensation(LI-SCPEC)and Lagrange interpolation and extended Kalman filter(LRI-EKF)algorithms,has superior suppression effect.
文摘This paper shows that the sequence of Lagrange interpolation polynomials corresponding to the rune tion f（z） =｜x｜^α（1〈α〈2） on [-1,1] can diverge everywhere in the interval except at zero and the end-points.
文摘The acoustic Doppler current profilers(ADCP)as a new type of flow measuring equipment,can measure the flow velocity of the channel section directly.ADCP has the advantages of short measuring time and wide measuring range.The traditional ADCP processing system uses analog method to realize demodulation and filtering,which will introduce extra errors.While digital processing system will greatly increase the computation and slow down the speed of data processing.To solve this problem,an efficient real-time broadband ADCP digital signal processing system is proposed based on the low computational cascade integrator comb(CIC)cascade and interpolated second-order polynomial(ISOP)filter banks.The digital in-phase and quadrature(IQ)demodulation,CIC filter banks,and complex autocorrelation operation steps are cascaded with a pipelined method in the system,which greatly improves the system operating speed while avoiding the high memory occupation of non-real-time systems.
文摘Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.
基金This work is financially supported by National Nature Science Foundation of China (Grant No. 50175027).
文摘Subpixel accuracy for V-groove center in robot welding is researched and a software measure to increase the accuracy of seam tracking by laser is presented. LOG （ Laplacian of Gaussian ） operator is adopted to detect image edge. Vgroove center is extracted by corner detection of extremum curvature. Subpixel position is obtained by Lagarange polynomial interpolation algorithm. Experiment results show that the method is brief and applied, and is sufficient for the real time of robot welding by laser sensors.
文摘We study the optimal order of approximation for|x|α(0<α<1)by Lagrange interpolation polynomials based on Chebyshev nodes of the first kind.It is proved that the Jackson order of approximation is attained.
文摘The Fourier p-element method is an improvement to the finite element method,and is particularly suitable for vibration analysis due to the well-behaved Fourier series.In this paper,an iteration procedure is presented for solving the resulting nonlinear eigenvalue problem.Three types of Fourier version shape functions are constructed for analyzing the circular shaft torsional vibration,the plate in-plane vibration and annular plate flexural vibration modes,respectively. The numerical results show that this method can achieve higher accuracy and converge much faster than the FEM based on polynomial interpolation,especially for higher mode analysis.
