As a branch of quantum image processing,quantum image scaling has been widely studied.However,most of the existing quantum image scaling algorithms are based on nearest-neighbor interpolation and bilinear interpolatio...As a branch of quantum image processing,quantum image scaling has been widely studied.However,most of the existing quantum image scaling algorithms are based on nearest-neighbor interpolation and bilinear interpolation,the quantum version of bicubic interpolation has not yet been studied.In this work,we present the first quantum image scaling scheme for bicubic interpolation based on the novel enhanced quantum representation(NEQR).Our scheme can realize synchronous enlargement and reduction of the image with the size of 2^(n)×2^(n) by integral multiple.Firstly,the image is represented by NEQR and the original image coordinates are obtained through multiple CNOT modules.Then,16 neighborhood pixels are obtained by quantum operation circuits,and the corresponding weights of these pixels are calculated by quantum arithmetic modules.Finally,a quantum matrix operation,instead of a classical convolution operation,is used to realize the sum of convolution of these pixels.Through simulation experiments and complexity analysis,we demonstrate that our scheme achieves exponential speedup over the classical bicubic interpolation algorithm,and has better effect than the quantum version of bilinear interpolation.展开更多
Aim To study wind tunnel test data interpolation methods for flight vehicle with aerodynamic axial asymmetry. Methods For different body aerodynamic roll angles, proper wind tunnel test schemes were selected and ...Aim To study wind tunnel test data interpolation methods for flight vehicle with aerodynamic axial asymmetry. Methods For different body aerodynamic roll angles, proper wind tunnel test schemes were selected and trigonometric series were used for aerodynamic interpolation. Results and Conclusion A simple and effective scheme for wind tunnel test and an accurate aerodynamic interpolation method are developed with satisfactory results.展开更多
The traditional algorithms for formation flying satellites treat the satellite position and attitude sepa- rately. A novel algorithm combining satellite attitude with position is proposed. The principal satellite traj...The traditional algorithms for formation flying satellites treat the satellite position and attitude sepa- rately. A novel algorithm combining satellite attitude with position is proposed. The principal satellite trajectory is obtained by dual quaternion interpolation, then the relative position and attitude of the deputy satellite are ob- tained by dual quaternion modeling on the principal satellite. Through above process, relative position and atti- tude are unified. Compared with the orbital parameter and the quaternion methods, the simulation result proves that the algorithm can unify position and attitude, and satisfy the precision requirement of formation flying satel- lites.展开更多
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
The generating motion of the generating gear and the work gear on spiral bevel gear NC machining is analyzed. The mathematical model of the tooth surface of spiral bevel gear is presented. A direct interpolation algor...The generating motion of the generating gear and the work gear on spiral bevel gear NC machining is analyzed. The mathematical model of the tooth surface of spiral bevel gear is presented. A direct interpolation algorithm of spiral bevel gear NC machining is proposed, thus establishing the relationship between the motion of the cutter-head center and the rotation of the work gear. The interpolation algorithm is implemented to control the gear cutting on self-developed spiral bevel gear NC cutting machine. An example is given to verify the mathematical model and the interpolation algorithm.展开更多
Based on the construction of reference e le ment and bilinear transformation, a quasi-Wilson element for arbitrary narrow q uadrilateral is presented. Using the interpolation Theorem for narrow quadrilate ral isoparam...Based on the construction of reference e le ment and bilinear transformation, a quasi-Wilson element for arbitrary narrow q uadrilateral is presented. Using the interpolation Theorem for narrow quadrilate ral isoparametric finite element and related methods, the bounds of interpolatio n error for arbitrary narrow quadrilateral quasi-Wilson element are obtained in case when the condition ρ K/h K≥σ 0】0 is not satisfied, where h K is the diameter of the element K and ρ K is the diameter of an ins cribed circle in K. The interpolation error is O(h2 K) in the L2( K)-norm and O(h K) in the H1(K) -norm provided that the in terpolated function belongs to H2(K).展开更多
基金Project supported by the Scientific Research Fund of Hunan Provincial Education Department,China (Grant No.21A0470)the Natural Science Foundation of Hunan Province,China (Grant No.2023JJ50268)+1 种基金the National Natural Science Foundation of China (Grant Nos.62172268 and 62302289)the Shanghai Science and Technology Project,China (Grant Nos.21JC1402800 and 23YF1416200)。
文摘As a branch of quantum image processing,quantum image scaling has been widely studied.However,most of the existing quantum image scaling algorithms are based on nearest-neighbor interpolation and bilinear interpolation,the quantum version of bicubic interpolation has not yet been studied.In this work,we present the first quantum image scaling scheme for bicubic interpolation based on the novel enhanced quantum representation(NEQR).Our scheme can realize synchronous enlargement and reduction of the image with the size of 2^(n)×2^(n) by integral multiple.Firstly,the image is represented by NEQR and the original image coordinates are obtained through multiple CNOT modules.Then,16 neighborhood pixels are obtained by quantum operation circuits,and the corresponding weights of these pixels are calculated by quantum arithmetic modules.Finally,a quantum matrix operation,instead of a classical convolution operation,is used to realize the sum of convolution of these pixels.Through simulation experiments and complexity analysis,we demonstrate that our scheme achieves exponential speedup over the classical bicubic interpolation algorithm,and has better effect than the quantum version of bilinear interpolation.
文摘Aim To study wind tunnel test data interpolation methods for flight vehicle with aerodynamic axial asymmetry. Methods For different body aerodynamic roll angles, proper wind tunnel test schemes were selected and trigonometric series were used for aerodynamic interpolation. Results and Conclusion A simple and effective scheme for wind tunnel test and an accurate aerodynamic interpolation method are developed with satisfactory results.
基金Supported by the National Natural Science Foundation of China(60974107)the Research Foundation of Nanjing University of Aeronautics and Astronautics(2010219)~~
文摘The traditional algorithms for formation flying satellites treat the satellite position and attitude sepa- rately. A novel algorithm combining satellite attitude with position is proposed. The principal satellite trajectory is obtained by dual quaternion interpolation, then the relative position and attitude of the deputy satellite are ob- tained by dual quaternion modeling on the principal satellite. Through above process, relative position and atti- tude are unified. Compared with the orbital parameter and the quaternion methods, the simulation result proves that the algorithm can unify position and attitude, and satisfy the precision requirement of formation flying satel- lites.
文摘The paper is given the interpolation of operators between weighted Hardy spaces and weighted L p spaces when w∈A 1 by Calderon Zygmund decomposition.
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The generating motion of the generating gear and the work gear on spiral bevel gear NC machining is analyzed. The mathematical model of the tooth surface of spiral bevel gear is presented. A direct interpolation algorithm of spiral bevel gear NC machining is proposed, thus establishing the relationship between the motion of the cutter-head center and the rotation of the work gear. The interpolation algorithm is implemented to control the gear cutting on self-developed spiral bevel gear NC cutting machine. An example is given to verify the mathematical model and the interpolation algorithm.
文摘Based on the construction of reference e le ment and bilinear transformation, a quasi-Wilson element for arbitrary narrow q uadrilateral is presented. Using the interpolation Theorem for narrow quadrilate ral isoparametric finite element and related methods, the bounds of interpolatio n error for arbitrary narrow quadrilateral quasi-Wilson element are obtained in case when the condition ρ K/h K≥σ 0】0 is not satisfied, where h K is the diameter of the element K and ρ K is the diameter of an ins cribed circle in K. The interpolation error is O(h2 K) in the L2( K)-norm and O(h K) in the H1(K) -norm provided that the in terpolated function belongs to H2(K).
