A new application of Chebyshev polynomials of second kind Un(x) to functions of two-dimensional operators is derived and discussed. It is related to the Hamilton-Cayley identity for operators or matrices which allows ...A new application of Chebyshev polynomials of second kind Un(x) to functions of two-dimensional operators is derived and discussed. It is related to the Hamilton-Cayley identity for operators or matrices which allows to reduce powers and smooth functions of them to superpositions of the first N-1 powers of the considered operator in N-dimensional case. The method leads in two-dimensional case first to the recurrence relations for Chebyshev polynomials and due to initial conditions to the application of Chebyshev polynomials of second kind Un(x). Furthermore, a new general class of Generating functions for Chebyshev polynomials of first and second kind Un(x) comprising the known Generating function as special cases is constructed by means of a derived identity for operator functions f(A) of a general two-dimensional operator A. The basic results are Formulas (9.5) and (9.6) which are then specialized for different examples of functions f(x). The generalization of the theory for three-dimensional operators is started to attack and a partial problem connected with the eigenvalue problem and the Hamilton-Cayley identity is solved in an Appendix. A physical application of Chebyshev polynomials to a problem of relativistic kinematics of a uniformly accelerated system is solved. All operator calculations are made in coordinate-invariant form.展开更多
Training neural network to recognize targets needs a lot of samples.People usually get these samples in a non-systematic way,which can miss or overemphasize some target information.To improve this situation,a new meth...Training neural network to recognize targets needs a lot of samples.People usually get these samples in a non-systematic way,which can miss or overemphasize some target information.To improve this situation,a new method based on virtual model and invariant moments was proposed to generate training samples.The method was composed of the following steps：use computer and simulation software to build target object＇s virtual model and then simulate the environment,light condition,camera parameter,etc.;rotate the model by spin and nutation of inclination to get the image sequence by virtual camera;preprocess each image and transfer them into binary image;calculate the invariant moments for each image and get a vectors＇ sequence.The vectors＇ sequence which was proved to be complete became the training samples together with the target outputs.The simulated results showed that the proposed method could be used to recognize the real targets and improve the accuracy of target recognition effectively when the sampling interval was short enough and the circumstance simulation was close enough.展开更多
It is very important to improve the penetration depth and fueling efficiency of supersonic molecular beam injection（SMBI） especially for the next generation fusion devices such as ITER. Two components, a fast compon...It is very important to improve the penetration depth and fueling efficiency of supersonic molecular beam injection（SMBI） especially for the next generation fusion devices such as ITER. Two components, a fast component（FC） and a slow component（SC）, have been observed in the HL-2A SMBI experiments for several years, and the FC can penetrate much more deeply than the common SMBIs which draws a great deal of attention for a better fueling method. It is the first time to the FC and SC of SMBI have been simulated and interpreted in theory and simulation in this paper with the trans-neut module of the BOUT＋＋ code. The simulation results of the FC and SC are clear and distinguishable in the same way as the observation in experiment. For the major mechanism of the FC and SC, it is found that although the difference in the injection velocity has some effect on the penetration depth difference between the FC and SC, it is mainly caused by the self-blocking effect of the first ionized SMB. We also discuss the influence of the initial plasma density on the FC and SC,and the variation of the SC penetration depth with its injection velocity.展开更多
文摘A new application of Chebyshev polynomials of second kind Un(x) to functions of two-dimensional operators is derived and discussed. It is related to the Hamilton-Cayley identity for operators or matrices which allows to reduce powers and smooth functions of them to superpositions of the first N-1 powers of the considered operator in N-dimensional case. The method leads in two-dimensional case first to the recurrence relations for Chebyshev polynomials and due to initial conditions to the application of Chebyshev polynomials of second kind Un(x). Furthermore, a new general class of Generating functions for Chebyshev polynomials of first and second kind Un(x) comprising the known Generating function as special cases is constructed by means of a derived identity for operator functions f(A) of a general two-dimensional operator A. The basic results are Formulas (9.5) and (9.6) which are then specialized for different examples of functions f(x). The generalization of the theory for three-dimensional operators is started to attack and a partial problem connected with the eigenvalue problem and the Hamilton-Cayley identity is solved in an Appendix. A physical application of Chebyshev polynomials to a problem of relativistic kinematics of a uniformly accelerated system is solved. All operator calculations are made in coordinate-invariant form.
基金Supported by the Ministerial Level Research Foundation(404040401)
文摘Training neural network to recognize targets needs a lot of samples.People usually get these samples in a non-systematic way,which can miss or overemphasize some target information.To improve this situation,a new method based on virtual model and invariant moments was proposed to generate training samples.The method was composed of the following steps：use computer and simulation software to build target object＇s virtual model and then simulate the environment,light condition,camera parameter,etc.;rotate the model by spin and nutation of inclination to get the image sequence by virtual camera;preprocess each image and transfer them into binary image;calculate the invariant moments for each image and get a vectors＇ sequence.The vectors＇ sequence which was proved to be complete became the training samples together with the target outputs.The simulated results showed that the proposed method could be used to recognize the real targets and improve the accuracy of target recognition effectively when the sampling interval was short enough and the circumstance simulation was close enough.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11575055,11375053,and 11472519)the Chinese National Fusion Project for ITER(Grant Nos.2013GB111005,2013GB107001,2014GB108004,2014GB110004,and 2015GB110001)the International S&T Cooperation Program of China(Grant No.2015DFA61760)
文摘It is very important to improve the penetration depth and fueling efficiency of supersonic molecular beam injection（SMBI） especially for the next generation fusion devices such as ITER. Two components, a fast component（FC） and a slow component（SC）, have been observed in the HL-2A SMBI experiments for several years, and the FC can penetrate much more deeply than the common SMBIs which draws a great deal of attention for a better fueling method. It is the first time to the FC and SC of SMBI have been simulated and interpreted in theory and simulation in this paper with the trans-neut module of the BOUT＋＋ code. The simulation results of the FC and SC are clear and distinguishable in the same way as the observation in experiment. For the major mechanism of the FC and SC, it is found that although the difference in the injection velocity has some effect on the penetration depth difference between the FC and SC, it is mainly caused by the self-blocking effect of the first ionized SMB. We also discuss the influence of the initial plasma density on the FC and SC,and the variation of the SC penetration depth with its injection velocity.
