Evidence for the long-term optical curve variability and colour behaviour of the BL Lac object Mkn 421 is presented. Our results show that the amplitude of the optical variations of Mkn 421 is only about △B=4.7 magni...Evidence for the long-term optical curve variability and colour behaviour of the BL Lac object Mkn 421 is presented. Our results show that the amplitude of the optical variations of Mkn 421 is only about △B=4.7 magnitude in the B-band for its photometric history from 1899 to 2002. The results of optical photometric monitoring of the Mkn 421 from April 2000 to Jan 2002 are provided. During our observation, Mkn 421 shows significant rapid variations and exhibits short time variability of 2.42 hours in the B band. A strong correlation between the B - V colour index and the magnitude in the B band is found. Our charge coupled device （CCD） photometry of Mkn 421 shows that the measured results are in good agreement with the predicted optical variability period of about 23 years.展开更多
This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization.In order to deal with large scale problems,a reduced Hessian matrix is ...This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization.In order to deal with large scale problems,a reduced Hessian matrix is approximated by BFGS updates.The new method assures global convergence without using a merit function.By Lagrangian function in the filter and nonmonotone scheme,the authors prove that the method can overcome Maratos effect without using second order correction step so that the locally superlinear convergence is achieved.The primary numerical experiments are reported to show effectiveness of the proposed algorithm.展开更多
基金Project supported by an CRCG grant of the University of Hong Kong, Yunnan Provincial Foundation of Science of China （Grant No 2004A0027M） and the National Natural Science Foundation of China（Grant No 10363002）, and the Natural Science Foundation of China Education Department（Grant No 02142）.
文摘Evidence for the long-term optical curve variability and colour behaviour of the BL Lac object Mkn 421 is presented. Our results show that the amplitude of the optical variations of Mkn 421 is only about △B=4.7 magnitude in the B-band for its photometric history from 1899 to 2002. The results of optical photometric monitoring of the Mkn 421 from April 2000 to Jan 2002 are provided. During our observation, Mkn 421 shows significant rapid variations and exhibits short time variability of 2.42 hours in the B band. A strong correlation between the B - V colour index and the magnitude in the B band is found. Our charge coupled device （CCD） photometry of Mkn 421 shows that the measured results are in good agreement with the predicted optical variability period of about 23 years.
基金supported by the National Science Foundation of China under Grant No.10871130the Ph.D Foundation under Grant No.20093127110005+1 种基金the Shanghai Leading Academic Discipline Project under Grant No.S30405the Innovation Program of Shanghai Municipal Education Commission under Grant No.12YZ174
文摘This paper proposes a nonmonotone line search filter method with reduced Hessian updating for solving nonlinear equality constrained optimization.In order to deal with large scale problems,a reduced Hessian matrix is approximated by BFGS updates.The new method assures global convergence without using a merit function.By Lagrangian function in the filter and nonmonotone scheme,the authors prove that the method can overcome Maratos effect without using second order correction step so that the locally superlinear convergence is achieved.The primary numerical experiments are reported to show effectiveness of the proposed algorithm.
