The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc. In this article, the general procedure of quantum Fourier trans...The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc. In this article, the general procedure of quantum Fourier transform and phase estimation are investigated for high dimensional case run in a qudit quantum computer, and the quantum circuits are They can be seen as subroutines in a main program given.展开更多
The special structure in some coupled equations makes it possible to drop partial smallness assumption of the initial data to gain the global well-posedness.In this paper,we study the Cauchy problem for generalized De...The special structure in some coupled equations makes it possible to drop partial smallness assumption of the initial data to gain the global well-posedness.In this paper,we study the Cauchy problem for generalized Debye-Hückel system in Fourier-Besov spaces.Under more generalized index range,we obtain the global solution with small initial data and local solution with arbitrary initial.Besides,by constructing some weighted function,we prove that the global well-posedness still holds under the small assumption of the charge of initial data.Thus we show that although the initial densities and the hole in electrolytes are large,the equation is still global well-posedness.展开更多
Spectrometer is an essential and necessary optical element used for measuring the chemical components and content of the matter. The development of miniature spectrometers can be traced back to 1980s. The development ...Spectrometer is an essential and necessary optical element used for measuring the chemical components and content of the matter. The development of miniature spectrometers can be traced back to 1980s. The development state and different manufacturing methods of micro-spectrometers are presented. Finally, we analyze the miniaturization trend of spectrometers. Some groundwork for the scientific research is offered by introducing micro-spectrometers development.展开更多
We investigate the low regularity local and global well-posedness of the Cauchy problem for the coupled Klein-Gordon-Schr¨odinger system with fractional Laplacian in the Schr¨odinger equation in R^（1＋1）. ...We investigate the low regularity local and global well-posedness of the Cauchy problem for the coupled Klein-Gordon-Schr¨odinger system with fractional Laplacian in the Schr¨odinger equation in R^（1＋1）. We use Bourgain space method to study this problem and prove that this system is locally well-posed for Schr¨odinger data in H^（s_1） and wave data in H^（s_2） × H^（s_2-1）for 3/4- α ＆lt; s_1≤0 and-1/2 ＆lt; s_2 ＆lt; 3/2, where α is the fractional power of Laplacian which satisfies 3/4 ＆lt; α≤1. Based on this local well-posedness result, we also obtain the global well-posedness of this system for s_1 = 0 and-1/2 ＆lt; s_2 ＆lt; 1/2 by using the conservation law for the L^2 norm of u.展开更多
In the theory of signal analysis, the existence of the advanced response, whose appearance is earlier than the input, violates the law of causation. It is believed that the presence of advanced response is due to unre...In the theory of signal analysis, the existence of the advanced response, whose appearance is earlier than the input, violates the law of causation. It is believed that the presence of advanced response is due to unreasonable setting of the characteristic of the system. Hereof, by means of nonstandard analysis, it is concluded that the advanced response arises from the course of Fourier analysis other than the transmission process of the signal.展开更多
基金Supported by the National Natural Science Foundation of China Grant No.10874098the National Basic Research Program of China under Grant Nos.2009CB929402 and 2011CB9216002
文摘The quantum Fourier transform and quantum phase estimation are the key components for many quantum algorithms, such as order-finding, factoring, and etc. In this article, the general procedure of quantum Fourier transform and phase estimation are investigated for high dimensional case run in a qudit quantum computer, and the quantum circuits are They can be seen as subroutines in a main program given.
基金Supported by Natural Science Foundation of Jiangsu Province(No.BK20200587)。
文摘The special structure in some coupled equations makes it possible to drop partial smallness assumption of the initial data to gain the global well-posedness.In this paper,we study the Cauchy problem for generalized Debye-Hückel system in Fourier-Besov spaces.Under more generalized index range,we obtain the global solution with small initial data and local solution with arbitrary initial.Besides,by constructing some weighted function,we prove that the global well-posedness still holds under the small assumption of the charge of initial data.Thus we show that although the initial densities and the hole in electrolytes are large,the equation is still global well-posedness.
文摘Spectrometer is an essential and necessary optical element used for measuring the chemical components and content of the matter. The development of miniature spectrometers can be traced back to 1980s. The development state and different manufacturing methods of micro-spectrometers are presented. Finally, we analyze the miniaturization trend of spectrometers. Some groundwork for the scientific research is offered by introducing micro-spectrometers development.
基金supported by National Natural Science Foundation of China (Grant No. 11201498)
文摘We investigate the low regularity local and global well-posedness of the Cauchy problem for the coupled Klein-Gordon-Schr¨odinger system with fractional Laplacian in the Schr¨odinger equation in R^（1＋1）. We use Bourgain space method to study this problem and prove that this system is locally well-posed for Schr¨odinger data in H^（s_1） and wave data in H^（s_2） × H^（s_2-1）for 3/4- α ＆lt; s_1≤0 and-1/2 ＆lt; s_2 ＆lt; 3/2, where α is the fractional power of Laplacian which satisfies 3/4 ＆lt; α≤1. Based on this local well-posedness result, we also obtain the global well-posedness of this system for s_1 = 0 and-1/2 ＆lt; s_2 ＆lt; 1/2 by using the conservation law for the L^2 norm of u.
文摘In the theory of signal analysis, the existence of the advanced response, whose appearance is earlier than the input, violates the law of causation. It is believed that the presence of advanced response is due to unreasonable setting of the characteristic of the system. Hereof, by means of nonstandard analysis, it is concluded that the advanced response arises from the course of Fourier analysis other than the transmission process of the signal.
