A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being int...A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators partial derivative(t) and its dual, creation operators partial derivative(t)*.展开更多
In this paper, the structure of a new chaotic bitwise dynamical system （CBDS） is described. Compared to our previous research work, it uses various random bitwise operations instead of only one. The chaotic behavior...In this paper, the structure of a new chaotic bitwise dynamical system （CBDS） is described. Compared to our previous research work, it uses various random bitwise operations instead of only one. The chaotic behavior of CBDS is mathemat- ically proven according to the Devaney＇s definition, and its statistical properties are verified both for uniformity and by a comprehensive, reputed and stringent battery of tests called TestU01. Furthermore, a systematic methodology developing the parallel computations is proposed for FPGA platform-based realization of this CBDS. Experiments finally validate the proposed systematic methodology.展开更多
文摘A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators partial derivative(t) and its dual, creation operators partial derivative(t)*.
基金Project supported by China Postdoctoral Science Foundation(Grant No.2014M552175)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,Chinese Education Ministry+1 种基金the National Natural Science Foundation of China(Grant No.61172023)the Specialized Research Foundation of Doctoral Subjects of Chinese Education Ministry(Grant No.20114420110003)
文摘In this paper, the structure of a new chaotic bitwise dynamical system （CBDS） is described. Compared to our previous research work, it uses various random bitwise operations instead of only one. The chaotic behavior of CBDS is mathemat- ically proven according to the Devaney＇s definition, and its statistical properties are verified both for uniformity and by a comprehensive, reputed and stringent battery of tests called TestU01. Furthermore, a systematic methodology developing the parallel computations is proposed for FPGA platform-based realization of this CBDS. Experiments finally validate the proposed systematic methodology.
