Linear transfer function approximations of the fractional integrators 1Is~ with m ^- 0.80-0.99 with steps of 0.01 are calculated systemically from the fractional order calculus and frequency-domain approximation metho...Linear transfer function approximations of the fractional integrators 1Is~ with m ^- 0.80-0.99 with steps of 0.01 are calculated systemically from the fractional order calculus and frequency-domain approximation method. To illustrate the effectiveness for fractional functions, the magnitude Bode diagrams of the actual and approximate transfer functions 1Ism with a slope of -20m dB//decade are depicted. By using the transfer function approxima- tions of the fractional integrators, a new fractional-order nonlinear system is investigated through the bifurcation diagram and Lyapunov exponent. The corresponding circuit of the fractional-order system is designed and the experimental results match perfectly with the numerical simulations.展开更多
This paper addresses the mathematical relation on a set of periods and temporal indexing construc- tions as well as their applications.First we introduce two concepts, i.e.the temporal connection and temporal inclusio...This paper addresses the mathematical relation on a set of periods and temporal indexing construc- tions as well as their applications.First we introduce two concepts, i.e.the temporal connection and temporal inclusion, which are equivalence relation and preorder relation respectively.Second, by study- ing some basic topics such as the division of ＂large＂ equivalence classes and the overlaps of preorder relational sets, we propose a temporal data index model （TDIM） with a tree-structure consisting of a root node, equivalence class nodes and linearly ordered branch nodes.Third, we study algorithms for the temporal querying and incremental updating as well as dynamical management within the framework of TDIM.Based on a proper mathematical supporting, TDIM can be applied to researching some significant practical cases such as temporal relational and temporal XML data and so on.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No 51475246the Natural Science Foundation of Jiangsu Province under Grant No Bk20131402the Ministry-of-Education Overseas Returnees Start-up Research Fund under Grant No[2012]1707
文摘Linear transfer function approximations of the fractional integrators 1Is~ with m ^- 0.80-0.99 with steps of 0.01 are calculated systemically from the fractional order calculus and frequency-domain approximation method. To illustrate the effectiveness for fractional functions, the magnitude Bode diagrams of the actual and approximate transfer functions 1Ism with a slope of -20m dB//decade are depicted. By using the transfer function approxima- tions of the fractional integrators, a new fractional-order nonlinear system is investigated through the bifurcation diagram and Lyapunov exponent. The corresponding circuit of the fractional-order system is designed and the experimental results match perfectly with the numerical simulations.
基金Supported by the National Natural Science Foundation of China (Grant Nos 60373081, 60673135)the Natural Science Foundation of Guangdong Province (Grant No 05003348)the Program of New Century Excellent Person Supporting of Ministery of Education of China(GrantNo.NCET-04-0805)
文摘This paper addresses the mathematical relation on a set of periods and temporal indexing construc- tions as well as their applications.First we introduce two concepts, i.e.the temporal connection and temporal inclusion, which are equivalence relation and preorder relation respectively.Second, by study- ing some basic topics such as the division of ＂large＂ equivalence classes and the overlaps of preorder relational sets, we propose a temporal data index model （TDIM） with a tree-structure consisting of a root node, equivalence class nodes and linearly ordered branch nodes.Third, we study algorithms for the temporal querying and incremental updating as well as dynamical management within the framework of TDIM.Based on a proper mathematical supporting, TDIM can be applied to researching some significant practical cases such as temporal relational and temporal XML data and so on.
