We designed the window function of the optimal Gabor transform based on the time-frequency rotation property of the fractional Fourier transform. Thus, we obtained the adaptive optimal Gabor transform in the fractiona...We designed the window function of the optimal Gabor transform based on the time-frequency rotation property of the fractional Fourier transform. Thus, we obtained the adaptive optimal Gabor transform in the fractional domain and improved the time-frequency concentration of the Gabor transform. The algorithm first searches for the optimal rotation factor, then performs the p-th FrFT of the signal and, finally, performs time and frequency analysis of the FrFT result. Finally, the algorithm rotates the plane in the fractional domain back to the normal time-frequency plane. This promotes the application of FrFT in the field of high-resolution reservoir prediction. Additionally, we proposed an adaptive search method for the optimal rotation factor using the Parseval principle in the fractional domain, which simplifies the algorithm. We carried out spectrum decomposition of the seismic signal, which showed that the instantaneous frequency slices obtained by the proposed algorithm are superior to the ones obtained by the traditional Gabor transform. The adaptive time frequency analysis is of great significance to seismic signal processing.展开更多
The scheduling efficiency of the tracking and data relay satellite system(TDRSS)is strictly limited by the scheduling degrees of freedom(DoF),including time DoF defined by jobs' flexible time windows and spatial ...The scheduling efficiency of the tracking and data relay satellite system(TDRSS)is strictly limited by the scheduling degrees of freedom(DoF),including time DoF defined by jobs' flexible time windows and spatial DoF brought by multiple servable tracking and data relay satellites(TDRSs).In this paper,ageneralized multiple time windows(GMTW)model is proposed to fully exploit the time and spatial DoF.Then,the improvements of service capability and job-completion probability based on the GMTW are theoretically proved.Further,an asymmetric path-relinking(APR)based heuristic job scheduling framework is presented to maximize the usage of DoF provided by the GMTW.Simulation results show that by using our proposal 11%improvement of average jobcompletion probability can be obtained.Meanwhile,the computing time of the time-to-target can be shorten to 1/9 of the GRASP.展开更多
In this paper, we use the Mittag-Leffler addition formula to solve the Green function of generalized time fractional diffusion equation in the whole plane and prove the convergence of the Green function.
The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9(t) ~ t^γ, 0 ≤ γ 〈...The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9(t) ~ t^γ, 0 ≤ γ 〈 2, and the probability density function ω(t) of a particle's waiting time t follows a power law form for large t: ω(t) ~t^-(1+α), 0 〈 α 〈 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent 7 and the long-tailed index α of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.展开更多
In this paper, the inhomogeneous structure of generalized seismic strain release time series (GSSRTS) of earth- quakes in East, West China and their subtectonic regions as Xinjiang, Qinghai-Xizang (Tibetan) Plateau, N...In this paper, the inhomogeneous structure of generalized seismic strain release time series (GSSRTS) of earth- quakes in East, West China and their subtectonic regions as Xinjiang, Qinghai-Xizang (Tibetan) Plateau, Northeast China, North China, South China and Taiwan have been analyzed by using the method of significant analysis on zero crossings of derivatives (SiZer). Results show that when index η for estimating GSSRTS is close to zero and bandwidth is large enough, GSSRTSs feature significant increasing in Xinjiang, Northeast China, South China and Taiwan tectonic regions and decreasing in Qinghai-Xizang (Tibetan Platean) and North China tectonic regions from January 1, 1970 to January 1, 2000. While with the dwindling of bandwidth GSSRTSs in all the above tec- tonic regions characterize clustering, that is to say, significant increasing and decreasing emerge alternatively. When η is large enough, GSSRTSs would have no significant statistical variation in most of above tectonic regions except Qinghai-Xizang (Tibetan Platean) and Taiwan where significant increasing or decreasing hold in several time intervals within limited bandwidths.展开更多
Major disasters such as wildfire, tornado, hurricane, tropical storm, and flooding cause disruptions in infrastructure systems such as power and water supply, wastewater management, telecommunication, and transportati...Major disasters such as wildfire, tornado, hurricane, tropical storm, and flooding cause disruptions in infrastructure systems such as power and water supply, wastewater management, telecommunication, and transportation facilities. Disruptions in electricity infrastructure have negative impacts on sectors throughout a region, including education, medical services,financial services, and recreation. In this study, we introduced a novel approach to investigate the factors that can be associated with longer restoration time of power service after a hurricane. Considering restoration time as the dependent variable and using a comprehensive set of county-level data, we estimated a generalized accelerated failure time(GAFT) model that accounts for spatial dependence among observations for time to event data. The model fit improved by 12% after considering the effects of spatial correlation in time to event data. Using the GAFT model and Hurricane Irma's impact on Florida as a case study, we examined:(1) differences in electric power outages and restoration rates among different types of power companies—investor-owned power companies, rural and municipal cooperatives;(2) the relationship between the duration of power outage and power system variables;and(3) the relationship between the duration of power outage and socioeconomic attributes. The findings of this study indicate that counties with a higher percentage of customers served by investor-owned electric companies and lower median household income faced power outage for a longer time. This study identified the key factors to predict restoration time of hurricane-induced power outages, allowing disaster management agencies to adopt strategies required for restoration process.展开更多
In this paper, we consider the distribution of the maximum surplus before ruin in a generalized Erlang(n) risk process (i.e., convolution of n exponential distributions with possibly different parameters) perturbe...In this paper, we consider the distribution of the maximum surplus before ruin in a generalized Erlang(n) risk process (i.e., convolution of n exponential distributions with possibly different parameters) perturbed by diffusion. It is shown that the maximum surplus distribution before ruin satisfies the integro-differential equation with certain boundary conditions. Explicit expressions are obtained when claims amounts are rationally distributed. Finally, the surplus distribution at the time of ruin and the surplus distribution immediately before ruin are presented.展开更多
In this paper we use the spectral method to analyse the generalized Kuramoto-Sivashinsky equations. We prove the existence and uniqueness of global smooth solution of the equations. Finally, we obtain the error estima...In this paper we use the spectral method to analyse the generalized Kuramoto-Sivashinsky equations. We prove the existence and uniqueness of global smooth solution of the equations. Finally, we obtain the error estimation between spectral approximate solution and exact solution on large time.展开更多
This paper reports a new derivative in the Eulerian description in flat space-the generalized covariant derivative with respect to time. The following contents are included:(a) the restricted covariant derivative with...This paper reports a new derivative in the Eulerian description in flat space-the generalized covariant derivative with respect to time. The following contents are included:(a) the restricted covariant derivative with respect to time for Eulerian component is defined;(b) the postulate of the covariant form invariability in time field is set up;(c) the generalized covariant derivative with respect to time for generalized Eulerian component is defined;(d) the algebraic structure of the generalized covariant derivative with respect to time is made clear;(e) the covariant differential transformation group in time filed is derived. These progresses reveal the covariant form invariability of Eulerian space and time.展开更多
The previous paper reported a new derivative in the Eulerian description in flat space—the generalized covariant derivative of generalized Eulerian component with respect to time. This paper extends the thought from ...The previous paper reported a new derivative in the Eulerian description in flat space—the generalized covariant derivative of generalized Eulerian component with respect to time. This paper extends the thought from the Eulerian description to the Lagrangian description:on the basis of the postulate of covariant form invariability in time field, we define a new derivative in the Lagrangian description in flat space—the generalized covariant derivative of generalized Lagrangian component with respect to time. Besides, the covariant differential transformation group is set up. The covariant form invariability of Lagrangian space-time is ascertained.展开更多
The generalized fractional Burgers equation is studied in this paper. Using the classical Lie symmetry method, all of the vector fields and symmetry reduction of the equation with nonlinearity are constructed. In part...The generalized fractional Burgers equation is studied in this paper. Using the classical Lie symmetry method, all of the vector fields and symmetry reduction of the equation with nonlinearity are constructed. In particular, an exact solution & provided by using the ansatz method. In addition, other types of exact solution are obtained via the invariant subspace method. Finally, conservation laws for this equation are derived.展开更多
“The time-fractional generalized Burger-Fisher equation(TF-GBFE)”is used in various applied sciences and physical applications,including simulation of gas dynamics,financial mathematics,fluid mechan-ics,and ocean en...“The time-fractional generalized Burger-Fisher equation(TF-GBFE)”is used in various applied sciences and physical applications,including simulation of gas dynamics,financial mathematics,fluid mechan-ics,and ocean engineering.This equation represents a concept for the coordination of reaction systems,as well as advection,and conveys the understanding of dissipation.The Fractional Reduced Differential Transform Method(FRDTM)is used to evaluate“the time-fractional generalized Burger-Fisher equation(TF-GBFE).”Todeterminethemethod’s validity,whenthesolutionsareobtained,theyarecorrelatedto exact solutions ofα=1 order,and even for various values ofα.Three-dimensional graphs are used to depict the solutions.Additionally,the analysis of exact and FRDTM solutions indicates that the proposed approach is very accurate.展开更多
In this paper, a generalized time fractional nonlinear foam drainage equation is investigated by means of the Lie group analysis method. Based on the Riemann–Liouville derivative, the Lie point symmetries and symmetr...In this paper, a generalized time fractional nonlinear foam drainage equation is investigated by means of the Lie group analysis method. Based on the Riemann–Liouville derivative, the Lie point symmetries and symmetry reductions of the equation are derived, respectively. Furthermore, conservation laws with two kinds of independent variables of the equation are performed by making use of the nonlinear self-adjointness method.展开更多
基金supported by national natural science foundation of China(No.41274127,41301460,40874066,and 40839905)
文摘We designed the window function of the optimal Gabor transform based on the time-frequency rotation property of the fractional Fourier transform. Thus, we obtained the adaptive optimal Gabor transform in the fractional domain and improved the time-frequency concentration of the Gabor transform. The algorithm first searches for the optimal rotation factor, then performs the p-th FrFT of the signal and, finally, performs time and frequency analysis of the FrFT result. Finally, the algorithm rotates the plane in the fractional domain back to the normal time-frequency plane. This promotes the application of FrFT in the field of high-resolution reservoir prediction. Additionally, we proposed an adaptive search method for the optimal rotation factor using the Parseval principle in the fractional domain, which simplifies the algorithm. We carried out spectrum decomposition of the seismic signal, which showed that the instantaneous frequency slices obtained by the proposed algorithm are superior to the ones obtained by the traditional Gabor transform. The adaptive time frequency analysis is of great significance to seismic signal processing.
基金Supported by the National Natural Science Foundation of China(91338101,91338108,61132002,6132106)Research Fund of Tsinghua University(2011Z05117)Co-innovation Laboratory of Aerospace Broadband Network Technology
文摘The scheduling efficiency of the tracking and data relay satellite system(TDRSS)is strictly limited by the scheduling degrees of freedom(DoF),including time DoF defined by jobs' flexible time windows and spatial DoF brought by multiple servable tracking and data relay satellites(TDRSs).In this paper,ageneralized multiple time windows(GMTW)model is proposed to fully exploit the time and spatial DoF.Then,the improvements of service capability and job-completion probability based on the GMTW are theoretically proved.Further,an asymmetric path-relinking(APR)based heuristic job scheduling framework is presented to maximize the usage of DoF provided by the GMTW.Simulation results show that by using our proposal 11%improvement of average jobcompletion probability can be obtained.Meanwhile,the computing time of the time-to-target can be shorten to 1/9 of the GRASP.
文摘In this paper, we use the Mittag-Leffler addition formula to solve the Green function of generalized time fractional diffusion equation in the whole plane and prove the convergence of the Green function.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11605003 and 11547231
文摘The generalized master equation for the space-time coupled continuous time random walk is derived analytically, in which the space-time coupling is considered through the correlated function 9(t) ~ t^γ, 0 ≤ γ 〈 2, and the probability density function ω(t) of a particle's waiting time t follows a power law form for large t: ω(t) ~t^-(1+α), 0 〈 α 〈 1. The results indicate that the expressions of the generalized master equation are determined by the correlation exponent 7 and the long-tailed index α of the waiting time. Moreover, the diffusion results obtained from the generalized master equation are in accordance with the previous known results and the numerical simulation results.
基金Natural Science Foundation of Shandong Province (Y2002E01), Key Project for Earthquake Prevention and Disaster Mitigation in Shandong (SD10503-02-05) and Project of China-Greece International Cooperation of Science and Technology from 2003 to 2005.
文摘In this paper, the inhomogeneous structure of generalized seismic strain release time series (GSSRTS) of earth- quakes in East, West China and their subtectonic regions as Xinjiang, Qinghai-Xizang (Tibetan) Plateau, Northeast China, North China, South China and Taiwan have been analyzed by using the method of significant analysis on zero crossings of derivatives (SiZer). Results show that when index η for estimating GSSRTS is close to zero and bandwidth is large enough, GSSRTSs feature significant increasing in Xinjiang, Northeast China, South China and Taiwan tectonic regions and decreasing in Qinghai-Xizang (Tibetan Platean) and North China tectonic regions from January 1, 1970 to January 1, 2000. While with the dwindling of bandwidth GSSRTSs in all the above tec- tonic regions characterize clustering, that is to say, significant increasing and decreasing emerge alternatively. When η is large enough, GSSRTSs would have no significant statistical variation in most of above tectonic regions except Qinghai-Xizang (Tibetan Platean) and Taiwan where significant increasing or decreasing hold in several time intervals within limited bandwidths.
基金the U.S.National Science Foundation for the Grant CMMI-1832578 to support the research presented in this article。
文摘Major disasters such as wildfire, tornado, hurricane, tropical storm, and flooding cause disruptions in infrastructure systems such as power and water supply, wastewater management, telecommunication, and transportation facilities. Disruptions in electricity infrastructure have negative impacts on sectors throughout a region, including education, medical services,financial services, and recreation. In this study, we introduced a novel approach to investigate the factors that can be associated with longer restoration time of power service after a hurricane. Considering restoration time as the dependent variable and using a comprehensive set of county-level data, we estimated a generalized accelerated failure time(GAFT) model that accounts for spatial dependence among observations for time to event data. The model fit improved by 12% after considering the effects of spatial correlation in time to event data. Using the GAFT model and Hurricane Irma's impact on Florida as a case study, we examined:(1) differences in electric power outages and restoration rates among different types of power companies—investor-owned power companies, rural and municipal cooperatives;(2) the relationship between the duration of power outage and power system variables;and(3) the relationship between the duration of power outage and socioeconomic attributes. The findings of this study indicate that counties with a higher percentage of customers served by investor-owned electric companies and lower median household income faced power outage for a longer time. This study identified the key factors to predict restoration time of hurricane-induced power outages, allowing disaster management agencies to adopt strategies required for restoration process.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10901164 and 11071037), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry and Natural Science Foundation of CQ CSTC (Grant No. 2009BB8221)
文摘In this paper, we consider the distribution of the maximum surplus before ruin in a generalized Erlang(n) risk process (i.e., convolution of n exponential distributions with possibly different parameters) perturbed by diffusion. It is shown that the maximum surplus distribution before ruin satisfies the integro-differential equation with certain boundary conditions. Explicit expressions are obtained when claims amounts are rationally distributed. Finally, the surplus distribution at the time of ruin and the surplus distribution immediately before ruin are presented.
文摘In this paper we use the spectral method to analyse the generalized Kuramoto-Sivashinsky equations. We prove the existence and uniqueness of global smooth solution of the equations. Finally, we obtain the error estimation between spectral approximate solution and exact solution on large time.
基金Project supported by the National Natural Sciences Foundation of China(No.11272175)the Specialized Research Found for Doctoral Program of Higher Education(No.20130002110044)
文摘This paper reports a new derivative in the Eulerian description in flat space-the generalized covariant derivative with respect to time. The following contents are included:(a) the restricted covariant derivative with respect to time for Eulerian component is defined;(b) the postulate of the covariant form invariability in time field is set up;(c) the generalized covariant derivative with respect to time for generalized Eulerian component is defined;(d) the algebraic structure of the generalized covariant derivative with respect to time is made clear;(e) the covariant differential transformation group in time filed is derived. These progresses reveal the covariant form invariability of Eulerian space and time.
基金Project supported by the National Natural Sciences Foundation of China(No.11272175)the Specialized Research Found for Doctoral Program of Higher Education(No.20130002110044)
文摘The previous paper reported a new derivative in the Eulerian description in flat space—the generalized covariant derivative of generalized Eulerian component with respect to time. This paper extends the thought from the Eulerian description to the Lagrangian description:on the basis of the postulate of covariant form invariability in time field, we define a new derivative in the Lagrangian description in flat space—the generalized covariant derivative of generalized Lagrangian component with respect to time. Besides, the covariant differential transformation group is set up. The covariant form invariability of Lagrangian space-time is ascertained.
文摘The generalized fractional Burgers equation is studied in this paper. Using the classical Lie symmetry method, all of the vector fields and symmetry reduction of the equation with nonlinearity are constructed. In particular, an exact solution & provided by using the ansatz method. In addition, other types of exact solution are obtained via the invariant subspace method. Finally, conservation laws for this equation are derived.
文摘“The time-fractional generalized Burger-Fisher equation(TF-GBFE)”is used in various applied sciences and physical applications,including simulation of gas dynamics,financial mathematics,fluid mechan-ics,and ocean engineering.This equation represents a concept for the coordination of reaction systems,as well as advection,and conveys the understanding of dissipation.The Fractional Reduced Differential Transform Method(FRDTM)is used to evaluate“the time-fractional generalized Burger-Fisher equation(TF-GBFE).”Todeterminethemethod’s validity,whenthesolutionsareobtained,theyarecorrelatedto exact solutions ofα=1 order,and even for various values ofα.Three-dimensional graphs are used to depict the solutions.Additionally,the analysis of exact and FRDTM solutions indicates that the proposed approach is very accurate.
基金Supported by the National Training Programs of Innovation and Entrepreneurship for Undergraduates under Grant No.201410290039the Fundamental Research Funds for the Central Universities under Grant Nos.2015QNA53 and 2015XKQY14+2 种基金the Fundamental Research Funds for Postdoctoral at the Key Laboratory of Gas and Fire Control for Coal Minesthe General Financial Grant from the China Postdoctoral Science Foundation under Grant No.2015M570498Natural Sciences Foundation of China under Grant No.11301527
文摘In this paper, a generalized time fractional nonlinear foam drainage equation is investigated by means of the Lie group analysis method. Based on the Riemann–Liouville derivative, the Lie point symmetries and symmetry reductions of the equation are derived, respectively. Furthermore, conservation laws with two kinds of independent variables of the equation are performed by making use of the nonlinear self-adjointness method.