In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system...In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system of linear equations and they can be used to compute Jordan basis.展开更多
Using the method of the Jordan-Wigner transformation for solving different spin-spin correlation functions, we have investigated the generation of next-nearest-neighbouring entanglement in a one-dimensional quantum Is...Using the method of the Jordan-Wigner transformation for solving different spin-spin correlation functions, we have investigated the generation of next-nearest-neighbouring entanglement in a one-dimensional quantum Ising spin chain with the Gaussian distribution impurities of exchange couplings and external magnetic fields taken into account. The maximal value of entanglement between the next-nearest-neighbouring qubits in the transverse Ising model was analysed in detail by varying the effectively controlled parameters such as interchange coupling, magnetic field and the system impurity. For such systems, where both exchange couplings and external magnetic field disorder appear, we show that it is possible to achieve next-nearest-neighbouring entanglement better than the previously discussed pure Ising spin chain case. We also show that the Gaussian distribution impurity can induce next-nearest-neighbouring entanglement, which can be used as a means to characterize quantum phase transition.展开更多
Jordan is very vulnerable to drought because of its location in the arid to semi-arid part of the Middle East. Droughts coupled with water scarcity are becoming a serious threat to the economic growth, social cohesion...Jordan is very vulnerable to drought because of its location in the arid to semi-arid part of the Middle East. Droughts coupled with water scarcity are becoming a serious threat to the economic growth, social cohesion and political stability. Rainfall time series from four rain stations covering the Jordan River Basin were analyzed for drought characterization and forecasting using standardized precipitation index (SPI), Markov chain and autoregressive integrated moving average (ARIMA) model. The 7-year moving average of Amman data showed a decreasing trend while data from the other three stations were stable or showed an increasing trend. The frequency analysis indicated 2-year return period for near zero SPI values while the return period for moderate drought was 7 years. Successive droughts had occurred at least three times during the past 40 years. Severe droughts are expected once every 20 - 25 year period at all rain stations. The extreme droughts were rare events with return periods between 80 and 115 years. There are equal occurrence probabilities for drought and wet conditions in any given year, irrespective, of the condition in the previous year. The results showed that ARIMA model was successful in predicting the overall statistics with a given period at annual scales. The overall number of predicted/observed droughts during the validation periods were 2/2 severe droughts for Amman station and, 0/1, 1/1, 0/1 extreme droughts for Amman, Irbid and Mafraq stations, respectively. In addition, the ARIMA model also predicted 3 out of 4 actual moderate droughts for Amman and Mafraq stations. It was concluded that early warning of developing droughts can be deduced form the monthly Markov transitional probabilities. ARIMA models can be used as a forecasting tool of the future drought trends. Using the first and second order Markov probabilities can complement the ARIMA predictions.展开更多
基金Foundation item： Supported by the Science Foundation of Liuzhou Vocational Institute of Technology（2007C03）
文摘In this paper, we introduce a method to define generalized characteristic matrices of a defective matrix by the common form of Jordan chains. The generalized characteristic matrices can be obtained by solving a system of linear equations and they can be used to compute Jordan basis.
基金supported by the Foundation for Scientific and Technological Research Programme,Education Department of Hubei Province,China (Grant No Z200722001)the Postgraduate Programme of Hubei Normal University of China (Grant No 2007D20)
文摘Using the method of the Jordan-Wigner transformation for solving different spin-spin correlation functions, we have investigated the generation of next-nearest-neighbouring entanglement in a one-dimensional quantum Ising spin chain with the Gaussian distribution impurities of exchange couplings and external magnetic fields taken into account. The maximal value of entanglement between the next-nearest-neighbouring qubits in the transverse Ising model was analysed in detail by varying the effectively controlled parameters such as interchange coupling, magnetic field and the system impurity. For such systems, where both exchange couplings and external magnetic field disorder appear, we show that it is possible to achieve next-nearest-neighbouring entanglement better than the previously discussed pure Ising spin chain case. We also show that the Gaussian distribution impurity can induce next-nearest-neighbouring entanglement, which can be used as a means to characterize quantum phase transition.
文摘Jordan is very vulnerable to drought because of its location in the arid to semi-arid part of the Middle East. Droughts coupled with water scarcity are becoming a serious threat to the economic growth, social cohesion and political stability. Rainfall time series from four rain stations covering the Jordan River Basin were analyzed for drought characterization and forecasting using standardized precipitation index (SPI), Markov chain and autoregressive integrated moving average (ARIMA) model. The 7-year moving average of Amman data showed a decreasing trend while data from the other three stations were stable or showed an increasing trend. The frequency analysis indicated 2-year return period for near zero SPI values while the return period for moderate drought was 7 years. Successive droughts had occurred at least three times during the past 40 years. Severe droughts are expected once every 20 - 25 year period at all rain stations. The extreme droughts were rare events with return periods between 80 and 115 years. There are equal occurrence probabilities for drought and wet conditions in any given year, irrespective, of the condition in the previous year. The results showed that ARIMA model was successful in predicting the overall statistics with a given period at annual scales. The overall number of predicted/observed droughts during the validation periods were 2/2 severe droughts for Amman station and, 0/1, 1/1, 0/1 extreme droughts for Amman, Irbid and Mafraq stations, respectively. In addition, the ARIMA model also predicted 3 out of 4 actual moderate droughts for Amman and Mafraq stations. It was concluded that early warning of developing droughts can be deduced form the monthly Markov transitional probabilities. ARIMA models can be used as a forecasting tool of the future drought trends. Using the first and second order Markov probabilities can complement the ARIMA predictions.
