This paper considers the scalar differential delay equation x（t） -μ x（t）-f（x（t-τ））, where f（x） is a decreasing continuous function. By proving that all solutions will beultimately in some interval, we give...This paper considers the scalar differential delay equation x（t） -μ x（t）-f（x（t-τ））, where f（x） is a decreasing continuous function. By proving that all solutions will beultimately in some interval, we give tile conditions under which the unique equilibrium pointof the differential delay equation is globally attractive.展开更多
On the basis of strict mathematical description about Failure_Free Period Life Test (FFPLT), the statistical properties of the tests and optimal confidence limit of the parameter are discussed in detail and correspond...On the basis of strict mathematical description about Failure_Free Period Life Test (FFPLT), the statistical properties of the tests and optimal confidence limit of the parameter are discussed in detail and corresponding calculating formulae are found out.展开更多
The wind speed is measured with the help of three anemometers S30, S45, S60 placed at 30 m, 45 m, and 60 m height. Mean values are recorded and stored for every hour using a data logger. For accounting wind turbine ge...The wind speed is measured with the help of three anemometers S30, S45, S60 placed at 30 m, 45 m, and 60 m height. Mean values are recorded and stored for every hour using a data logger. For accounting wind turbine generator （WTG.） tower height, data recorded from S60 anemometer at 60 m height is used for analysis purpose. This paper analyzes the probability distribution of wind speed data recorded by maharashtra energy development agency （MEDA） wind farm at Ahmednagar （India）. The main objective is to validate the wind energy probability by using probability distribution function （PDF） of available wind potential. The energy generated from wind for any time interval is equal to the area tinder power curve multiplied by time in hours for that time interval. To estimate the wind energy probability, hourly wind speed data tbr one year interval is selected. Weibull distribution is adopted in this study to best fit the wind speed data. The scale and shape paranleters are estimated by using maximum likelihood method. The goodness of fit tests based on the probability density function （PDF） is conducted to show that the distribution adequately fits the data. It is found from the curve fitting test that, although the two distributions are all suitable for describing the probability distribution of wind speed data, the two-parameter weibull distribution is more appropriate than the lognormal distribution.展开更多
It is known that a strictly piecewise monotone function with nonmonotonicity height ≥ 2 on a compact interval has no iterative roots of order greater than the number of forts. An open question is: Does it have iterat...It is known that a strictly piecewise monotone function with nonmonotonicity height ≥ 2 on a compact interval has no iterative roots of order greater than the number of forts. An open question is: Does it have iterative roots of order less than or equal to the number of forts? An answer was given recently in the case of "equal to". Since many theories of resultant and algebraic varieties can be applied to computation of polynomials, a special class of strictly piecewise monotone functions, in this paper we investigate the question in the case of "less than" for polynomials. For this purpose we extend the question from a compact interval to the whole real line and give a procedure of computation for real polynomial iterative roots. Applying the procedure together with the theory of discriminants, we find all real quartic polynomials of non-monotonicity height 2 which have quadratic polynomial iterative roots of order 2 and answer the question.展开更多
The aim of this paper is to develop some basic theories of stochastic functional differential equations (SFDEs) under the local Lipschitz condition in continuous functions space C. Firstly, we establish a global exist...The aim of this paper is to develop some basic theories of stochastic functional differential equations (SFDEs) under the local Lipschitz condition in continuous functions space C. Firstly, we establish a global existence-uniqueness lemma for the SFDEs under the global Lipschitz condition in C without the linear growth condition. Then, under the local Lipschitz condition in C, we show that the non-continuable solution of SFDEs still exists if the drift coefficient and diffusion coefficient are square-integrable with respect to t when the state variable equals zero. And the solution of the considered equation must either explode at the end of the maximum existing interval or exist globally. Furthermore, some more general sufficient conditions for the global existence-uniqueness are obtained. Our conditions obtained in this paper are much weaker than some existing results. For example, we need neither the linear growth condition nor the continuous condition on the time t. Two examples are provided to show the effectiveness of the theoretical results.展开更多
文摘This paper considers the scalar differential delay equation x（t） -μ x（t）-f（x（t-τ））, where f（x） is a decreasing continuous function. By proving that all solutions will beultimately in some interval, we give tile conditions under which the unique equilibrium pointof the differential delay equation is globally attractive.
文摘On the basis of strict mathematical description about Failure_Free Period Life Test (FFPLT), the statistical properties of the tests and optimal confidence limit of the parameter are discussed in detail and corresponding calculating formulae are found out.
文摘The wind speed is measured with the help of three anemometers S30, S45, S60 placed at 30 m, 45 m, and 60 m height. Mean values are recorded and stored for every hour using a data logger. For accounting wind turbine generator （WTG.） tower height, data recorded from S60 anemometer at 60 m height is used for analysis purpose. This paper analyzes the probability distribution of wind speed data recorded by maharashtra energy development agency （MEDA） wind farm at Ahmednagar （India）. The main objective is to validate the wind energy probability by using probability distribution function （PDF） of available wind potential. The energy generated from wind for any time interval is equal to the area tinder power curve multiplied by time in hours for that time interval. To estimate the wind energy probability, hourly wind speed data tbr one year interval is selected. Weibull distribution is adopted in this study to best fit the wind speed data. The scale and shape paranleters are estimated by using maximum likelihood method. The goodness of fit tests based on the probability density function （PDF） is conducted to show that the distribution adequately fits the data. It is found from the curve fitting test that, although the two distributions are all suitable for describing the probability distribution of wind speed data, the two-parameter weibull distribution is more appropriate than the lognormal distribution.
基金supported by the National Basic Research Program of China (Grant No. 2011CB302402)National Natural Science Foundation of China (Grant Nos. 61021004 and 10825104)Shanghai Leading Academic Discipline Project (Grant No. B412)
文摘It is known that a strictly piecewise monotone function with nonmonotonicity height ≥ 2 on a compact interval has no iterative roots of order greater than the number of forts. An open question is: Does it have iterative roots of order less than or equal to the number of forts? An answer was given recently in the case of "equal to". Since many theories of resultant and algebraic varieties can be applied to computation of polynomials, a special class of strictly piecewise monotone functions, in this paper we investigate the question in the case of "less than" for polynomials. For this purpose we extend the question from a compact interval to the whole real line and give a procedure of computation for real polynomial iterative roots. Applying the procedure together with the theory of discriminants, we find all real quartic polynomials of non-monotonicity height 2 which have quadratic polynomial iterative roots of order 2 and answer the question.
基金supported by National Natural Science Foundation of China (Grant Nos.11271270, 11201320 and 11101298)Youth Foundation of Sichuan University (Grant No. 2011SCU11111)
文摘The aim of this paper is to develop some basic theories of stochastic functional differential equations (SFDEs) under the local Lipschitz condition in continuous functions space C. Firstly, we establish a global existence-uniqueness lemma for the SFDEs under the global Lipschitz condition in C without the linear growth condition. Then, under the local Lipschitz condition in C, we show that the non-continuable solution of SFDEs still exists if the drift coefficient and diffusion coefficient are square-integrable with respect to t when the state variable equals zero. And the solution of the considered equation must either explode at the end of the maximum existing interval or exist globally. Furthermore, some more general sufficient conditions for the global existence-uniqueness are obtained. Our conditions obtained in this paper are much weaker than some existing results. For example, we need neither the linear growth condition nor the continuous condition on the time t. Two examples are provided to show the effectiveness of the theoretical results.
