Some polar coordinates are used to determine the domain and the ball of convergence of a multiple Taylor series. In this domain and in this ball the series converges, converges absolutely and converges uniformly on an...Some polar coordinates are used to determine the domain and the ball of convergence of a multiple Taylor series. In this domain and in this ball the series converges, converges absolutely and converges uniformly on any compact set properties of the series may also be studied. For some random multiple are some corresponding properties. Growth and other Taylor series there展开更多
The formulas of the lower orders of Dirichlet series are given by means of the exponents and the convex regularized sequences of the logarithms and the convex regularized sequences of the logarithms of the moduli of t...The formulas of the lower orders of Dirichlet series are given by means of the exponents and the convex regularized sequences of the logarithms and the convex regularized sequences of the logarithms of the moduli of the coefficients. Corresponding results are obtained for some random Dirichlet series.展开更多
Under the conditions(without independence): (i) There Exists alpha > 0, such that sup E\Z(n)\(alpha) < +infinity, (ii) There Exists beta > 0, such that sup E\Z(n)\(-beta) < +infinity, the random series Sig...Under the conditions(without independence): (i) There Exists alpha > 0, such that sup E\Z(n)\(alpha) < +infinity, (ii) There Exists beta > 0, such that sup E\Z(n)\(-beta) < +infinity, the random series Sigma a(n) Z(n)e(-lambda n) and series' Sigma a(n)e(-lambda ns) a.s. have the same abscissa of convergence, the (R) order, lower order and type.展开更多
In this paper,we study the relations between the coefficients and the growth of zero order and finite order Dirichlet series and random Dirichlet series in the whole plane. And when the random variable sequence {Xn {...In this paper,we study the relations between the coefficients and the growth of zero order and finite order Dirichlet series and random Dirichlet series in the whole plane. And when the random variable sequence {Xn {ω}} satisfies the certain condition, in the whole plane, the growth of the random entire function which is determined by the zero order and finite order random Dirichlet series is almost surely same with corresponding growth of random Dirichlet series on any horizontal straight line.展开更多
In this article, the authors study the vector-valued random power series on the unit ball of C^n and get vector-valued Salem-Zygmund theorem for them by using martingale technique. Further, the relationships between v...In this article, the authors study the vector-valued random power series on the unit ball of C^n and get vector-valued Salem-Zygmund theorem for them by using martingale technique. Further, the relationships between vector-valued random power series and several function spaces are also studied.展开更多
For some random Dirichlet series of order (R) infinite almost surely every horizontal line is a Borel line of order (R) infinite and without exceptional values
This paper deals with the value distribution of random Dirichlet series whose coefficients are a martingale difference sequence, and which is of neutral growth.
This paper studies the value distribution of random analytic Dirichlet series f(s) = Zn()e-sn, where {Zn} is a sequence of independent random variables, n = 1 with moments zero, such that infE{Zn}/E1/2{Zn2≥ α > ...This paper studies the value distribution of random analytic Dirichlet series f(s) = Zn()e-sn, where {Zn} is a sequence of independent random variables, n = 1 with moments zero, such that infE{Zn}/E1/2{Zn2≥ α > 0. Suppose [h*(σ)]2 = n converges for any α > 0, and diverges for = 0. It is shown that if = ρ E (0, ), then with probability one, where β is a constant depending only upon the constant α.展开更多
Suppose that {X(n)(omega)} are independent random complex variable sequence, E(X(n)) = 0 and [GRAPHICS] (V(X(n) = sigma(n)2). If reversed capital E-epsilon > 0 such that for all P (H) > 1-epsilon, we have [GRAPH...Suppose that {X(n)(omega)} are independent random complex variable sequence, E(X(n)) = 0 and [GRAPHICS] (V(X(n) = sigma(n)2). If reversed capital E-epsilon > 0 such that for all P (H) > 1-epsilon, we have [GRAPHICS] Then the circle {\Z\ = rho} is almost surely a natural boundary of the random series [GRAPHICS]展开更多
In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary rando...In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.展开更多
In this article, the uniqueness theorem of Dirichlet series is proved. Then the random Dirichlet series in the right half plane is studied, and the result that the random Dirichlet series of finite order has almost su...In this article, the uniqueness theorem of Dirichlet series is proved. Then the random Dirichlet series in the right half plane is studied, and the result that the random Dirichlet series of finite order has almost surely（a.s.） no deficient functions is proved.展开更多
This paper deals with random Taylor series whose coefficients consist of independent random variables {X n} with the property: αE 1/2 {|X n| 2}≤E{|X n|}<∞, E{X n}=0 (n ) for some positive cons...This paper deals with random Taylor series whose coefficients consist of independent random variables {X n} with the property: αE 1/2 {|X n| 2}≤E{|X n|}<∞, E{X n}=0 (n ) for some positive constant α. The convergence, growth, and value distribution of the series are investigated.展开更多
This note implies only a moment condition upon the coefficients of random Dirichlet series to study the convergence and growth of the series. The condition needs the coefficients to satisfy the so-called inverse H?lde...This note implies only a moment condition upon the coefficients of random Dirichlet series to study the convergence and growth of the series. The condition needs the coefficients to satisfy the so-called inverse H?lder inequality, which need not be independent. The note uses a method whose feature is to compare the convergence of two series, and obtains two theorems, one dealing with the convergence of the random Dirichlet series, another the growth of the random analytic function represented by the series. These results can be used to improve essentially some known conclusions.展开更多
Kahane has studied the value distribution of the Gauss-Taylor serieswhere {Xn} is a complex Gauss sequence and In this paper, by trans-forming the right half plane into the unit disc and setting up some important ineq...Kahane has studied the value distribution of the Gauss-Taylor serieswhere {Xn} is a complex Gauss sequence and In this paper, by trans-forming the right half plane into the unit disc and setting up some important inequal-ities, the value distribution of the Dirichlet series is studied where {Xn}is a sequence of some non-degenerate independent random variable satisfying conditions:EXn = 0; Xn or ReXn or ImAn of bounded density. Thereexists α> 0 such that Vn : (the classic Gauss and Steinhaus random variables are special cases of such random variables). The important results are obtained that every point on the line Res = 0 is a Picard point of the series without finite exceptional value a.s..展开更多
We study the random Taylor series whose random variable sequence in |z|＜1 belongs to a class of non equal distributions which are general enough, and proved that they have not almost surely exceptioinal fu nction.
A kind of method of modal identification subject to ambient excitation is presented. A new synthesis stationary signal based on structural response wavelet transform and wavelet coefficient processes co-integration is...A kind of method of modal identification subject to ambient excitation is presented. A new synthesis stationary signal based on structural response wavelet transform and wavelet coefficient processes co-integration is obtained. The new signal instead of structural response is used in identifying the modal parameters of a non- stationary system, combined with the method of modal identification under stationary random excitation-the NExT method and the adjusted continuous least square method. The numerical results show that the method can eliminate the non-stationarity of structural response subject to non-stationary random excitation to a great extent, and is highly precise and robust.展开更多
On the assumption that random interruptions in the observation process are modeled by a sequence of independent Bernoulli random variables, we firstly generalize two kinds of nonlinear filtering methods with random in...On the assumption that random interruptions in the observation process are modeled by a sequence of independent Bernoulli random variables, we firstly generalize two kinds of nonlinear filtering methods with random interruption failures in the observation based on the extended Kalman filtering （EKF） and the unscented Kalman filtering （UKF）, which were shortened as GEKF and CUKF in this paper, respectively. Then the nonlinear filtering model is established by using the radial basis function neural network （RBFNN） prototypes and the network weights as state equation and the output of RBFNN to present the observation equation. Finally, we take the filtering problem under missing observed data as a special case of nonlinear filtering with random intermittent failures by setting each missing data to be zero without needing to pre-estimate the missing data, and use the GEKF-based RBFNN and the GUKF-based RBFNN to predict the ground radioactivity time series with missing data. Experimental results demonstrate that the prediction results of GUKF-based RBFNN accord well with the real ground radioactivity time series while the prediction results of GEKF-based RBFNN are divergent.展开更多
A generalized antithetic time series theory for exponentially derived antithetic random variables is developed. The correlation function between a generalized gamma distributed random variable and its pth exponent is ...A generalized antithetic time series theory for exponentially derived antithetic random variables is developed. The correlation function between a generalized gamma distributed random variable and its pth exponent is derived. We prove that the correlation approaches minus one as the exponent approaches zero from the left and the shape parameter approaches infinity.展开更多
This work applies non-stationary random processes to resilience of power distribution under severe weather. Power distribution, the edge of the energy infrastructure, is susceptible to external hazards from severe wea...This work applies non-stationary random processes to resilience of power distribution under severe weather. Power distribution, the edge of the energy infrastructure, is susceptible to external hazards from severe weather. Large-scale power failures often occur, resulting in millions of people without electricity for days. However, the problem of large-scale power failure, recovery and resilience has not been formulated rigorously nor studied systematically. This work studies the resilience of power distribution from three aspects. First, we derive non-stationary random processes to model large-scale failures and recoveries. Transient Little’s Law then provides a simple approximation of the entire life cycle of failure and recovery through a queue at the network-level. Second, we define time-varying resilience based on the non-stationary model. The resilience metric characterizes the ability of power distribution to remain operational and recover rapidly upon failures. Third, we apply the non-stationary model and the resilience metric to large-scale power failures caused by Hurricane Ike. We use the real data from the electric grid to learn time-varying model parameters and the resilience metric. Our results show non-stationary evolution of failure rates and recovery times, and how the network resilience deviates from that of normal operation during the hurricane.展开更多
文摘Some polar coordinates are used to determine the domain and the ball of convergence of a multiple Taylor series. In this domain and in this ball the series converges, converges absolutely and converges uniformly on any compact set properties of the series may also be studied. For some random multiple are some corresponding properties. Growth and other Taylor series there
文摘The formulas of the lower orders of Dirichlet series are given by means of the exponents and the convex regularized sequences of the logarithms and the convex regularized sequences of the logarithms of the moduli of the coefficients. Corresponding results are obtained for some random Dirichlet series.
文摘Under the conditions(without independence): (i) There Exists alpha > 0, such that sup E\Z(n)\(alpha) < +infinity, (ii) There Exists beta > 0, such that sup E\Z(n)\(-beta) < +infinity, the random series Sigma a(n) Z(n)e(-lambda n) and series' Sigma a(n)e(-lambda ns) a.s. have the same abscissa of convergence, the (R) order, lower order and type.
基金Supported by the National Natural Science Foundation of China（10471048）
文摘In this paper,we study the relations between the coefficients and the growth of zero order and finite order Dirichlet series and random Dirichlet series in the whole plane. And when the random variable sequence {Xn {ω}} satisfies the certain condition, in the whole plane, the growth of the random entire function which is determined by the zero order and finite order random Dirichlet series is almost surely same with corresponding growth of random Dirichlet series on any horizontal straight line.
文摘In this article, the authors study the vector-valued random power series on the unit ball of C^n and get vector-valued Salem-Zygmund theorem for them by using martingale technique. Further, the relationships between vector-valued random power series and several function spaces are also studied.
基金the Doctoral Programme Fundation and by theNational Natural Science Fundation of China
文摘For some random Dirichlet series of order (R) infinite almost surely every horizontal line is a Borel line of order (R) infinite and without exceptional values
基金the National Natural Science Foundation of China and the Doctoral Foundation of China.
文摘This paper deals with the value distribution of random Dirichlet series whose coefficients are a martingale difference sequence, and which is of neutral growth.
基金Project supported by the National Natural Science Foundationof China
文摘This paper studies the value distribution of random analytic Dirichlet series f(s) = Zn()e-sn, where {Zn} is a sequence of independent random variables, n = 1 with moments zero, such that infE{Zn}/E1/2{Zn2≥ α > 0. Suppose [h*(σ)]2 = n converges for any α > 0, and diverges for = 0. It is shown that if = ρ E (0, ), then with probability one, where β is a constant depending only upon the constant α.
文摘Suppose that {X(n)(omega)} are independent random complex variable sequence, E(X(n)) = 0 and [GRAPHICS] (V(X(n) = sigma(n)2). If reversed capital E-epsilon > 0 such that for all P (H) > 1-epsilon, we have [GRAPHICS] Then the circle {\Z\ = rho} is almost surely a natural boundary of the random series [GRAPHICS]
基金supported by the Shenzhen sustainable development project:KCXFZ 20201221173013036 and the National Natural Science Foundation of China(91746107).
文摘In this paper,we mainly discuss a discrete estimation of the average differential entropy for a continuous time-stationary ergodic space-time random field.By estimating the probability value of a time-stationary random field in a small range,we give an entropy estimation and obtain the average entropy estimation formula in a certain bounded space region.It can be proven that the estimation of the average differential entropy converges to the theoretical value with a probability of 1.In addition,we also conducted numerical experiments for different parameters to verify the convergence result obtained in the theoretical proofs.
文摘In this article, the uniqueness theorem of Dirichlet series is proved. Then the random Dirichlet series in the right half plane is studied, and the result that the random Dirichlet series of finite order has almost surely（a.s.） no deficient functions is proved.
文摘This paper deals with random Taylor series whose coefficients consist of independent random variables {X n} with the property: αE 1/2 {|X n| 2}≤E{|X n|}<∞, E{X n}=0 (n ) for some positive constant α. The convergence, growth, and value distribution of the series are investigated.
文摘This note implies only a moment condition upon the coefficients of random Dirichlet series to study the convergence and growth of the series. The condition needs the coefficients to satisfy the so-called inverse H?lder inequality, which need not be independent. The note uses a method whose feature is to compare the convergence of two series, and obtains two theorems, one dealing with the convergence of the random Dirichlet series, another the growth of the random analytic function represented by the series. These results can be used to improve essentially some known conclusions.
文摘Kahane has studied the value distribution of the Gauss-Taylor serieswhere {Xn} is a complex Gauss sequence and In this paper, by trans-forming the right half plane into the unit disc and setting up some important inequal-ities, the value distribution of the Dirichlet series is studied where {Xn}is a sequence of some non-degenerate independent random variable satisfying conditions:EXn = 0; Xn or ReXn or ImAn of bounded density. Thereexists α> 0 such that Vn : (the classic Gauss and Steinhaus random variables are special cases of such random variables). The important results are obtained that every point on the line Res = 0 is a Picard point of the series without finite exceptional value a.s..
基金The NSF (19971029) of China abd the Guangdong Provincial NSF (990444) of China.
文摘We study the random Taylor series whose random variable sequence in |z|＜1 belongs to a class of non equal distributions which are general enough, and proved that they have not almost surely exceptioinal fu nction.
基金The National Natural Science Foundation of China(No50278017)
文摘A kind of method of modal identification subject to ambient excitation is presented. A new synthesis stationary signal based on structural response wavelet transform and wavelet coefficient processes co-integration is obtained. The new signal instead of structural response is used in identifying the modal parameters of a non- stationary system, combined with the method of modal identification under stationary random excitation-the NExT method and the adjusted continuous least square method. The numerical results show that the method can eliminate the non-stationarity of structural response subject to non-stationary random excitation to a great extent, and is highly precise and robust.
基金Project supported by the State Key Program of the National Natural Science of China (Grant No. 60835004)the Natural Science Foundation of Jiangsu Province of China (Grant No. BK2009727)+1 种基金the Natural Science Foundation of Higher Education Institutions of Jiangsu Province of China (Grant No. 10KJB510004)the National Natural Science Foundation of China (Grant No. 61075028)
文摘On the assumption that random interruptions in the observation process are modeled by a sequence of independent Bernoulli random variables, we firstly generalize two kinds of nonlinear filtering methods with random interruption failures in the observation based on the extended Kalman filtering （EKF） and the unscented Kalman filtering （UKF）, which were shortened as GEKF and CUKF in this paper, respectively. Then the nonlinear filtering model is established by using the radial basis function neural network （RBFNN） prototypes and the network weights as state equation and the output of RBFNN to present the observation equation. Finally, we take the filtering problem under missing observed data as a special case of nonlinear filtering with random intermittent failures by setting each missing data to be zero without needing to pre-estimate the missing data, and use the GEKF-based RBFNN and the GUKF-based RBFNN to predict the ground radioactivity time series with missing data. Experimental results demonstrate that the prediction results of GUKF-based RBFNN accord well with the real ground radioactivity time series while the prediction results of GEKF-based RBFNN are divergent.
文摘A generalized antithetic time series theory for exponentially derived antithetic random variables is developed. The correlation function between a generalized gamma distributed random variable and its pth exponent is derived. We prove that the correlation approaches minus one as the exponent approaches zero from the left and the shape parameter approaches infinity.
文摘This work applies non-stationary random processes to resilience of power distribution under severe weather. Power distribution, the edge of the energy infrastructure, is susceptible to external hazards from severe weather. Large-scale power failures often occur, resulting in millions of people without electricity for days. However, the problem of large-scale power failure, recovery and resilience has not been formulated rigorously nor studied systematically. This work studies the resilience of power distribution from three aspects. First, we derive non-stationary random processes to model large-scale failures and recoveries. Transient Little’s Law then provides a simple approximation of the entire life cycle of failure and recovery through a queue at the network-level. Second, we define time-varying resilience based on the non-stationary model. The resilience metric characterizes the ability of power distribution to remain operational and recover rapidly upon failures. Third, we apply the non-stationary model and the resilience metric to large-scale power failures caused by Hurricane Ike. We use the real data from the electric grid to learn time-varying model parameters and the resilience metric. Our results show non-stationary evolution of failure rates and recovery times, and how the network resilience deviates from that of normal operation during the hurricane.
