A model of nonlinear differential systems with impulsive effect on random moments is considered. The extensions of qualitative analysis of the model is mainly focused on and three modified sufficient conditions are pr...A model of nonlinear differential systems with impulsive effect on random moments is considered. The extensions of qualitative analysis of the model is mainly focused on and three modified sufficient conditions are presented about p-moment boundedness in the process by Liapunov method with nonlinear item dependent on the impulsive effects, which may gain wider use in industrial engineering, physics, etc. At last, an example is given to show an theoretical application of the obtained results.展开更多
Benford's law is logarithmic law for distribution of leading digits formulated by P[D=d]= log(1+1/d) where d is leading digit or group of digits. It's named by Frank Albert Benford (1938) who formulated mathema...Benford's law is logarithmic law for distribution of leading digits formulated by P[D=d]= log(1+1/d) where d is leading digit or group of digits. It's named by Frank Albert Benford (1938) who formulated mathematical model of this probability. Befbre him, the same observation was made by Simon Newcomb. This law has changed usual preasumption of equal probability of each digit on each position in number.The main characteristic properties of this law are base, scale, sum, inverse and product invariance. Base invariance means that logarithmic law is valid for any base. Inverse invariance means that logarithmic law for leading digits holds for inverse values in sample. Multiplication invariance means that if random variable X follows Benford's law and Y is arbitrary random variable with continuous density then XY follows Benford's law too. Sum invariance means that sums of significand are the same for any leading digit or group of digits. In this text method of testing sum invariance property is proposed.展开更多
Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers.In this paper,motived by the notion of indepen...Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers.In this paper,motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng(2008),we introduce the concept of negative dependence of random variables and establish Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations.As an application,we show that Kolmogorov's strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite.展开更多
Security issues in networked control systems(NCSs) have received increasing attention in recent years.However, security protection often requires extra energy consumption, computational overhead, and time delays,whi...Security issues in networked control systems(NCSs) have received increasing attention in recent years.However, security protection often requires extra energy consumption, computational overhead, and time delays,which could adversely affect the real-time and energy-limited system. In this paper, random cryptographic protection is implemented. It is less expensive with respect to computational overhead, time, and energy consumption,compared with persistent cryptographic protection. Under the consideration of weak attackers who have little system knowledge, ungenerous attacking capability and the desire for stealthiness and random zero-measurement attacks are introduced as the malicious modification of measurements into zero signals. NCS is modeled as a stochastic system with two correlated Bernoulli distributed stochastic variables for implementation of random cryptographic protection and occurrence of random zero-measurement attacks; the stochastic stability can be analyzed using a linear matrix inequality(LMI) approach. The proposed stochastic stability analysis can help determine the proper probability of running random cryptographic protection against random zero-measurement attacks with a certain probability. Finally, a simulation example is presented based on a vertical take-off and landing(VTOL) system. The results show the effectiveness, robustness, and application of the proposed method, and are helpful in choosing the proper protection mechanism taking into account the time delay and in determining the system sampling period to increase the resistance against such attacks.展开更多
基金The Special Research Funds for Young Col-lege Teacher of Shanghai (No. 355877)
文摘A model of nonlinear differential systems with impulsive effect on random moments is considered. The extensions of qualitative analysis of the model is mainly focused on and three modified sufficient conditions are presented about p-moment boundedness in the process by Liapunov method with nonlinear item dependent on the impulsive effects, which may gain wider use in industrial engineering, physics, etc. At last, an example is given to show an theoretical application of the obtained results.
文摘Benford's law is logarithmic law for distribution of leading digits formulated by P[D=d]= log(1+1/d) where d is leading digit or group of digits. It's named by Frank Albert Benford (1938) who formulated mathematical model of this probability. Befbre him, the same observation was made by Simon Newcomb. This law has changed usual preasumption of equal probability of each digit on each position in number.The main characteristic properties of this law are base, scale, sum, inverse and product invariance. Base invariance means that logarithmic law is valid for any base. Inverse invariance means that logarithmic law for leading digits holds for inverse values in sample. Multiplication invariance means that if random variable X follows Benford's law and Y is arbitrary random variable with continuous density then XY follows Benford's law too. Sum invariance means that sums of significand are the same for any leading digit or group of digits. In this text method of testing sum invariance property is proposed.
基金supported by National Natural Science Foundation of China(Grant No.11225104)the Fundamental Research Funds for the Central Universities
文摘Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers.In this paper,motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng(2008),we introduce the concept of negative dependence of random variables and establish Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of negatively dependent random variables under the sub-linear expectations.As an application,we show that Kolmogorov's strong law of larger numbers holds for independent and identically distributed random variables under a continuous sub-linear expectation if and only if the corresponding Choquet integral is finite.
基金supported by the National Natural Science Foundation of China(No.61433006)the Key Research Project of Zhejiang Province,China(No.2017C01062)+3 种基金the Open Research Project of the State Key Laboratory of Industrial Control Technology,Zhejiang University,China(No.ICT1800422)the Opening Project of Shanghai Key Laboratory of Integrated Administration Technologies for Information Security,China(No.AGK2018003)the Department of Education of Zhejiang Province,China(No.Y201840611)the Zhejiang Provincial Natural Science Foundation of China(No.LY16F020019)
文摘Security issues in networked control systems(NCSs) have received increasing attention in recent years.However, security protection often requires extra energy consumption, computational overhead, and time delays,which could adversely affect the real-time and energy-limited system. In this paper, random cryptographic protection is implemented. It is less expensive with respect to computational overhead, time, and energy consumption,compared with persistent cryptographic protection. Under the consideration of weak attackers who have little system knowledge, ungenerous attacking capability and the desire for stealthiness and random zero-measurement attacks are introduced as the malicious modification of measurements into zero signals. NCS is modeled as a stochastic system with two correlated Bernoulli distributed stochastic variables for implementation of random cryptographic protection and occurrence of random zero-measurement attacks; the stochastic stability can be analyzed using a linear matrix inequality(LMI) approach. The proposed stochastic stability analysis can help determine the proper probability of running random cryptographic protection against random zero-measurement attacks with a certain probability. Finally, a simulation example is presented based on a vertical take-off and landing(VTOL) system. The results show the effectiveness, robustness, and application of the proposed method, and are helpful in choosing the proper protection mechanism taking into account the time delay and in determining the system sampling period to increase the resistance against such attacks.