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Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The existence and uniqueness of the solutions to high-dimensional McKean-Vlasov stochastic differential equations with discontinuous drift coefficients and corresponding particle systems, were investigated. With the drift coefficient being piecewise Lipschitz continuous about the space variable, through Zvonkin’s transformation, the original equation was converted into a new McKean-Vlasov stochastic differential equation with Lipschitz continuous coefficients. Therefore, the new equation has a unique solution. Moreover, the existence and Lipschitz continuity of the inverse function were proven according to the transformation function characteristics. Finally, based on the It’s formula and the inverse function characteristics, the existence and uniqueness of the solutions to the McKean-Vlasov stochastic differential equation and the corresponding particle system were obtained. [ABSTRACT FROM AUTHOR]

The random source inverse method and properties for a class of stochastic differential equations driven by the fractional Brownian motion with Hurst index H∈(0, 1). This problem can be obtained from the transform of many stochastic models and is a widely followed problem. For the direct problem, the mild solution to the equation was obtained by means of constant variation, and according to the statistical properties of the mild solution, the well-posedness of the direct problem was discussed. For the inverse problem, some statistics of the random source term were determined from the random data at the final moment, to prove the uniqueness of the inverse problem, and the stability of the inverse problem with a(x) in different ranges was discussed. [ABSTRACT FROM AUTHOR]

This paperinvestigatedk-Hilfer fractional differential equations with Poisson jumps. By making use of the properties of fractional calculus, theDoob martingale measure inequality, theboundedness theorem and theCauchy-Schwarz inequality, the averaging principle of the system under considerationwas obtained. Finally, an example was given to illustrate the result. [ABSTRACT FROM AUTHOR]

For a class of unstable stochastic differential equations (SDEs)with jumps, the problem of stabilization with linear time-delay feedback controller is studied. Such an equation will have a unique solution, provided that its coefficients satisfy polynomial growth condition and Khasminskii type condition. By constructing integral Lyapunov functional, the coefficient matrix and time delay of the controller are determined. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Using the idea of step method, we discassed the existence and uniqueness of solutions of fractional neutral stochastic delay differential equations in the interval [0,τ],[τ,2τ],…,[（n-1）τ,nτ]. Combining Picard iterative method and integral operator theory, we proved that the solutions of fractional neutral stochastic delay differential equations are in existence and unique. The conclusions in existing literature are generalized and improved. [ABSTRACT FROM AUTHOR]

The asymptotic properties of the solutions to a class of perturbed stochastic impulsive functional differential equations were investigated. Through comparison of the solution to the perturbed equation with the solution to the corresponding unperturbed one, the sufficient conditions for these solutions to be close in a finite time interval were derived. Then, when small perturbations approach zero and the length of the time interval approaches infinity, the 2 solutions will still be close to each other. Finally, an example illustrates the effectiveness of the results. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Based on the deterministic network infectious disease model, a stochastic network infectious disease model under the influence of white noise was established, and the existence and uniqueness of the global solution to the model were proved. With the theory of stochastic differential equations, sufficient conditions for stochastic extinction and persistence of infectious diseases were obtained. The results show that, white noise has a great impact on the transmission dynamics of network infectious diseases. White noise can effectively suppress the spread of infectious diseases, and large white noise can even make the original persistent infectious diseases become extinct. Finally, the theoretical results were verified through numerical simulations. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The existent route convergence models are mainly deterministic ones, and various phenomena, such as packet losses, link noises, and sudden changes in interconnecting topology will occur in the route convergence process. Aimed at these random problems, a new stochastic dynamic system model was proposed by means of the Bernoulli white sequence distribution, the Wiener process and the Markov process. Based on the stochastic differential equation theory and the stochastic analysis methods, the sufficient conditions for the route convergence were given. The results prove that, the convergence of the routing state in a random environment is closely related to the Laplacian matrix of the router connection topology, the smooth distribution of the Markov switching, the successful transmission rate of the data packets, and the noise intensity in the network. Finally, a numerical example illustrates the effectiveness of the results. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Donghua University (Natural Science Edition) is the property of Journal of Donghua University (Natural Science) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Donghua University (Natural Science Edition) is the property of Journal of Donghua University (Natural Science) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A modified Euler-Maruyama ( EM) scheme was constructed for a class of multi-term fractional non-linear stochastic differential equations with weak singularity kernels, and the strong convergence of this modified EM scheme was proved. Specifically, according to the sufficient condition for stochastic integral decomposition, the multi-term fractional stochastic differential equation was equivalently transformed into the stochastic Volterra integral equation, and then the corresponding modified EM scheme and its strong convergence were derived and proved, respectively. The order of strong convergence is an, - αm - αm-1 where αi is the index of fractional derivative satisfying 0 < α1, < ... < αm-1 <α1 <1. Finally, numerical experiments verify the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Donghua University (Natural Science Edition) is the property of Journal of Donghua University (Natural Science) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The stabilization problem of a class of nonlinear stochastic delay differential equations driven by G? Brownain motion(G?SDDEs) was studied. Firstly,a delay feedback control was designed in the drift term of an unstable nonlinear G?SDDE, and the controlled system was therefore obtained. Then, with the Lyapunov technique,sufficient conditions for the asymptotical stability of the controlled system were given. Finally,two examples were presented to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

A stochastic uncertain dynamic model was put forward for power systems with asynchronous wind turbines. Based on the stochastic differential equation, matrix theory and other related theories, a Lyapunov function was constructed according to the probability stability theorem, and the stochastic small disturbance interval stability of the asynchronous wind turbine with parameter perturbation was analyzed by differential operator. Simulation results verified the validity of the proposed probabilistic stability theorem for power systems with parameter perturbation. [ABSTRACT FROM AUTHOR]

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The existence and uniqueness of solutions for a class fractional stochastic delay differential equations dx(t)=b(x(t),x(t-τ),t)dt+σ1(x(t),x(t-τ),t)dB(t)+σ2(x(t),x(t-τ),t)(dt)α of orderα∈(0,1) were studied. By introducing two new integral operators, the existence and uniqueness of solution of the equation was proved by using Picard successive approximation method and integral operator theory. The continuous dependence of the solution of the equation on the initial value was discussed. [ABSTRACT FROM AUTHOR]

Truncated Euler-Maruyama ( EM) method is an effective one for solving highly nonlinear stochastic differential equations. However, in such models as biological populations and stock prices, it is of practical significance when the solution of stochastic differential equation is positive. Therefore, it is significant to study the positivity preserving property of numerical solutions of stochastic differential equations with truncated EM method. By logarithmic transformation of stochastic differential equation, the exponential integrability of numerical solution and analytical solution of stochastic differential equation is proved under the condition of ensuring the convergence of truncated EM method, and the result that numerical solution can keep the positive of analytical solution is obtained. [ABSTRACT FROM AUTHOR]

The convergence of numerical solutions for Milstein Neutral Stochastic Delay Differential Equations with nonlinear coefficients is studied. A truncated Milstein numerical scheme is constructed for neutral stochastic delay differential equations with highly nonlinear coefficients by combining the truncation idea with the Milstein numerical scheme. Under the local Lipschitz condition and Khasminskii condition, it is proved that the truncated Milstein numerical solution Lp converges strongly to the exact solution for a neutral stochastic delay differential equation. The correctness of the conclusion is verified by numerical simulation for a specific neutral stochastic delay differential equation. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Guangdong University of Technology is the property of Journal of Guangdong University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to reflect the change process of the actual financial asset price, and solve the problem thal the return rate has no independent and stationarity increace and the random volatility of the actual financial asset price series, and improve the shortcomings of the traditional option pricing model in practical applications. Considers that the asset price follows stochastic differential equations driven by sub-fractional Brownian motion, and the volatility satisfied the Ornstein-Uhlenback (O-U) process, Stochastic analysis theory and Monte Carlo method are used to study European option, the empirical analysis is discussed using the 50ETF option. The Monte Carlo method is used to simulate European option prices, and compared with the European option price in other models. The result show that extended model is more adapted to the real financial market. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Jilin University (Science Edition) / Jilin Daxue Xuebao (Lixue Ban) is the property of Zhongguo Xue shu qi Kan (Guang Pan Ban) Dian zi Za zhi She and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Basic Sciences Journal of Textile Universities / Fangzhi Gaoxiao Jichu Kexue Xuebao is the property of Basic Sciences Journal of Textile Universities and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Xinyang Normal University Natural Science Edition is the property of Journal of Xinyang Normal University Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Based on the dynamics of inter-bank money flow, a bank money storage network model driven by fractional Brownian motion and involving central bank is proposed. Each bank borrows money from other banks at a specific rate and, in certain circumstances, can borrow money from the central bank, but that creates borrowing costs. The money store of the bank in the system satisfies the stochastic differential equation given in the paper. The mathematical expression of system risk index-the overall probability of bankruptcy and total system activity is given, the optimal cost of borrowing funds from the central bank is obtained by linear quadratic control method. [ABSTRACT FROM AUTHOR]

This paper describes atomic clock models and frequency stability analyses methods. The time de⁃ viation observation model is comprised of the deterministic part (the time deviation, the frequency devia⁃ tion, the linear frequency drift and the periodical part), the stochastic part which is the clock noise and the observation noise. This paper gives the Allan deviation expressions of these parts. The principle of utilizing Kalman filter to estimate the clock status is not illustrated in some paper clearly. Thus, this paper describes the atomic clock stochastic differential equations and parameters in detail. Then, we propose a method to estimate the clock noises and observation noise levels by means of the Kalman filter estimation results and Allan deviation pictures. Three methods of estimating the linear frequency drift level are proposed and vali⁃ dated by measurements. This paper also proposes the method of estimating the period and level of the peri⁃ odical part by means of the atomic clock stochastic differential equations, the Kalman filter estimation results and Allan deviation pictures. The real measurements of two domestic hydrogen masers are used to validate these methods. The principles of these methods are distinct. They are practical and easily to be realized. The methods can be used to obtain the estimated Allan deviation values at any observation interval. This research is the basis of a series of successive researches such as time scale algorithms, clock prediction algo⁃ rithms, steering algorithms. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Zhengzhou University (Natural Science Edition) is the property of Journal of Zhengzhou University (Natural Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Henan University of Science & Technology, Natural Science is the property of Editorial Office of Journal of Henan University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Basic Sciences Journal of Textile Universities / Fangzhi Gaoxiao Jichu Kexue Xuebao is the property of Basic Sciences Journal of Textile Universities and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Basic Sciences Journal of Textile Universities / Fangzhi Gaoxiao Jichu Kexue Xuebao is the property of Basic Sciences Journal of Textile Universities and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Henan University of Science & Technology, Natural Science is the property of Editorial Office of Journal of Henan University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Basic Sciences Journal of Textile Universities / Fangzhi Gaoxiao Jichu Kexue Xuebao is the property of Basic Sciences Journal of Textile Universities and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

An analog-equation-method (AEM)-based numerical scheme was proposed for initial value problems of stochastic fractional differential equations with 2 fractional derivative terms. 2 stochastic analog equations comprising respective undetermined functions were introduced, to convert the problem to a fractional differential equation with only 1 fractional derivative term. The Laplace transform and its inverse were employed to get the integration representations for the solution to the fractional differential equation and establish the relation between the 2 analog equations. In view of the initial conditions, an iterative algorithm to solve the initial value problem of the stochastic fractional differential equation was obtained. In a typical case, the numerical solution to a linear stochastic ordinary differential equation with 2 fractional derivative terms was derived based on the AEM. The numerical results of both the definite and stochastic systems demonstrate the effectiveness, stability and accuracy of the presented AEM scheme, of which the error only lies in the truncation error of the integration approximation and the rounding error of the computation software. [ABSTRACT FROM AUTHOR]

Via the analysis of the structure of networked control systems it presents the linear mathematic model with stochastic delay and packet losses. Based on the model the stochastic control problem with quadratic criteria of the networked control systems was analyzed. The expressions of optimal gain and op-timal performance index were given. Ultimately, the stochastic control effect of networked control systems with delay and diiferent probability of packet looses rate were compared by simulation. The simulation re-sults of Matlab show the eefectivenes of the stochastic control algorithm and the range of the critical value of the packet loos rate. [ABSTRACT FROM AUTHOR]

The Euler approximated solutions of stochastic differential equations with Markovian switching driven by Levy process are studied. The convergence of the Euler approximated solutions to the analytical solutions in the mean-square sense under non-Lipschitz conditions is obtained. Some known results are generalized and improved. [ABSTRACT FROM AUTHOR]

Auction is a realizable way of venture capital equity exit. The problems of information asymmetry and the indefinite nature of external environment in venture capital equity auction make it difficult for the outside investors to accurately price the risk corporate equity. Given this, the equity bidding system can be considered as an open system, thus the changing state of outside investors' bidding strategies can be described by stochastic differential equations. On this basis, this paper constructs a venture capital exit equity auction model, then discusses the formation mechanism of the corporate equity clearing price and its influence factors such as the degree of information disclosure, bidder's susceptible extent and so on, and finally analyses the expected revenue of venture capitalist by means of calculus of variations. [ABSTRACT FROM AUTHOR]

As uncertainties of inherent factors (such as loads, environment and material properties) always exist during driving axle's lifetime, a time-dependent model incorporating such uncertainties was established based on stochastic differential equation theory. Combined with the distribution parameters of multiple random variables, the time-dependent design method of driving axle parts under uncertainties in stress and strength was presented and it was illustrated by taking the shaft's time-dependent design as an example. It is indicated that this method, with good prospects, can make dynamic security evaluation of reliability for driving axle products. The shaft's time-dependent design reveals the impact of time scale on the design. Under the premise of meeting the performance requirements, it could effectively reduce the size of parts. [ABSTRACT FROM AUTHOR]

For 1/2≤θ≤1,by using the technique of stopping time and Burkholder-Davis-Gundy inequality as well as the theory of stochastic differential delay equation,the strong convergence of Caratheodory approximation solution of the mean-reverting θ process with delay in sense of p-th moment（p≥2） is proved. [ABSTRACT FROM AUTHOR]

Starting from numerical stability ,a]most sure exponential stability conditions of the Euler-Maruyama method for linear scalar SDEs are proved, and the stability regions of numerical solution for linear scalar SDEs are identi-ed, By comparing with the mean-square stability regions reported by Saito and Mitsui ,the almostsure stability regions in this paper is larger than the corresponding mean-square stability regions, andtherefore they are more valuable. [ABSTRACT FROM AUTHOR]

Stochastic differential equations(SDE) are applied to generate correlated random variables as receiver taper of fading channels. It is assumed that the random phases can be modeled through a Langevin equation and the amplitude gains follow a reasonable distribution, which are characterized by SDE. We further prove that the band-passed signals of tap in multiipath channel still follow Rayleigh distribution. Simulation results of statistical characteristics of correlated fading channel, such as correlation function and Doppler power spectrum, agree well with the theoretic values. The random phase is correlated Gaussian variables and the taper is the independent Rayleigh variables, which demonstrate the applicability of the proposed methodology. [ABSTRACT FROM AUTHOR]

The robust D-stability and H∞ control of uncertain discrete switched systems are studied in this paper. Based on multiple Lyapunov functions theory, a sufficient condition in form of multiple convex constraints of LMI is derived from robust D-stability and H∞ performance under arbitrary switching. Furthermore, a state-feedback controller is designed to make the closed uncertain system have robust D-stability and H∞ performance. A simulation example illustrates the feasibility and effectiveness of the designed controller. [ABSTRACT FROM AUTHOR]