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Existence Results of Damped Second Order Impulsive Functional Differential Equations with Infinite Delay

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Acta Mathematicae Applicatae Sinica 2019年第3期35卷 564-579页

作者： Sheng-li xie Yi-ming xie School of Mathematics&Physics Urban Construction CollegeAnhui Jianzhu University School of Civil Engineering Anhui Jianzhu UniversityHefei 230601China

Using the Monch fixed point theorem and progressive estimation method,we study the existence,uniqueness and regularity of mild solutions for damped second order impulsive functional differential equations with infinite delay in Banach *** compactness assumption on associated family of operators and the impulsive term,some restrictive conditions on a priori estimation,noncompactness measure estimation and the impulsive term have not been used,our results are different from some known ***,a noncompact semigroup example explains the obtained results.

关键词： damped second order impulsive functional differential equations mild solution strong solution classical solution measure of noncompactness

Probability of rebound and eject of sand particles in wind-blown sand movement

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Acta Mechanica Sinica 2007年第5期23卷 471-475页

作者： li xie Xiaojing Zheng Key Laboratory of Mechanics on Western Disaster and Environment Lanzhou University Lanzhou 730000 China

When incident particles impact into a sand bed in wind-blown sand movement, rebound of the incident particles and eject of the sand particles by the incident particles affect directly the development of wind sand flux. In order to obtain rebound and eject lift-off probability of the sand particles, we apply the particle-bed stochastic collision model presented in our pervious works to derive analytic solutions of velocities of the incident and impacted particles in the postcollision bed. In order to describe randomness inherent in the real particle-bed collision, we take the incident angle, the impact position and the direction of resultant action of sand particles in sand bed on the impacted sand particle as ran- dom variables, and calculate the rebound and eject velocities, angles and coefficients （ratio of rebound and eject velocity to incident velocity）. Numerical results are found in accordance with current experimental results. The rebound and eject liftoff probabilities versus the incident and creeping velocities are predicted.

关键词： Wind-blown sand movement Rebound andeject coefficient Rebound and eject lift-off probability

PEAK COVARIANCE STABIliTY OF A RANDOM RICCATI EQUATION ARISING FROM KALMAN FILTERING WITH OBSERVATION LOSSES

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Journal of Systems Science & Complexity 2007年第2期20卷 262-272页

作者： li xie lihua xie School of Electrical and Electronic Engineering Nanyang Technological University Nanyang Avenue 639798 Singapore

We consider the stability of a random Riccati equation with a Markovian binary jump coefficient. More specifically, we are concerned with the boundedness of the solution of a random Riccati difference equation arising from Kalman filtering with measurement losses. A sufficient condition for the peak covariance stability is obtained which has a simpler form and is shown to be less conservative in some cases than a very recent result in existing literature. Furthermore, we show that a known sufficient condition is also necessary when the observability index equals one.

关键词： Kalman filtering observation losses Random Riccati equations stability stopping time

Extraction of vanadium from high calcium vanadium slag using direct roasting and soda leaching

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International Journal of Minerals,Metallurgy and Materials 2012年第7期19卷 595-601页

作者： Xin-sheng li Bing xie College of Materials Science and Engineering Chongqing University Chongqing 400044 China

The extraction of vanadium from high calcium vanadium slag was attempted by direct roasting and soda leaching. The oxidation process of the vanadium slag at different temperatures was investigated by X-ray diffraction （XRD）, scanning electron microscopy （SEM）, and energy dispersive spectroscopy （EDS）. The effects of roasting temperature, roasting time, Na2CO3 concentration, leaching tem- perature, leaching time, and liquid to solid ratio on the extraction of vanadium were studied. The results showed that olivine phases and spinel phases in the vanadium slag were completely decomposed at 500 and 800℃, respectively. Vanadium-rich phases were formed at above 850℃. The leaching rate of vanadium reached above 90% under the optimum conditions： roasting temperature of 850℃, roasting time of 60 min, Na2CO3 concentration of 160 g/L, leaching temperature of 95℃, leaching time of 150 min, and liquid to solid ratio of 10：1 mL/g. The main impurities were Si and P in the leach liquor.

关键词： vanadium metallurgy extraction slag roasting leaching

A new three-dimensional Hoek-Brown strength criterion

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Acta Mechanica Sinica 2012年第2期28卷 393-406页

作者： Hua Jiang Yong-li xie Key Laboratory for Bridgeand Tunnel of Shaanxi Province Chang'an University710064 Xi'anChina

The Hoek-Brown （HB） strength criterion has been widely applied to the estimation of strength of intact rock and rock mass, while evolving ever since. However, negligence of the effect of the intermediate principal stress still remains in the criterion＇s latest version. At the same time, several three-dimensional （3D） HB strength, which can takes into account the influence of the intermediate principal stress, have already been proposed, among which the 3D HB criterion proposed by Zhang and Zhu seems to be the most reasonable one. However, the Zhang 3D HB criterion may have problems with some stress path close to triaxial extension state because of the non-convexity characteristic of its failure surface. In this paper, a new 3D HB strength criterion is presented based on a generalized form of the HB criterion, which also considers the effect of the intermediate principal stress and inherits all the merits of the original version of the HB criterion. In addition, this new criterion can remedy to some extent the shortcomings observed in the Zhang 3D HB criterion. Polyaxial tests for five different rocks from pub- lished literatures are used for evaluating this new criterion and comparing it with the Zhang 3D HB criterion. The re- sults show that this new criterion may over-predict or under- predict the polyaxial strength of rocks but the errors are rela- tively small, and similar results are also found for the Zhang 3D HB criterion, which one is better depends on the type of the rock under estimation.

关键词： Hoek-Brown criterion Rock strength Merid-ian plane Octahedral plane

Experimental study on detonation parameters and cellular structures of fuel cloud

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Acta Mechanica Sinica 2012年第2期28卷 438-443页

作者： li-Feng xie Bin li Yu-Lei Zhang School of Chemical Engineering Nanjing University of Science and Technology210094 NanjingChina

In this paper, detonation parameters of fuel cloud, such as propylene oxide （PO）, isopropyl nitrate （IPN）, hex- ane, 90# oil and decane were measured in a self-designed and constructed vertical shock tube. Results show that the deto- nation pressure and velocity of PO increase to a peak value and then decrease smoothly with increasing equivalence ra- tio. Several nitrate sensitizers were added into PO to make fuel mixtures, and test results indicated that the additives can efficiently enhance detonation velocity and pressure of fuel cloud and one type of additive n-propyl nitrate （NPN） played the best in the improvement. The critical initiation energy that directly initiated detonation of all the test liquid fuel clouds showed a U-shape curve relationship with equiva- lence ratios. The optimum concentration lies on the rich-fuel side （;b 〉 1）. The critical initiation energy is closely related to molecular structure and volatility of fuels. IPN and PO have similar critical values while that of alkanes are larger. Detonation cell sizes of PO were respectively investigated at 25;C, 35;C and 50;C with smoked foil technique. The cell width shows a U-shape curve relationship with equivalence ratios at all temperatures. The minimal cell width also lies on the rich-fuel side （;b 〉 1）. The cell width of PO vapor is slightly larger than that of PO cloud. Therefore, the deto- nation reaction of PO at normal temperature is controlled by gas phase reaction.

关键词： Cloud detonation Detonation velocity Deto- nation pressure - Critical initiation energy Cell size

Experimental analysis of sand particles' lift-off and incident velocities in wind-blown sand flux

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Acta Mechanica Sinica 2005年第6期21卷 564-573页

作者： li xie Zhibao Dong Xiaojing Zheng Key Laboratory of Mechanics on Western Disaster and Environment Ministry of EducationDepartment of Mechanics Lanzhou UniversityLanzhou Gansu 730000 China Laboratory of Blown Sand Physics and Desert Environments Cold and Arid Regions Environment and EngineeringResearch Institute Chinese Academy of SciencesLanzhou Gansu 730000 China

The probability distributions of sand particles＇ lift-off and incident velocities in a wind-blown sand flux play very important roles in the simulation of the wind-blown sand movement. In this paper, the vertical and the horizontal speeds of sand particles located at 1.0 mm above a sand-bed in a wind-blown sand flux are observed with the aid of Phase Doppler Anemometry （PDA） in a wind tunnel. Based on the experimental data, the probability distributions of not only the vertical lift-off speed but also the lift-off velocity as well as its horizontal component and the incident velocity as well as its vertical and horizontal components can be obtained by the equal distance histogram method. It is found, according to the results of the X^2-test for these probability distributions, that the probability density functions （pdf＇s） of the sand particles＇ lift-off and incident velocities as well as their vertical com- ponents are described by the Gamma density function with different peak values and shapes and the downwind incident and lift-off horizontal speeds, respectively, can be described by the lognormal and the Gamma density functions, These pdf＇s depend on not only the sand particle diameter but also the wind speed.

关键词： Wind-blown sand movement - Tunnel experiment- Incident velocity. lift-off velocity Probability density

A rapid calculation method for predicting roll deformation of six-high rolling mill

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Journal of Iron and Steel Research International 2018年第9期25卷 901-909页

作者： li xie An-rui He Chao liu National Engineering Research Center for Advanced Rolling Technology University of Science and Technology BeijingBeijing 100083 China

The method to predict roll deformation precisely and efficiently is vital for the strip shape control of a six-high rolling mill. Traditional calculation methods of roll deformation, such as the finite element method and the influence function method, have been widely used due to their accuracies. However, the required calculation time is too long to be applied to the realtime control. Therefore, a rapid calculation method for predicting roll deformation of a six-high rolling mill was proposed, which employed the finite difference method to calculate the roll deflection and used a polynomial to describe the nonlinear relationship between roll flattening and roll contact pressure. Furthermore, a new correction strategy was proposed in the iteration, where the roll center flattening and the roll flattening deviation were put forward and corrected simultaneously in the iteration process according to the static equilibrium of roll. Finally, by the comparison with traditional methods, the proposed method was proved to be more efficient and it was suitable for the online calculation of the strip shape control.

关键词： Six-high rolling mill Roll deformation Influence function method Rapid calculation method Online model

Time-varying formation tracking for uncertain second-order nonlinear multi-agent systems

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Frontiers of Information Technology & Electronic Engineering 2019年第1期20卷 76-87页

作者： Mao-peng RAN li-hua xie Jun-cheng li School of Electrical and Electronic Engineering Nanyang Technological University

Our study is concerned with the time-varying formation tracking problem for second-order multi-agent systems that are subject to unknown nonlinear dynamics and external disturbance, and the states of the followers form a predefined time-varying formation while tracking the state of the leader. The total uncertainty lumps the unknown nonlinear dynamics and the external disturbance, and is regarded as an extended state of the agent. To estimate the total uncertainty, we design an extended state observer(ESO). Then we propose a novel ESO based time-varying formation tracking protocol. It is proved that, under the proposed protocol, the ESO estimation error and the time-varying formation tracking error can be made arbitrarily small. An application to the target enclosing problem for multiple unmanned aerial vehicles(UAVs) verifies the effectiveness and superiority of the proposed approach.

关键词： Multi-agent system Time-varying formation Formation tracking Nonlinear dynamics Extended state observer(ESO)