We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small a-stable noises, observed at n regularly spaced time points ti = i/n, i = 1,...,n on [0, 1]. U...We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small a-stable noises, observed at n regularly spaced time points ti = i/n, i = 1,...,n on [0, 1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator （LSE） when a small dispersion parameter ε→0 and n →∞ simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal.展开更多
This paper studies the dynamic stress intensity factor （DSIF） at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the i...This paper studies the dynamic stress intensity factor （DSIF） at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the integral transform, the problem is reduced to algebraic equations and can be solved with the collocation dots method in the Laplace domain. Time response of DSIF is calculated with the inverse Laplace integral transform. The results show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, while decreases with the swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is -0.5 and independent on the material parameters, damage conditions of materials, and time. The oscillatory index is controlled by viscoelastic material parameters.展开更多
The movement of lubricated fibres in a fibre assembly is investigated theoretically and aviscous sliding model of friction is proposed.Previous work and experimental results are discussedin relation to the model.Resul...The movement of lubricated fibres in a fibre assembly is investigated theoretically and aviscous sliding model of friction is proposed.Previous work and experimental results are discussedin relation to the model.Results of drawing experiments carried out on wool slivers are also pres-ented and discussed.展开更多
Landslides are one of the most widespread and dangerous phenomena in the urbanized territories. In Moscow they affect about 3% of the most valuable territory, including churches and historical buildings located at hig...Landslides are one of the most widespread and dangerous phenomena in the urbanized territories. In Moscow they affect about 3% of the most valuable territory, including churches and historical buildings located at high banks of the Moskva River. Recently the landslide activation occurred. Normal functioning of city infrastructure and implementation of effective slope protection measures require special landslide monitoring. Mechanical-mathematical model of high viscous fluid was applied for the landslide-prone slopes modeling. Equation of continuityand an approximatedNavier-Stockes equation f or slow motions in a thin layer were used. The results of modelling give possibility to define the landslide section with upmost velocity that should be monitored in the first place. Some important parameters used for numerical modelling can be defined from monitoring data.展开更多
A transformation way of the Navier-Stokes differential equation was presented. The obtained result is the Cauchy momentum equation. The transformation was performed using a novel shorten mathematical notation presente...A transformation way of the Navier-Stokes differential equation was presented. The obtained result is the Cauchy momentum equation. The transformation was performed using a novel shorten mathematical notation presented at the beginning of the transformation.展开更多
基金supported by FAU Start-up funding at the C. E. Schmidt Collegeof Science
文摘We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small a-stable noises, observed at n regularly spaced time points ti = i/n, i = 1,...,n on [0, 1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator （LSE） when a small dispersion parameter ε→0 and n →∞ simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal.
基金the National Natural Science Foundation of China(No.10672027)the National Basic Research Program of China(No.2006CB601205)the National Science Fund for Distin-guished Young Scholars of China(No.50625414)
文摘This paper studies the dynamic stress intensity factor （DSIF） at the interface in an adhesive joint under shear loading. Material damage is considered. By introducing the dislocation density function and using the integral transform, the problem is reduced to algebraic equations and can be solved with the collocation dots method in the Laplace domain. Time response of DSIF is calculated with the inverse Laplace integral transform. The results show that the mode Ⅱ DSIF increases with the shear relaxation parameter, shear module and Poisson ratio, while decreases with the swell relaxation parameter. Damage shielding only occurs at the initial stage of crack propagation. The singular index of crack tip is -0.5 and independent on the material parameters, damage conditions of materials, and time. The oscillatory index is controlled by viscoelastic material parameters.
文摘The movement of lubricated fibres in a fibre assembly is investigated theoretically and aviscous sliding model of friction is proposed.Previous work and experimental results are discussedin relation to the model.Results of drawing experiments carried out on wool slivers are also pres-ented and discussed.
文摘Landslides are one of the most widespread and dangerous phenomena in the urbanized territories. In Moscow they affect about 3% of the most valuable territory, including churches and historical buildings located at high banks of the Moskva River. Recently the landslide activation occurred. Normal functioning of city infrastructure and implementation of effective slope protection measures require special landslide monitoring. Mechanical-mathematical model of high viscous fluid was applied for the landslide-prone slopes modeling. Equation of continuityand an approximatedNavier-Stockes equation f or slow motions in a thin layer were used. The results of modelling give possibility to define the landslide section with upmost velocity that should be monitored in the first place. Some important parameters used for numerical modelling can be defined from monitoring data.
文摘A transformation way of the Navier-Stokes differential equation was presented. The obtained result is the Cauchy momentum equation. The transformation was performed using a novel shorten mathematical notation presented at the beginning of the transformation.
