For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the paramet...For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the parametric equations of the system. First, the parametric equations of the Birkhoffian system in the event space are established, and the definition of integrating factors for the system is given; second the necessary conditions for the existence of conservation laws are studied in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the results.展开更多
Dynamical properties of liquid in nano-channels attract much interest because of their applications in engineering and biological systems. The transfer behavior of liquid confined within nanopores differs significantl...Dynamical properties of liquid in nano-channels attract much interest because of their applications in engineering and biological systems. The transfer behavior of liquid confined within nanopores differs significantly from that in the bulk. Based on the simple quasicrystal model of liquid, analytical expressions of self-diffusion coefficient both in bulk and in slit nanopore are derived from the Stokes–Einstein equation and the modified Eyring's equation for viscosity. The local self-diffusion coefficient in different layers of liquid and the global self-diffusion coefficient in the slit nanopore are deduced from these expressions. The influences of confinement by pore walls,pore widths, liquid density, and temperature on the self-diffusion coefficient are investigated. The results indicate that the self-diffusion coefficient in nanopore increases with the pore width and approaches the bulk value as the pore width is sufficiently large. Similar to that in bulk state, the self-diffusion coefficient in nanopore decreases with the increase of density and the decrease of temperature, but these dependences are weaker than that in bulk state and become even weaker as the pore width decreases. This work provides a simple method to capture the physical behavior and to investigate the dynamic properties of liquid in nanopores.展开更多
One of the most important reasons for the serious damage of embankment dams is their impermissible settlement.Therefore,it can be stated that the prediction of settlement of a dam is of paramount importance.This study...One of the most important reasons for the serious damage of embankment dams is their impermissible settlement.Therefore,it can be stated that the prediction of settlement of a dam is of paramount importance.This study aims to apply intelligent methods to predict settlement after constructing central core rockfill dams.Attempts were made in this research to prepare models for predicting settlement of these dams using the information of 35 different central core rockfill dams all over the world and Adaptive Neuro-Fuzzy Interface System(ANFIS) and Gene Expression Programming(GEP) methods.Parameters such as height of dam(H) and compressibility index(Ci) were considered as the input parameters.Finally,a form was designed using visual basic software for predicting dam settlement.With respect to the accuracy of the results obtained from the intelligent methods,they can be recommended for predicting settlement after constructing central core rockfill dams for the future plans.展开更多
The main purpose of current study is development of an intelligent model for estimation of shear wave velocity in limestone. Shear wave velocity is one of the most important rock dynamic parameters. Because rocks have...The main purpose of current study is development of an intelligent model for estimation of shear wave velocity in limestone. Shear wave velocity is one of the most important rock dynamic parameters. Because rocks have complicated structure, direct determination of this parameter takes time, spends expenditure and requires accuracy. On the other hand, there are no precise equations for indirect determination of it; most of them are empirical. By using data sets of several dams of Iran and neuro-genetic, adaptive neuro-fuzzy inference system (ANFIS), and gene expression programming (GEP) methods, models are rendered for prediction of shear wave velocity in limestone. Totally, 516 sets of data has been used for modeling. From these data sets, 413 ones have been utilized for building the intelligent model, and 103 have been used for their performance evaluation. Compressional wave velocity (Vp), density (7) and porosity (.n), were considered as input parameters. Respectively, the amount of R for neuro-genetic and ANFIS networks was 0.959 and 0.963. In addition, by using GEP, three equations are obtained; the best of them has 0.958R. ANFIS shows the best prediction results, whereas GEP indicates proper equations. Because these equations have accuracy, they could be used for prediction of shear wave velocity for limestone in the future.展开更多
In this paper, the author presents a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this proced...In this paper, the author presents a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can be reduced to some 2-dimensional Laplace-like equations or rotation and divergence equations, which are much convenient for the resolution.展开更多
Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational...Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational space curves and rational surfaces by implicitization with univaxiate resultant computations. This method is more efficient than the other algorithms in finding implicit equations for this class of rational curves and surfaces.展开更多
This paper deals with the estimation of crest settlement in a concrete face rockfill dam (CFRD), utilizing intelligent methods. Following completion of dam construction, considerable movements of the crest and the b...This paper deals with the estimation of crest settlement in a concrete face rockfill dam (CFRD), utilizing intelligent methods. Following completion of dam construction, considerable movements of the crest and the body of the dam can develop during the first impoundment of the reservoir. Although there is vast experience worldwide in CFRD design and construction, few accurate experimental relationships are available to predict the settlement in CFRD. The goal is to advance the development of intelligent methods to estimate the subsidence of dams at the design stage. Due to dam zonifieation and uncertainties in material properties, these methods appear to be the appropriate choice. In this study, the crest settlement behavior of CFRDs is analyzed based on compiled data of 24 CFRDs constructed during recent years around the world, along with the utilization of gene ex- pression programming (GEP) and adaptive neuro-fuzzy inference system (ANFIS) methods. In addition, dam height (H), shape factor (St), and time (t, time after first operation) are also assessed, being considered major factors in predicting the settlement behavior. From the relationships proposed, the values ofR2 for both equations of GEP (with and without constant) were 0.9603 and 0.9734, and for the three approaches of ANFIS (grid partitioning (GP), subtractive clustering method (SCM), and fuzzy c-means clustering (FCM)) were 0.9693, 0.8657, and 0.8848, respectively. The obtained results indicate that the overall behavior evaluated by this approach is consistent with the measured data of other CFRDs.展开更多
Einstein's equation,in its standard form,breaks down at the Big Bang singularity.A new version,equivalent to Einstein's whenever the latter is defined,but applicable in wider situations,is proposed.The new equation ...Einstein's equation,in its standard form,breaks down at the Big Bang singularity.A new version,equivalent to Einstein's whenever the latter is defined,but applicable in wider situations,is proposed.The new equation remains smooth at the Big Bang singularity of the Friedmann-Lemaatre-Robertson-Walker model.It is a tensor equation defined in terms of the Ricci part of the Riemann curvature.It is obtained by taking the Kulkarni-Nomizu product between Einstein's equation and the metric tensor.展开更多
基金the Natural Science Foundation of Higher Education Institution of Jiangsu Province of China under Grant Nos.04KJA130135 and 08KJB13002
文摘For a Birkhoffing system in the event space, a general approach to the construction of conservation laws is presented. The conservation laws are constructed by finding corresponding integrating factors for the parametric equations of the system. First, the parametric equations of the Birkhoffian system in the event space are established, and the definition of integrating factors for the system is given; second the necessary conditions for the existence of conservation laws are studied in detail, and the relation between the conservation laws and the integrating factors of the system is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the system are established, and an example is given to illustrate the application of the results.
基金Supported by Guangdong Science and Technology Project(2012B050600012)
文摘Dynamical properties of liquid in nano-channels attract much interest because of their applications in engineering and biological systems. The transfer behavior of liquid confined within nanopores differs significantly from that in the bulk. Based on the simple quasicrystal model of liquid, analytical expressions of self-diffusion coefficient both in bulk and in slit nanopore are derived from the Stokes–Einstein equation and the modified Eyring's equation for viscosity. The local self-diffusion coefficient in different layers of liquid and the global self-diffusion coefficient in the slit nanopore are deduced from these expressions. The influences of confinement by pore walls,pore widths, liquid density, and temperature on the self-diffusion coefficient are investigated. The results indicate that the self-diffusion coefficient in nanopore increases with the pore width and approaches the bulk value as the pore width is sufficiently large. Similar to that in bulk state, the self-diffusion coefficient in nanopore decreases with the increase of density and the decrease of temperature, but these dependences are weaker than that in bulk state and become even weaker as the pore width decreases. This work provides a simple method to capture the physical behavior and to investigate the dynamic properties of liquid in nanopores.
文摘One of the most important reasons for the serious damage of embankment dams is their impermissible settlement.Therefore,it can be stated that the prediction of settlement of a dam is of paramount importance.This study aims to apply intelligent methods to predict settlement after constructing central core rockfill dams.Attempts were made in this research to prepare models for predicting settlement of these dams using the information of 35 different central core rockfill dams all over the world and Adaptive Neuro-Fuzzy Interface System(ANFIS) and Gene Expression Programming(GEP) methods.Parameters such as height of dam(H) and compressibility index(Ci) were considered as the input parameters.Finally,a form was designed using visual basic software for predicting dam settlement.With respect to the accuracy of the results obtained from the intelligent methods,they can be recommended for predicting settlement after constructing central core rockfill dams for the future plans.
文摘The main purpose of current study is development of an intelligent model for estimation of shear wave velocity in limestone. Shear wave velocity is one of the most important rock dynamic parameters. Because rocks have complicated structure, direct determination of this parameter takes time, spends expenditure and requires accuracy. On the other hand, there are no precise equations for indirect determination of it; most of them are empirical. By using data sets of several dams of Iran and neuro-genetic, adaptive neuro-fuzzy inference system (ANFIS), and gene expression programming (GEP) methods, models are rendered for prediction of shear wave velocity in limestone. Totally, 516 sets of data has been used for modeling. From these data sets, 413 ones have been utilized for building the intelligent model, and 103 have been used for their performance evaluation. Compressional wave velocity (Vp), density (7) and porosity (.n), were considered as input parameters. Respectively, the amount of R for neuro-genetic and ANFIS networks was 0.959 and 0.963. In addition, by using GEP, three equations are obtained; the best of them has 0.958R. ANFIS shows the best prediction results, whereas GEP indicates proper equations. Because these equations have accuracy, they could be used for prediction of shear wave velocity for limestone in the future.
文摘In this paper, the author presents a framework for getting a series of exact vacuum solutions to the Einstein equation. This procedure of resolution is based on a canonical form of the metric. According to this procedure, the Einstein equation can be reduced to some 2-dimensional Laplace-like equations or rotation and divergence equations, which are much convenient for the resolution.
基金supported by the Natural Science Foundation of China under Grant No. 10901163the Knowledge Innovation Program of the Chinese Academy of Sciences
文摘Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational space curves and rational surfaces by implicitization with univaxiate resultant computations. This method is more efficient than the other algorithms in finding implicit equations for this class of rational curves and surfaces.
文摘This paper deals with the estimation of crest settlement in a concrete face rockfill dam (CFRD), utilizing intelligent methods. Following completion of dam construction, considerable movements of the crest and the body of the dam can develop during the first impoundment of the reservoir. Although there is vast experience worldwide in CFRD design and construction, few accurate experimental relationships are available to predict the settlement in CFRD. The goal is to advance the development of intelligent methods to estimate the subsidence of dams at the design stage. Due to dam zonifieation and uncertainties in material properties, these methods appear to be the appropriate choice. In this study, the crest settlement behavior of CFRDs is analyzed based on compiled data of 24 CFRDs constructed during recent years around the world, along with the utilization of gene ex- pression programming (GEP) and adaptive neuro-fuzzy inference system (ANFIS) methods. In addition, dam height (H), shape factor (St), and time (t, time after first operation) are also assessed, being considered major factors in predicting the settlement behavior. From the relationships proposed, the values ofR2 for both equations of GEP (with and without constant) were 0.9603 and 0.9734, and for the three approaches of ANFIS (grid partitioning (GP), subtractive clustering method (SCM), and fuzzy c-means clustering (FCM)) were 0.9693, 0.8657, and 0.8848, respectively. The obtained results indicate that the overall behavior evaluated by this approach is consistent with the measured data of other CFRDs.
文摘Einstein's equation,in its standard form,breaks down at the Big Bang singularity.A new version,equivalent to Einstein's whenever the latter is defined,but applicable in wider situations,is proposed.The new equation remains smooth at the Big Bang singularity of the Friedmann-Lemaatre-Robertson-Walker model.It is a tensor equation defined in terms of the Ricci part of the Riemann curvature.It is obtained by taking the Kulkarni-Nomizu product between Einstein's equation and the metric tensor.