We establish the dimension formula of the space of C^r bivsriate piecewise polynomials of total degree 3r defined on a so-called QT triangulation Δ*. Our approach is to construct a minimal determining set and an asso...We establish the dimension formula of the space of C^r bivsriate piecewise polynomials of total degree 3r defined on a so-called QT triangulation Δ*. Our approach is to construct a minimal determining set and an associated explicit basis for the space S3r^3(Δ*).展开更多
This paper establishes a short-term prediction model of weekly retail prices for eggs based on chaotic neural network with the weekly retail prices of eggs from January 2008 to December 2012 in China.In the process of...This paper establishes a short-term prediction model of weekly retail prices for eggs based on chaotic neural network with the weekly retail prices of eggs from January 2008 to December 2012 in China.In the process of determining the structure of the chaotic neural network,the number of input layer nodes of the network is calculated by reconstructing phase space and computing its saturated embedding dimension,and then the number of hidden layer nodes is estimated by trial and error.Finally,this model is applied to predict the retail prices of eggs and compared with ARIMA.The result shows that the chaotic neural network has better nonlinear fitting ability and higher precision in the prediction of weekly retail price of eggs.The empirical result also shows that the chaotic neural network can be widely used in the field of short-term prediction of agricultural prices.展开更多
For deep mining engineering, heat transfer of coal mass is a vital factor in the thermal environment of coal mines. In order to study the thermal conduction mechanism, we obtained gray images of coal mass microstructu...For deep mining engineering, heat transfer of coal mass is a vital factor in the thermal environment of coal mines. In order to study the thermal conduction mechanism, we obtained gray images of coal mass microstructure by scanning samples with a digital microscope. With the use of Matlab, these gray images were transformed into binary images, which were then transformed into a corresponding matrix consisting only of the values 0 and 1. According to the calculation method of box-counting dimension, we calculated the fractal dimension of the loose coal to be approximately 1.86. The thermal conductivity expressions of loose coal were derived based on the simulation method of thermal resistance. We calculated the thermal conductivity of loose coal by using a fractal model and compared the calculated values with our experimental data. The results show that the test data show an encourag-ing agreement with the calculated values. Hence fractal theory is a feasible method for studying thermal conductivity of loose coal.展开更多
A novel analytical model to determine the heat flux of subcooled pool boiling in fractal nanofluids is developed.The model considers the fractal character of nanofluids in terms of the fractal dimension of nanoparticl...A novel analytical model to determine the heat flux of subcooled pool boiling in fractal nanofluids is developed.The model considers the fractal character of nanofluids in terms of the fractal dimension of nanoparticles and the fractal dimension of active cavities on the heated surfaces;it also takes into account the effect of the Brownian motion of nanoparticles,which has no empirical constant but has parameters with physical meanings.The proposed model is expressed as a function of the subcooling of fluids and the wall superheat.The fractal analytical model is verified by a reasonable agreement with the experimental data and the results obtained from existing models.展开更多
One dimensional non-steady, non-Darcy flow of water in a rock stratum was reduced into a system described by six ordinary differential equations involving five controlling parameters. Through response computations and...One dimensional non-steady, non-Darcy flow of water in a rock stratum was reduced into a system described by six ordinary differential equations involving five controlling parameters. Through response computations and time series analysis, chaotic behavior in the reduced system was discussed in details. Firstly, the dynamical response of the reduced system under a set of parameters was calculated, and the power spectrum of the attractor was obtained through fast Lagrangian transformation; then the phase space was reconstructed by fixing embedding dimension to be 6 and delay time to range from 1 to 20, and the correlation dimension of the attractor was calculated based on the curves under the coordinates of logarithm of correlation integral vs. logarithm of covering radius; and lastly, the Lyapunov indices of the attractor were calculated by using Gram-Schmit's orthogonalization method. The results show that the power spectrum of the attractor is continuous; the correlation dimension of the attractor is equal to 2.36; among the Lyapunov indices, LE1, LE2, LE3 are positive, LE5, LE6 are negative, and LE4 fluctuates near zero. All the analysis indicates that there may exist chaos in the system of non-steady, non-Darcy flow.展开更多
In order to quantify the characteristics of the surface of jointed rock mass,new equipment,the three-dimensional laser surface topography instrument,was used to accurately measure surface morphology of joints.Scan pic...In order to quantify the characteristics of the surface of jointed rock mass,new equipment,the three-dimensional laser surface topography instrument,was used to accurately measure surface morphology of joints.Scan pictures and parameters were obtained to describe the rock joint surface characteristics,for example,the height frequency of surface,and mean square roughness.Using the method of fractal dimension,the values of joint roughness coefficient(JRC) were calculated based on the above parameters.It could access to the joint surface rock sample morphology of the main parameters of characteristic.The maximum peak height is 2.692 mm in the test joint plane.The maximum profile height is 4.408 mm.JRC value is 6.38 by fractal dimension computing.It belongs to the smooth joint surface.The results show that it is a kind of the effective method to quantitatively evaluate the surface topography by the three-dimensional laser surface topography instrument and the fractal dimension method.According to the results,during the process of underground large-scale mining,safe measures to prevent slip failure of the joint plane by controlling surface tension and shear mechanical response were proposed.展开更多
文摘We establish the dimension formula of the space of C^r bivsriate piecewise polynomials of total degree 3r defined on a so-called QT triangulation Δ*. Our approach is to construct a minimal determining set and an associated explicit basis for the space S3r^3(Δ*).
基金financially supported by the National KeyTechnology R&D Program during the 12th Five-Year Plan period(2012BAH20B04)the 948 Program of Ministry of Agriculture,China(2013-Z1)
文摘This paper establishes a short-term prediction model of weekly retail prices for eggs based on chaotic neural network with the weekly retail prices of eggs from January 2008 to December 2012 in China.In the process of determining the structure of the chaotic neural network,the number of input layer nodes of the network is calculated by reconstructing phase space and computing its saturated embedding dimension,and then the number of hidden layer nodes is estimated by trial and error.Finally,this model is applied to predict the retail prices of eggs and compared with ARIMA.The result shows that the chaotic neural network has better nonlinear fitting ability and higher precision in the prediction of weekly retail price of eggs.The empirical result also shows that the chaotic neural network can be widely used in the field of short-term prediction of agricultural prices.
基金support for this study, provided by the National Natural Science Foundation of China (Nos50534040 and 50974117)the Research Fund of the State Key Laboratory of Coal Resources & Mine Safety, CUMT (No07KF10)
文摘For deep mining engineering, heat transfer of coal mass is a vital factor in the thermal environment of coal mines. In order to study the thermal conduction mechanism, we obtained gray images of coal mass microstructure by scanning samples with a digital microscope. With the use of Matlab, these gray images were transformed into binary images, which were then transformed into a corresponding matrix consisting only of the values 0 and 1. According to the calculation method of box-counting dimension, we calculated the fractal dimension of the loose coal to be approximately 1.86. The thermal conductivity expressions of loose coal were derived based on the simulation method of thermal resistance. We calculated the thermal conductivity of loose coal by using a fractal model and compared the calculated values with our experimental data. The results show that the test data show an encourag-ing agreement with the calculated values. Hence fractal theory is a feasible method for studying thermal conductivity of loose coal.
基金Project supported by the National Natural Science Foundation of China (Grant No.11102100)the Natural Science Foundation of Fujian Province,China (Grant No.2012J01017)the Scientific Research Special Foundation for Provincial University of Education Department of Fujian Province,China (Grant No.JK2011056)
文摘A novel analytical model to determine the heat flux of subcooled pool boiling in fractal nanofluids is developed.The model considers the fractal character of nanofluids in terms of the fractal dimension of nanoparticles and the fractal dimension of active cavities on the heated surfaces;it also takes into account the effect of the Brownian motion of nanoparticles,which has no empirical constant but has parameters with physical meanings.The proposed model is expressed as a function of the subcooling of fluids and the wall superheat.The fractal analytical model is verified by a reasonable agreement with the experimental data and the results obtained from existing models.
基金supported by the National Natural Science Foundation of China (No.50874104)
文摘One dimensional non-steady, non-Darcy flow of water in a rock stratum was reduced into a system described by six ordinary differential equations involving five controlling parameters. Through response computations and time series analysis, chaotic behavior in the reduced system was discussed in details. Firstly, the dynamical response of the reduced system under a set of parameters was calculated, and the power spectrum of the attractor was obtained through fast Lagrangian transformation; then the phase space was reconstructed by fixing embedding dimension to be 6 and delay time to range from 1 to 20, and the correlation dimension of the attractor was calculated based on the curves under the coordinates of logarithm of correlation integral vs. logarithm of covering radius; and lastly, the Lyapunov indices of the attractor were calculated by using Gram-Schmit's orthogonalization method. The results show that the power spectrum of the attractor is continuous; the correlation dimension of the attractor is equal to 2.36; among the Lyapunov indices, LE1, LE2, LE3 are positive, LE5, LE6 are negative, and LE4 fluctuates near zero. All the analysis indicates that there may exist chaos in the system of non-steady, non-Darcy flow.
基金Project(2011QNZT087) supported by the Freedom Explore Program of Central South University of ChinaProject(51074178) supported by the National Natural Science Foundation of China+1 种基金Project(09JJ4025) supported by Hunan Provincial Natural Science Foundation of ChinaProject(2010QZZD001) supported by the Fundamental Research Funds for the Central Universities of China
文摘In order to quantify the characteristics of the surface of jointed rock mass,new equipment,the three-dimensional laser surface topography instrument,was used to accurately measure surface morphology of joints.Scan pictures and parameters were obtained to describe the rock joint surface characteristics,for example,the height frequency of surface,and mean square roughness.Using the method of fractal dimension,the values of joint roughness coefficient(JRC) were calculated based on the above parameters.It could access to the joint surface rock sample morphology of the main parameters of characteristic.The maximum peak height is 2.692 mm in the test joint plane.The maximum profile height is 4.408 mm.JRC value is 6.38 by fractal dimension computing.It belongs to the smooth joint surface.The results show that it is a kind of the effective method to quantitatively evaluate the surface topography by the three-dimensional laser surface topography instrument and the fractal dimension method.According to the results,during the process of underground large-scale mining,safe measures to prevent slip failure of the joint plane by controlling surface tension and shear mechanical response were proposed.
