Function S-rough sets(Function Singular rough sets) are defined by R-function equivalence class which has dynamic characteristic, and a function is s law, function S-rough sets have law characteristic. Function S-roug...Function S-rough sets(Function Singular rough sets) are defined by R-function equivalence class which has dynamic characteristic, and a function is s law, function S-rough sets have law characteristic. Function S-rough sets has these forms: function one direction S-rough sets, function two direction S-rough sets and dual of function one direction S-rough sets. This paper presents the law characteristic of function one direction S-rough sets and puts forward the theorems of law-chain-attribute and law-belt. Function S-rough sets is s new research direction of the rough sets theory.展开更多
The multifractality of energy and thermal dissipation of fully developed intermittent turbulence is investigated in the urban canopy layer under unstable conditions by the singularity spectrum for the fractal dimensio...The multifractality of energy and thermal dissipation of fully developed intermittent turbulence is investigated in the urban canopy layer under unstable conditions by the singularity spectrum for the fractal dimensions of sets of singularities characterizing multifractals. In order to obtain high-order moment properties of smallscale turbulent dissipation in the inertial range, an ultrasonic anemometer with a high sampling frequency of 100 Hz was used. The authors found that the turbulent signal could be singular everywhere. Moreover, the singular exponents of energy and thermal dissipation rates are most frequently encountered at around 0.2, which is significantly smaller than the singular exponents for a wind tunnel at a moderate Reynolds number. The evidence indicates a higher intermittency of turbulence in the urban canopy layer at a high Reynolds number, which is demonstrated by the data with high temporal resolution. Furthermore, the temperature field is more intermittent than the velocity field. In addition, a large amount of samples could be used for verification of the results.展开更多
The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitut...The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method （VSM）, and steepest descent integration method （SDIM） were used to evaluate this type of Green＇s function. For SDIM, the complex domain was restricted only on the 0-plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating struc- tures moving in waves.展开更多
基金Supported by the Nature Science Foundation of Henan Province(0511012700).
文摘Function S-rough sets(Function Singular rough sets) are defined by R-function equivalence class which has dynamic characteristic, and a function is s law, function S-rough sets have law characteristic. Function S-rough sets has these forms: function one direction S-rough sets, function two direction S-rough sets and dual of function one direction S-rough sets. This paper presents the law characteristic of function one direction S-rough sets and puts forward the theorems of law-chain-attribute and law-belt. Function S-rough sets is s new research direction of the rough sets theory.
基金supported by the National Natural Science Foundation of China(Grant Nos.11472272 and 91215302)the Special Fund for Meteorological Research in the Public Interest(Grant No.GYHY201206041)
文摘The multifractality of energy and thermal dissipation of fully developed intermittent turbulence is investigated in the urban canopy layer under unstable conditions by the singularity spectrum for the fractal dimensions of sets of singularities characterizing multifractals. In order to obtain high-order moment properties of smallscale turbulent dissipation in the inertial range, an ultrasonic anemometer with a high sampling frequency of 100 Hz was used. The authors found that the turbulent signal could be singular everywhere. Moreover, the singular exponents of energy and thermal dissipation rates are most frequently encountered at around 0.2, which is significantly smaller than the singular exponents for a wind tunnel at a moderate Reynolds number. The evidence indicates a higher intermittency of turbulence in the urban canopy layer at a high Reynolds number, which is demonstrated by the data with high temporal resolution. Furthermore, the temperature field is more intermittent than the velocity field. In addition, a large amount of samples could be used for verification of the results.
基金Project supported by the National Natural Science Foundation of China （No. 50879090）, and the Key Research Program of Hydrody- namics of China （No. 9140A 14030712JB 11044）
文摘The singularities and oscillatory performance of translating-pulsating source Green＇s function in Bessho form were analyzed. Relative numerical integration methods such as Gaussian quadrature rule, variable substitution method （VSM）, and steepest descent integration method （SDIM） were used to evaluate this type of Green＇s function. For SDIM, the complex domain was restricted only on the 0-plane. Meanwhile, the integral along the real axis was computed by use of the VSM to avoid the complication of a numerical search of the steepest descent line. Furthermore, the steepest descent line was represented by the B-spline function. Based on this representation, a new self-compatible integration method corresponding to parametric t was established. The numerical method was validated through comparison with other existing results, and was shown to be efficient and reliable in the calculation of the velocity potentials for the 3D seakeeping and hydrodynamic performance of floating struc- tures moving in waves.
