Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the followi...Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equationand f is a smooth function on M under the assumptionthat the m-dimensional nonnegative Bakry-Emery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Emery Ricci curva- ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].展开更多
This study was conducted to examine the nutritional content, contamination levels, and biological effects of 3 local prepared formulas. Formula (1) contained mixed nuts;formula (2) contained moghat, honey and royal je...This study was conducted to examine the nutritional content, contamination levels, and biological effects of 3 local prepared formulas. Formula (1) contained mixed nuts;formula (2) contained moghat, honey and royal jelly, while formula (3) contained honey, fenugreek and royal jelly. Groups of albino rats (90 rats) were randomly allocated to diets of control group or 1 - 3 treatment groups. The tested diets contained 15% carbohydrate. The weight and food intake were recorded. Blood tests were conducted to determine total cholesterol, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol, triglycerides, glucose, urea, creatinine, white blood cell count (WBC), red blood cell count (RBC), haemoglobin (HB), mean corpuscular volume (MCV), and haematocrit (HCT). Results showed that bacterial contamination was found in formula (1) and formula (3). Fungal contamination was detected in formula (2) and formula (3). Body weight increased significantly in the rats fed treatment formulas compared to the control group. The blood tests indicated significant increases in the levels of glucose, WBC, HCT, total cholesterol, LDL cholesterol, and triglycerides as well as a significant decrease in HDL level in the group (2) was fed formula (1) the control. In conclusion, these findings indicate that these local formulas may not be safe, and further studies are required to understand the consequences of a long-term consumption of these formulas.展开更多
A weighted Koppelman-Leray-Norguet formula of (r, s) differential forms on a local q-concave wedge in a complex manifold is obtained. By constructing the new weighted kernels, the authors give a new weighted Koppelman...A weighted Koppelman-Leray-Norguet formula of (r, s) differential forms on a local q-concave wedge in a complex manifold is obtained. By constructing the new weighted kernels, the authors give a new weighted Koppelman-Leray-Norguet formula without boundary integral of (r, s) differential forms, which is different from the classical one. The new weighted formula is especially suitable for the case of the local g-concave wedge with a non-smooth boundary, so one can avoid complex estimates of boundary integrals and the density of integral may be not defined on the boundary but only in the domain. Moreover, the weighted integral formulas have much freedom in applications such as in the interpolation of functions.展开更多
We investigate the highest weight representations of the q-deformed Virasoro algebra of Hom-type. In order to determine its unitarity and irreducible highest weight representations, we present its Kac determinant form...We investigate the highest weight representations of the q-deformed Virasoro algebra of Hom-type. In order to determine its unitarity and irreducible highest weight representations, we present its Kac determinant formula when q is nonzero and non-root of unity.展开更多
The single safety factor criteria for slope stability evaluation, derived from the rigid limit equilibrium method or finite element method （FEM）, may not include some important information, especially for steep slop...The single safety factor criteria for slope stability evaluation, derived from the rigid limit equilibrium method or finite element method （FEM）, may not include some important information, especially for steep slopes with complex geological conditions. This paper presents a new reliability method that uses sample weight analysis. Based on the distribution characteristics of random variables, the minimal sample size of every random variable is extracted according to a small sample t-distribution under a certain expected value, and the weight coefficient of each extracted sample is considered to be its contribution to the random variables. Then, the weight coefficients of the random sample combinations are determined using the Bayes formula, and different sample combinations are taken as the input for slope stability analysis. According to one-to-one mapping between the input sample combination and the output safety coefficient, the reliability index of slope stability can be obtained with the multiplication principle. Slope stability analysis of the left bank of the Baihetan Project is used as an example, and the analysis results show that the present method is reasonable and practicable for the reliability analysis of steep slopes with complex geological conditions.展开更多
Based on the development of the offshore water drive reservoir, the determination of reasonable water injection of monolayer and single well affects the distribution of remaining oil and development effect of oil fiel...Based on the development of the offshore water drive reservoir, the determination of reasonable water injection of monolayer and single well affects the distribution of remaining oil and development effect of oil field water flooding, so this paper, using the grey correlation analysis method, studies the main factors influencing the dividing coefficient of water-injection and weight. This method takes into account the effective thickness, permeability, injection-production well spacing, the number of injection-production wells, and the direction of formation coefficient factors such as the influence of the dividing coefficient for injection. The formula for water-injection multi-factor controlled is established, at the same time, applying water injection formula of this article and the conventional on injection allocation of A-platform offshore injection wells. And the difference of single-well injection-allocation quantity in layers is analyzed. Based on a platform offshore, layers exist in the process of water flooding and the problems such as the contradiction between the layers, put forward the necessity of layered water injection through this article to determine water injection formula and injection allocation on a platform of injection wells by implementing effect which can be found. A platform for water flooding development of water cut under control, natural decline rate reduced to verify the reliability and practicability of the formula to determine injection in this paper. It has certain guiding significance to the offshore for the water-injection development oilfield.展开更多
基金supported by the Fundamental Research Fund for the Central Universities
文摘Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equationand f is a smooth function on M under the assumptionthat the m-dimensional nonnegative Bakry-Emery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Emery Ricci curva- ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].
文摘This study was conducted to examine the nutritional content, contamination levels, and biological effects of 3 local prepared formulas. Formula (1) contained mixed nuts;formula (2) contained moghat, honey and royal jelly, while formula (3) contained honey, fenugreek and royal jelly. Groups of albino rats (90 rats) were randomly allocated to diets of control group or 1 - 3 treatment groups. The tested diets contained 15% carbohydrate. The weight and food intake were recorded. Blood tests were conducted to determine total cholesterol, low-density lipoprotein cholesterol, high-density lipoprotein cholesterol, triglycerides, glucose, urea, creatinine, white blood cell count (WBC), red blood cell count (RBC), haemoglobin (HB), mean corpuscular volume (MCV), and haematocrit (HCT). Results showed that bacterial contamination was found in formula (1) and formula (3). Fungal contamination was detected in formula (2) and formula (3). Body weight increased significantly in the rats fed treatment formulas compared to the control group. The blood tests indicated significant increases in the levels of glucose, WBC, HCT, total cholesterol, LDL cholesterol, and triglycerides as well as a significant decrease in HDL level in the group (2) was fed formula (1) the control. In conclusion, these findings indicate that these local formulas may not be safe, and further studies are required to understand the consequences of a long-term consumption of these formulas.
基金National Natural Science Foundation and Mathematical "Tian Yuan" Foundation of China (10271097 and TY10126033)
文摘A weighted Koppelman-Leray-Norguet formula of (r, s) differential forms on a local q-concave wedge in a complex manifold is obtained. By constructing the new weighted kernels, the authors give a new weighted Koppelman-Leray-Norguet formula without boundary integral of (r, s) differential forms, which is different from the classical one. The new weighted formula is especially suitable for the case of the local g-concave wedge with a non-smooth boundary, so one can avoid complex estimates of boundary integrals and the density of integral may be not defined on the boundary but only in the domain. Moreover, the weighted integral formulas have much freedom in applications such as in the interpolation of functions.
基金Supported by the National Natural Science Foundation of China(11047030)Supported by the Science and Technology Program of Henan Province(152300410061)
文摘We investigate the highest weight representations of the q-deformed Virasoro algebra of Hom-type. In order to determine its unitarity and irreducible highest weight representations, we present its Kac determinant formula when q is nonzero and non-root of unity.
基金supported by the National Natural Science Foundation of China (Grant No. 90510017)
文摘The single safety factor criteria for slope stability evaluation, derived from the rigid limit equilibrium method or finite element method （FEM）, may not include some important information, especially for steep slopes with complex geological conditions. This paper presents a new reliability method that uses sample weight analysis. Based on the distribution characteristics of random variables, the minimal sample size of every random variable is extracted according to a small sample t-distribution under a certain expected value, and the weight coefficient of each extracted sample is considered to be its contribution to the random variables. Then, the weight coefficients of the random sample combinations are determined using the Bayes formula, and different sample combinations are taken as the input for slope stability analysis. According to one-to-one mapping between the input sample combination and the output safety coefficient, the reliability index of slope stability can be obtained with the multiplication principle. Slope stability analysis of the left bank of the Baihetan Project is used as an example, and the analysis results show that the present method is reasonable and practicable for the reliability analysis of steep slopes with complex geological conditions.
文摘Based on the development of the offshore water drive reservoir, the determination of reasonable water injection of monolayer and single well affects the distribution of remaining oil and development effect of oil field water flooding, so this paper, using the grey correlation analysis method, studies the main factors influencing the dividing coefficient of water-injection and weight. This method takes into account the effective thickness, permeability, injection-production well spacing, the number of injection-production wells, and the direction of formation coefficient factors such as the influence of the dividing coefficient for injection. The formula for water-injection multi-factor controlled is established, at the same time, applying water injection formula of this article and the conventional on injection allocation of A-platform offshore injection wells. And the difference of single-well injection-allocation quantity in layers is analyzed. Based on a platform offshore, layers exist in the process of water flooding and the problems such as the contradiction between the layers, put forward the necessity of layered water injection through this article to determine water injection formula and injection allocation on a platform of injection wells by implementing effect which can be found. A platform for water flooding development of water cut under control, natural decline rate reduced to verify the reliability and practicability of the formula to determine injection in this paper. It has certain guiding significance to the offshore for the water-injection development oilfield.
