The changing law of internal forces during the whole deformation development process was analyzed. The process was divided into five stages based on the internal force state of the beam and the assumptions of internal...The changing law of internal forces during the whole deformation development process was analyzed. The process was divided into five stages based on the internal force state of the beam and the assumptions of internal force relationship of five stages were proposed. Then, the formulas for determining the midspan deflection of the steel beam under distributed load, which was restrained both in rotational and axial directions, were obtained using restraint coefficient method and rigid-plastic mechanism, thereby the deformation development process was expressed accurately in a quantified way. Priority was given to the analysis of the process from bending to tension-bending, then the final state totally depends on tension to resist the external loads, that is the problem of catenary action of the restrained beam under distributed load. Additionally, finite element analysis was carried out with soitware ABAQUS6.7 on a restrained steel beam under distributed load with different axial and rotational restraint coefficients. The accuracy of the formulas presented was verified by the results of the behavior of the restrained beams. Finally, error analysis was conducted and some formulas were corrected according to the reasons of errors. The calculated results of corrected formulas match the FEM analysis results better, thus the accuracy of these formulas is improve .展开更多
This study investigates the wind energy input, an important source of mechanical energy, in the coastal seas east of China. Using the wind field from the high-resolution sea surface meteorology dataset in the Bohai Se...This study investigates the wind energy input, an important source of mechanical energy, in the coastal seas east of China. Using the wind field from the high-resolution sea surface meteorology dataset in the Bohai Sea, Yellow Sea, and East China Sea, we studied the wind energy input through surface ageostrophic currents and surface waves. Using a simple analytical formula for the Ekman Spiral with time- dependent wind, the wind energy input through ageostrophic currents was estimated at -22 GW averaged from 1960 to 2007, and through use of an empirical formula, the wind energy input through surface waves was estimated at -169 GW. We also examined the seasonal variation and long-term tendency of mechanical energy from wind stress, and found that the wind energy input to the East China Sea decreased before the 1980s, and then subsequently increased, which is contrary to what has been found for the Bohai Sea and Yellow Sea. More complicated physical processes and varying diffusivity need to be taken into account in future studies.展开更多
Some complete variational formulas and approximation theorems for the first eigenvalue of elliptic operators in dimension one or a class of Markov chains are presented.
We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a...We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a（r） and Ramanujan＇s cubic transformation. Besides, a new cubic transformation formula of hypergeometric function is given, which complements the Ramanujan＇s cubic transformation.展开更多
This paper considers the problem of estimating the bounds on the average controlled direct effects （ACDEs） of a treatment variable on an unobserved response variable in the presence of unobserved confounders between...This paper considers the problem of estimating the bounds on the average controlled direct effects （ACDEs） of a treatment variable on an unobserved response variable in the presence of unobserved confounders between an intermediate variable and the response variable. When the response variable is observed, Cai, et al.（2008） derived the formulas for the sharp bounds on the ACDEs. When the response variable is unobserved, the authors propose a graphical criterion for selecting variables affected by the response variable to derive the formulas for the bounds on the ACDEs, which is an extension of the result of Kuroki（2005） to ACDEs. The results enable us not only to judge from the graph structure whether the bounds on the ACDEs can be expressed through observed variables when the response variable is unobserved, but also to provide their formulas when the answer is affirmative.展开更多
In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system...In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system of the admitted one-dimensional subalgebras.Secondly,by analyzing the reduced equation,three types of similarity solutions are derived,such as multi-soliton like solutions,variable separations solutions,and KdV type solutions.展开更多
基金Project(2006BAJ01B02)supported by the National Science and Technology Pillar Program during the Eleventh Five-Year Plan Period of China
文摘The changing law of internal forces during the whole deformation development process was analyzed. The process was divided into five stages based on the internal force state of the beam and the assumptions of internal force relationship of five stages were proposed. Then, the formulas for determining the midspan deflection of the steel beam under distributed load, which was restrained both in rotational and axial directions, were obtained using restraint coefficient method and rigid-plastic mechanism, thereby the deformation development process was expressed accurately in a quantified way. Priority was given to the analysis of the process from bending to tension-bending, then the final state totally depends on tension to resist the external loads, that is the problem of catenary action of the restrained beam under distributed load. Additionally, finite element analysis was carried out with soitware ABAQUS6.7 on a restrained steel beam under distributed load with different axial and rotational restraint coefficients. The accuracy of the formulas presented was verified by the results of the behavior of the restrained beams. Finally, error analysis was conducted and some formulas were corrected according to the reasons of errors. The calculated results of corrected formulas match the FEM analysis results better, thus the accuracy of these formulas is improve .
基金Supported by the National 111 Project of China(No.B07036)the National Natural Science Foundation of China(Nos.40930844,40976004)the Research Fund for the Doctoral Program of Higher Education of China(No.20110132130001)
文摘This study investigates the wind energy input, an important source of mechanical energy, in the coastal seas east of China. Using the wind field from the high-resolution sea surface meteorology dataset in the Bohai Sea, Yellow Sea, and East China Sea, we studied the wind energy input through surface ageostrophic currents and surface waves. Using a simple analytical formula for the Ekman Spiral with time- dependent wind, the wind energy input through ageostrophic currents was estimated at -22 GW averaged from 1960 to 2007, and through use of an empirical formula, the wind energy input through surface waves was estimated at -169 GW. We also examined the seasonal variation and long-term tendency of mechanical energy from wind stress, and found that the wind energy input to the East China Sea decreased before the 1980s, and then subsequently increased, which is contrary to what has been found for the Bohai Sea and Yellow Sea. More complicated physical processes and varying diffusivity need to be taken into account in future studies.
基金This work was supported in part bythe National Natural Science Foundation of China (Grant No. 19631060) Mathematical Tian Yuan Foundation, Qiu Shi Science & Technology Foundation, RFDP and MCEC.
文摘Some complete variational formulas and approximation theorems for the first eigenvalue of elliptic operators in dimension one or a class of Markov chains are presented.
基金supported by National Natural Science Foundation of China(Grant Nos.11371125,11171307 and 61374086)Natural Science Foundation of Zhejiang Province(Grant No.LY13A010004)+1 种基金Natural Science Foundation of Hunan Province(Grant No.12C0577)PhD Students Innovation Foundation of Hunan Province(Grant No.CX2012B153)
文摘We study the quotient of hypergeometric functions in the theory of Ramanujan＇s generalized modular equation for a ∈ （0, 1/2], and find an infinite product for- mula for μ1/3（r） by use of the properties of μ＊a（r） and Ramanujan＇s cubic transformation. Besides, a new cubic transformation formula of hypergeometric function is given, which complements the Ramanujan＇s cubic transformation.
基金This research was partially supported by the National Natural Science Foundation of China under Grant Nos. 10871038, 10926186, and 11025102, the National 973 Key Project of China under Grant No. 2007CB311002, and the Jilin Project （20100401）.
文摘This paper considers the problem of estimating the bounds on the average controlled direct effects （ACDEs） of a treatment variable on an unobserved response variable in the presence of unobserved confounders between an intermediate variable and the response variable. When the response variable is observed, Cai, et al.（2008） derived the formulas for the sharp bounds on the ACDEs. When the response variable is unobserved, the authors propose a graphical criterion for selecting variables affected by the response variable to derive the formulas for the bounds on the ACDEs, which is an extension of the result of Kuroki（2005） to ACDEs. The results enable us not only to judge from the graph structure whether the bounds on the ACDEs can be expressed through observed variables when the response variable is unobserved, but also to provide their formulas when the answer is affirmative.
基金Supported by Shandong Provincial Natural Science Foundation under Grant Nos. ZR2011AQ017 and ZR2010AM028
文摘In this paper,some new formal similarity reduction solutions for the(2+1)-dimensional Nizhnik-Novikov-Veselov equation are derived.Firstly,we derive the similarity reduction of the NNV equation with the optimal system of the admitted one-dimensional subalgebras.Secondly,by analyzing the reduced equation,three types of similarity solutions are derived,such as multi-soliton like solutions,variable separations solutions,and KdV type solutions.
