To the serf-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium, when the hydraulic head at the boundary behaved like a power of time, Barenblatt obtained a powe...To the serf-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium, when the hydraulic head at the boundary behaved like a power of time, Barenblatt obtained a power series solution. However, he listed only the first three coefficients and did not give the recurrent formula among the coefficients. A formal proof of convergence of the series did not appear in his works. In this paper, the recurrent formula for the coefficients is obtained by using the method of power series expansion, and the convergence of the series is proven. The results can be easily understood and used by engineers in the catchment hydrology and baseflow studies as well as to solve agricultural drainage problems.展开更多
Based on the“three box”exergy analysis model,a black box-gray box hierarchical exergy analysis and evaluation method is put forward in this paper,which is applied to evaluate the power generation technology of diffe...Based on the“three box”exergy analysis model,a black box-gray box hierarchical exergy analysis and evaluation method is put forward in this paper,which is applied to evaluate the power generation technology of differential pressure produced by natural gas expansion.By using the exergy analysis theory,the black box-gray box hierarchical exergy analysis models of three differential pressure power generation technologies are established respectively.Firstly,the“black box”analysis models of main energy consuming equipment are established,and then the“gray box”analysis model of the total system is established.Based on the calculation results of exergy analysis indexes,the weak energy consumption equipment in the whole power generation process is accurately located.Taking a gas field in southwest China as an example,the comprehensive energy consumption evaluation of the three power generation technologies is carried out,and the technology with the best energy consumption condition among the three technologies is determined.Finally,the rationalization improvement measures are put forward from improving the air tightness,replacing the deflector and reducing the flow loss.展开更多
Numerous privacy-preserving issues have emerged along with the fast development of Internet, both in theory and in real-life applications. To settle the privacy-preserving problems, secure multi-party computation is e...Numerous privacy-preserving issues have emerged along with the fast development of Internet, both in theory and in real-life applications. To settle the privacy-preserving problems, secure multi-party computation is essential and critical. In this paper, we have solved two problems regarding to how to determine the position relation between points and curves without revealing any private information. Two protocols have been proposed in order to solve the problems in different conditions. In addition, some building blocks have been developed, such as scalar product protocol, so that we can take advantage of them to settle the privacy-preserving computational geometry problems which are a kind of special secure multi-party computation problems. Moreover, oblivious transfer and power series expansion serve as significant parts in our protocols. Analyses and proofs have also been given to argue our conclusion.展开更多
Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional (1D) equations for a piezoelectric semiconductor beam are obtained. The...Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional (1D) equations for a piezoelectric semiconductor beam are obtained. These derived equations are universal, in which extension, flexure, and shear deformations are all included, and can be degen- erated to a number of special cases, e.g., extensional motion, coupled extensional and flexural motion with shear deformations, and elementary flexural motion without shear deformations. As a typical application, the extensional motion of a ZnO beam is analyzed sequentially. It is revealed that semi-conduction has a great effect on the performance of the piezoelectric semiconductor beam, including static deformations and dynamic be- haviors. A larger initial carrier density will evidently lead to a lower resonant frequency and a smaller displacement response, which is a little similar to the dissipative effect. Both the derived approximate equations and the corresponding qualitative analysis are general and widely applicable, which can clearly interpret the inner physical mechanism of the semiconductor in the piezoelectrics and provide theoretical guidance for further experimental design.展开更多
Presented in this paper is a convergence theorem for a kind of composite power series expansions whose coefficients can be expressed by using Faa` di Bruno’s formula. A related problem is proposed as a remark, and a ...Presented in this paper is a convergence theorem for a kind of composite power series expansions whose coefficients can be expressed by using Faa` di Bruno’s formula. A related problem is proposed as a remark, and a few examples are given as applications.展开更多
基金Project supported by the National Natural Science Foundation of China (No.50425926)
文摘To the serf-similar analytical solution of the Boussinesq equation of groundwater flow in a semi-infinite porous medium, when the hydraulic head at the boundary behaved like a power of time, Barenblatt obtained a power series solution. However, he listed only the first three coefficients and did not give the recurrent formula among the coefficients. A formal proof of convergence of the series did not appear in his works. In this paper, the recurrent formula for the coefficients is obtained by using the method of power series expansion, and the convergence of the series is proven. The results can be easily understood and used by engineers in the catchment hydrology and baseflow studies as well as to solve agricultural drainage problems.
基金financially supported by the National Natural Science Foundation of China(52074089 and 51534004)Natural Science Foundation of Heilongjiang Province of China(LH2019E019)。
文摘Based on the“three box”exergy analysis model,a black box-gray box hierarchical exergy analysis and evaluation method is put forward in this paper,which is applied to evaluate the power generation technology of differential pressure produced by natural gas expansion.By using the exergy analysis theory,the black box-gray box hierarchical exergy analysis models of three differential pressure power generation technologies are established respectively.Firstly,the“black box”analysis models of main energy consuming equipment are established,and then the“gray box”analysis model of the total system is established.Based on the calculation results of exergy analysis indexes,the weak energy consumption equipment in the whole power generation process is accurately located.Taking a gas field in southwest China as an example,the comprehensive energy consumption evaluation of the three power generation technologies is carried out,and the technology with the best energy consumption condition among the three technologies is determined.Finally,the rationalization improvement measures are put forward from improving the air tightness,replacing the deflector and reducing the flow loss.
基金Supported by the National Natural Science Foundation of China (No. 61070189, 60673065)the National High Technology Development Program (No. 2008AA01Z419)
文摘Numerous privacy-preserving issues have emerged along with the fast development of Internet, both in theory and in real-life applications. To settle the privacy-preserving problems, secure multi-party computation is essential and critical. In this paper, we have solved two problems regarding to how to determine the position relation between points and curves without revealing any private information. Two protocols have been proposed in order to solve the problems in different conditions. In addition, some building blocks have been developed, such as scalar product protocol, so that we can take advantage of them to settle the privacy-preserving computational geometry problems which are a kind of special secure multi-party computation problems. Moreover, oblivious transfer and power series expansion serve as significant parts in our protocols. Analyses and proofs have also been given to argue our conclusion.
基金Project supported by the National Natural Science Foundation of China(Nos.11672223,11402187,and 51178390)the China Postdoctoral Science Foundation(No.2014M560762)the Fundamental Research Funds for the Central Universities of China(No.xjj2015131)
文摘Within the framework of continuum mechanics, the double power series ex- pansion technique is proposed, and a series of reduced one-dimensional (1D) equations for a piezoelectric semiconductor beam are obtained. These derived equations are universal, in which extension, flexure, and shear deformations are all included, and can be degen- erated to a number of special cases, e.g., extensional motion, coupled extensional and flexural motion with shear deformations, and elementary flexural motion without shear deformations. As a typical application, the extensional motion of a ZnO beam is analyzed sequentially. It is revealed that semi-conduction has a great effect on the performance of the piezoelectric semiconductor beam, including static deformations and dynamic be- haviors. A larger initial carrier density will evidently lead to a lower resonant frequency and a smaller displacement response, which is a little similar to the dissipative effect. Both the derived approximate equations and the corresponding qualitative analysis are general and widely applicable, which can clearly interpret the inner physical mechanism of the semiconductor in the piezoelectrics and provide theoretical guidance for further experimental design.
文摘Presented in this paper is a convergence theorem for a kind of composite power series expansions whose coefficients can be expressed by using Faa` di Bruno’s formula. A related problem is proposed as a remark, and a few examples are given as applications.