The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coeifficients. Several theore...The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coeifficients. Several theorems on the existence of solutions are obtained, which perfect the solution theory of linear complex differential equations.展开更多
Using value distribution theory and techniques,the problem of the algebroid solutions of second order algebraic differential equation is investigated.Examples show that the results are sharp.
Soil infiltration and redistribution are important processes in field water cycle, and it is necessary to develop a simple model to describe the processes. In this study, an algebraic solution for one-dimensional wate...Soil infiltration and redistribution are important processes in field water cycle, and it is necessary to develop a simple model to describe the processes. In this study, an algebraic solution for one-dimensional water infiltration and redistribution without evaporation in unsaturated soil was developed based on Richards equation. The algebraic solution had three parameters, namely, the saturated water conductivity, the comprehensive shape coefficient of the soil water content distribution, and the soil suction allocation coefficient. To analyze the physical features of these parameters, a relationship between the Green-Ampt model and the algebraic solution was established. The three parameters were estimated based on experimental observations, whereas the soil water content and the water infiltration duration were calculated using the algebraic solution. The calculated soil water content and infiltration duration were compared with the experimental observations, and the results indicated that the algebraic solution accurately described the unsaturated soil water flow processes.展开更多
This paper discusses the existence and uniqueness of the generalized solution in the sense of Colombeau to the Benjamin-Ono (B-O) equation and the relationship between the new generalized solution and the classical so...This paper discusses the existence and uniqueness of the generalized solution in the sense of Colombeau to the Benjamin-Ono (B-O) equation and the relationship between the new generalized solution and the classical solution.展开更多
This paper considers the global existence and nonexistence of positive solutions for the following volterra integral equations wbers Matrix B is called a positive definite one, if all the principal minors have positi...This paper considers the global existence and nonexistence of positive solutions for the following volterra integral equations wbers Matrix B is called a positive definite one, if all the principal minors have positive detechants. By considering the existence of positivve solutions for algebra equations, it is proved that if I-A is a positive definite matrix,where I is an identity matrix, then (I) bas global positive solution 1 Otherwise, (I)has no continous nbndeereasing positive solution.展开更多
Many applications for locating a radio signal source employ Global Navigation Satellite System(GNSS)to obtain a sensor’s position.By using GNSS,a sensor can also synchronize with other sensors.For a sensor that is eq...Many applications for locating a radio signal source employ Global Navigation Satellite System(GNSS)to obtain a sensor’s position.By using GNSS,a sensor can also synchronize with other sensors.For a sensor that is equipped with a GNSS receiver,it can be independent and is readily to be loaded on a flexible platform,such as an unmanned aerial vehicle(UAV).In this paper,we consider using such sensors and timeof-arrival(TOA)techniques to locate a radio signal source,and analyze the performance limit of source localization.Besides the performance analysis,this paper provides the geometric interpretation of the performance limit,which can illustrate how a sensor contributes to the source localization accuracy.The performance analysis and the geometric interpretation together give important insights into how to make better use of GNSS receiver for passive localization.Another contribution is we propose a modified closedform solution for this localization problem.Compared with previous literature,this solution takes both sensor position and synchronization uncertainty into account,and it does not need proper initial guess of source position and is computationally efficient.Our simulation results validate the efficiency of this solution.展开更多
We study the number and distribution of critical points as we Ⅱ as algebraic solutions of a cubic system close related to the general quadratic system.
基金Supported by Guangdong Natural Science Foundation(2015A030313628,S2012010010376)Training plan for Distinguished Young Teachers in Higher Education of Guangdong(Yqgdufe1405)+1 种基金Guangdong Education Science Planning Project(2014GXJK091,GDJG20142304)the National Natural Science Foundation of China(11301140,11101096)
文摘The main purpose of this paper is to study the problems on the existence of algebraic solutions for some second-order complex differential equations with entire algebraic function element coeifficients. Several theorems on the existence of solutions are obtained, which perfect the solution theory of linear complex differential equations.
文摘Using value distribution theory and techniques,the problem of the algebroid solutions of second order algebraic differential equation is investigated.Examples show that the results are sharp.
基金supported by the Knowledge Innovation Program of the Chinese Academy of Sciences (No.KSCX2-YW-N-003)the National Basic Research Program of China (No.2005CB121103)the National Natural Science Foundation ofChina (No.50879067).
文摘Soil infiltration and redistribution are important processes in field water cycle, and it is necessary to develop a simple model to describe the processes. In this study, an algebraic solution for one-dimensional water infiltration and redistribution without evaporation in unsaturated soil was developed based on Richards equation. The algebraic solution had three parameters, namely, the saturated water conductivity, the comprehensive shape coefficient of the soil water content distribution, and the soil suction allocation coefficient. To analyze the physical features of these parameters, a relationship between the Green-Ampt model and the algebraic solution was established. The three parameters were estimated based on experimental observations, whereas the soil water content and the water infiltration duration were calculated using the algebraic solution. The calculated soil water content and infiltration duration were compared with the experimental observations, and the results indicated that the algebraic solution accurately described the unsaturated soil water flow processes.
基金Project supported by the National Natural Science Foundation ofChina (No. 60103015) and SRF for ROCS+2 种基金 SEM China
文摘This paper discusses the existence and uniqueness of the generalized solution in the sense of Colombeau to the Benjamin-Ono (B-O) equation and the relationship between the new generalized solution and the classical solution.
文摘This paper considers the global existence and nonexistence of positive solutions for the following volterra integral equations wbers Matrix B is called a positive definite one, if all the principal minors have positive detechants. By considering the existence of positivve solutions for algebra equations, it is proved that if I-A is a positive definite matrix,where I is an identity matrix, then (I) bas global positive solution 1 Otherwise, (I)has no continous nbndeereasing positive solution.
基金supported by the National Natural Science Foundation of China(Grant No.61973181)Tsinghua University Initiative Scientific Research Program(Grant No.2018Z05JZY004).
文摘Many applications for locating a radio signal source employ Global Navigation Satellite System(GNSS)to obtain a sensor’s position.By using GNSS,a sensor can also synchronize with other sensors.For a sensor that is equipped with a GNSS receiver,it can be independent and is readily to be loaded on a flexible platform,such as an unmanned aerial vehicle(UAV).In this paper,we consider using such sensors and timeof-arrival(TOA)techniques to locate a radio signal source,and analyze the performance limit of source localization.Besides the performance analysis,this paper provides the geometric interpretation of the performance limit,which can illustrate how a sensor contributes to the source localization accuracy.The performance analysis and the geometric interpretation together give important insights into how to make better use of GNSS receiver for passive localization.Another contribution is we propose a modified closedform solution for this localization problem.Compared with previous literature,this solution takes both sensor position and synchronization uncertainty into account,and it does not need proper initial guess of source position and is computationally efficient.Our simulation results validate the efficiency of this solution.
文摘We study the number and distribution of critical points as we Ⅱ as algebraic solutions of a cubic system close related to the general quadratic system.
