We define discrete total differential forms on lattice space by. changing coefficients of discrete differential forms from functions only of n to functions also of dependent variables un and their partial differences....We define discrete total differential forms on lattice space by. changing coefficients of discrete differential forms from functions only of n to functions also of dependent variables un and their partial differences. And the discrete exterior derivative extends to be discrete total differential map which is also nilpotent. Then a discrete horizontal complex can be derived and be proved to be exact by constructing homotopy operators.展开更多
The novel free-form deformation (FFD) technique presented in the paper uses scalar fields definedby skeletons with arbitrary topology. The technique embeds objects into the scalar field by assigning a field value to e...The novel free-form deformation (FFD) technique presented in the paper uses scalar fields definedby skeletons with arbitrary topology. The technique embeds objects into the scalar field by assigning a field value to each point of the objects. When the space of the skeleton is changed, the distribution of the scalar field changes accordingly, which implicitly defines a deformation of the space. The generality of skeletons assures that the technique can freely define deformable regions to produce a broader range of shape deformations.展开更多
A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman tr...A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal eurvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.展开更多
Borehole inclinometers are important observation instruments used to measure ground tilt movement and monitor crustal deformation of solid tides and geological landslide disasters.They are widely used in oil explorati...Borehole inclinometers are important observation instruments used to measure ground tilt movement and monitor crustal deformation of solid tides and geological landslide disasters.They are widely used in oil exploration,mineral resource drilling,well logging,exploration and other fields.There is potential for development of rock stress strain monitoring tools.Many types of tiltmeters have been installed,such as SQ-7,FSQ,VS and JB.However,these tiltmeters are generally installed in a deep cave to avoid the interference of temperature,humidity,and human activities.With the urbanization of human society,suitable installation locations are difficult to find.To solve the problem,a two-component borehole tiltmeter,named the CBT-type tiltmeter,is proposed in this paper.It can be installed in a borehole less than500 m deep to eliminate environmental influences.The tiltmeter is composed of two sophisticated gravitational swing and two capacitive transducers.From preliminary theory and experiment analysis,its linear correlation coefficient is higher than 0.99,its co-seismic response is rapid and its noise level is up to 10 4arc seconds in practice.展开更多
Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried ...Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations,the majority of the results deal with polynomial types.Limited research has been reported regarding such equations of rational type.In this paper we present an adaptation of the(G /G)-expansion method to solve nonlinear rational differential-difference equations.The procedure is demonstrated using two distinct equations.Our approach allows one to construct three types of exact traveling wave solutions(hyperbolic,trigonometric,and rational) by means of the simplified form of the auxiliary equation method with reduced parameters.Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.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
文摘We define discrete total differential forms on lattice space by. changing coefficients of discrete differential forms from functions only of n to functions also of dependent variables un and their partial differences. And the discrete exterior derivative extends to be discrete total differential map which is also nilpotent. Then a discrete horizontal complex can be derived and be proved to be exact by constructing homotopy operators.
文摘The novel free-form deformation (FFD) technique presented in the paper uses scalar fields definedby skeletons with arbitrary topology. The technique embeds objects into the scalar field by assigning a field value to each point of the objects. When the space of the skeleton is changed, the distribution of the scalar field changes accordingly, which implicitly defines a deformation of the space. The generality of skeletons assures that the technique can freely define deformable regions to produce a broader range of shape deformations.
文摘A new family of exact solutions to the wave equation representing relatively undistorted progressive waves is constructed using separation of variables in the elliptic cylindrical coordinates and one of the Bateman transforms. The general form of this Bateman transform in an orthogonal eurvilinear cylindrical coordinate system is discussed and a specific problem of physical feasibility of the obtained solutions, connected with their dependence on the cyclic coordinate, is addressed. The limiting case of zero eccentricity, in which the elliptic cylindrical coordinates turn into their circular cylindrical counterparts, is shown to correspond to the focused wave modes of the Bessel-Gauss type.
基金the research grant from Institute of Crustal Dynamics,CEA (No.ZDJ2013-07)Key Project of the National Twelfth-Five Year Research Program of China (No.2012BAK19B)
文摘Borehole inclinometers are important observation instruments used to measure ground tilt movement and monitor crustal deformation of solid tides and geological landslide disasters.They are widely used in oil exploration,mineral resource drilling,well logging,exploration and other fields.There is potential for development of rock stress strain monitoring tools.Many types of tiltmeters have been installed,such as SQ-7,FSQ,VS and JB.However,these tiltmeters are generally installed in a deep cave to avoid the interference of temperature,humidity,and human activities.With the urbanization of human society,suitable installation locations are difficult to find.To solve the problem,a two-component borehole tiltmeter,named the CBT-type tiltmeter,is proposed in this paper.It can be installed in a borehole less than500 m deep to eliminate environmental influences.The tiltmeter is composed of two sophisticated gravitational swing and two capacitive transducers.From preliminary theory and experiment analysis,its linear correlation coefficient is higher than 0.99,its co-seismic response is rapid and its noise level is up to 10 4arc seconds in practice.
文摘Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations,the majority of the results deal with polynomial types.Limited research has been reported regarding such equations of rational type.In this paper we present an adaptation of the(G /G)-expansion method to solve nonlinear rational differential-difference equations.The procedure is demonstrated using two distinct equations.Our approach allows one to construct three types of exact traveling wave solutions(hyperbolic,trigonometric,and rational) by means of the simplified form of the auxiliary equation method with reduced parameters.Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.
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.
