In this paper we introduce the notions of mean dimension and metric mean dimension for non-autonomous iterated function systems(NAIFSs for short)on countably infinite alphabets which can be regarded as generalizations...In this paper we introduce the notions of mean dimension and metric mean dimension for non-autonomous iterated function systems(NAIFSs for short)on countably infinite alphabets which can be regarded as generalizations of the mean dimension and the Lindenstrauss metric mean dimension for non-autonomous iterated function systems.We also show the relationship between the mean topological dimension and the metric mean dimension.展开更多
Let X (t)(t∈R^N) be a d-dimensional fractional Brownian motion. A contiunous function f:R^N→R^d is called a polar function of X(t)(t∈R^N) if P{ t∈R^N\{0},X(t)=t(t)}=0. In this paper, the characteristies of the cla...Let X (t)(t∈R^N) be a d-dimensional fractional Brownian motion. A contiunous function f:R^N→R^d is called a polar function of X(t)(t∈R^N) if P{ t∈R^N\{0},X(t)=t(t)}=0. In this paper, the characteristies of the class of polar functions are studied. Our theorem 1 improves the previous results of Graversen and Legall. Theorem2 solves a problem of Legall (1987) on Brownian motion.展开更多
In this paper, we introduce the A, weights into the tent space, many important results in the tent space are generalized. Also, new relations between the A, weights and Carleson measures are obtained.
Spin-orbit scattering effects in a layered quasi-2D disordered electron system have been investigated by the diagrammatic techniques in perturbation theory. The expression of Cooperon (propagator in particle-particle ...Spin-orbit scattering effects in a layered quasi-2D disordered electron system have been investigated by the diagrammatic techniques in perturbation theory. The expression of Cooperon (propagator in particle-particle channel) is obtained as the function of interlayer coupling. The analytical result for the quantum correction to Hall conductivity has been obtained as functions of elastic, inelastic and spin-orbit scattering times. It is shown that the strong and weak couplings correspond, respectively, to the 3D and 2D situations. The Hall coefficient is shown to vanish. The relevant dimensional crossover behavior from 3D to 2D with decreasing the interlayer coupling has been discussed, and the condition for the crossover has been obtained. The present theory is expected to apply for the electronic transport in tunneling superlattices.展开更多
In this paper we elaborate a general expression of the conditional expectation related to pricing problem of the American options using the Malliavin derivative （without localization）. This work is a generalization ...In this paper we elaborate a general expression of the conditional expectation related to pricing problem of the American options using the Malliavin derivative （without localization）. This work is a generalization of paper of Bally et al. （2005） [ 1 ] for the one dimensional case. Basing on the density function of the asset price, Bally and al. used the Malliavin calculus to evaluate the conditional expectation related to pricing American option problem, but in our work we use the Malliavin derivative to resolve the previous problem.展开更多
The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further...The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3)Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*, B). Then the functional dimension of (B*, σ(B*, B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.展开更多
Over the past 2 decades,tight restriction has been imposed on strength criteria of concrete by the combination of plasticity and damage in one theory.The present study aims at constructing plastic/damage loading funct...Over the past 2 decades,tight restriction has been imposed on strength criteria of concrete by the combination of plasticity and damage in one theory.The present study aims at constructing plastic/damage loading functions for elastoplastic damage models for concrete that can perform more satisfactorily in 3D stress states.Numerous strength criteria of concrete are reorganized according to their simplest representations as Cartesian,cylindrical,mixed cylindrical-Cartesian,and other forms,and the homogeneity of loading functions discussed.It is found that under certain supplementary conditions from physical meanings,an unambiguous definition of the cohesion in a strength criterion,which is demanded in an elastoplastic damage model,is usually available in an explicit or implicit form,and in each case the loading function is still homogeneous.To apply and validate the presented theory,we construct the respective homogeneous damage and plastic loading functions and implant them into some widely used elastoplastic damage models for concrete,and their performances in triaxial compression prove to have improved significantly.展开更多
This paper presents a method for extracting geometrical features of the joint probability density function(PDF)of two-dimensional systems based on its contour lines,with particular interests given to the number and po...This paper presents a method for extracting geometrical features of the joint probability density function(PDF)of two-dimensional systems based on its contour lines,with particular interests given to the number and position of peaks and craters.In order to detect those two types of structures,a series of horizontal planes are applied to truncate the joint PDF with contour lines generated.Starting with the analysis of contour lines in a single plane,shape characteristics of the peak and the crater can be reflected on the contour lines in the aspects of gradient direction and inclusion relationship.Aided by the properties of PDF,the information about gradient direction and inclusion relationship of contour lines can be obtained simultaneously if the contour tree is built.According to the contour tree,the contour lines can be classified as two groups.Then the corresponding relation between contour lines in different planes is discussed.Based on the corresponding relation,clustering analysis about contour lines belonging to the same group but having different heights is performed.Two sets of contour lines are finally obtained as the simplest expression of geometrical characteristics of a joint PDF.They can be used to obtain the number and position of each peak and crater.Three oscillators of different types are chosen to test this method,which shows that this method can pave the way for numerical calculation about the stochastic P-bifurcation of multi-dimensional systems.展开更多
文摘In this paper we introduce the notions of mean dimension and metric mean dimension for non-autonomous iterated function systems(NAIFSs for short)on countably infinite alphabets which can be regarded as generalizations of the mean dimension and the Lindenstrauss metric mean dimension for non-autonomous iterated function systems.We also show the relationship between the mean topological dimension and the metric mean dimension.
文摘Let X (t)(t∈R^N) be a d-dimensional fractional Brownian motion. A contiunous function f:R^N→R^d is called a polar function of X(t)(t∈R^N) if P{ t∈R^N\{0},X(t)=t(t)}=0. In this paper, the characteristies of the class of polar functions are studied. Our theorem 1 improves the previous results of Graversen and Legall. Theorem2 solves a problem of Legall (1987) on Brownian motion.
文摘In this paper, we introduce the A, weights into the tent space, many important results in the tent space are generalized. Also, new relations between the A, weights and Carleson measures are obtained.
文摘Spin-orbit scattering effects in a layered quasi-2D disordered electron system have been investigated by the diagrammatic techniques in perturbation theory. The expression of Cooperon (propagator in particle-particle channel) is obtained as the function of interlayer coupling. The analytical result for the quantum correction to Hall conductivity has been obtained as functions of elastic, inelastic and spin-orbit scattering times. It is shown that the strong and weak couplings correspond, respectively, to the 3D and 2D situations. The Hall coefficient is shown to vanish. The relevant dimensional crossover behavior from 3D to 2D with decreasing the interlayer coupling has been discussed, and the condition for the crossover has been obtained. The present theory is expected to apply for the electronic transport in tunneling superlattices.
文摘In this paper we elaborate a general expression of the conditional expectation related to pricing problem of the American options using the Malliavin derivative （without localization）. This work is a generalization of paper of Bally et al. （2005） [ 1 ] for the one dimensional case. Basing on the density function of the asset price, Bally and al. used the Malliavin calculus to evaluate the conditional expectation related to pricing American option problem, but in our work we use the Malliavin derivative to resolve the previous problem.
基金Project supported by the National Natural Science Foundation of China (No.10071088, No.10171098).
文摘The functional dimension of countable Hilbert spaces has been discussed by some authors. They showed that every countable Hilbert space with finite functional dimension is nuclear. In this paper the authors do further research on the functional dimension, and obtain the following results: (1) They construct a countable Hilbert space, which is nuclear, but its functional dimension is infinite. (2) The functional dimension of a Banach space is finite if and only if this space is finite dimensional. (3)Let B be a Banach space, B* be its dual, and denote the weak * topology of B* by σ(B*, B). Then the functional dimension of (B*, σ(B*, B)) is 1. By the third result, a class of topological linear spaces with finite functional dimension is presented.
基金supported by the National Natural Science Foundation of China-National Science Foundation Joint Project(Grant No.51261120374)the National Natural Science Foundation of China(Grant Nos.51108336 and 51378377)
文摘Over the past 2 decades,tight restriction has been imposed on strength criteria of concrete by the combination of plasticity and damage in one theory.The present study aims at constructing plastic/damage loading functions for elastoplastic damage models for concrete that can perform more satisfactorily in 3D stress states.Numerous strength criteria of concrete are reorganized according to their simplest representations as Cartesian,cylindrical,mixed cylindrical-Cartesian,and other forms,and the homogeneity of loading functions discussed.It is found that under certain supplementary conditions from physical meanings,an unambiguous definition of the cohesion in a strength criterion,which is demanded in an elastoplastic damage model,is usually available in an explicit or implicit form,and in each case the loading function is still homogeneous.To apply and validate the presented theory,we construct the respective homogeneous damage and plastic loading functions and implant them into some widely used elastoplastic damage models for concrete,and their performances in triaxial compression prove to have improved significantly.
基金supported by the National Program on Key Basic Research Project(Grant No.2014CB046805)National Natural Science Foundation of China(Grant No.11372211).
文摘This paper presents a method for extracting geometrical features of the joint probability density function(PDF)of two-dimensional systems based on its contour lines,with particular interests given to the number and position of peaks and craters.In order to detect those two types of structures,a series of horizontal planes are applied to truncate the joint PDF with contour lines generated.Starting with the analysis of contour lines in a single plane,shape characteristics of the peak and the crater can be reflected on the contour lines in the aspects of gradient direction and inclusion relationship.Aided by the properties of PDF,the information about gradient direction and inclusion relationship of contour lines can be obtained simultaneously if the contour tree is built.According to the contour tree,the contour lines can be classified as two groups.Then the corresponding relation between contour lines in different planes is discussed.Based on the corresponding relation,clustering analysis about contour lines belonging to the same group but having different heights is performed.Two sets of contour lines are finally obtained as the simplest expression of geometrical characteristics of a joint PDF.They can be used to obtain the number and position of each peak and crater.Three oscillators of different types are chosen to test this method,which shows that this method can pave the way for numerical calculation about the stochastic P-bifurcation of multi-dimensional systems.
