This article discusses the perturbation of a non-symmetric Dirichlet form, （ε, D（ε））, by a signed smooth measure u, where u=u1 -u2 with u1 and u2 being smooth measures. It gives a sufficient condition for the pe...This article discusses the perturbation of a non-symmetric Dirichlet form, （ε, D（ε））, by a signed smooth measure u, where u=u1 -u2 with u1 and u2 being smooth measures. It gives a sufficient condition for the perturbed form （ε^u ,D（ε^u）） （for some a0 ≥ 0） to be a coercive closed form.展开更多
Nakao＇s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting. ItS＇s formula in terms of the ext...Nakao＇s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting. ItS＇s formula in terms of the extended stochastic integrals is obtained.展开更多
Using variational methods and Morse theory, we obtain some existence results of multiple solutions for certain semilinear problems associated with general Dirichlet forms.
A creating technology of the part forming was discussed and finite volume method(FVM)was used to simulate the forming process of the non-symmetrical axostyle spring core-bar.The results show that the no-even radial fl...A creating technology of the part forming was discussed and finite volume method(FVM)was used to simulate the forming process of the non-symmetrical axostyle spring core-bar.The results show that the no-even radial flange on the top part of the eccentric peachy surface can remarkably block the metal flow and the eccentric peachy can be filled contentedly.Increasing the radius of punch near the inner pocket,the head bulge also can be filled contentedly.The temperature distribution in the part and the forming force,which helps to decide the forming temperature and to select the equipment,was also analyzed.The comparison between the simulation and the experiment result shows that they are accordant.展开更多
Suppose that X is a right process which is associated with a semi-Dirichlet form （ε, D（ε）） on L2（E; m）. Let J be the jumping measure of （ε, D（ε）） satisfying J（E x E- d） 〈 ∞. Let u E D（ε）b ：= D（...Suppose that X is a right process which is associated with a semi-Dirichlet form （ε, D（ε）） on L2（E; m）. Let J be the jumping measure of （ε, D（ε）） satisfying J（E x E- d） 〈 ∞. Let u E D（ε）b ：= D（ε） N L（E; m）, we have the following Pukushima＇s decomposition u（Xt）-u（X0） --- Mut ＋ Nut. Define Pu f（x） = Ex[eNT f（Xt）]. Let Qu（f,g） = ε（f,g）＋ε（u, fg） for f, g E D（ε）b. In the first part, under some assumptions we show that （Qu, D（ε）b） is lower semi-bounded if and only if there exists a constant a0 〉 0 such that /Put/2 ≤eaot for every t 〉 0. If one of these assertions holds, then （Put〉0is strongly continuous on L2（E;m）. If X is equipped with a differential structure, then under some other assumptions, these conclusions remain valid without assuming J（E x E - d） 〈 ∞. Some examples are also given in this part. Let At be a local continuous additive functional with zero quadratic variation. In the second part, we get the representation of At and give two sufficient conditions for PAf（x） = Ex[eAtf（Xt）] to be strongly continuous.展开更多
In this paper, we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric spac...In this paper, we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric spaces. Extensions to the processes associated with semi-Dirichlet forms and nearly symmetric right processes on Lusin spaces including infinite dimensional spaces are mentioned at the end of this paper.展开更多
In the present paper the transformation of symmetric Markov processes by symmetric martingale multiplicative functionals is studied and the corresponding Dirichlet form is formulated.
We characterize A-linear symmetric and contraction module operator semigroup{Tt}t∈R+L(l2(A)),where A is a finite-dimensional C-algebra,and L(l2(A))is the C-algebra of all adjointable module maps on l2(A).Next,we intr...We characterize A-linear symmetric and contraction module operator semigroup{Tt}t∈R+L(l2(A)),where A is a finite-dimensional C-algebra,and L(l2(A))is the C-algebra of all adjointable module maps on l2(A).Next,we introduce the concept of operator-valued quadratic forms,and give a one to one correspondence between the set of non-positive definite self-adjoint regular module operators on l2(A)and the set of non-negative densely defined A-valued quadratic forms.In the end,we obtain that a real and strongly continuous symmetric semigroup{Tt}t∈R+L(l2(A))being Markovian if and only if the associated closed densely defined A-valued quadratic form is a Dirichlet form.展开更多
In this paper, we introduce the concept of operator-valued quadratic form based on Hilbert W＊-module l2 A, and give a one to one correspondence between the set of positive self-adjoint regular module operators on l2 ...In this paper, we introduce the concept of operator-valued quadratic form based on Hilbert W＊-module l2 A, and give a one to one correspondence between the set of positive self-adjoint regular module operators on l2 A and the set of regular quadratic forms, where A is a finite and a-finite von Neumann algebra. Furthermore, we obtain that a strict continuous symmetric regular module operator semigroup （Tt）t∈R＋ C L（l2 A） is Markovian if and only if the associated A-valued quadratic form is a Dirichlet form, where L（l2 A） is the yon Neumann algebra of all adjointable module maps on l2 A.展开更多
Let (X_l) be an m-symmetric Hunt process associated with a regular Dirichlet form on L^2(X; m). S_0 denotes the family of all Radon measures of finite energy integral. It is shown that μ∈S_0 iff α>0 such that μ...Let (X_l) be an m-symmetric Hunt process associated with a regular Dirichlet form on L^2(X; m). S_0 denotes the family of all Radon measures of finite energy integral. It is shown that μ∈S_0 iff α>0 such that μRα<<m and d(μR_α)/dm∈. We have U_αμ=d(μR_α)/dm if μ∈S_0. As an application, we obtain some criteria for conservativeness of (X_l).展开更多
We introduce the quasi-homeomorphisms of generalized Dirichlet forms and prove that any quasi-regular generalized Dirichlet form is quasi-homeomorphic to a semi-regular generalized Dirichlet form. Moreover. we apply t...We introduce the quasi-homeomorphisms of generalized Dirichlet forms and prove that any quasi-regular generalized Dirichlet form is quasi-homeomorphic to a semi-regular generalized Dirichlet form. Moreover. we apply this quasi-homeomorphism method to study the measures of finite energy integrals of generalized Dirichlet forms. We show that any 1-coexcessive function which is dominated by a function in is associated with a measure of finite energy integral. Consequently, we prove that a Borel set B is-exceptional if and only if μ(B)=0 for any measure μ of finite energy integral.展开更多
A sufficient condition for the Mosco limit of a sequence of quasi-regular Dirichlet forms to be quasi-regular is given. In particular, a Dirichlet form is a quasi-regular Dirchlet form if and only if its Yosida approx...A sufficient condition for the Mosco limit of a sequence of quasi-regular Dirichlet forms to be quasi-regular is given. In particular, a Dirichlet form is a quasi-regular Dirchlet form if and only if its Yosida approximation sequency satisfies the conditon. Furthermore, conditions for the Mosco limit of a sequence of symmetric (strictly strong) local quasi-regular Dirichlet forms to be (strictly strong) local are also presented. This paper extends the results of [1] from regular Dirichlet space to quasi-regular Dirichlet space.展开更多
基金This research is supported by the NSFC andNSF of Hainan Province (Nos. 80529 and 10001)
文摘This article discusses the perturbation of a non-symmetric Dirichlet form, （ε, D（ε））, by a signed smooth measure u, where u=u1 -u2 with u1 and u2 being smooth measures. It gives a sufficient condition for the perturbed form （ε^u ,D（ε^u）） （for some a0 ≥ 0） to be a coercive closed form.
基金supported by National Natural Science Foundation of China (Grant No.10961012)Natural Sciences and Engineering Research Council of Canada (Grant No. 311945-2008)
文摘Nakao＇s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting. ItS＇s formula in terms of the extended stochastic integrals is obtained.
基金supported by National Natural Science Foundation of China - NSAF (10976026)National Natural Science Foundation of China (11271305)
文摘Using variational methods and Morse theory, we obtain some existence results of multiple solutions for certain semilinear problems associated with general Dirichlet forms.
基金Project of Science and Technology Foundation of Shanghai Committee,China(No.04NB14)
文摘A creating technology of the part forming was discussed and finite volume method(FVM)was used to simulate the forming process of the non-symmetrical axostyle spring core-bar.The results show that the no-even radial flange on the top part of the eccentric peachy surface can remarkably block the metal flow and the eccentric peachy can be filled contentedly.Increasing the radius of punch near the inner pocket,the head bulge also can be filled contentedly.The temperature distribution in the part and the forming force,which helps to decide the forming temperature and to select the equipment,was also analyzed.The comparison between the simulation and the experiment result shows that they are accordant.
基金supported by NSFC(11201102,11326169,11361021)Natural Science Foundation of Hainan Province(112002,113007)
文摘Suppose that X is a right process which is associated with a semi-Dirichlet form （ε, D（ε）） on L2（E; m）. Let J be the jumping measure of （ε, D（ε）） satisfying J（E x E- d） 〈 ∞. Let u E D（ε）b ：= D（ε） N L（E; m）, we have the following Pukushima＇s decomposition u（Xt）-u（X0） --- Mut ＋ Nut. Define Pu f（x） = Ex[eNT f（Xt）]. Let Qu（f,g） = ε（f,g）＋ε（u, fg） for f, g E D（ε）b. In the first part, under some assumptions we show that （Qu, D（ε）b） is lower semi-bounded if and only if there exists a constant a0 〉 0 such that /Put/2 ≤eaot for every t 〉 0. If one of these assertions holds, then （Put〉0is strongly continuous on L2（E;m）. If X is equipped with a differential structure, then under some other assumptions, these conclusions remain valid without assuming J（E x E - d） 〈 ∞. Some examples are also given in this part. Let At be a local continuous additive functional with zero quadratic variation. In the second part, we get the representation of At and give two sufficient conditions for PAf（x） = Ex[eAtf（Xt）] to be strongly continuous.
基金supported by National Natural Science Foundation of China (Grant No.10721101)National Basic Research Program of China (Grant No.2006CB805900)+1 种基金Key Lab of Random Complex Structures and Data Science,Chinese Academy of Sciences (Grant No.2008DP173182)Sino-Germany IGK Project
文摘In this paper, we extend the equivalence of the analytic and probabilistic notions of harmonicity in the context of Hunt processes associated with non-symmetric Dirichlet forms on locally compact separable metric spaces. Extensions to the processes associated with semi-Dirichlet forms and nearly symmetric right processes on Lusin spaces including infinite dimensional spaces are mentioned at the end of this paper.
基金in partby the National Natural Science Founda-tion of China(1 950 1 0 36)
文摘In the present paper the transformation of symmetric Markov processes by symmetric martingale multiplicative functionals is studied and the corresponding Dirichlet form is formulated.
基金supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Remin University of China(Grant No.10XNJ033)
文摘We characterize A-linear symmetric and contraction module operator semigroup{Tt}t∈R+L(l2(A)),where A is a finite-dimensional C-algebra,and L(l2(A))is the C-algebra of all adjointable module maps on l2(A).Next,we introduce the concept of operator-valued quadratic forms,and give a one to one correspondence between the set of non-positive definite self-adjoint regular module operators on l2(A)and the set of non-negative densely defined A-valued quadratic forms.In the end,we obtain that a real and strongly continuous symmetric semigroup{Tt}t∈R+L(l2(A))being Markovian if and only if the associated closed densely defined A-valued quadratic form is a Dirichlet form.
基金supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(Grant No.10XNJ033,"Study of Dirichlet forms and quantum Markov semigroups based on Hilbert C-modules")
文摘In this paper, we introduce the concept of operator-valued quadratic form based on Hilbert W＊-module l2 A, and give a one to one correspondence between the set of positive self-adjoint regular module operators on l2 A and the set of regular quadratic forms, where A is a finite and a-finite von Neumann algebra. Furthermore, we obtain that a strict continuous symmetric regular module operator semigroup （Tt）t∈R＋ C L（l2 A） is Markovian if and only if the associated A-valued quadratic form is a Dirichlet form, where L（l2 A） is the yon Neumann algebra of all adjointable module maps on l2 A.
基金Project supported by the National Natural Science Foundation of China.
文摘Let (X_l) be an m-symmetric Hunt process associated with a regular Dirichlet form on L^2(X; m). S_0 denotes the family of all Radon measures of finite energy integral. It is shown that μ∈S_0 iff α>0 such that μRα<<m and d(μR_α)/dm∈. We have U_αμ=d(μR_α)/dm if μ∈S_0. As an application, we obtain some criteria for conservativeness of (X_l).
文摘We introduce the quasi-homeomorphisms of generalized Dirichlet forms and prove that any quasi-regular generalized Dirichlet form is quasi-homeomorphic to a semi-regular generalized Dirichlet form. Moreover. we apply this quasi-homeomorphism method to study the measures of finite energy integrals of generalized Dirichlet forms. We show that any 1-coexcessive function which is dominated by a function in is associated with a measure of finite energy integral. Consequently, we prove that a Borel set B is-exceptional if and only if μ(B)=0 for any measure μ of finite energy integral.
文摘A sufficient condition for the Mosco limit of a sequence of quasi-regular Dirichlet forms to be quasi-regular is given. In particular, a Dirichlet form is a quasi-regular Dirchlet form if and only if its Yosida approximation sequency satisfies the conditon. Furthermore, conditions for the Mosco limit of a sequence of symmetric (strictly strong) local quasi-regular Dirichlet forms to be (strictly strong) local are also presented. This paper extends the results of [1] from regular Dirichlet space to quasi-regular Dirichlet space.
