one of the central questions in CAGD[1] is blending surfaces whichprovides the theoretical baJsis for the design technology of space surfaces. We willdiscuss the general theories and algorithms for multivariate hyperf...one of the central questions in CAGD[1] is blending surfaces whichprovides the theoretical baJsis for the design technology of space surfaces. We willdiscuss the general theories and algorithms for multivariate hyperfinite interpolationand their aPplication to the blending of implicit algebraic surfaces, and investigate theexistence conditions of hyperfinite interpolation. Based on Wu's theory on blendingimplicit algebraic surfaces, the problem of blending two quadric surfaces is studied.The conditions for the coefficient of gi under which there exists the cubic blendingsurface S(f) (the lowest degree) are obtained and the concrete expressions of f arepresented if they exist. These results can be applied directly to CAGD.展开更多
Given a free ergodic action of a discrete abelian group G on a measure space (X, 7), the crossed product LX (X, 7)p G contains two distinguished maximal abelian subalgebras. We discuss what kind of information about t...Given a free ergodic action of a discrete abelian group G on a measure space (X, 7), the crossed product LX (X, 7)p G contains two distinguished maximal abelian subalgebras. We discuss what kind of information about the action can be extracted from the positions of these two subalgebras inside the crossed product algebra.展开更多
It is proved that everyσ-weakly continuous local derivation from triangular subalgebra A of hyperfinite von Neumann algebra B into A(or B)is a derivation.Morevoer,if A is also aσ-Dirichlet subalgebra,each local deri...It is proved that everyσ-weakly continuous local derivation from triangular subalgebra A of hyperfinite von Neumann algebra B into A(or B)is a derivation.Morevoer,if A is also aσ-Dirichlet subalgebra,each local derivation from A into A is an inner derivation.展开更多
Here concerned is a certain kind of non-standard measure defined on the n-dimensional Euclidean space (Rn), which (with n = 1) can be used to show that any standard linear point-set or the usual ordered field R of rea...Here concerned is a certain kind of non-standard measure defined on the n-dimensional Euclidean space (Rn), which (with n = 1) can be used to show that any standard linear point-set or the usual ordered field R of real numbers is of measure zero. The proposition just mentioned is basically consistent with Poincare's famous remark which renders a deep insight into the paradoxical structural nature of Cantor's continuum consisting precisely of all distinct real numbers.展开更多
Let L be a type II1 factor with separable predual and r be a normal faithful tracial state of c~. We first show that the set of subfactors of L with property F, the set of type II1 subfactors of L with similarity prop...Let L be a type II1 factor with separable predual and r be a normal faithful tracial state of c~. We first show that the set of subfactors of L with property F, the set of type II1 subfactors of L with similarity property and the set of all McDuff sub/actors of t are open and closed in the Hausdorff metric d2 induced by the trace norm; then we show that the set of all hyperfinite von Neumann subalgebras of L is closed in d2. We also consider the connection of perturbation of operator algebras under d2 with the fundamental group and the generator problem of type II1 factors. When M is a finite yon Neumann algebra with a normal faithful trace, the set of all von Neumann subalgebras B of M such that B ∪→ M is rigid is closed in the Hausdorff metric d2.展开更多
We use methods from nonstandard analysis to obtain a short and simple derivation of the Levy-Khintchine formula via an explicit construction of certain laws of the infinitesimal increments. Consequently, any arbitrary...We use methods from nonstandard analysis to obtain a short and simple derivation of the Levy-Khintchine formula via an explicit construction of certain laws of the infinitesimal increments. Consequently, any arbitrary Levy process is representable as the standard part of a hyperfinite sum of infinitesimal increments.展开更多
We introduce two notions of the pressure in operator algebras, one is the pressure Pα（π, T） for an automorphism α of a unital exact C^＊-algebra A at a self-adjoint element T in A with respect to a faithful unit...We introduce two notions of the pressure in operator algebras, one is the pressure Pα（π, T） for an automorphism α of a unital exact C^＊-algebra A at a self-adjoint element T in A with respect to a faithful unital ＊-representation π the other is the pressure Pτ,α（T） for an automorphism α of a hyperfinite von Neumann algebra M at a self-adjoint element T in M with respect to a faithful normal α-invariant state τ. We give some properties of the pressure, show that it is a conjugate invaxiant, and also prove that the pressure of the implementing inner automorphism of a crossed product A×α Z at a self-adjoint operator T in A equals that of α at T.展开更多
Let A be a unital C^(∗)-algebra and B a unital C^(∗)-algebra with a faithful traceτ.Let n be a positive integer.We give the definition of weakly approximate diagonalization(with respect toτ)of a unital homomorphism...Let A be a unital C^(∗)-algebra and B a unital C^(∗)-algebra with a faithful traceτ.Let n be a positive integer.We give the definition of weakly approximate diagonalization(with respect toτ)of a unital homomorphismφ:A→Mn(B).We give an equivalent characterization of McDuff Ⅱ_(1) factors.We show that,if A is a unital nuclear C^(∗)-algebra and B is a type Ⅱ_(1) factor with faithful traceτ,then every unital^(∗)-homomorphism φ:A→M_(n)(B)is weakly approximately diagonalizable.If B is a unital simple infinite dimensional separable nuclear C^(∗)-algebra,then any finitely many elements in Mn(B)can be simultaneously weakly approximately diagonalized while the elements in the diagonals can be required to be the same.展开更多
文摘one of the central questions in CAGD[1] is blending surfaces whichprovides the theoretical baJsis for the design technology of space surfaces. We willdiscuss the general theories and algorithms for multivariate hyperfinite interpolationand their aPplication to the blending of implicit algebraic surfaces, and investigate theexistence conditions of hyperfinite interpolation. Based on Wu's theory on blendingimplicit algebraic surfaces, the problem of blending two quadric surfaces is studied.The conditions for the coefficient of gi under which there exists the cubic blendingsurface S(f) (the lowest degree) are obtained and the concrete expressions of f arepresented if they exist. These results can be applied directly to CAGD.
文摘Given a free ergodic action of a discrete abelian group G on a measure space (X, 7), the crossed product LX (X, 7)p G contains two distinguished maximal abelian subalgebras. We discuss what kind of information about the action can be extracted from the positions of these two subalgebras inside the crossed product algebra.
文摘It is proved that everyσ-weakly continuous local derivation from triangular subalgebra A of hyperfinite von Neumann algebra B into A(or B)is a derivation.Morevoer,if A is also aσ-Dirichlet subalgebra,each local derivation from A into A is an inner derivation.
基金Supperted by Special Foundation of Dalian Univ. of Technology.
文摘Here concerned is a certain kind of non-standard measure defined on the n-dimensional Euclidean space (Rn), which (with n = 1) can be used to show that any standard linear point-set or the usual ordered field R of real numbers is of measure zero. The proposition just mentioned is basically consistent with Poincare's famous remark which renders a deep insight into the paradoxical structural nature of Cantor's continuum consisting precisely of all distinct real numbers.
基金supported by National Natural Science Foundation of China(Grant No.11371222)Natural Science Foundation of Shandong Province(Grant No.ZR2012AM024)
文摘Let L be a type II1 factor with separable predual and r be a normal faithful tracial state of c~. We first show that the set of subfactors of L with property F, the set of type II1 subfactors of L with similarity property and the set of all McDuff sub/actors of t are open and closed in the Hausdorff metric d2 induced by the trace norm; then we show that the set of all hyperfinite von Neumann subalgebras of L is closed in d2. We also consider the connection of perturbation of operator algebras under d2 with the fundamental group and the generator problem of type II1 factors. When M is a finite yon Neumann algebra with a normal faithful trace, the set of all von Neumann subalgebras B of M such that B ∪→ M is rigid is closed in the Hausdorff metric d2.
基金Work completed at BiBoS Universitat Bielefeld in 2004 with support from Norway-SA Grant 2067063
文摘We use methods from nonstandard analysis to obtain a short and simple derivation of the Levy-Khintchine formula via an explicit construction of certain laws of the infinitesimal increments. Consequently, any arbitrary Levy process is representable as the standard part of a hyperfinite sum of infinitesimal increments.
基金the NNSF of China (Grant No.A0324614)NSF of Shandong (Grant No.Y2006A03)NSF of QFNU (Grant No.xj0502)
文摘We introduce two notions of the pressure in operator algebras, one is the pressure Pα（π, T） for an automorphism α of a unital exact C^＊-algebra A at a self-adjoint element T in A with respect to a faithful unital ＊-representation π the other is the pressure Pτ,α（T） for an automorphism α of a hyperfinite von Neumann algebra M at a self-adjoint element T in M with respect to a faithful normal α-invariant state τ. We give some properties of the pressure, show that it is a conjugate invaxiant, and also prove that the pressure of the implementing inner automorphism of a crossed product A×α Z at a self-adjoint operator T in A equals that of α at T.
基金supported by the Natural Science Foundation of Chongqing Science and Technology Commission(Grant No.cstc2020jcyj-msxmX0723)the Research Foundation of Chongqing Educational Committee(Grant No.KJQN2021000529)supported by the National Natural Science Foundation of China(Grant Nos.11871127,11971463)。
文摘Let A be a unital C^(∗)-algebra and B a unital C^(∗)-algebra with a faithful traceτ.Let n be a positive integer.We give the definition of weakly approximate diagonalization(with respect toτ)of a unital homomorphismφ:A→Mn(B).We give an equivalent characterization of McDuff Ⅱ_(1) factors.We show that,if A is a unital nuclear C^(∗)-algebra and B is a type Ⅱ_(1) factor with faithful traceτ,then every unital^(∗)-homomorphism φ:A→M_(n)(B)is weakly approximately diagonalizable.If B is a unital simple infinite dimensional separable nuclear C^(∗)-algebra,then any finitely many elements in Mn(B)can be simultaneously weakly approximately diagonalized while the elements in the diagonals can be required to be the same.
