Let M and N be two factor von Neumann algebras that their dimensions are large than 1,η≠-1 a non zero complex number and Φa(not necessary linear)bijection between two factor von Neumann algebras satisfying Φ(I)=I....Let M and N be two factor von Neumann algebras that their dimensions are large than 1,η≠-1 a non zero complex number and Φa(not necessary linear)bijection between two factor von Neumann algebras satisfying Φ(I)=I.For all A,B∈M,define by A■B=AB+BA the Jordan product of A and B,A·_(η)B=AB+ηBA^(*)the Jordan η-*-product of A and B,respectively.Let Φ and Φ^(-1)preserve the mixed Jordan triple η-*-products.It is proved that Φ is a linear *-isomorphism if η is not real and Φ is the sum of a linear *-isomorphism and a conjugate linear *-isomorphism if η is real.展开更多
本文研究了在von Neumann代数框架下,投影运算后等价的保持情形,特别是在不同类型的von Neumann代数中投影等价的刻画及其性质。设E、F、N为von Neumann代数ℳ中的三个有限投影,且E~F。当NE=NF=0时,那么有N+E~N+F,N∧E~N∧F,N∨E~N∨F成...本文研究了在von Neumann代数框架下,投影运算后等价的保持情形,特别是在不同类型的von Neumann代数中投影等价的刻画及其性质。设E、F、N为von Neumann代数ℳ中的三个有限投影,且E~F。当NE=NF=0时,那么有N+E~N+F,N∧E~N∧F,N∨E~N∨F成立。当NE,NF时,那么有N∧E~N∧F,N∨E~N∨F成立。当EN,FN时,那么有N−E~N−F,N∧E~N∧F,N∨E~N∨F成立。本文进一步推至N为von Neumann代数ℳ中的无限投影,并且考虑了von Neumann代数ℳ中四个投影运算的情况。This paper studies the conditions of equivalents after projection operations under the framework of von Neumann algebra, especially the characterization and properties of projection equivalents in different types of von Neumann algebras. Let E,F,Nbe three finite projections in von Neumann algebra ℳ, and E~F. If NE=NF=0, then it follows that N+E~N+F, N∧E~N∧F, N∨E~N∨Fholds. If NE, NF, then it follows that N∧E~N∧F, N∨E~N∨Fholds. If EN, FN, then it follows that N−E~N−F, N∧E~N∧F, N∨E~N∨Fholds. This paper further extends these results to infinite projections Nin von Neumann algebras ℳand considers the case of four projection operations within von Neumann algebras ℳ.展开更多
设ℳ和N是无I1或I2型中心直和项的von Neumann代数,其单位元分别为I和I′。本文证明非线性双射Φ:ℳ→N混合Lie可乘,即Φ([ [ A,B ],C ]∗)=[ [ Φ(A),Φ(B) ],Φ(C) ]∗,∀A,B,C∈ℳ,当且仅当存在线性*-同构和共轭线性*-同构的直和Ψ:ℳ→N使...设ℳ和N是无I1或I2型中心直和项的von Neumann代数,其单位元分别为I和I′。本文证明非线性双射Φ:ℳ→N混合Lie可乘,即Φ([ [ A,B ],C ]∗)=[ [ Φ(A),Φ(B) ],Φ(C) ]∗,∀A,B,C∈ℳ,当且仅当存在线性*-同构和共轭线性*-同构的直和Ψ:ℳ→N使得Φ(A)=Φ(I)Ψ(A),∀A∈ℳ,其中Φ(I)∈N是可逆中心元且Φ(I)2=I′。该结论将因子von Neumann代数上的非线性混合Lie可乘双射的结果推广到无I1或I2型中心直和项的von Neumann代数。Let ℳand Nbe von Neumann algebras with no central summands of type I1or I2, Iand I′be the identities of them. This paper proves that a bijective map Φ:ℳ→Nis mixed Lie multiplicative, that is, Φ([ [ A,B ],C ]∗)=[ [ Φ(A),Φ(B) ],Φ(C) ]∗,∀A,B,C∈ℳif and only if Φ(A)=Φ(I)Ψ(A)for all A∈ℳ, where Ψ:ℳ→Nis a direct sum of a linear *-isomorphism and a conjugate linear *-isomorphism, Φ(I)is a central element in Nwith Φ(I)2=I′. The results about mixed Lie multiplicative maps on factor von Neumann algebras are generalized to von Neumann algebras with no central summands of type I1or I2.展开更多
本文在有限von Neumann代数的情形下应用广义奇异值的方法证明了一类迹函数的若干性质。特别地,我们将Hansen的主要结果推广至有限von Neumann代数的情形。In this paper, via the method of generalized singular values, we prove som...本文在有限von Neumann代数的情形下应用广义奇异值的方法证明了一类迹函数的若干性质。特别地,我们将Hansen的主要结果推广至有限von Neumann代数的情形。In this paper, via the method of generalized singular values, we prove some properties of a class of trace functions defined over finite von Neumann algebras. In particular, we extend the main results of Hansen to the context of finite von Neumann algebras.展开更多
研究一类退化Hessian商方程Neumann问题,通过选取恰当的辅助函数,利用极大值原理和基本对称函数的性质,在条件f1/k−l∈C1(Ω¯×ℝn)下得到该方程当f依赖于x,Du时解的全局梯度估计。In this paper, degenerate Hessian quotient ...研究一类退化Hessian商方程Neumann问题,通过选取恰当的辅助函数,利用极大值原理和基本对称函数的性质,在条件f1/k−l∈C1(Ω¯×ℝn)下得到该方程当f依赖于x,Du时解的全局梯度估计。In this paper, degenerate Hessian quotient equations with Neumann problem has studied. By choosing suitable auxiliary functions, using the maximum principle and the properties of basic symmetric functions, with the f1/k−l∈C1(Ω¯×ℝn)condition, the global gradient estimation for the admissible solution of the equations with dependent on x and Du has obtained.展开更多
We develop universal quantum computing models that form a family of quantum von Neumann architectures,with modular units of memory,control,CPU,and internet,besides input and output.This family contains three generatio...We develop universal quantum computing models that form a family of quantum von Neumann architectures,with modular units of memory,control,CPU,and internet,besides input and output.This family contains three generations characterized by dynamical quantum resource theory,and it also circumvents no-go theorems on quantum programming and control.Besides universality,such a family satisfies other desirable engineering requirements on system and algorithm design,such as modularity and programmability,hence serves as a unique approach to building universal quantum computers.展开更多
We prove the existence of solutions of the system for nonlocal Neumann problems with Minkowski-curvature operator(r^(N−1) u′/√(p 1−u′^(2)))′=r^(N−1)f(r,u),r 2(0,1),u′(0)=0,u′(1)=∫_(0)^(-) u′(s)dg(s),where k,N...We prove the existence of solutions of the system for nonlocal Neumann problems with Minkowski-curvature operator(r^(N−1) u′/√(p 1−u′^(2)))′=r^(N−1)f(r,u),r 2(0,1),u′(0)=0,u′(1)=∫_(0)^(-) u′(s)dg(s),where k,N≥1 are integers,f:[0,1]×R^(k)→R^(k) is continuous and g:[0,1]→R^(k) is a function of bounded variation.Our proof is based on the perturbation method.展开更多
We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bound...Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .展开更多
We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner...We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.展开更多
文摘Let M and N be two factor von Neumann algebras that their dimensions are large than 1,η≠-1 a non zero complex number and Φa(not necessary linear)bijection between two factor von Neumann algebras satisfying Φ(I)=I.For all A,B∈M,define by A■B=AB+BA the Jordan product of A and B,A·_(η)B=AB+ηBA^(*)the Jordan η-*-product of A and B,respectively.Let Φ and Φ^(-1)preserve the mixed Jordan triple η-*-products.It is proved that Φ is a linear *-isomorphism if η is not real and Φ is the sum of a linear *-isomorphism and a conjugate linear *-isomorphism if η is real.
文摘本文研究了在von Neumann代数框架下,投影运算后等价的保持情形,特别是在不同类型的von Neumann代数中投影等价的刻画及其性质。设E、F、N为von Neumann代数ℳ中的三个有限投影,且E~F。当NE=NF=0时,那么有N+E~N+F,N∧E~N∧F,N∨E~N∨F成立。当NE,NF时,那么有N∧E~N∧F,N∨E~N∨F成立。当EN,FN时,那么有N−E~N−F,N∧E~N∧F,N∨E~N∨F成立。本文进一步推至N为von Neumann代数ℳ中的无限投影,并且考虑了von Neumann代数ℳ中四个投影运算的情况。This paper studies the conditions of equivalents after projection operations under the framework of von Neumann algebra, especially the characterization and properties of projection equivalents in different types of von Neumann algebras. Let E,F,Nbe three finite projections in von Neumann algebra ℳ, and E~F. If NE=NF=0, then it follows that N+E~N+F, N∧E~N∧F, N∨E~N∨Fholds. If NE, NF, then it follows that N∧E~N∧F, N∨E~N∨Fholds. If EN, FN, then it follows that N−E~N−F, N∧E~N∧F, N∨E~N∨Fholds. This paper further extends these results to infinite projections Nin von Neumann algebras ℳand considers the case of four projection operations within von Neumann algebras ℳ.
文摘设ℳ和N是无I1或I2型中心直和项的von Neumann代数,其单位元分别为I和I′。本文证明非线性双射Φ:ℳ→N混合Lie可乘,即Φ([ [ A,B ],C ]∗)=[ [ Φ(A),Φ(B) ],Φ(C) ]∗,∀A,B,C∈ℳ,当且仅当存在线性*-同构和共轭线性*-同构的直和Ψ:ℳ→N使得Φ(A)=Φ(I)Ψ(A),∀A∈ℳ,其中Φ(I)∈N是可逆中心元且Φ(I)2=I′。该结论将因子von Neumann代数上的非线性混合Lie可乘双射的结果推广到无I1或I2型中心直和项的von Neumann代数。Let ℳand Nbe von Neumann algebras with no central summands of type I1or I2, Iand I′be the identities of them. This paper proves that a bijective map Φ:ℳ→Nis mixed Lie multiplicative, that is, Φ([ [ A,B ],C ]∗)=[ [ Φ(A),Φ(B) ],Φ(C) ]∗,∀A,B,C∈ℳif and only if Φ(A)=Φ(I)Ψ(A)for all A∈ℳ, where Ψ:ℳ→Nis a direct sum of a linear *-isomorphism and a conjugate linear *-isomorphism, Φ(I)is a central element in Nwith Φ(I)2=I′. The results about mixed Lie multiplicative maps on factor von Neumann algebras are generalized to von Neumann algebras with no central summands of type I1or I2.
文摘本文在有限von Neumann代数的情形下应用广义奇异值的方法证明了一类迹函数的若干性质。特别地,我们将Hansen的主要结果推广至有限von Neumann代数的情形。In this paper, via the method of generalized singular values, we prove some properties of a class of trace functions defined over finite von Neumann algebras. In particular, we extend the main results of Hansen to the context of finite von Neumann algebras.
文摘研究一类退化Hessian商方程Neumann问题,通过选取恰当的辅助函数,利用极大值原理和基本对称函数的性质,在条件f1/k−l∈C1(Ω¯×ℝn)下得到该方程当f依赖于x,Du时解的全局梯度估计。In this paper, degenerate Hessian quotient equations with Neumann problem has studied. By choosing suitable auxiliary functions, using the maximum principle and the properties of basic symmetric functions, with the f1/k−l∈C1(Ω¯×ℝn)condition, the global gradient estimation for the admissible solution of the equations with dependent on x and Du has obtained.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12047503 and 12105343)。
文摘We develop universal quantum computing models that form a family of quantum von Neumann architectures,with modular units of memory,control,CPU,and internet,besides input and output.This family contains three generations characterized by dynamical quantum resource theory,and it also circumvents no-go theorems on quantum programming and control.Besides universality,such a family satisfies other desirable engineering requirements on system and algorithm design,such as modularity and programmability,hence serves as a unique approach to building universal quantum computers.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11901464,12361040)the National Science Foundation of Gansu Province(Grant Nos.20JR10RA100,21JR1RA230)the Department of Education University Innovation Fund of Gansu Province(Grant Nos.2022A-218,2021A-006)。
文摘We prove the existence of solutions of the system for nonlocal Neumann problems with Minkowski-curvature operator(r^(N−1) u′/√(p 1−u′^(2)))′=r^(N−1)f(r,u),r 2(0,1),u′(0)=0,u′(1)=∫_(0)^(-) u′(s)dg(s),where k,N≥1 are integers,f:[0,1]×R^(k)→R^(k) is continuous and g:[0,1]→R^(k) is a function of bounded variation.Our proof is based on the perturbation method.
文摘We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.
文摘Given a compact and regular Hausdorff measure space (X, μ), with μ a Radon measure, it is known that the generalised space M(X) of all the positive Radon measures on X is isomorphic to the space of essentially bounded functions L<sup>∞</sup>(X, μ) on X. We confirm that the commutative von Neumann algebras M⊂B(H), with H=L<sup>2</sup>(X, μ), are unitary equivariant to the maximal ideals of the commutative algebra C(X). Subsequenly, we use the measure groupoid to formulate the algebraic and topological structures of the commutative algebra C(X) following its action on M(X) and define its representation and ergodic dynamical system on the commutative von Neumann algebras of M of B(H) .
文摘We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.
