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
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
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
Von Hippel-Lindau病(VHL病)是VHL基因变异导致的遗传肿瘤综合征。VHL病相关肿瘤常为多发,其常规治疗方法为手术,但术后易复发。VHL基因具有缺氧诱导因子(HIF)依赖及HIF非依赖的肿瘤抑制作用,关于VHL病遗传学机制的研究为该病的治疗奠...Von Hippel-Lindau病(VHL病)是VHL基因变异导致的遗传肿瘤综合征。VHL病相关肿瘤常为多发,其常规治疗方法为手术,但术后易复发。VHL基因具有缺氧诱导因子(HIF)依赖及HIF非依赖的肿瘤抑制作用,关于VHL病遗传学机制的研究为该病的治疗奠定了基础。近年来针对VHL病遗传学机制靶向药物的出现,为该病的治疗提供了新的思路,作用于缺氧诱导通路的小分子靶向药物,如belzutifan、酪氨酸激酶抑制剂,在临床试验中对VHL病的治疗展示了良好的应用前景。本文对VHL病遗传学机制及相关治疗进展进行总结。针对VHL病靶向药物更深入的临床研究将会为该病患者提供更多的治疗选择。展开更多
Retinal hemangioblastomas(RHs)are among the most common manifestations of von Hippel-Lindau(VHL)disease,an autosomal dominant genetic disorder that predisposes individuals to various tumors,particularly in the retina,...Retinal hemangioblastomas(RHs)are among the most common manifestations of von Hippel-Lindau(VHL)disease,an autosomal dominant genetic disorder that predisposes individuals to various tumors,particularly in the retina,central nervous system,kidney,adrenal gland,pancreas,and reproductive tract.VHL disease arises from variants in the VHL tumor suppressor gene,leading to the loss of VHL protein function.This protein regulates the degradation of hypoxia-inducible factors(HIFs)under normal oxygen conditions,but,in VHL disease,the loss of functional VHL protein results in the stabilization of HIFs,particularly HIF-2α,even in normoxia.The persistent activity of HIF-2αdrives the overexpression of factors including transforming growth factor alpha(TGF-α),platelet-derived growth factor beta(PDGF-β),epidermal growth factor receptor(EGFR),glucose transporter 1(GLUT-1)and vascular endothelial growth factor(VEGF)and others.Histologically,these tumors consist of tightly packed capillaries surrounded by stromal cells,which are the primary neoplastic components.Clinically,RHs often represent one of the earliest manifestations of VHL disease and can lead to significant visual impairment or blindness if untreated.Current conventional treatment approaches include ablative therapies such as laser photocoagulation and cryotherapy,both of which are destructive,and can be successful if the tumors are of amenable size and location.Intravitreal anti-VEGF therapies are administered to reduce retinal edema.Effective therapies for large tumors and those located on the optic nerve are severely limited.However,recent advances in our understanding of the HIF-VEGF pathway have led to the development of targeted therapies,such as HIF-2αinhibitors like belzutifan,which have demonstrated promising results in reducing tumor burden and improving outcomes.These novel treatments offer hope for more effective and less invasive management of RHs within the broader context of VHL disease.展开更多
This article explores Adam Schall von Bell’s Investigations of the Earth’s Interior(Kunyu gezhi坤輿格致,1639-1640),a significant Jesuit work aimed at reforming the Chinese mining and smelting industry by introducing...This article explores Adam Schall von Bell’s Investigations of the Earth’s Interior(Kunyu gezhi坤輿格致,1639-1640),a significant Jesuit work aimed at reforming the Chinese mining and smelting industry by introducing relevant European technologies during the late Ming period.After being lost for centuries,the recent rediscovery of a partial manuscript housed in the Nanjing Library has reinvigorated scholarly interest in this treatise.The authors present findings on the manuscript’s origins,dating,and its reliance on Georgius Agricola’s De re metallica alongside other Renaissance works,such as those by Lazarus Ercker or Vannoccio Biringuccio.They challenge claims that the Investigations of the Earth’s Interior introduced the Western concept of“minerals”(kuangwu礦物)to China,arguing that the term retained its traditional meaning of“ores and materials.”Additionally,the article presents new historical documents revealing attempts to implement the treatise’s methods and the bureaucratic challenges that prevented its widespread adoption.These topics shed light on the Investigations of the Earth’s Interior’s role in early global knowledge transmission and its potential impact on China’s mining and metallurgical practices during the Ming-Qing transition.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.
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.
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) .
基金supported by the intramural research program of the National Eye Institute。
文摘Retinal hemangioblastomas(RHs)are among the most common manifestations of von Hippel-Lindau(VHL)disease,an autosomal dominant genetic disorder that predisposes individuals to various tumors,particularly in the retina,central nervous system,kidney,adrenal gland,pancreas,and reproductive tract.VHL disease arises from variants in the VHL tumor suppressor gene,leading to the loss of VHL protein function.This protein regulates the degradation of hypoxia-inducible factors(HIFs)under normal oxygen conditions,but,in VHL disease,the loss of functional VHL protein results in the stabilization of HIFs,particularly HIF-2α,even in normoxia.The persistent activity of HIF-2αdrives the overexpression of factors including transforming growth factor alpha(TGF-α),platelet-derived growth factor beta(PDGF-β),epidermal growth factor receptor(EGFR),glucose transporter 1(GLUT-1)and vascular endothelial growth factor(VEGF)and others.Histologically,these tumors consist of tightly packed capillaries surrounded by stromal cells,which are the primary neoplastic components.Clinically,RHs often represent one of the earliest manifestations of VHL disease and can lead to significant visual impairment or blindness if untreated.Current conventional treatment approaches include ablative therapies such as laser photocoagulation and cryotherapy,both of which are destructive,and can be successful if the tumors are of amenable size and location.Intravitreal anti-VEGF therapies are administered to reduce retinal edema.Effective therapies for large tumors and those located on the optic nerve are severely limited.However,recent advances in our understanding of the HIF-VEGF pathway have led to the development of targeted therapies,such as HIF-2αinhibitors like belzutifan,which have demonstrated promising results in reducing tumor burden and improving outcomes.These novel treatments offer hope for more effective and less invasive management of RHs within the broader context of VHL disease.
文摘This article explores Adam Schall von Bell’s Investigations of the Earth’s Interior(Kunyu gezhi坤輿格致,1639-1640),a significant Jesuit work aimed at reforming the Chinese mining and smelting industry by introducing relevant European technologies during the late Ming period.After being lost for centuries,the recent rediscovery of a partial manuscript housed in the Nanjing Library has reinvigorated scholarly interest in this treatise.The authors present findings on the manuscript’s origins,dating,and its reliance on Georgius Agricola’s De re metallica alongside other Renaissance works,such as those by Lazarus Ercker or Vannoccio Biringuccio.They challenge claims that the Investigations of the Earth’s Interior introduced the Western concept of“minerals”(kuangwu礦物)to China,arguing that the term retained its traditional meaning of“ores and materials.”Additionally,the article presents new historical documents revealing attempts to implement the treatise’s methods and the bureaucratic challenges that prevented its widespread adoption.These topics shed light on the Investigations of the Earth’s Interior’s role in early global knowledge transmission and its potential impact on China’s mining and metallurgical practices during the Ming-Qing transition.
