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Takesaki-Takai Duality Theorem in Hilbert C^＊-Modules

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Acta Mathematica Sinica,English Series 2004年第6期20卷 1079-1088页

作者： mao zheng guo Xiao Xia ZHANG LMAM Department of Mathematics Peking University Department of Mathematics Yantai University

In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a unitary operator on H,and if E is an (?)-compatible Hilbert (?)-module, then E×(?)×(?)K(H),where K(H) is the set of all compact operators on H,and (?) and (?) are Hopf C~*-algebras corresponding to the Kac-system (H,V,U).

关键词： Coaction Crossed product Multiplicative unitary operator Hilbert C~*-module

The Characterization of a Class of Quantum Markov Semigroups and the Associated Operator-Valued Dirichlet Forms Based on Hilbert W＊-Module

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Acta Mathematica Sinica,English Series 2013年第5期29卷 857-866页

作者： Lun Chuan ZHANG mao zheng guo School of Information Science Renmin University of China School of Mathematical Science Peking University

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.

关键词： Hilbert W*-module quantum Markov semigroup operator-valued Dirichlet forms

The Galois Correspondence in Field Algebra of G-spin Model

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Acta Mathematica Sinica,English Series 2005年第4期21卷 673-680页

作者： Li Ning JIANG mao zheng guo Department of Mathematics Beijing Institute of Technology Beijing 100081. P. R. China LMAM Department of Mathematics Peking University. Beijing 100871. P. R. China

Suppose that G is a finite group and D（G） the double algebra of G. For a given subgroup H of G, there is a sub-Hopf algebra D（G; H） of D（G）. This paper gives the concrete construction of a D（G; H）-invariant su... 详细信息

关键词： G-spin model Double algebra Observable algebra Galois closed

Semi-Fredholm Spectrum and Weyl＇s Theorem for Operator Matrices

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Acta Mathematica Sinica,English Series 2006年第1期22卷 169-178页

作者： Xiao Hong CAO mao zheng guo Bin MENG College of Mathematics and Information Science Shanxi Normal University Xi'an 710062 P. R. China LMAM School of Mathematical Sciences Peking University Beijing 100871 P. R. China

When A ∈ B（H） and B ∈ B（K） are given, we denote by Mc an operator acting on the Hilbert space HΘ K of the form Me = （ A0 CB）. In this paper, first we give the necessary and sufficient condition for Mc to be an upper semi-Fredholm （lower semi-Fredholm, or Fredholm） operator for some C ∈B（K,H）. In addition, let σSF＋（A） = {λ ∈ C ： A-λI is not an upper semi-Fredholm operator} bc the upper semi-Fredholm spectrum of A ∈ B（H） and let σrsF- （A） = {λ∈ C ： A-λI is not a lower semi-Fredholm operator} be the lower semi Fredholm spectrum of A. We show that the passage from σSF±（A） U σSF±（B） to σSF±（Mc） is accomplished by removing certain open subsets of σSF-（A） ∩σSF＋（B） from the former, that is, there is an equality σSF±（A） ∪σSF± （B） = σSF± （Mc） ∪＆ where L is the union of certain of the holes in σSF±（Mc） which ilappen to be subsets of σSF- （A） A σSF＋（B）. Weyl＇s theorem and Browder＇s theorem are liable to fail for 2 × 2 operator matrices. In this paper, we also explore how Weyl＇s theorem, Browder＇s theorem, a-Weyl＇s theorem and a-Browder＇s theorem survive for 2 × 2 upper triangular operator matrices on the Hilbert space.

关键词： Semi-Fredholm operator Fredholm operator Spectrum Weyl's theorem

本刊英文版Vol.21(2005),No.4论文摘要(英文)

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数学学报（中文版） 2005年第5期48卷 1035-1040页

作者： Li Ning JIANG mao zheng guo The Galois Correspondence in Field Algebra of G-spin Model

Defect Engineering with Rational Dopants Modulation for High‑Temperature Energy Harvesting in Lead‑Free Piezoceramics

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Nano-Micro Letters 2025年第3期17卷 87-101页

作者： Kaibiao Xi Jianzhe guo Mupeng zheng Mankang Zhu Yudong Hou Key Laboratory of Advanced Functional Materials Ministry of EducationCollege of Materials Science and EngineeringBeijing University of TechnologyBeijing 100124People’s Republic of China

High temperature piezoelectric energy harvester(HTPEH)is an important solution to replace chemical battery to achieve independent power supply of HT wireless ***,simultaneously excellent performances,including high figure of merit(FOM),insulation resistivity(ρ)and depolarization temperature(Td)are indispensable but hard to achieve in lead-free piezoceramics,especially operating at 250°C has not been reported ***,well-balanced performances are achieved in BiFeO3–BaTiO3 ceramics via innovative defect engineering with respect to delicate manganese *** to the synergistic effect of enhancing electrostrictive coefficient by polarization configuration optimization,regulating iron ion oxidation state by high valence manganese ion and stabilizing domain orientation by defect dipole,comprehensive excellent electrical performances(Td=340°C,ρ250°C>10^(7)Ωcm and FOM_(250°C)=4905×10^(–15)m^(2)N^(−1))are realized at the solid solubility limit of manganese *** HT-PEHs assembled using the rationally designed piezoceramic can allow for fast charging of commercial electrolytic capacitor at 250°C with high energy conversion efficiency(η=11.43%).These characteristics demonstrate that defect engineering tailored BF-BT can satisfy high-end HT-PEHs requirements,paving a new way in developing selfpowered wireless sensors working in HT environments.

关键词： Lead-free piezoceramic Defect engineering Dopants modulation High-temperature Piezoelectric energy harvester

CaH2-promoted activity of Ni-carbonate interface for CO2 methanation

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Journal of Energy Chemistry 2025年第1期100卷 522-532页

作者： Jin-Peng Wang guo-Cui mao Hui-Lin Jiang Bao-Xia Dong Yun-Lei Teng School of Chemistry and Chemical Engineering Yangzhou University

Transition metal-carbonate interfaces often act as active sites in heterogeneous catalytic *** interface between transition metal and metal carbonate exhibits a dynamic equilibrium during the CO2hydrogenation reaction,involving surface carbonate hydrogenation and ***,there have been few reports on engineering the activity of the interface between transition metal and alkaline earth metal carbonate for catalytic *** work demonstrated that the incorporation of CaH2in Ni/CaCO3enhances the CO2methanation activity of the *** CO2conversion for Ni/CaH2-CaCO3reached 68.5%at 400°C,which was much higher than that of the Ni/CaCO3（31.6%） and Ni/CaH2-CaO （42.4%） ***,the Ni/CaH2-CaCO3catalysts remained stable during the stability test for 24 h at 400°C and 8 *** research revealed that CaH2played a crucial role in promoting the activity of the Ni-carbonate interface for ***2could modify the electronic structure of Ni and tune the structural properties of CaCO3to generate medium basic sites （OH groups）,which are favorable for the activation of H2and ***-situ Fourier transform infrared spectroscopy （FTIR） analysis combined with density functional theory calculations demonstrated that CO2activation occurs at the hydroxyl group （OH） on the CaH2-modified Ni-carbonate surface,leading to the formation of CO3H****,our study has confirmed that CO2methanation over the Ni/CaH2-CaCO3catalysts proceeds via the formate pathway.

关键词： CO 2 methanation Metal hydride Ni catalysts Carbonate Metal-carbonate interface

闭子模的酉等价与遗传C*-子代数的稳定同构问题

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数学学报（中文版） 2010年第6期53卷 1041-1044页

作者：张伦传郭懋正中国人民大学信息学院北京100872 北京大学数学科学学院北京100871

在Hilbert C~＊-模框架下,给出了闭子模之间的酉等价与相应的遗传C~＊-子代数的＊同构,及对应的开投影的等价性的关系定理.

关键词： C~*-模遗传C~*-子代数标准模框架

Synergistic effect of bonding heterogeneity and phonon localization in introducing excellent thermoelectric properties in layered heteroanionic NdZnSbO material

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Journal of Energy Chemistry 2025年第1期100卷 259-272页

作者： Da Wan Shuwei Tang Shulin Bai Xiaodong Li Peng Ai Wanrong guo Tuo zheng College of Materials Science and Engineering Liaoning Technical University Faculty of Chemistry Northeast Normal University

Layered rare-earth metal oxides, harnessing the dual properties of oxides and two-dimensional layered materials, exhibit remarkable thermal stability and quantum confinement effects. Therefore, this work adopts the first-principles calculation combined with the Boltzmann transport theory to predict the thermoelectric properties of NdZnSbO compound. The coexistence of weak interlayer van der Waals interactions, robust intralayer ionic bonding, and partial covalent bonding leads to remarkable bonding heterogeneity, which engenders pronounced phonon scattering and imposes constraints on thermal transport along the out-of-plane direction. The weakened chemical bonds induced by the antibonding states, together with the rattling-like behavior of the Zn atom, culminate in the profound anharmonicity in the layered NdZnSbO compound. The weakening bond and heavy element contribute to the softness of phonon modes, which significantly diminishes the phonon group velocity. The redistribution-dominated four-phonon scattering process spans a large optical gap, which effectively reduces the lattice thermal conductivity. The NdZnSbO compound exhibits direct semiconductor characteristic with a bandgap of 0.73 e V by adopting the Heyd-Scuseria-Ernzerhof(HSE06) functional in combination with spin–orbit coupling(SOC) effect. The multi-valley feature of NdZnSbO compound augur favorably for band degeneracy, thus amplifying the power factor. Consequently, an optimal figure-of-merit(ZT) of 3.40 at 900 K is achieved for the n-type NdZnSbO compound. The present study delves deeply insights into the origins for the low thermal conductivity of NdZnSbO compound and proposes an optimization scheme to enhance overall thermoelectric performance.

关键词： Bond strength (chemical)