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Bi-Frobenius Algebra Structures on Quantum Complete Intersections

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1481-1504页

作者： hai JIN Pu zhang School of Mathematical Sciences Shanghai Jiao Tong UniversityShanghai 200240P.R.China

This paper is to look for bi-Frobenius algebra structures on quantum complete intersections over field *** find a class of comultiplications,such that if√−1∈k,then a quantum complete intersection becomes a bi-Frobenius algebra with comultiplication of this form if and only if all the parameters qij=±***,it is proved that if√−1∈k then a quantum exterior algebra in two variables admits a bi-Frobenius algebra structure if and only if the parameter q=±√*** if−1/∈k,then the exterior algebra with two variables admits no bi-Frobenius algebra *** prove that the quantum complete intersections admit a bialgebra structure if and only if it admits a Hopf algebra structure,if and only if it is commutative,the characteristic of k is a prime p,and every ai a power of *** also provides a large class of examples of bi-Frobenius algebras which are not bialgebras(and hence not Hopf algebras).In commutative case,other two comultiplications on complete intersection rings are given,such that they admit non-isomorphic bi-Frobenius algebra structures.

关键词： Bi-Frobenius algebras coalgebras bialgebras Hopf algebras quantum complete intersections quantum exterior algebras

Dynamics of a Reaction-diffusion-ODE System in a Heterogeneous Media

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 275-301页

作者： Cong-hui zhang hai-fe.g zhang Mei-rong zhang School of Science Beijing University of Civil Engineering and ArchitectureBeijing 102616China Institute of Applied System Analysis Jiangsu UniversityZhenjiang 212013China Department of Mathematical Sciences Tsinghua UniversityBeijing 100084China

The existence and stability of stationary solutions for a reaction-diffusion-ODE system are investigated in this *** first show that there exist both continuous and discontinuous stationary *** a good understanding of the stability of discontinuous stationary solutions is gained under an appropriate *** addition,we demonstrate the influences of the diffusion coefficient on stationary *** results we obtained are based on the super-/sub-solution method and the generalized mountain pass ***,some numerical simulations are given to illustrate the theoretical results.

关键词： reaction-diffusion-ODE system discontinuous stationary solutions stability asymptotic behavior monotone solutions

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Discovery of the choristodere Hyphalosaurus baitaigouensis from the Lower Cretaceous Jiufotang Formation of western Liaoning,China and its paleobiogeographic significance

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Journal of Palaeogeography 2024年第3期13卷 547-562页

作者： Li-Jun zhang Shu-An Ji hai-Chun zhang South China Sea Culture Museum Hainan Tropical Ocean UniversitySanya 572022Hainan ProvinceChina Key Laboratory of Stratigraphy and Paleontology Ministry of Natural ResourcesInstitute of GeologyChinese Academy of Geological SciencesBeijing 100037China State Key Laboratory of Palaeobiology and Stratigraphy Nanjing Institute of Geology and Palaeontology and Center for Excellence in Life and PaleoenvironmentChinese Academy of SciencesNanjing 210008Jiangsu ProvinceChina

The water-living reptile genus Hyphalosaurus was previously discovered in the Lower Cretaceous Yixian Formation bearing the middle Jehol Biota in western Liaoning,*** complete skeletons of Hyphalosaurus are reported for the first time from the Jiufotang Formation bearing the late Jehol Biota at two sites in western *** show the typical characteristics of Hyphalosaurus baitaigouensis in terms of the contact between some cranial bones and the number of cervical and dorsal vertebrae,and therefore are assigned to *** discovery extends the stratigraphic range of this species from the Yixian Formation to the overlying Jiufotang *** paper further briefly compares the main characteristics of the two skeletons,summarizes the temporal and spatial distribution of Hyphalosaurus,and discusses the palaeogeographic evolution of western Liaoning at the middle and late Jehol Biota stages based on the aquatic habits of Hyphalosaurus and the geological background of western *** analytical results show that the volcanic downwarped lakes,with distinct geographical divisions in western Liaoning during the deposition of the Yixian Formation,had not completely disappeared till the deposition of the Jiufotang *** palaeo-lake in the Fuxin-Yixian Basin underwent the process of generation,expansion and shrinkage during the depositional period of the Yixian Formation and finally merged into a large *** palaeo-Dalinghe River,which connected the main basins in western Liaoning during the depositional period of the Jiufotang Formation,was formed simultaneously.

关键词： Western liaoning Jehol biota Jiufotang formation Hyphalosaurus baitaigouensis Palaeobiogeography

Derivation of Expanded Isospectral-Nonisospectral Integrable Hierarchies via the Column-vector Loop Algebra

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 778-800页

作者： hai-fe.g WANg Yu-fe.g zhang School of Science Jimei UniversityXiamen 361021China School of Mathematics China University of Mining and TechnologyXuzhou 221116China

A scheme for generating nonisospectral integrable hierarchies is *** on the method,we deduce a nonisospectral hierarchy of soliton equations by considering a linear spectral *** follows that the corresponding expanded isospectral and nonisospectral integrable hierarchies are deduced based on a 6 dimensional complex linear space ■.By reducing these integrable hierarchies,we obtain the expanded isospectral and nonisospectral derivative nonlinear Schr?dinger *** using the trace identity,the biHamiltonian structure of these two hierarchies are also ***,some symmetries and conserved quantities of the resulting hierarchy are discussed.

关键词： expanded isospectral-nonisospectral integrable hierarchies column-vector loop algebra bi-Hamiltonian structure symmetry

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Design optimization of a hexapod vibration isolation system for electro-optical payload

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Chinese Journal of Aeronautics 2024年第2期37卷 330-342页

作者： Jing LI Weipeng LI Xiaoyan zhang hai HUANg School of Astronautics Beihang UniversityBeijing 100191China

The electro-optical payloads on mobile platforms generally suffer undesirable vibrations generated by maneuvers and *** vibrations are in six degrees of freedom and cause line-of-sight jitters,resulting in image blurring and loss of tracking *** this paper,a Hexapod Vibration Isolation System(HVIS)is proposed and optimized to solve this *** optimization aims to centralize and minimize the natural frequencies of HVIS,for expanding the vibration isolation bandwidth and improving the vibration isolation in the higher frequency *** that the design space for HVIS is limited and interfered with the frames of the mobile platform,a non-collision algorithm is proposed and applied in the optimization to obtain the feasible optimal *** optimization result shows that the natural frequency bandwidth has been reduced by 42.9%,and the maximum natural frequency is reduced by 30.2%.The prototypes of initial and optimal designs are manufactured and *** simulated and experimental results demonstrate the validity of the optimization,and the optimal design provides a maximum of 15 dB more isolation in rotation direction than the initial design.

关键词： Electro-optical payload Vibrations Isolation system Hexapod Optimization Non-collision design

Learning topological defects formation with neural networks in a quantum phase transition

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Communications in Theoretical Physics 2024年第5期76卷 68-76页

作者： Han-Qing Shi hai-Qing zhang Center for gravitational Physics Department of Space ScienceBeihang UniversityBeijing 100191China Peng Huanwu Collaborative Center for Research and Education Beihang UniversityBeijing 100191China

Neural networks possess formidable representational power,rendering them invaluable in solving complex quantum many-body *** they excel at analyzing static solutions,nonequilibrium processes,including critical dynamics during a quantum phase transition,pose a greater challenge for neural *** address this,we utilize neural networks and machine learning algorithms to investigate time evolutions,universal statistics,and correlations of topological defects in a one-dimensional transverse-field quantum Ising ***,our analysis involves computing the energy of the system during a quantum phase transition following a linear quench of the transverse magnetic field *** excitation energies satisfy a power-law relation to the quench rate,indicating a proportional relationship between the excitation energy and the kink ***,we establish a universal power-law relationship between the first three cumulants of the kink numbers and the quench rate,indicating a binomial distribution of the ***,the normalized kink-kink correlations are also investigated and it is found that the numerical values are consistent with the analytic formula.

关键词： neural networks machine learning transverse-field quantum Ising model kibble-zurek mechanism

Synthesis of hierarchically porous carbon materials by zinc salts-assisted carbonization of biomass and organic solid wastes

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Particuology 2024年第1期84卷 45-52页

作者： Le-Le zhang Lei Tong Yanwei Ding Wanqun zhang hai-Wei Liang Hefei National Research Center for Physical Sciences at the Microscale Department of ChemistryUniversity of Science and Technology of ChinaHefei230026China

Hierarchically porous carbons(HPCs)with multimodal pores have attracted considerable attention due to their unique physical and chemical properties and various application potentials in heterogeneous catalysis,environmental treatment,and energy storage and ***,we report a general and simple zinc salts-assisted method for the synthesis of HPCs with varied porosity and chemical func-tionalities by the direct carbonization of diverse biomass and *** the carbonization,zinc salts are thermally decomposed into nanoparticles that serve as in-situ templates to introduce nanopores in *** prepared HPCs exhibit high specific surface areas(up to 2432 m2 g-1),large pore volumes(up to 4.30 cm^(3)g^(-1)),and broad pore size ***,the zinc salts can be recovered and recycled,supporting the sustainable production of HPCs on large *** prepared HPCs-supported catalysts with atomically dispersed metal sites exhibit promising electrocatalytic performance for the oxygen reduction reaction.

关键词： Hierarchical porous carbon Zinc salts Biomass Wastes Electrocatalysis

Possibilities for the synthesis of superheavy element Z=121 in fusion reactions

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Nuclear Science and Techniques 2024年第6期35卷 90-100页

作者： Ming-Hao zhang Yu-hai zhang Ying Zou Xiu-Xiu Yang gen zhang fe.g-Shou zhang The Key Laboratory of Beam Technology of Ministry of Education College of Nuclear Science and TechnologyBeijing Normal UniversityBeijing 100875China Institute of Radiation Technology Beijing Academy of Science and TechnologyBeijing 100875China School of Physical Science and Technology Guangxi UniversityNanning 530004China National Laboratory of Heavy Ion Accelerator of Lanzhou Center of Theoretical Nuclear PhysicsLanzhou 730000China

Based on the dinuclear system model,the calculated evaporation residue cross sections matched well with the current experimental *** synthesis of superheavy elements Z=121 was systematically studied through combinations of stable projectiles with Z=21-30 and targets with half-lives exceeding 50 *** influence of mass asymmetry and isotopic dependence on the projectile and target nuclei was investigated in *** reactions^(254)Es(^(46)Ti,3n)^(297)121 and^(252)Es(^(46)Ti,3n)^(295)121 were found to be experimentally feasible for synthesizing superheavy element Z=121,with maximal evaporation residue cross sections of 6.619 and 4.123 fb at 219.9 and 223.9 MeV,respectively.

关键词： Superheavy nuclei Dinuclear system model Fusion reaction Evaporation residue cross section

ferromagnetism and insulating behavior with a logarithmic temperature dependence of resistivity in Pb_(10-x)Cux(PO_(4))_(6)O

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Science China(Physics,Mechanics & Astronomy) 2024年第1期67卷 106-111页

作者： Yuhang zhang Cong Liu Xiyu Zhu hai-Hu Wen Center for Superconducting Physics and Materials National Laboratory of Solid State Microstructures and Department of PhysicsNational Collaborative Innovation Center of Advanced MicrostructuresNanjing UniversityNanjing 210093China

Recent claim of discovering above-room-temperature superconductivity(Tc≈400 K)at ambient pressure in copper doped apatite Pb10(PO_(4))_(6)O has stimulated world-wide enthusiasm and impulse of motion.A lot of follow-up works have been carried out with controversial *** check whether superconductivity is really present or absent in the material,we need samples which should have a rather pure phase of Pb_(10-x)Cux(PO_(4))_(6)*** we report the characterization results from the Pb_(10-x)Cux(PO_(4))_(6)O with a fraction of about 97 wt.%inferred from the fitting to the X-ray diffraction pattern,if assuming Cu2S as the only *** resistivity measurements show that it is a semiconductor characterized roughly by a ln(1/T)temperature dependence in wide temperature region without trace of *** measurements show that it has a general ferromagnetic signal with a weak superparamagnetic *** grains of the sample show clear interactions with a Nb fe B *** detected Cu concentration is much lower than the expected nominal *** results show the absence of metallicity and superconductivity in Pb_(10-x)Cux(PO_(4))_(6)O at ambient pressure,and suggest the presence of strong correlation effect.

关键词： superconductivity Pb10(PO4)6O ferromagnetic correlation effect