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Equivariant Chern Classes of Orientable Toric Origami Manifolds

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Chinese Annals of mathematics,Series B 2024年第2期45卷 221-234页

作者： Yueshan XIONG Haozhi ZENG school of mathematics and StatisticsHuazhong University of science and Technology Wuhan 430074China

A toric origami manifold,introduced by Cannas da Silva,Guillemin and Pires,is a generalization of a toric symplectic *** a toric symplectic manifold,its equivariant Chern classes can be described in terms of the corresponding Delzant polytope and the stabilization of its tangent bundle splits as a direct sum of complex line *** in general a toric origami manifold is not simply connected,so the algebraic topology of a toric origami manifold is more difficult than a toric symplectic *** this paper they give an explicit formula of the equivariant Chern classes of an oriented toric origami manifold in terms of the corresponding origami ***,they prove the stabilization of the tangent bundle of an oriented toric origami manifold also splits as a direct sum of complex line bundles.

关键词： Equivariant Chern classes Toric origami manifolds Unitary structures Spin structures

Semisymmetric Graphs of Order 2p^(3)with Valency p^(2)

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Algebra Colloquium 2024年第2期31卷 199-208页

作者： Li Wang Songtao Guo Genghua Fan school of mathematics and Information science Henan Polytechnic University JiaozuoHenan 454000China school of mathematics and Statistics Henan University of Science and Technology LuoyangHenan 471023China 不详

A simple undirected regular graph is said to be semisymmetric if it is edge-transitive but not *** a semisymmetric graphΓof order 2p^(3),p a prime,it is well known thatΓis bipartite with two biparts having equal *** complete classification of such graphs has been given for the full automorphism group Aut(Γ)acting unfaithfully on at least one bipart ofΓ,which shows that there is only one infinite family of such graphs with valency p^(2).The graphs of this kind have been determined when Aut(Γ)acts faithfully and primitively on at least one bipart ofΓ,and thus there is only one remaining case for classifying such graphs of valency p^(2),Aut(Γ)acting faithfully and imprimitively on both biparts ofΓ,which is dealt with in this *** a result,there is only one infinite family of semisymmetric graphs of order 2p^(3)with valency p^(2).

关键词： semisymmetric graph semitransitive graph bi-coset graph

One-step hydrothermal synthesis of Cit-NaYbF_(4):Er^(3+)nanocrystals with enhanced red upconversion emission for in vivo fluorescence molecular tomography

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Journal of Rare Earths 2024年第1期42卷 36-45,I0002页

作者： Xiaoli Luo Qichen Chen Hongbo Guo Heng Zhang Xiaowei He Wu Zhao school of mathematics and Computer science Ningxia Normal UniversityGuyuan756099China school of Information science and Technology Northwest UniversityXi'an710127China

Fluorescence imaging techniques represent essential tools in in vitro,preclinical,and clinical *** this study,an improved one-step hydrothermal method to synthesize citric acid(CA)modifiedα-NaYbF_(4):2%Er^(3+)nanocrystals was *** introduction of various doping ions into NaYbF_(4):2%Er^(3+)and the different valence states of the same ions affect both the crystal size and upconversion luminesce *** fore,we investigated the upconversion luminesce nce enha ncement of NaYbF_(4):2%Er^(3+)by ion doping and find that the upconversion luminescence intensity of the upconversion nanoparticles(UCNPs)co-doped with 5 mol%Fe^(2+)ions shows the greatest enhancement,especially for red emission at654 ***,HeLa cells incubated with UCNPs allow for imaging with strong red upconversion emission detectio *** laser scanning microscope(CLSM)fluorescent images of HeLa cells indicate that NaYbF_(4):2%Er/5%Fe^(2+)leads to a clear outline and improves visualization of the cell *** addition,the CA coated NaYbF_(4):2%Er^(3+)/5%Fe^(2+)nanoparticles and NaYbF_(4):2%Er^(3+)/5%Fe^(2+)show low cytotoxicity in HeLa *** imaging reveals the efficiency of these UCNPs to analyze the lungs,liver,and ***,these results indicate that the Cit-NaYbF_(4):2%Er^(3+)/5%Fe^(2+)UCNPs are efficient nanoprobes for fluorescence molecular to mography.

关键词： Hydrothermal method Fe^(2+)ion doping Tuning size Nanoprobes Fluorescence imaging Rare earths

An anti-aliasing filtering of quantum images in spatial domain using a pyramid structure

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Chinese Physics B 2024年第5期33卷 223-237页

作者：吴凯周日贵罗佳 College of Information Engineering Shanghai Maritime UniversityShanghai 201306China Research Center of Intelligent Information Processing and Quantum Intelligent Computing Shanghai 201306China school of mathematics and computational science Shangrao Normal UniversityShangrao 334001China

As a part of quantum image processing,quantum image filtering is a crucial technology in the development of quantum ***-pass filtering can effectively achieve anti-aliasing effects on ***,most quantum image filterings are based on classical domains and grayscale images,and there are relatively fewer studies on anti-aliasing in the quantum *** paper proposes a scheme for anti-aliasing filtering based on quantum grayscale and color image scaling in the spatial *** achieves the effect of anti-aliasing filtering on quantum images during the scaling ***,we use the novel enhanced quantum representation(NEQR)and the improved quantum representation of color images(INCQI)to represent classical *** aliasing phenomena are more pronounced when images are scaled down,this paper focuses only on the anti-aliasing effects in the case of ***,we perform anti-aliasing filtering on the quantum representation of the original image and then use bilinear interpolation to scale down the image,achieving the anti-aliasing *** constructed pyramid model is then used to select an appropriate image for upscaling to the original image ***,the complexity of the circuit is *** to the images experiencing aliasing effects solely due to scaling,applying anti-aliasing filtering to the images results in smoother and clearer ***,the anti-aliasing filtering allows for manual intervention to select the desired level of image smoothness.

关键词： quantum color image processing anti-aliasing filtering algorithm quantum multiplier pyramid model

Improved error estimates for a modified exponential Euler method for the semilinear stochastic heat equation with rough initial data

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science China mathematics 2024年

作者： Xinping Gui Buyang Li Jilu Wang Beijing computational science Research Center Department of Applied mathematics The Hong Kong Polytechnic University school of science Harbin Institute of Technology

A class of stochastic Besov spaces BpL2(Ω;H~α(O)), 1≤ p ≤∞ and α ∈ [-2, 2], is introduced to characterize the regularity of the noise in the semilinear stochastic heat equation du-△udt = f(u)dt + d W(t),under the following conditions for some α ∈(0, 1]:‖(∫t)0e~(-(t-s)A)dW(S)‖_(L2(Ω;L2(O)))≤Cta/2and ‖(∫t)0e~(-(t-s)A)dW(S)‖_(B~∞L2(Ω;H~α(O)))≤C The conditions above are shown to be satisfied by both trace-class noises(with α = 1) and one-dimensional space-time white noises(with α =1/2). The latter would fail to satisfy the conditions with α =1/2 if the stochastic Besov norm ∥·∥_(B~∞L2(Ω;H~α(O)))is replaced by the classical Sobolev norm ∥·∥_(L2(Ω;H~α(O))), and this often causes reduction of the convergence order in the numerical analysis of the semilinear stochastic heat equation. In this paper, the convergence of a modified exponential Euler method, with a spectral method for spatial discretization,is proved to have order α in both the time and space for possibly nonsmooth initial data in L4(Ω;H~β(O)) withβ >-1, by utilizing the real interpolation properties of the stochastic Besov spaces and a class of locally refined stepsizes to resolve the singularity of the solution at t = 0.

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ANALYSIS OF THE IMPLICIT-EXPLICIT ULTRA-WEAK DISCONTINUOUS GALERKIN METHOD FOR CONVECTION-DIFFUSION PROBLEMS

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Journal of computational mathematics 2024年第1期42卷 1-23页

作者： Haijin Wang Anping Xu Qi Tao school of science Nanjing University of Posts and TelecommunicationsNanjing 210023China Beijing computational science Research Center Beijing 100193China

In this paper,we first present the optimal error estimates of the semi-discrete ultra-weak discontinuous Galerkin method for solving one-dimensional linear convection-diffusion ***,coupling with a kind of Runge-Kutta type implicit-explicit time discretization which treats the convection term explicitly and the diffusion term implicitly,we analyze the stability and error estimates of the corresponding fully discrete *** fully discrete schemes are proved to be stable if the time-stepτ≤τ0,whereτ0 is a constant independent of the mesh-size ***,by the aid of a special projection and a careful estimate for the convection term,the optimal error estimate is also obtained for the third order fully discrete *** experiments are displayed to verify the theoretical results.

关键词： The ultra-weak discontinuous Galerkin method Convection-diffusion Implicitexplicit time discretization Stability Error estimate

THE LIMIT CYCLE BIFURCATIONS OF A WHIRLING PENDULUM WITH PIECEWISE SMOOTH PERTURBATIONS

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Acta Mathematica Scientia 2024年第3期44卷 1115-1144页

作者：杨纪华 school of mathematics and Computer science Ningxia Normal UniversityGuyuan756000China Ningxia Basic science Research Center of mathematics Yinchuan750000China

This paper deals with the problem of limit cycles for the whirling pendulum equation x=y,y=sin x(cosx-r)under piecewise smooth perturbations of polynomials of cos x,sin x and y of degree n with the switching line x=*** upper bounds of the number of limit cycles in both the oscillatory and the rotary regions are obtained using the Picard-Fuchs equations,which the generating functions of the associated first order Melnikov functions ***,the exact bound of a special case is given using the Chebyshev *** the end,some numerical simulations are given to illustrate the existence of limit cycles.

关键词： whirling pendulum limit cycle Melnikov function Picard-Fuchs equation Chebyshev system

On limit fractional Volterra hierarchies

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Communications in Theoretical Physics 2024年第1期76卷 7-16页

作者： Lixiang Zhang Chuanzhong Li school of mathematics and Statistics Ningbo UniversityNingbo315211China College of mathematics and Systems science Shandong University of Science and TechnologyQingdao266590China

For the limit fractional Volterra(LFV)hierarchy,we construct the n-fold Darboux transformation and the soliton ***,we extend the LFV hierarchy to the noncommutative LFV(NCLFV)hierarchy,and construct the Darboux transformation expressed by quasi determinant of the noncommutative ***,we establish the relationship between new and old solutions of the NCLFV ***,the quasi determinant solutions of the NCLFV hierarchy are obtained.

关键词： limit fractional Volterra hierarchy noncommutative limit fractional Volterra hierarchy Darboux transformation soliton solution quasi determinant solution

Digital signal acquisition system for complex nuclear reaction experiments

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Nuclear science and Techniques 2024年第1期35卷 124-133页

作者： Wei-Liang Pu Yan-Lin Ye Jian-Ling Lou Jia-Hao Chen school of Physics and State Key Laboratory of Nuclear Physics and Technology Peking UniversityBeijing 100871China Institute of Applied Physics and computational mathematics Beijing 100094China

A digital data-acquisition system based on XIA LLC products was used in a complex nuclear reaction experiment using radioactive ion beams.A flexible trigger system based on a field-programmable gate array(FPGA)parametrization was developed to adapt to different experimental sizes.A user-friendly interface was implemented,which allows converting script language expressions into FPGA internal control *** proposed digital system can be combined with a conventional analog data acquisition system to provide more *** performance of the combined system was veri-fied using experimental data.

关键词： Digital signal acquisition system Trigger Programmable logic Timestamp