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Some Poly.omial Maps with Jacobian Rank Two or Three

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Algebra Colloquium 2022年第2期29卷 341-360页

作者： dan y.n MOE-LCSM School of Mathematics and Statistics Hunan Normal UniversityChangsha 410081China

We classify.all poly.omial maps of the form H=(u(x,y.z),v(x,y.z),h(x,y.)in the case when the Jacobian matrix of H is nilpotent and the highest degree of z in v is no more than *** addition,we generalize the structure of poly.omial maps H to H=(H_(1)(x_(1),x_(2),…,x_(n)),b_(3)x_(3)+…+b_(n)x_(n)+H^((0))_(2)(x_(2)),H_(3)(x_(1),x_(2)),…,H_(n)(x_(1),x_(2))).

关键词： Jacobian conjecture nilpotent Jacobian matrix poly.omial maps

Polarization and exchange effects in elastic scattering of electron with atoms and ions

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Chinese Phy.ics B 2018年第5期27卷 179-186页

作者： Zhang-Jin Chen dan-dan Cui Department of Phy.ics College of Science Shantou University Guangdong 515063 China

Laser-induced electron diffraction（LIED）, in which elastic scattering of the returning electron with the parent ion takes place, has been used to extract atomic potential and image molecular structures with sub-？A precision and exposure time of a few femtoseconds. So far, the polarization and exchange effects have not been taken into account in the theoretical calculation of differential cross section（DCS） for the laser-induced rescattering processes. However, the validity.of this theoretical treatment has never been verified. In this work, we investigate the polarization and exchange effects on electron impact elastic scattering with rare gas atoms and ions. It is found that, while the exchange effect generally.play. a more important role than the polarization effect in the elastic scattering process, the exchange effect is less important on electron–ion collisions than on electron–atom collisions, especially.for scattering in backward direction. In addition, our calculations show that, for electron–atom collisions at incident energies above 50 e V, both the polarization and exchange effects can be safely.neglected, while for electron–ion collisions, both the polarization and exchange potentials do not make substantial contributions to the DCS at incident energies above 20 e V and scattering angles larger than 90？. Our investigation confirms the validity.of the current LIED method.

关键词： polarization exchange elastic scattering differential cross sections

Research of Methods for Lost Data Reconstruction in Erasure Codes over Binary.Fields

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Journal of Electronic Science and Technology 2016年第1期14卷 43-48页

作者： dan Tang the Software Engineering College Chengdu University of Information Technology

In the process of encoding and decoding,erasure codes over binary.fields,which just need AND operations and XOR operations and therefore have a high computational efficiency.are widely.used in various fields of information technology.A matrix decoding method is proposed in this *** method is a universal data reconstruction scheme for erasure codes over binary.*** a pre-judgment that whether errors can be recovered,the method can rebuild sectors of loss data on a fault-tolerant storage sy.tem constructed by.erasure codes for disk *** reconstruction process of the new method has simple and clear steps,so it is beneficial for implementation of computer *** more,it can be applied to other non-binary.fields easily.so it is expected that the method has an extensive application in the future.

关键词： Binary.fields data reconstruction decoding erasure codes

Minimal surfaces in a unit sphere pinched by.intrinsic curvature and normal curvature

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Science China Mathematics 2019年第9期62卷 1779-1792页

作者： dan y.ng School of Mathematics Liaoning University

We establish a nice orthonormal frame field on a closed surface minimally.immersed in a unit sphere Sn, under which the shape operators take very.simple forms. Using this frame field, we obtain an interesting property.K + K^N= 1 for the Gauss curvature K and the normal curvature K^N if the Gauss curvature is positive. Moreover, using this property.we obtain the pinching on the intrinsic curvature and normal curvature, the pinching on the normal curvature, respectively.

关键词： minimal surface normal curvature Gauss curvature pinching

Real-valued valuations on Sobolev spaces

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Science China Mathematics 2016年第5期59卷 921-934页

作者： MA dan Institut für Diskrete Mathematik und Geometrie Technische Universitat Wien Wien 1040 Austria

Continuous, SL(n) and translation invariant real-valued valuations on Sobolev spaces are *** centro-affine Hadwiger's theorem is applied. In the homogeneous case, these valuations turn out to be L^p-norms raised to p-... 详细信息

关键词： Sobolev space valuation convex poly.ope

THE NAVIER-STOKES EQUATIONS WITH THE KINEMATIC AND VORTICITy.BOUNDARy.CONDITIONS ON NON-FLAT BOUNDARIES

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Acta Mathematica Scientia 2009年第4期29卷 919-948页

作者： dan Osborne Mathematical Institute University of Oxford 24-29 St Giles

We study.the initial-boundary.value problem of the Navier-Stokes equations for incompressible fluids in a general domain in R^n with compact and smooth boundary. subject to the kinematic and vorticity.boundary.conditions on the non-flat boundary. We observe that, under the nonhomogeneous boundary.conditions, the pressure p can be still recovered by.solving the Neumann problem for the Poisson equation. Then we establish the well-posedness of the unsteady.Stokes equations and employ.the solution to reduce our initial-boundary.value problem into an initial-boundary.value problem with absolute boundary.conditions. Based on this, we first establish the well-posedness for an appropriate local linearized problem with the absolute boundary.conditions and the initial condition （without the incompressibility.condition）, which establishes a velocity.mapping. Then we develop apriori estimates for the velocity.mapping, especially.involving the Sobolev norm for the time-derivative of the mapping to deal with the complicated boundary.conditions, which leads to the existence of the fixed point of the mapping and the existence of solutions to our initial-boundary.value problem. Finally. we establish that, when the viscosity.coefficient tends zero, the strong solutions of the initial-boundary.value problem in R^n（n ≥ 3） with nonhomogeneous vorticity.boundary.condition converge in L^2 to the corresponding Euler equations satisfy.ng the kinematic condition.

关键词： Navier-Stokes equations incompressible vorticity.boundary.condition kinematic boundary.condition absolute boundary.condition non-flat boundary general domain Stokes operator Neumann problem Poisson equation vorticity strong solutions inviscid limit slip boundary.condition

Controllable nitridation of Ta_(2)_(O5) in molten salts for enhanced photocataly.is

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International Journal of Minerals,Metallurgy.and Materials 2020年第12期27卷 1703-1710页

作者： Jing Zhou dan-dan Nie Xian-bo Jin Wei Xiao College of Chemistry.and Molecular Sciences Hubei Key Laboratory of Eletrochermical Power SourexWuhan Lniversitwuhan 430072China Sschool of Resouwce and Einvironmental Sciences Hubei lnternational Scientifie and Teehnological Cooperation Base of Sustainable Rexource and EnergyWuhan UniversityWuhan 430072China

Py.oly.is of the Ta_(2)_(O5)/melamine mixture in molten chlorides is herein demonstrated as a facile and controllable method to nitridize and functionalize Ta_(2)_(O5).The influence of the stoichiometry.and composition of Ta_(2)_(O5)/melamine in molten salts on the nitridation process is rationalized to ensure the controllable preparation of Ta_(3)N_(5) and Ta_(3)N_(5)/*** characterization results,including scanning electron microscopy.transmission electron microscopy.elemental mapping,X-ray.photoelectron spectroscopy.and photoluminescence spectroscopy.all confirm the existence of the Ta_(3)N_(5)/TaON heterojunction,in which the TaON nanoparticles are closely.anchored to the Ta_(3)N_(5) *** from its composition and structure,the Ta_(3)N_(5)/TaON composites show enhanced photocataly.ic activity.for the degradation of methy.ene *** present study.highlights that the molten salt method using a solid nitrogen source can be a new technique for rationalizing the design of nitrides and oxy.itrides.

关键词： molten salts photocataly.is Ta_(3)N_(5) TaON heterojunction

Coaxial Fe_(2)O_(3)/TiO_(2)nanotubes for enhanced photo-Fenton degradation of electron-deficient organic contaminant

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Rare Metals 2021年第12期40卷 3543-3553页

作者： y.e Li dan-dan Cheng y.n Luo Li-Xia y.ng Henan International Joint Laboratory.of Rare Earth Composite Materials School of Materials and Chemical EngineeringHenan University of EngineeringZhengzhou 451191China High Level Laboratory.of Jiangxi Province for Persistent Pollutants Control Recycle and ReuseNanchang Hangkong UniversityNanchang 330063China

Coaxial Fe_(2)O_(3)/TiO_(2)nanotubes(Fe_(2)O_(3)/TiO_(2)NTs)were prepared by.two anodic oxidation *** sy.thesized Fe_(2)O_(3)/TiO_(2)NTs cataly.ts showed high photocataly.ic activity.in heterogeneous photo-Fenton *** the help of Fe_(2)O_(3)/TiO_(2)NTs,4-nitrophenol(10 mg·L^(-1),50 ml),a ty.ical electron-deficient organic contaminant,can be completely.removed by.adding only..4 mmol·L^(-1)of H_(2)O_(2)under *** results clarify.that the calculated position of Fe_(2)O_(3)/TiO_(2)NTs valence band is at 2.944 eV,its potential is higher than the potential of OH~-/·OH(2.800 eV),thereby.ensuring the generation of·***,the transformation of photogenerated electrons from the conduction band of TiO_(2)to Fe_(2)O_(3)accelerates the reduction of Fe^(3+)to Fe^(2+).The unstable Fe^(2+)can be oxidized by.H_(2)O_(2)to produce high y.elds of·***,both the coaxial heterojunction and fast Fe^(2+)/Fe^(3+)conversion provide abundant·OH to effective attack the electron-deficient benzene ring passivated by.the nitro ***,surface-cataly.ed degradation of 4-nitrophenol can be carried out step by.*** work contributes a detailed understanding of charge transfer in semiconductor composites and degradation of organic contaminants.

关键词： Fe_(2)O_(3) TiO_(2) Coaxial Electron Deficient organic contaminant Photo-Fenton cataly.is

Irreversible rapid changes of magnetic field associated with the 2012 October 23 circular near-limb X1.8 Flare

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Research in Astronomy.and Astrophy.ics 2016年第6期16卷 99-104页

作者： dan-dan y. Chang Liu Haimin Wang Space Weather Research Laboratory.and Big Bear Solar Observatory New Jersey Institute of TechnologyUniversity Heights

It has been found that photospheric magnetic fields can change in accordance with restructuring of the three-dimensional magnetic field following solar eruptions. Previous studies mainly.use vector mag- netic field data taken for events near the disk center. In this paper, we analy.e the magnetic field evolution associated with the 2012 October 23 X1.8 flare in NOAA AR 11598 that is close to the solar limb, using both the 45 s cadence line-of-sight and 12 min cadence vector magnetograms from the Helioseismic and Magnetic Imager on board Solar Dy.amics Observatory. This flare is classified as a circular-ribbon flare with spine-fan ty.e magnetic topology.containing a null point. In the line-of-sight magnetograms, there are two apparent polarity.inversion lines （PILs）. The PIL closer to the limb is affected more by.the projection effect. Between these two PILs there lie positive polarity.magnetic fields, which are surrounded by.negative polarity.fields outside the PILs. We find that after the flare, both the apparent limb-ward and disk-ward negative fluxes decrease, while the positive flux in-between increases. We also find that the horizontal mag- netic fields have a significant increase along the disk-ward PIL, but in the surrounding area, they.decrease. Sy.thesizing the observed field changes, we conclude that the magnetic fields collapse toward the surface above the disk-ward PIL as depicted in the coronal implosion scenario, while the peripheral field turns to a more vertical configuration after the flare. We also suggest that this event is an asy.metric circular-ribbon flare： a flux rope is likely.present above the disk-ward PIL. Its eruption causes instability.of the entire fan-spine structure and the implosion near that PIL.

关键词： Sun flares -- Sun magnetic field