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General Solutions of First-Order Algebraic ODEs in Simple Constant Extensions

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系统科学与复杂性学报:英文版 2023年第4期36卷 1769-1788页

作者： MITTERAMSKOGLER Johann Josef winkler franz Research Institute for Symbolic Computation(RISC) Johannes Kepler Universität LinzA-4040 LinzAustria

If a first-order algebraic ODE is defined over a certain differential field,then the most elementary solution class,in which one can hope to find a general solution,is given by the adjunction of a single arbitrary constant to this *** of this type give rise to a particular kind of generic point—a rational parametrization—of an algebraic curve which is associated in a natural way to the ODE’s defining *** for the opposite direction,we show that a suitable rational parametrization of the associated curve can be extended to a general solution of the ODE if and only if one can find a certain automorphism of the solution *** automorphisms are determined by linear rational functions,i.e.,Möbius *** properties of rational parametrizations,in combination with the particular shape of such automorphisms,lead to a number of necessary conditions on the existence of general solutions in this solution ***,the desired linear rational function can be determined by solving a comparatively simple differential system over the ODE’s field of *** results hold for arbitrary differential fields of characteristic zero.

关键词： Algebraic curve algebraic differential equation general solution Möbius transformation rational parametrization

RATIONAL GENERAL SOLUTIONS OF HIGHER ORDER ALGEBRAIC ODES

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Journal of Systems Science & Complexity 2013年第2期26卷 261-280页

作者： HUANG Yanli NG L X Chu winkler franz School of Computer Science and Software Engineering Tianjin Polytechnic University Research Institute for Symbolic Computation(RISC) Johannes Kepler University Department of Mathematics Quy Nhon University

This paper generalizes the method of Ng6 and winkler （2010, 2011） for finding rational general solutions of a first order non-autonomous algebraic ordinary differential equation （AODE） to the case of a higher order AODE, provided a proper parametrization of its solution hypersurface. The authors reduce the problem of finding the rational general solution of a higher order AODE to finding the rational general solution of an associated system. The rational general solutions of the original AODE and its associated system are in computable 1-1 correspondence. The authors give necessary and sufficient conditions for the associated system to have a rational solution based on proper reparametrization of invariant algebraic space curves. The authors also relate invariant space curves to first integrals and characterize rationally solvable systems by rational first integrals.

关键词： Algebraic ODE associated system invariant algebraic space curve rational first integral rational general solution.

Grbner bases in difference-differential modules and difference-differential dimension polynomials

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Science China Mathematics 2008年第9期51卷 1732-1752页

作者： franz winkler RISC-Linz J. Kepler University Linz A-4040 Linz Austria

In this paper we extend the theory of Grbner bases to difference-differential modules and present a new algorithmic approach for computing the Hilbert function of a finitely generated difference-differential module equipped with the natural filtration. We present and verify algorithms for construct-ing these Grbner bases counterparts. To this aim we introduce the concept of "generalized term order" on Nm ×Zn and on difference-differential modules. Using Grbner bases on difference-differential mod-ules we present a direct and algorithmic approach to computing the difference-differential dimension polynomials of a difference-differential module and of a system of linear partial difference-differential equations.

关键词： Grbner basis generalized term order difference-differential module difference-differential dimension polynomial

B-cell and antibody responses to SARS-CoV-2:infection,vaccination,and hybrid immunity

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Cellular & Molecular Immunology 2024年第2期21卷 144-158页

作者： Dennis Lapuente Thomas H.winkler Matthias Tenbusch Institut für klinische und molekulare Virologie Universitätsklinikum Erlangen und Friedrich-Alexander-Universität(FAU)Erlangen-NürnbergSchlossgarten 491054 ErlangenGermany Department of Biology Division of GeneticsNikolaus-Fiebiger-Center for Molecular MedicineFriedrich-Alexander-Universität Erlangen-Nürnberg(FAU)ErlangenGermany Medical Immunology Campus Erlangen Friedrich-Alexander-Universität(FAU)Erlangen-NürnbergSchlossplatz 191054 ErlangenGermany

The emergence of severe acute respiratory syndrome coronavirus 2(SARS-CoV-2)in 2019 prompted scientific,medical,and biotech communities to investigate infection-and vaccine-induced immune responses in the context of this pathogen.B-cell and antibody responses are at the center of these investigations,as neutralizing antibodies(nAbs)are an important correlate of protection(COP)from infection and the primary target of SARS-CoV-2 vaccine *** addition to absolute levels,nAb longevity,neutralization breadth,immunoglobulin isotype and subtype composition,and presence at mucosal sites have become important topics for scientists and health policy *** recent pandemic was and still is a unique setting in which to study de novo and memory B-cell(MBC)and antibody responses in the dynamic interplay of infection-and vaccine-induced *** also provided an opportunity to explore new vaccine platforms,such as mRNA or adenoviral vector vaccines,in unprecedented cohort *** with the technological advances of recent years,this situation has provided detailed mechanistic insights into the development of B-cell and antibody responses but also revealed some unexpected *** this review,we summarize the key findings of the last 2.5 years regarding infection-and vaccine-induced B-cell immunity,which we believe are of significant value not only in the context of SARS-CoV-2 but also for future vaccination approaches in endemic and pandemic settings.

关键词： SARS-CoV-2 neutralizing antibodies memory responses vaccines IgG4

Spontaneous mutations and mutational responses to penicillin treatment in the bacterial pathogen Streptococcus pneumoniae D39

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Marine Life Science & Technology 2024年第3期6卷 198-211页

作者： Wanyue Jiang Tongtong Lin Jiao Pan Caitlyn ERivera Clayton Tincher Yaohai Wang Yu Zhang Xiang Gao Yan Wang Ho‑Ching T.Tsui Malcolm E.winkler Michael Lynch Hongan Long Institute of Evolution and Marine Biodiversity KLMMEOcean University of ChinaQingdao 266003China Laboratory for Marine Biology and Biotechnology Laoshan LaboratoryQingdao 266237China Department of Biology Indiana UniversityBloomingtonIN 47405USA School of Mathematics Science Ocean University of ChinaQingdao 266000China State Key Laboratory of Microbial Technology Microbial Technology InstituteSchool of Life ScienceShandong UniversityQingdao 266237China Biodesign Center for Mechanisms of Evolution Arizona State UniversityTempeAZ 85281USA

Bacteria with functional DNA repair systems are expected to have low mutation rates due to strong natural selection for genomic ***,our study of the wild-type Streptococcus pneumoniae D39,a pathogen responsible for many common diseases,revealed a high spontaneous mutation rate of 0.02 per genome per cell division in mutation-accumulation(MA)*** rate is orders of magnitude higher than that of other non-mutator bacteria and is characterized by a high mutation bias in the A/T *** high mutation rate may have resulted from a reduction in the overall efficiency of selection,conferred by the tiny effective population size in *** line with this,*** D39 also exhibited the lowest DNA mismatch-repair(MMR)efficiency among *** with the antibiotic penicillin did not elevate the mutation rate,as penicillin did not induce DNA damage and *** lacks a stress response *** findings suggested that the MA results are applicable to within-host scenarios and provide insights into pathogen evolution.

关键词： Neutral evolution Mutation spectrum Antibiotics DNA mismatch repair Oxidative damage repair

阿尔卑斯古近纪火山活动的沉积记录及其地质意义

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地球科学 2024年

作者：芦刚高亮王长城陈兴聪卢喜和 Wilfried winkler 成都理工大学能源学院山东石油化工学院石油工程学院瑞士苏黎世联邦理工大学

在始新世中期至渐新世早期，欧洲板块和亚得里亚板块发生碰撞，导致了阿尔卑斯造山带的大规模岩浆活动，由于后期隆升剥蚀无法保存，而弧后盆地中同时期的沉积火山碎屑岩记录了这一构造事件。本文针对该套沉积火山碎屑岩，开展了地质年... 详细信息

在始新世中期至渐新世早期，欧洲板块和亚得里亚板块发生碰撞，导致了阿尔卑斯造山带的大规模岩浆活动，由于后期隆升剥蚀无法保存，而弧后盆地中同时期的沉积火山碎屑岩记录了这一构造事件。本文针对该套沉积火山碎屑岩，开展了地质年代学与地球化学等方面的研究，揭示了阿尔卑斯造山带的火山活动和构造演化特征。本次研究表明：火山碎屑岩中的锆石年龄峰值主要集中在～47Ma、40Ma和37Ma，并且锆石的Hf同位素呈现负值，说明其主要形成于板块俯冲过程中部分地壳熔融的岩浆中。此外，通过对岩浆锆石同位素计算地壳厚度的变化，说明了阿尔卑斯造山带不仅存在由于板块俯冲碰撞引起的地壳垂直挤压增厚，还存在俯冲板片拉伸引起的地壳伸展变薄。

关键词：火山碎屑岩岩浆锆石 U-Pb年龄 Eu值地壳厚度

Immediate regularization of measure-type population densities in a two-dimensional chemotaxis systemwith signal consumption

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Science China Mathematics 2021年第4期64卷 725-746页

作者： Yulan Wang Michael winkler Zhaoyin Xiang School of Science Xihua UniversityChengdu 610039China Institut für Mathematik Universität PaderbornPaderbom 33098Germany School of Mathematical Sciences University of Electronic Science and Technology of ChinaChengdu 611731China

This paper deals with the Neumann initial-boundary value problem for a classical chemotaxis system with signal consumption in a *** contrast to previous studies which have established a comprehensive theory of global classical solutions for suitably regular nonnegative initial data,the focus in the present work is on the question to which extent initially prescribed singularities can be regularized despite the presence of the nonlinear cross-diffusive *** main result in this paper asserts that at least in the framework of radial solutions immediate regularization occurs under an essentially optimal condition on the initial distribution of the population *** precisely,it will turn out that for any radially symmetric initial data belonging to the space of regular signed Borel measures for the population density and to L^(2) for the signal density,there exists a classical solution to the Neumann initial-boundary value problem,which is smooth and approaches the given initial data in an appropriate trace sense.

关键词： chemotaxis measure valued initial data instantaneous smoothing global existence

A Smallness Condition Ensuring Boundedness in a Two-dimensional Chemotaxis-Navier-Stokes System involving Dirichlet Boundary Conditions for the Signal

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Acta Mathematica Sinica,English Series 2022年第6期38卷 985-1001页

作者： Yu Lan WANG Michael winkler Zhao Yin XIANG School of Science Xihua UniversityChengdu 610039P.R.China Institut fur Mathematik Universitat Paderborn33098 PaderbornGermany School of Mathematical Sciences University of Electronic Science and Technology of ChinaChengdu 611731P.R.China

The chemotaxis-Navier-Stokes system{nt+u・∇n=Δn−∇・(n∇c),ct+u・∇c=Δc−nc,ut+(u・∇)u=Δu+∇P+n∇φ,∇・u=0is considered in a smoothly bounded planar domainΩunder the boundary conditions(∇n−n∇c)・ν=0,c=c,u=0,x∈∂Ω,t>0,with a given nonnegative constant c_(*).It is shown that if(n_(0),c_(0),u_(0))is sufficiently regular and such that the product||n_(0)||L^(1)(Ω)||c_(0)||^(2)L^(∞)(Ω)is suitably small,an associated initial value problem possesses a bounded classical solution with(n,c,u)|_(t=0)=(n_(0),c_(0),u_(0)).

关键词： Chemotaxis Navier-Stokes system Dirichlet boundary condition

Topology of triple-point metals

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Chinese Physics B 2019年第7期28卷 54-72页

作者： Georg W.winkler Sobhit Singh Alexey A.Soluyanov Microsoft Quantum Microsoft Station Q University of California Santa Barbara California 93106-6105 USA Department of Physics and Astronomy Rutgers University Piscutuwny New Jersey 08854 USA Institute of Physics University of Zurich. Winterthurerstrasse 190 8057 Zurich Switzerland Department of Physics. St. Petersburg State University St. Petersburg 199034Russia

We discuss and illustrate the appearance of topological fermions and bosons in triple-point metals where a band crossing of three electronic bands occurs close to the Fermi *** bosons appear in the phonon spectrum of certain triple-point metals, depending on the mass of atoms that form the binary triple-point *** first provide a classification of possible triple-point electronic topological phases possible in crystalline compounds and discuss the consequences of these topological phases, seen in Fermi arcs, topological Lifshitz transitions, and transport *** we show how the topological phase of phonon modes can be extracted and proven for relevant ***,we show how the interplay of electronic and phononic topologies in triple-point metals puts these metallic materials into the list of the most efficient metallic thermoelectrics known to date.

关键词： topological metals topological phonons electronic structure thermoelectrics