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The Algebro-Geometric Method for Solving Algebraic Differential Equations——A Survey

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Journal of Systems Science & Complexity 2019年第1期32卷 256-270页

作者： winkler franz Research Institute for Symbolic Computation J.Kepler University

This paper presents the algebro-geometric method for computing explicit formula solutions for algebraic differential equations(ADEs). An algebraic differential equation is a polynomial relation between a function, some of its partial derivatives, and the variables in which the function is de?*** all these quantities as unrelated variables, the polynomial relation leads to an algebraic relation de?ning a hypersurface on which the solution is to be found. A solution in a certain class of functions, such as rational or algebraic functions, determines a parametrization of the hypersurface in this class. So in the algebro-geometric method the author ?rst decides whether a given ADE can be parametrized with functions from a given class; and in the second step the author tries to transform a parametrization into one respecting also the differential conditions. This approach is relatively well understood for rational and algebraic solutions of single algebraic ordinary differential equations(AODEs). First steps are taken in a generalization to systems and to partial differential equations.

关键词： Algebraic differential equation exact solution parametrization of curves

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2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

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

Traction-assisted endoscopic mucosal resection for polypectomy in the large intestine

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World Journal of Gastroenterology 2010年第43期16卷 5462-5466页

作者： Bernhard Dauser Thomas winkler Behrooz Salehi Stefan Riss franz Beer Friedrich Herbst Department of Surgery St. John of God Hospital Department of Surgery Medical University of Vienna Kerjaschki Laboratory of Pathology

AIM: To evaluate if traction-assisted endoscopic mucosal resection (TA-EMR) is feasible and if it enables en bloc resection of colorectal lesions. METHODS: Seven patients with a total of 12 colorectal adenomas were prospectively enrolled. All lesions were removed by TA-EMR: one hemostatic clip tied to a white silk suture was applied to the base of the lesion to allow traction through the working channel of the colonoscope. A conventional polypectomy snare was mounted over the suture and the lesion was pulled into the snare and resected in one piece. RESULTS: All 12 lesions (nine sessile) were resected en bloc with free lateral and vertical margins by using this novel technique, including five lesions (5/12, 41.6%) in less-accessible positions, where TA-EMR enabled complete visualization of the base before resection. Mean longest lesion and specimen sizes were 9 mm (range: 6-25 mm) and 11 mm in diameter (range: 7-17 mm),respectively. No serious procedure-related complications were observed. CONCLUSION: TA-EMR through the endoscope using a hemostatic clip and suture material is technically feasible. Visualization of colorectal lesions in less-accessible locations can be improved.

关键词： Traction-assisted Endoscopic mucosal resection Colon polyp Colonoscopy

Stochastic Runge-Kutta–Munthe-Kaas Methods in the Modelling of Perturbed Rigid Bodies

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Advances in Applied Mathematics and Mechanics 2022年第2期14卷 528-538页

作者： Michelle Muniz Matthias Ehrhardt Michael Günther Renate winkler Institute of Mathematical Modelling Analysis and Computational Mathematics(IMACM)Applied Mathematics and Numerical AnalysisBergische Universität WuppertalGaußstraße 2042119 WuppertalGermany

In this paper we present how nonlinear stochastic Itˆo differential equations arising in the modelling of perturbed rigid bodies can be solved numerically in such a way that the solution evolves on the correct *** this end,we formulate an approach based on Runge-Kutta–Munthe-Kaas(RKMK)schemes for ordinary differ-ential equations on ***,we provide a proof of the mean-square convergence of this stochastic version of the RKMK schemes applied to the rigid body problem and illustrate the effectiveness of our proposed schemes by demonstrating the structure preservation of the stochastic RKMK schemes in contrast to the stochastic Runge-Kutta methods.

关键词： Stochastic Runge-Kutta method Runge-Kutta–Munthe-Kaas scheme nonlinear Itˆo SDEs rigid body problem