FRG: Collaborative Research: Model Theory of Differential and Difference Equations with Applications
FRG:协作研究:微分方程和差分方程的模型理论及其应用
基本信息
- 批准号:1760448
- 负责人:
- 金额:$ 27.16万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2018
- 资助国家:美国
- 起止时间:2018-07-15 至 2023-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This project is concerned with differential equations, which relate a quantity to its rate of change with respect to continuous time; difference equations, which relate a quantity to its rate of change with respect to discrete time; and combinations of these. Systems of such equations describe or model behavior and phenomena throughout the sciences; epidemiology, population dynamics, mechanics etc. The project will use methods from model theory, a branch of mathematical logic, to develop or improve procedures for showing consistency (existence of solutions) of systems of such equations, for identifying auxiliary parameters in systems of such equations, and for eliminating unknowns from such systems. The project will also extend the existing classification of sets of solutions from the case of over-determined (or finite-dimensional) systems to under-determined (or infinite-dimensional systems). In this focused research group project, the team of researchers studies differential, difference, and differential-difference equations, from the point of view of model theory in the sense of mathematical logic. Among the aims is to provide decision procedures or improve existing decision procedures regarding consistency and elimination. Applications to a variety of modelling problems for physical systems are expected. The proposed research is threefold. The first is to develop efficient algorithms in cases where the existing methods from theories of differential or difference fields provide algorithms in principle. The second is to extend the existing model-theoretic classification of finite-dimensional solution spaces of systems to infinite-dimensional solution spaces, as well as developing methods to apply the classification in practice. The third is to introduce and study new first order theories of rings with operators, whose decision procedures will apply to new examples arising in applications.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
该项目涉及微分方程,它将一个量与其相对于连续时间的变化率联系起来;差分方程,它将一个量与其相对于离散时间的变化率联系起来;以及这些方程的组合。这些方程的系统描述或模型的行为和现象在整个科学;流行病学,人口动态学,力学等该项目将使用模型理论的方法,数学逻辑的一个分支,以开发或改进程序,以显示一致性(存在的解决方案)的系统,这些方程的系统,确定辅助参数,并消除未知数从这些系统。该项目还将扩展现有的解决方案集的分类,从超定(或有限维)系统的情况下,欠定(或无限维系统)。在这个重点研究小组项目中,研究人员团队从数学逻辑意义上的模型论的角度研究微分,差分和微分差分方程。其目的之一是提供决策程序或改进有关一致性和消除的现有决策程序。预计各种物理系统的建模问题的应用。拟议的研究有三个方面。第一个是开发有效的算法的情况下,现有的方法从理论上的微分或差场提供算法的原则。第二是将现有的有限维系统解空间的模型理论分类扩展到无限维解空间,以及开发将分类应用于实践的方法。第三个奖项是介绍和研究新的一阶环理论与运营商,其决策程序将适用于新的例子中出现的应用。这个奖项反映了NSF的法定使命,并已被认为是值得支持的,通过评估使用基金会的智力价值和更广泛的影响审查标准。
项目成果
期刊论文数量(42)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Separating variables in bivariate polynomial ideals
- DOI:10.1145/3373207.3404028
- 发表时间:2020-02
- 期刊:
- 影响因子:0
- 作者:Manfred Buchacher;Manuel Kauers;G. Pogudin
- 通讯作者:Manfred Buchacher;Manuel Kauers;G. Pogudin
Quadratization of ODEs: Monomial vs. Non-Monomial
ODE 的二次化:单项式与非单项式
- DOI:10.1137/20s1360578
- 发表时间:2021
- 期刊:
- 影响因子:0
- 作者:Alauddin, Foyez
- 通讯作者:Alauddin, Foyez
Degree bound for toric envelope of a linear algebraic group
线性代数群的复曲面包络的度界
- DOI:10.1090/mcom/3695
- 发表时间:2021
- 期刊:
- 影响因子:2
- 作者:Amzallag, Eli;Minchenko, Andrei;Pogudin, Gleb
- 通讯作者:Pogudin, Gleb
Optimal Monomial Quadratization for ODE Systems
ODE 系统的最优单项式二次化
- DOI:10.1007/978-3-030-79987-8_9
- 发表时间:2021
- 期刊:
- 影响因子:0
- 作者:Bychkov, Andrey;Pogudin, Gleb
- 通讯作者:Pogudin, Gleb
Expansive dynamics on profinite groups
有限群的扩张动力学
- DOI:10.4064/fm15-1-2021
- 发表时间:2021
- 期刊:
- 影响因子:0.6
- 作者:Wibmer, Michael
- 通讯作者:Wibmer, Michael
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Alexey Ovchinnikov其他文献
Tannakian Approach to Linear Differential Algebraic Groups
- DOI:
10.1007/s00031-008-9010-4 - 发表时间:
2008-06-03 - 期刊:
- 影响因子:0.400
- 作者:
Alexey Ovchinnikov - 通讯作者:
Alexey Ovchinnikov
On bounds for the effective differential Nullstellensatz
- DOI:
10.1016/j.jalgebra.2015.10.009 - 发表时间:
2016-03-01 - 期刊:
- 影响因子:
- 作者:
Omar León Sánchez;Alexey Ovchinnikov - 通讯作者:
Alexey Ovchinnikov
High-molecular weight bottlebrushes emvia/em continuous flow photoiniferter polymerization of macromonomers
高分子量瓶刷通过大分子单体的 emvia/em 连续流光引发聚合
- DOI:
10.1039/d3py00042g - 发表时间:
2023-01-01 - 期刊:
- 影响因子:3.900
- 作者:
Alexey Sivokhin;Dmitry Orekhov;Oleg Kazantsev;Ksenia Otopkova;Olga Sivokhina;Yuri Chesnokov;Michael Smirnov;Alexey Ovchinnikov;Ilya Makhov - 通讯作者:
Ilya Makhov
Tannakian Categories, Linear Differential Algebraic Groups, and Parametrized Linear Differential Equations
- DOI:
10.1007/s00031-008-9042-9 - 发表时间:
2008-11-27 - 期刊:
- 影响因子:0.400
- 作者:
Alexey Ovchinnikov - 通讯作者:
Alexey Ovchinnikov
Technique of cluster validity for Text Mining
文本挖掘的聚类有效性技术
- DOI:
10.1109/confluence.2016.7508139 - 发表时间:
2016 - 期刊:
- 影响因子:0
- 作者:
G. Chernyshova;Gennady Smorodin;Alexey Ovchinnikov - 通讯作者:
Alexey Ovchinnikov
Alexey Ovchinnikov的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Alexey Ovchinnikov', 18)}}的其他基金
Collaborative Research: CCF: AF: Medium: Validated Soft Approaches to Parametric ODE Solving
协作研究:CCF:AF:中:经过验证的参数 ODE 求解软方法
- 批准号:
2212460 - 财政年份:2022
- 资助金额:
$ 27.16万 - 项目类别:
Continuing Grant
Collaborative Research: Efficient Methods for Identifiability of Dynamic Models
协作研究:动态模型可识别性的有效方法
- 批准号:
1853650 - 财政年份:2019
- 资助金额:
$ 27.16万 - 项目类别:
Standard Grant
International Symposium on Symbolic and Algebraic Computation
符号与代数计算国际研讨会
- 批准号:
1708884 - 财政年份:2017
- 资助金额:
$ 27.16万 - 项目类别:
Standard Grant
AF: Medium: Collaborative Research: Numerical Algebraic Differential Equations
AF:媒介:协作研究:数值代数微分方程
- 批准号:
1563942 - 财政年份:2016
- 资助金额:
$ 27.16万 - 项目类别:
Continuing Grant
Algebraic Theory of Differential and Functional Equations: from Foundations to Computation
微分方程和泛函方程的代数理论:从基础到计算
- 批准号:
1606334 - 财政年份:2016
- 资助金额:
$ 27.16万 - 项目类别:
Standard Grant
Computational Differential and Difference Algebra, a special session at the Applications of Computer Algebra 2014 Conference, July 9 - 12, 2014.
计算微分和差分代数,2014 年计算机代数应用会议的特别会议,2014 年 7 月 9 日至 12 日。
- 批准号:
1413859 - 财政年份:2014
- 资助金额:
$ 27.16万 - 项目类别:
Standard Grant
CAREER: CISE-CCF-AF-Algebra: DMS-Algebra: Computational Differential Algebra
职业:CISE-CCF-AF-代数:DMS-代数:计算微分代数
- 批准号:
0952591 - 财政年份:2010
- 资助金额:
$ 27.16万 - 项目类别:
Continuing Grant
CISE-CCF-AF-Algebra: SGER: Computational Methods for Systems of Difference Equations
CISE-CCF-AF-代数:SGER:差分方程组的计算方法
- 批准号:
0901175 - 财政年份:2009
- 资助金额:
$ 27.16万 - 项目类别:
Standard Grant
CISE-CCF-AF-Algebra: SGER: Computational Methods for Systems of Difference Equations
CISE-CCF-AF-代数:SGER:差分方程组的计算方法
- 批准号:
0964875 - 财政年份:2009
- 资助金额:
$ 27.16万 - 项目类别:
Standard Grant
相似海外基金
FRG: Collaborative Research: New birational invariants
FRG:协作研究:新的双有理不变量
- 批准号:
2244978 - 财政年份:2023
- 资助金额:
$ 27.16万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2245017 - 财政年份:2023
- 资助金额:
$ 27.16万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245111 - 财政年份:2023
- 资助金额:
$ 27.16万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245077 - 财政年份:2023
- 资助金额:
$ 27.16万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2244879 - 财政年份:2023
- 资助金额:
$ 27.16万 - 项目类别:
Standard Grant
FRG: Collaborative Research: New Birational Invariants
FRG:合作研究:新的双理性不变量
- 批准号:
2245171 - 财政年份:2023
- 资助金额:
$ 27.16万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2403764 - 财政年份:2023
- 资助金额:
$ 27.16万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2245021 - 财政年份:2023
- 资助金额:
$ 27.16万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245097 - 财政年份:2023
- 资助金额:
$ 27.16万 - 项目类别:
Continuing Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245147 - 财政年份:2023
- 资助金额:
$ 27.16万 - 项目类别:
Continuing Grant