Well-Posed Inverse Problems

适定反问题

基本信息

  • 批准号:
    9209738
  • 负责人:
  • 金额:
    $ 6万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    1992
  • 资助国家:
    美国
  • 起止时间:
    1992-07-15 至 1994-06-30
  • 项目状态:
    已结题

项目摘要

The problem of determining a quantum mechanical potential from its scattering amplitude goes back to the beginning of quantum mechanics. One aspect of the problem which has received little attention is finding data sets for which the problem is well-posed, i.e., that the mapping from the potential to the scattering data set is continuously invertible. This work focuses on one such set, the so-called backscattering data. It is the data which occurs from the restriction of the scattering amplitude to the direction opposite to the direction of the incident plane wave. In dimensions three and higher, the relationship of the backscattering and potential is well documented. In two dimensions or in cases where the data is restricted to half-spaces, there are obstacles which will be analyzed during the course of this project. Other work on inverse scattering will focus on the wave equation with variable speed of sound and the Schrodinger equation with both electric and magnetic potential. A second line of investigation concerns hyperbolic partial differential equations defined in domains with wedgelike boundaries and the propagation of singularities of solutions of initial-boundary value problems for second order equations in the presence of boundary wedges. Partial differential equations form the backbone of mathematical modeling in the physical sciences. Phenomena which involve continuous change such as that seen in motion, materials and energy are known to obey certain general laws which are expressible in terms of the interactions and relationships between partial derivatives. The inverse problems described in this proposal play a central role in these studies. Their object is not to state the relationships, but rather, to extract qualitative and quantitative meaning from them.
确定量子力学势的问题 从它的散射振幅可以追溯到 量子力学 问题的一个方面, 很少有人注意到的是, 适定的,即,从势能到 散射数据集是连续可逆的。 这项工作 集中在一个这样的集合,所谓的后向散射数据。 它 是从散射的限制中产生的数据 的方向相反的方向上的振幅 入射平面波 在三维和更高的维度中, 后向散射与电势有良好的关系 记录在案。 在二维空间中,或者在数据 限制在半空间,有障碍,这将是 在这个项目的过程中进行了分析。 上的其他工作 逆散射将集中在波动方程与变量 声速和薛定谔方程, 磁势。第二条调查线涉及 双曲型偏微分方程 楔形边界和奇点的传播 二阶初边值问题的解 方程中存在边界楔。 偏微分方程是 物理科学中的数学建模。 的现象 包括连续变化,如运动、材料 和能量都服从某些普遍规律, 可以用相互作用和关系来表达 偏导数之间的关系 中描述的逆问题 这一建议在这些研究中发挥了核心作用。其对象 并不是陈述它们之间的关系,而是提取 定性和定量的意义。

项目成果

期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)

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James Ralston其他文献

Iatrogenic aortic dissection after minimally invasive aortic valve replacement: a case report
  • DOI:
    10.1186/s13019-016-0531-y
  • 发表时间:
    2016-08-24
  • 期刊:
  • 影响因子:
    1.500
  • 作者:
    Mohamed Ehab Ramadan;Lamia Buohliqah;Juan Crestanello;James Ralston;David Igoe;Hamdy Awad
  • 通讯作者:
    Hamdy Awad
Hyponatremia decreases left ventricular ejection fraction after ischemia by modulating NO production
  • DOI:
    10.1016/j.jamcollsurg.2012.06.114
  • 发表时间:
    2012-09-01
  • 期刊:
  • 影响因子:
  • 作者:
    Weiping Ye;Daniel Lee;James Ralston;Jay Zweier;Juan Crestanello
  • 通讯作者:
    Juan Crestanello
Experimental Validation of Cryobot Thermal Models for the Exploration of Ocean Worlds
用于海洋世界探索的低温机器人热模型的实验验证
  • DOI:
    10.3847/psj/acc2b7
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Paula do Vale Pereira;Michael J. Durka;B. Hogan;K. Richmond;Miles W. E. Smith;D. Winebrenner;W. T. Elam;Benjamin J. Hockman;A. Lopez;Neal Tanner;Joshua Moor;James Ralston;Miriam Alexander;W. Zimmerman;Nolan Flannery;William Kuhl;Sarah E. Wielgosz;K. Cahoy;T. Cwik;W. Stone
  • 通讯作者:
    W. Stone
P390: Health system direct contact of relatives for cascade testing: Reach and initial acceptability in a prospective intervention study*
  • DOI:
    10.1016/j.gimo.2023.100426
  • 发表时间:
    2023-01-01
  • 期刊:
  • 影响因子:
  • 作者:
    Nora Henrikson;Jamilyn Zepp;Paula Blasi;Melissa Anderson;Aaron Scrol;Jane Grafton;John Ewing;James Ralston;Stephanie Fullerton;Kathleen Leppig
  • 通讯作者:
    Kathleen Leppig
P679: “I would have had no idea”: Families’ experiences with a new US health system-mediated direct contact program
  • DOI:
    10.1016/j.gimo.2023.100751
  • 发表时间:
    2023-01-01
  • 期刊:
  • 影响因子:
  • 作者:
    Paula Blasi;Jamilyn Zepp;Aaron Scrol;Melissa Anderson;John Ewing;James Ralston;Stephanie Fullerton;Kathleen Leppig;Nora Henrikson
  • 通讯作者:
    Nora Henrikson

James Ralston的其他文献

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{{ truncateString('James Ralston', 18)}}的其他基金

Spectral Asymptotics for Non-self-adjoint Semiclassical Operators
非自伴半经典算子的谱渐近
  • 批准号:
    0304970
  • 财政年份:
    2003
  • 资助金额:
    $ 6万
  • 项目类别:
    Standard Grant
Inverse Boundary Value and Inverse Scattering Problems
逆边界值和逆散射问题
  • 批准号:
    0139192
  • 财政年份:
    2002
  • 资助金额:
    $ 6万
  • 项目类别:
    Continuing Grant
Inverse Scattering for Obstacles and Related Problems
障碍物和相关问题的逆散射
  • 批准号:
    9970565
  • 财政年份:
    1999
  • 资助金额:
    $ 6万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Scattering Theory for N-particle Systems
数学科学:N 粒子系统的散射理论
  • 批准号:
    9896076
  • 财政年份:
    1997
  • 资助金额:
    $ 6万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Inverse Scattering Problems
数学科学:逆散射问题
  • 批准号:
    9622310
  • 财政年份:
    1996
  • 资助金额:
    $ 6万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Scattering Theory for N-particle Systems
数学科学:N 粒子系统的散射理论
  • 批准号:
    9501033
  • 财政年份:
    1995
  • 资助金额:
    $ 6万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Well-Posed Inverse Problems
数学科学:适定反问题
  • 批准号:
    9305882
  • 财政年份:
    1993
  • 资助金额:
    $ 6万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Well-Posed Inverse Problems
数学科学:适定反问题
  • 批准号:
    8902246
  • 财政年份:
    1989
  • 资助金额:
    $ 6万
  • 项目类别:
    Continuing Grant
Mathematical Sciences: Partial Differential Equations of Mathematical Physics
数学科学:数学物理偏微分方程
  • 批准号:
    8703500
  • 财政年份:
    1987
  • 资助金额:
    $ 6万
  • 项目类别:
    Standard Grant
Mathematical Sciences: Partial Differential Equations of Mathematical Physics
数学科学:数学物理偏微分方程
  • 批准号:
    8502326
  • 财政年份:
    1985
  • 资助金额:
    $ 6万
  • 项目类别:
    Continuing Grant

相似海外基金

Best basis construction and comparison of trial functions for ill-posed inverse problems in Earth sciences - studied at the examples of global-scale seismic tomography and gravitational field modelling
地球科学中不适定反问题的最佳基础构建和试验函数比较——以全球尺度地震层析成像和重力场建模为例进行研究
  • 批准号:
    437390524
  • 财政年份:
    2019
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    $ 6万
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    Research Grants
Regularisation methods for solving nonlinear ill-posed inverse problems
求解非线性不适定反问题的正则化方法
  • 批准号:
    DE120101707
  • 财政年份:
    2012
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    $ 6万
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    Discovery Early Career Researcher Award
Numerical optimization for large-scale experimental design of ill-posed inverse problems
不适定反问题大规模实验设计的数值优化
  • 批准号:
    0915121
  • 财政年份:
    2009
  • 资助金额:
    $ 6万
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    Continuing Grant
Solution of ill-posed inverse problems using complex-valuednetwork inversion
使用复值网络反演求解不适定反演问题
  • 批准号:
    21700260
  • 财政年份:
    2009
  • 资助金额:
    $ 6万
  • 项目类别:
    Grant-in-Aid for Young Scientists (B)
Numerical optimization for large-scale experimental design of ill-posed inverse problems
不适定反问题大规模实验设计的数值优化
  • 批准号:
    0914987
  • 财政年份:
    2009
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    $ 6万
  • 项目类别:
    Standard Grant
Establishment of New Numerical Methods for Applied Inverse and Ill-Posed Problems
应用逆问题和不适定问题的新数值方法的建立
  • 批准号:
    16340024
  • 财政年份:
    2004
  • 资助金额:
    $ 6万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Numerical and Mathematical Analysis for the reconstruction for solutions of inverse and ill-posed problems by regularization methods
通过正则化方法重构逆问题和病态问题解的数值和数学分析
  • 批准号:
    13440031
  • 财政年份:
    2001
  • 资助金额:
    $ 6万
  • 项目类别:
    Grant-in-Aid for Scientific Research (B)
Local Regularization Methods for Ill-Posed Inverse Problems: Fast Algorithms and Adaptive Parameter Selection
不适定反问题的局部正则化方法:快速算法和自适应参数选择
  • 批准号:
    0104003
  • 财政年份:
    2001
  • 资助金额:
    $ 6万
  • 项目类别:
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Mathematical Sciences: Computational Methods for Ill-Posed Inverse Problems
数学科学:不适定反问题的计算方法
  • 批准号:
    9622119
  • 财政年份:
    1996
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    $ 6万
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    Standard Grant
Mathematical Sciences: Well-Posed Inverse Problems
数学科学:适定反问题
  • 批准号:
    9305882
  • 财政年份:
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