关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

where A represents the magnetic vector potential, is an integral of the hydromagnetic equations. This -integral made it possible to formulate a variational principle for the force-free magnetic fields. The integral expresses the fact that motions cannot transform a given field in an entirely arbitrary different field, if the conductivity of the medium isconsidered infinite. In this paper we shall show that the full set of hydromagnetic equations admit five more integrals, besides the energy integral, if dissipative processes are absent. These integrals, as we shall presently verify, are I2 =fbHvdV, (2)

Proceedings of the National Academy of Sciences

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Methods Of Modern Mathematical Physics

Thank you for downloading regularization of inverse problems. Maybe you have knowledge that, people have search hundreds times for their favorite novels like this regularization of inverse problems, but end up in malicious downloads. Rather than reading a good book with a cup of tea in the afternoon, instead they juggled with some infectious bugs inside their computer. regularization of inverse problems is available in our book collection an online access to it is set as public so you can download it instantly. Our book servers spans in multiple locations, allowing you to get the most less latency time to download any of our books like this one. Kindly say, the regularization of inverse problems is universally compatible with any devices to read.

Regularization Of Inverse Problems

The use of parallel imaging for scan time reduction in MRI faces problems with image degradation when using GRAPPA or SENSE for high acceleration factors. Although an inherent loss of SNR in parallel MRI is inevitable due to the reduced measurement time, the sensitivity to image artifacts that result from severe undersampling can be ameliorated by alternative reconstruction methods. While the introduction of GRAPPA and SENSE extended MRI reconstructions from a simple unitary transformation (Fourier transform) to the inversion of an ill-conditioned linear system, the next logical step is the use of a nonlinear inversion. Here, a respective algorithm based on a Newton-type method with appropriate regularization terms is demonstrated to improve the performance of autocalibrating parallel MRI--mainly due to a better estimation of the coil sensitivity profiles. The approach yields images with considerably reduced artifacts for high acceleration factors and/or a low number of reference lines.

/pdf/image-reconstruction-by-regularized-nonlinear-inversion-1kriyfuhqd.pdf

Image reconstruction by regularized nonlinear inversion--joint estimation of coil sensitivities and image content.

Previously, the convergence analysis for linear statistical inverse problems has mainly focused on spectral cut-off and Tikhonov-type estimators. Spectral cut-off estimators achieve minimax rates for a broad range of smoothness classes and operators, but their practical usefulness is limited by the fact that they require a complete spectral decomposition of the operator. Tikhonov estimators are simpler to compute but still involve the inversion of an operator and achieve minimax rates only in restricted smoothness classes. In this paper we introduce a unifying technique to study the mean square error of a large class of regularization methods (spectral methods) including the aforementioned estimators as well as many iterative methods, such as $\nu$-methods and the Landweber iteration. The latter estimators converge at the same rate as spectral cut-off but require only matrix-vector products. Our results are applied to various problems; in particular we obtain precise convergence rates for satellite gradiometry, $L^2$-boosting, and errors in variable problems.

/pdf/convergence-rates-of-general-regularization-methods-for-2210drx00r.pdf

Convergence Rates of General Regularization Methods for Statistical Inverse Problems and Applications

We introduce a framework for the preparation, coherent manipulation and characterization of free-electron quantum states, experimentally demonstrating attosecond pulse trains for electron microscopy. Specifically, we employ phase-locked single-color and two-color optical fields to coherently control the electron wave function along the beam direction. We establish a new variant of quantum state tomography - "SQUIRRELS" - to reconstruct the density matrices of free-electron ensembles and their attosecond temporal structure. The ability to tailor and quantitatively map electron quantum states will promote the nanoscale study of electron-matter entanglement and the development of new forms of ultrafast electron microscopy and spectroscopy down to the attosecond regime.

Attosecond Electron Pulse Trains and Quantum State Reconstruction in Ultrafast Transmission Electron Microscopy

Convergence and logarithmic convergence rates of the iteratively regularized Gauss - Newton method in a Hilbert space setting are proven provided a logarithmic source condition is satisfied. This method is applied to an inverse potential and an inverse scattering problem, and the source condition is interpreted as a smoothness condition in terms of Sobolev spaces for the case where the domain is a circle. Numerical experiments yield convergence and convergence rates of the form expected by our general convergence theorem.

http://iopscience.iop.org/article/10.1088/0266-5611/13/5/012/pdf

Logarithmic convergence rates of the iteratively regularized Gauss - Newton method for an inverse potential and an inverse scattering problem

Ultrafast electron and X-ray imaging and spectroscopy are the basis for an ongoing revolution in the understanding of dynamical atomic-scale processes in matter. The underlying technology relies heavily on laser science for the generation and characterization of ever shorter pulses. Recent findings suggest that ultrafast electron microscopy with attosecond-structured wavefunctions may be feasible. However, such future technologies call for means to both prepare and fully analyse the corresponding free-electron quantum states. Here, we introduce a framework for the preparation, coherent manipulation and characterization of free-electron quantum states, experimentally demonstrating attosecond electron pulse trains. Phase-locked optical fields coherently control the electron wavefunction along the beam direction. We establish a new variant of quantum state tomography—‘SQUIRRELS’—for free-electron ensembles. The ability to tailor and quantitatively map electron quantum states will promote the nanoscale study of electron–matter entanglement and new forms of ultrafast electron microscopy down to the attosecond regime. Attosecond electron pulse trains in electron microscopy are demonstrated through the coupling of phase-locked multicolour optical fields with electron pulses. A new variant of quantum state tomography for free-electron ensembles is established.

Thorsten Hohage

Papers

Image reconstruction by regularized nonlinear inversion--joint estimation of coil sensitivities and image content.

Convergence Rates of General Regularization Methods for Statistical Inverse Problems and Applications

Attosecond Electron Pulse Trains and Quantum State Reconstruction in Ultrafast Transmission Electron Microscopy

Logarithmic convergence rates of the iteratively regularized Gauss - Newton method for an inverse potential and an inverse scattering problem

Attosecond electron pulse trains and quantum state reconstruction in ultrafast transmission electron microscopy