相关论文: New inversion methods for the Lorentz Integral Tra…
Elementary methods are used to examine some nontrivial mathematical issues underpinning the Lorentz transformation. Its eigen-system is characterized through the exponential of a $G$-skew symmetric matrix, underlining its unconnectedness at…
The inversion of nabla Laplace transform, corresponding to a causal sequence, is considered. Two classical methods, i.e., residual calculation method and partial fraction method are developed to perform the inverse nabla Laplace transform.…
In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…
The iterative Boltzmann inversion is an iterative scheme to determine an effective pair potential for an ensemble of identical particles in thermal equilibrium from the corresponding radial distribution function. Although the method is…
This article reviews the concept of Lorentz invariant relative velocity that is often misunderstood or unknown in high energy physics literature. The properties of the relative velocity allow to formulate the invariant flux and cross…
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
In this paper a new method for inverting the Laplace transform from the real axis is formulated. This method is based on a quadrature formula. We assume that the unknown function $f(t)$ is continuous with (known) compact support. An…
The quantum measurement procedure based on the Lorentz transformation formalism and weak perturbation of the system is considered. In the simple case of a single-qubit it turns out that one can perform 4-dimension pseudo-rotation along with…
According to the postulates of the special theory of relativity (STR), physical quantities such as proper times and Doppler shifts can be obtained from any inertial frame by regarding it as isotropic. Nonetheless many inconsistencies arise…
The focus of this book is on the analysis of regularization methods for solving \emph{nonlinear inverse problems}. Specifically, we place a strong emphasis on techniques that incorporate supervised or unsupervised data derived from prior…
We discuss in detail and from the geometrical point of view the issues of gauge invariance and Lorentz covariance raised by the approach proposed recently by Chen et al. to the proton spin decomposition. We show that the gauge invariance of…
A new method of derivation of Lorentz Transformation (LT) is given based on both axioms of special relativity (SR) and physical intuitions. The essence of the transformation is established and the crucial role played by the presumptions is…
We consider perturbed nonlinear ill-posed equations in Hilbert spaces, with operators that are monotone on a given closed convex subset. A simple stable approach is Lavrentiev regularization, but existence of solutions of the regularized…
Like many other advanced imaging methods, x-ray phase contrast imaging and tomography require mathematical inversion of the observed data to obtain real-space information. While an accurate forward model describing the generally nonlinear…
A novel theoretical framework, the inverse problem approach, is proposed to calculate non-perturbative quantities in quantum chromodynamics (QCD). Based on the dispersion relation of quantum field theory, this approach determines unknown…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
While an explicit basis is common in the study of Euclidean spaces, it is usually implied in the study of inertial relativistic systems. There are some conceptual advantages to including the basis in the study of special relativistic…
In classical mechanics, a procedure for simultaneous synchronization in all inertial frames is consistent with the Galilean transformation. However, if one attempts to achieve such a synchronization utilizing light signals, he will be…
Iterative regularization exploits the implicit bias of an optimization algorithm to regularize ill-posed problems. Constructing algorithms with such built-in regularization mechanisms is a classic challenge in inverse problems but also in…
Inverse problems arise in a variety of imaging applications including computed tomography, non-destructive testing, and remote sensing. The characteristic features of inverse problems are the non-uniqueness and instability of their…