The goal of this work is to develop digital image processing tools for improving the quality of the images provided by the Göttingen transmission X-ray microscope at BESSY [1, 2]. We first present a method for correcting the inhomogeneous illumination. Then, we present results of image restoration techniques applied to X-ray microscopy images of test objects and of biological specimens containi...

A numerical analysis of non-Darcian flow to a pumping well in a confined aquifer using the strong-form mesh-free (MFREE) method is described. This technique is targeted at problems that use advanced numerical approaches for modeling non-Darcian flow and it supports the assumption that the non-Darcian flow follows the Forchheimer equation. Interpolation functions including the multi-quadrics (MQ...

We show that the error probability of reconstructing kernel matrices from Random Fourier Features for any shift-invariant kernel function is at most O(exp(−D)), where D is the number of random features. We also provide a matching informationtheoretic method-independent lower bound of Ω(exp(−D)) for standard Gaussian distributions. Compared to prior work, we are the first to show that the error ...

By an extension of the Bethe ansatz method used by Gwa and Spohn, we obtain an exact expression for the large deviation function of the time averaged current for the fully asymmetric exclusion process in a ring containing N sites and p particles. Using this expression we easily recover the exact diffusion constant obtained earlier and calculate as well some higher cumulants. The distribution of...

A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method provides a more systematical and convenient handling of the solution process of nonlinear equations, unifying the tanhfunction type methods, the homogeneous balance method, the exp-function method, the mapping method, and the F-expansion type m...

In this study, we have applied the modified exp -expansion function method (MEFM) to obtain exact travelling wave solutions for (3+1) dimensional Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation and (3+1)-dimensional Jimbo-Miwa (JM) equation. Dark soliton solution, dark-bright hyperbolic solution trigonometric of KZK JM been found by using method. After that, scratched 2D 3D graphs all obtained i...