The Tychonoff uniqueness theorem for the G-heat equation

In this paper, we obtain the Tychonoff uniqueness theorem for the G-heat equation

Non-Spinning Black Holes in Alternative Theories of Gravity

We study two large classes of alternative theories, modifying the action through algebraic, quadratic curvature invariants coupled to scalar fields. We find one class that admits solutions that solve the vacuum Einstein equations and another that does not. In the latter, we find a deformation to the Schwarzschild metric that solves the modified field equations in the small coupling approximation. We calculate the event horizon shift, the innermost stable circular orbit shift, and corrections to gravitational waves, mapping them to the parametrized post-Einsteinian framework.Comment: 7 pages, submitted to PR

The use of the Kalman filter in the automated segmentation of EIT lung images

In this paper, we present a new pipeline for the fast and accurate segmentation of impedance images of the lungs using electrical impedance tomography (EIT). EIT is an emerging, promising, non-invasive imaging modality that produces real-time, low spatial but high temporal resolution images of impedance inside a body. Recovering impedance itself constitutes a nonlinear ill-posed inverse problem, therefore the problem is usually linearized, which produces impedance-change images, rather than static impedance ones. Such images are highly blurry and fuzzy along object boundaries. We provide a mathematical reasoning behind the high suitability of the Kalman filter when it comes to segmenting and tracking conductivity changes in EIT lung images. Next, we use a two-fold approach to tackle the segmentation problem. First, we construct a global lung shape to restrict the search region of the Kalman filter. Next, we proceed with augmenting the Kalman filter by incorporating an adaptive foreground detection system to provide the boundary contours for the Kalman filter to carry out the tracking of the conductivity changes as the lungs undergo deformation in a respiratory cycle. The proposed method has been validated by using performance statistics such as misclassified area, and false positive rate, and compared to previous approaches. The results show that the proposed automated method can be a fast and reliable segmentation tool for EIT imaging

An efficient numerical model for the simulation of coupled heat, air and moisture transfer in porous media

41 pages, 13 figures, 2 tables, 32 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/This article proposes an efficient explicit numerical model with a relaxed stability condition for the simulation of heat, air and moisture transfer in porous material. Three innovative approaches are combined to solve the system of three partial differential equations. The Du Fort-Frankel scheme is used to solve the diffusion equation, providing an explicit scheme with an extended stability region. The two advection--diffusion equations are solved using both Scharfetter-Gummel numerical scheme for the space discretisation and the two-step Runge-Kutta method for the time variable. This combination enables to relax the stability condition by one order. The proposed numerical model is evaluated on three case studies. The first one considers quasi-linear coefficients to confirm the theoretical results by numerical computations. The stability condition is relaxed by a factor of 40 compared to the standard approach. The second case provides an analytical solution for weakly nonlinear problem. A very satisfactory accuracy is observed between the reference solution and the one provided by the numerical model. The last case study assumes more realistic application with nonlinear coefficients and Robin-type boundary conditions. The computational time is reduced 10 times by using the proposed model in comparison with the explicit Euler method