This article studies the existence and uniqueness of a weak solution of the time-fractional cancer invasion system with nonlocal diffusion operator. Existence and uniqueness results are ensured by adapting the Faedo-Galerkin method and some a priori estimates. Further, finite element numerical scheme is implemented for the considered system. Finally, various numerical computations are performed along with the convergence analysis of the scheme.
The authors carried out the study of the state of systemic and cerebral hemodynamics in normal conditions and in various neurosurgical pathologies using modern signal processing methods. The results characterize the condition for the mechanisms of cerebral circulation Institute of Computer Science and Control, Higher School of Cyber-Physical Systems and Control regulation, which allows for finding a solution to fundamental and specific clinical problems for the effective treatment of patients with various pathologies. The proposed method is based on the continuous wavelet transform of systemic arterial pressure and blood flow velocity signals in the middle cerebral artery recorded by non-invasive methods of photoplethysmography and transcranial doppler ultrasonography. The study of these signals in real-time in the frequency range of Mayer waves makes it possible to determine the cerebral autoregulation state in certain diseases before and after surgical interventions. The proposed method uses a cross-wavelet spectrum, which helps obtain wavelet coherence and a phase shift between the wavelet coefficients of systemic arterial pressure signals and blood flow velocity in the Mayer wave range. The obtained results enable comparing the proposed method with that based on the short-time Fourier transform. The comparison showed that the proposed method has higher sensitivity to changes in cerebral autoregulation and better localization of changes in time and frequency.
A systematic approach to reducing the risk of flooding is considered. The main idea of it is to switch from the flood control only by the one hydro system on the main river but to control the whole river system, including many adjacent river basins at various levels. This proposal expands the possibility of using a flood control system of self-regulating hydro systems distributed on adjacent drainage basins at multiple levels by organizing their joint work, ensuring that the maximum allowable water flow in the control sections of the river system is not exceeded. Using the proposed approach will allow protecting from flooding significant areas of land in the lower pool of the main hydroelectric complex in the context of climate change.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.