Altybay, Arshyn Ruzhansky, Michael Sebih, Mohammed Elamine Tokmagambetov, Niyaz

In this paper, we consider the heat equation with strongly singular potentials and prove that it has a "very weak solution". Moreover, we show the uniqueness and consistency results in some appropriate sense. The cases of positive and negative potentials are studied. Numerical simulations are done: one suggests so-called "laser heating and cooling"...

Sheng, Yin Huang, Tingwen Zeng, Zhigang Li, Peng

This article investigates the global exponential stabilization (GES) of inertial memristive neural networks with discrete and distributed time-varying delays (DIMNNs). By introducing the inertial term into memristive neural networks (MNNs), DIMNNs are formulated as the second-order differential equations with discontinuous right-hand sides. Via a v...

Mondal, Shyam Swarup Kumar, Vishvesh
Published in
Complex Analysis and Operator Theory

Let (S,B,m)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(S, {\mathcal {B}}, m)$$\end{document} be a finite measure space. In this paper we show that every bounded li...

Duckworth, H Sharp, DJ Ghajari, M

The Cerebrospinal Fluid (CSF) can undergo shear deformations under head motions. Finite Element (FE) models, which are commonly used to simulate biomechanics of the brain, including traumatic brain injury, employ solid elements to represent the CSF. However, the limited number of elements paired with shear deformations in CSF can decrease the accur...

Farouki, RT Pelosi, F Sampoli, ML

The clothoid is a planar curve with the intuitive geometrical property of a linear variation of the curvature with arc length, a feature that is important in many geometric design applications. However, the exact parameterization of the clothoid is defined in terms of the irreducible Fresnel integrals, which are computationally expensive to evaluat...

Bokhari, Ahmad H. Berggren, Martin Noreland, Daniel Wadbro, Eddie
Published in
Scientific Reports

A subwoofer generates the lowest frequency range in loudspeaker systems. Subwoofers are used in audio systems for live concerts, movie theatres, home theatres, gaming consoles, cars, etc. During the last decades, numerical simulations have emerged as a cost- and time-efficient complement to traditional experiments in the design process of different...

Ketokivi, Mikko Bromiley, Philip Awaysheh, Amrou

We argue that in analyzing panel-data econometric models, researchers rely excessively on statistical criteria to determine model specification, treating it primarily as a matter of statistical inference. This inferential emphasis is most obvious in the common practice of using statistical tests (e.g., the Hausman test) to choose between fixed- and...

Hoang, Luan T Titi, Edriss S

We study the three-dimensional Navier--Stokes equations of rotating incompressible viscous fluids with periodic boundary conditions. The asymptotic expansions, as time goes to infinity, are derived in all Gevrey spaces for any Leray-Hopf weak solutions in terms of oscillating, exponentially decaying functions. The results are established for all no...

Liu, X Titi, ES

This work is devoted to establishing the local-in-time well-posedness of strong solutions to the three-dimensional compressible primitive equations of atmospheric dynamics. It is shown that strong solutions exist, are unique, and depend continuously on the initial data, for a short time in two cases: with gravity but without vacuum, and with vacuum...

Kirane, Mokhtar Torebek, Berikbol