Current Issue : January-March Volume : 2022 Issue Number : 1 Articles : 5 Articles
We introduce some new oscillation criteria for a third-order linear differential equation with variable coefficients in this study. We found out the corollary as a result of the Storm comparison theory and used it to prove some theorems. Through it, we were able to achieve the necessary conditions for oscillation. We concluded that the solution to the differential equation is oscillating if it Q(x) is bounded from below, and also if the discriminant D(x) of the equation is negative, its solution is oscillatory. We have given examples illustrating these results....
Functional brain networks (FBNs) provide a potential way for understanding the brain organizational patterns and diagnosing neurological diseases. Due to its importance, many FBN construction methods have been proposed currently, including the low-order Pearson’s correlation (PC) and sparse representation (SR), as well as the high-order functional connection (HoFC). However, most existing methods usually ignore the information of topological structures of FBN, such as low-rank structure which can reduce the noise and improve modularity to enhance the stability of networks. In this paper, we propose a novel method for improving the estimated FBNs utilizing matrix factorization (MF). More specifically, we firstly construct FBNs based on three traditional methods, including PC, SR, and HoFC. Then, we reduce the rank of these FBNs via MF model for estimating FBN with low-rank structure. Finally, to evaluate the effectiveness of the proposed method, experiments have been conducted to identify the subjects with mild cognitive impairment (MCI) and autism spectrum disorder (ASD) from norm controls (NCs) using the estimated FBNs. The results on Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset and Autism Brain Imaging Data Exchange (ABIDE) dataset demonstrate that the classification performances achieved by our proposed method are better than the selected baseline methods....
Beam equation can describe the deformation of beams and reflect various bending problems and it has been widely used in large engineering projects, bridge construction, aerospace and other fields. It has important engineering practice value and scientific significance for the design of numerical schemes. In this paper, a scheme for vibration equation of viscoelastic beam is developed by using the Hermite finite element. Based on an elliptic projection, the errors of semi-discrete scheme and fully discrete scheme are analyzed respectively, and the optimal L2-norm error estimates are obtained. Finally, a numerical example is given to verify the theoretical predictions and the validity of the scheme....
The aim of this work is to prove the well-posedness of some linear and nonlinear mixed problems with integral conditions defined only on two parts of the considered boundary. First, we establish for the associated linear problem a priori estimate and prove that the range of the operator generated by the considered problem is dense using a functional analysis method. Then by applying an iterative process based on the obtained results for the linear problem, we establish the existence, uniqueness and continuous dependence of the weak solution of the nonlinear problem....
One of the methods of mathematical analysis in many cases makes it possible to reduce the study of differential operators, pseudo-differential operators and certain types of integral operators and the solution of equations containing them, to an examination of simpler algebraic problems. The development and systematic use of operational calculus began with the work of O. Heaviside (1892), who proposed formal rules for dealing with the differentiation operator d/dt and solved a number of applied problems. However, he did not give operational calculus a mathematical basis; this was done with the aid of the Laplace transform; J. Mikusiński (1953) put operational calculus into algebraic form, using the concept of a function ring [1]. Thereupon I’m suggesting here the use of the integration operator dt to make an extension for the systematic use of operational calculus. Throughout designing and analyzing a control system, we need to treat the functionality of the system with respect to time. The reaction of the system instructs us how to stable it by amplifiers and feedbacks [2], thereafter the Differential Transform is a good tool for doing this, and it’s a technique to frustrate difficulties we may bump into, also it has the methods to find the immediate reaction of the system with respect to infinitesimal (tiny) time which spares us from the hard work in finding the time dependent function, this could be done by producing finite series....
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