scholarly journals SYNTHESIS OF SYSTEMS OF CORRELATED SIGNALS USING A SUPPLEMENTATION FOR THE GRAM-SCHMIDT ORTHOGONALIZATION PROCEDURE

2019 ◽  
Vol 40 (4) ◽  
Author(s):  
О. Г. Голубничий
Keyword(s):  
Schmidt Orthogonalization ◽  
Correlated Signals ◽  
Orthogonalization Procedure

scholarly journals The study of chaotic and regular regimes of the fractal oscillators FitzHugh-Nagumo

2018 ◽  
Vol 62 ◽  
pp. 02017 ◽  
Author(s):  
Olga Lipko ◽  
Roman Parovik
Keyword(s):  
Mathematical Model ◽  
Lyapunov Exponents ◽  
Nerve Impulse ◽  
Chaotic Attractors ◽  
Control Parameters ◽  
Schmidt Orthogonalization ◽  
Non Local ◽  
Explicit Finite Difference ◽  
Maximum Lyapunov Exponents ◽  
Orthogonalization Procedure

In this paper we study the conditions for the existence of chaotic and regular oscillatory regimes of the hereditary oscillator FitzHugh-Nagumo (FHN), a mathematical model for the propagation of a nerve impulse in a membrane. To achieve this goal, using the non-local explicit finite-difference scheme and Wolf’s algorithm with the Gram-Schmidt orthogonalization procedure and the spectra of the maximum Lyapunov exponents were also constructed depending on the values of the control parameters of the model of the FHN. The results of the calculations showed that there are spectra of maximum Lyapunov exponents both with positive values and with negative values. The results of the calculations were also confirmed with the help of oscillograms and phase trajectories, which indicates the possibility of the existence of both chaotic attractors and limit cycles.

Vibration of Nonhomogeneous Orthotropic Elliptic and Circular Plates With Variable Thickness

2006 ◽  
Vol 129 (2) ◽  
pp. 256-259 ◽  
Author(s):  
S. Chakraverty ◽  
Ragini Jindal ◽  
V. K. Agarwal
Keyword(s):  
Variable Thickness ◽  
Ritz Method ◽  
Thickness Variation ◽  
Circular Plates ◽  
Plate Material ◽  
Orthotropic Plates ◽  
Various Boundary Conditions ◽  
Vibrational Characteristics ◽  
Schmidt Orthogonalization ◽  
Orthogonalization Procedure

In this paper, study of nonhomogeneity as well as variable thickness in elliptic and circular orthotropic plates is undertaken. Nonhomogeneity of plate material is assumed to be a quadratic variation of Young’s modulii and density whereas shear modulus, is considered to vary linearly along both the axes. The quadratic thickness variation in orthotropic nonhomogeneous plates is also considered. Effect of variation of these parameters on vibrational characteristics are analyzed for various boundary conditions at the edges. Results are obtained using boundary characteristic orthogonal polynomials generated by using Gram-Schmidt orthogonalization procedure in Rayleigh-Ritz method.

Orthogonal Signals and the Orthogonalization Procedure

2021 ◽  
pp. 18-55
Author(s):  
Stevan Berber
Keyword(s):  
Spread Spectrum ◽  
Communication Systems ◽  
Orthogonal Frequency Division Multiplexing ◽  
Theory And Practice ◽  
Schmidt Orthogonalization ◽  
Code Division Multiple ◽  
Digital Communication Systems ◽  
Spreading Sequences ◽  
Multiplexing Systems ◽  
Orthogonalization Procedure

Chapter 2 is dedicated to the principle of signal orthogonalization, because orthogonal signals are widely used in telecommunication theory and practice, like the carriers of baseband signals, subcarriers in orthogonal frequency division multiplexing systems, and the spreading sequences in spread-spectrum and code division multiple access (CDMA) systems. The orthonormal basis functions are defined and the procedure of the vector representation of signals is demonstrated. The Gram–Schmidt orthogonalization procedure and construction of the space diagram are presented in detail. Using orthonormal signals, signal synthesizers and analysers that can be used to form discrete-time transmitters and receivers are theoretically founded. Understanding of this chapter is a prerequisite for understanding Chapters 4–10, because the orthonormal signals defined in this chapter will be used throughout the book. The basis harmonic orthonormal functions will define the carriers in the discrete and digital communication systems.

scholarly journals Analysis of Feature Influence on Covid-19 Death Rate Per Country Using a Novel Orthogonalization Technique

2021 ◽  
Author(s):  
Gaston Gonnet ◽  
John Stewart ◽  
Joseph Lafleur ◽  
Stephen Keith ◽  
Mark McLellan ◽  
...  
Keyword(s):  
Death Rate ◽  
Economic Factors ◽  
New Approach ◽  
Preventative Measures ◽  
Feature Importance ◽  
Schmidt Orthogonalization ◽  
A New Technique ◽  
Proper Context ◽  
Over Time ◽  
Orthogonalization Procedure

We have developed a new technique of Feature Importance, a topic of machine learning, to analyze the possible causes of the Covid-19 pandemic based on country data. This new approach works well even when there are many more features than countries and is not affected by high correlation of features. It is inspired by the Gram-Schmidt orthogonalization procedure from linear algebra. We study the number of deaths, which is more reliable than the number of cases at the onset of the pandemic, during Apr/May 2020. This is while countries started taking measures, so more light will be shed on the root causes of the pandemic rather than on its handling. The analysis is done against a comprehensive list of roughly 3,200 features. We find that globalization is the main contributing cause, followed by calcium intake, economic factors, environmental factors, preventative measures, and others. This analysis was done for 20 different dates and shows that some factors, like calcium, phase in or out over time. We also compute row explainability, i.e. for every country, how much each feature explains the death rate. Finally we also study a series of conditions, e.g. comorbidities, immunization, etc. which have been proposed to explain the pandemic and place them in their proper context. While there are many caveats to this analysis, we believe it sheds light on the possible causes of the Covid-19 pandemic.

scholarly journals An attractive numerical algorithm for solving nonlinear Caputo–Fabrizio fractional Abel differential equation in a Hilbert space

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohammed Al-Smadi ◽  
Nadir Djeddi ◽  
Shaher Momani ◽  
Shrideh Al-Omari ◽  
Serkan Araci
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Reproducing Kernel ◽  
Numerical Approach ◽  
Accurate Solution ◽  
Stability And Convergence ◽  
Type Model ◽  
Schmidt Orthogonalization ◽  
And Performance ◽  
Abel Differential Equation

AbstractOur aim in this paper is presenting an attractive numerical approach giving an accurate solution to the nonlinear fractional Abel differential equation based on a reproducing kernel algorithm with model endowed with a Caputo–Fabrizio fractional derivative. By means of such an approach, we utilize the Gram–Schmidt orthogonalization process to create an orthonormal set of bases that leads to an appropriate solution in the Hilbert space $\mathcal{H}^{2}[a,b]$ H 2 [ a , b ] . We investigate and discuss stability and convergence of the proposed method. The n-term series solution converges uniformly to the analytic solution. We present several numerical examples of potential interests to illustrate the reliability, efficacy, and performance of the method under the influence of the Caputo–Fabrizio derivative. The gained results have shown superiority of the reproducing kernel algorithm and its infinite accuracy with a least time and efforts in solving the fractional Abel-type model. Therefore, in this direction, the proposed algorithm is an alternative and systematic tool for analyzing the behavior of many nonlinear temporal fractional differential equations emerging in the fields of engineering, physics, and sciences.

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