Sign Stability of Dual Switching Linear Continuous-Time Positive Systems

This paper investigates 1-moment exponential stability and exponential mean-square stability (EMS stability) under average dwell time (ADT) and the preset deterministic switching mechanism of dual switching linear continuous-time positive systems when a numerical realization does not exist. The signs of subsystem matrices, but not their structures of magnitude, are key information that causes a qualitative concept of stability called sign stability. Both 1-moment exponential stability and EMS stability, which are the traditional stability concepts, are generalized intrinsically. Hence, both 1-moment exponential sign stability and EMS sign stability are introduced and are proven based on sign equivalency. It is shown that they are symmetrically and qualitatively stable. Notably, the notion of stability can be checked quantitatively using some examples.

On a Hilfer Type Fractional Differential Equation with Nonlinear Right-Hand Side

In this article we consider the questions of one-valued solvability and numerical realization of initial value problem for a nonlinear Hilfer type fractional differential equation with maxima. By the aid of uncomplicated integral transformation based on Dirichlet formula, this initial value problem is reduced to the nonlinear Volterra type fractional integral equation. The theorem of existence and uniqueness of the solution of given initial value problem in the segment under consideration is proved. For numerical realization of solution the generalized Jacobi–Galerkin method is applied. Illustrative examples are provided.

Pseudospin-dependent Acoustic Topological Insulator by Sonic Crystals With Same Hexagonal Rods

We report the experimental and numerical realization of a pseudospin-dependent acoustic topological insulator based on two sonic crystals constructed by the same regular hexagonal rods. Based on the zone folding mechanism, we obtain double Dirac cones with a four-fold deterministic degeneracy in the sonic crystal, and realize a band inversion and topological phase transition by rotating the rods. We observe the topologically protected one-way sound propagation of pseudospin-dependent edge states in a designed topological insulator composed of two selected sonic crystals with different rotation angles of the rods. Furthermore, we experimentally demonstrate the robustness of topological sound propagation against two types of defects, in which the edge states are almost immune to backscattering, and remain pseudospin-dependent characteristics. Our work provides a diverse route for designing tunable topological functional sound devices.

Applying the constant strength doublet method to resolve a steady flow around an airfoil

In the paper hereby, a numerical (panel) method is applied to analyze steady two-dimensional flow of ideal gas around an airfoil. Initially, the airfoil is divided into a finite number of panels. Then the panels are replaced by doublets with constant strength. In addition, a wake panel is added to fulfill Kutta condition at the airfoil trailing edge. In order to implement this, a numerical realization is developed and built by means of Tiny C Compiler. To work out a solution to the linear non-homogeneous algebraic system, direct schemes for lower-upper factorization/decomposition of matrix of coefficients were applied, namely Crout, Doolittle, and Cholesky. The obtained results are validated against exact solution and shown for various values of angle of attack and Reynolds number.

Analytical reconstruction formula with efficient implementation for a modality of Compton scattering tomography with translational geometry

<p style='text-indent:20px;'>In this paper, we address an alternative formulation for the exact inverse formula of the Radon transform on circle arcs arising in a modality of Compton Scattering Tomography in translational geometry proposed by Webber and Miller (Inverse Problems (36)2, 025007, 2020). The original study proposes a first method of reconstruction, using the theory of Volterra integral equations. The numerical realization of such a type of inverse formula may exhibit some difficulties, mainly due to stability issues. Here, we provide a suitable formulation for exact inversion that can be straightforwardly implemented in the Fourier domain. Simulations are carried out to illustrate the efficiency of the proposed reconstruction algorithm.</p>

A Fast Method for Numerical Realization of Fourier Tools

This chapter presents new application of author’s recent algorithms for fast summations of truncated Fourier series. A complete description of this method is given, and an algorithm for numerical implementation with a given accuracy for the Fourier transform is proposed.

Approximation of a function describing a quality criterion of the thermo-mechanical fusible interfacing process

The present work aims to investigate the function describing the relationship between a quality criterion and input factors of the thermo-mechanical fusible /TMF/ interfacing process and to derive its effective approximation. An approximation by interpolation was applied for the purpose of the study. A numerical realization of a linear and exponential approximation of the mathematical model describing the TMF interfacing process was performed. An effective linear approximation of the function connecting the quality criterion with the input factors of the TMF interfacing process was found. This creates conditions for replacing the relatively complex function (describing the TMF interfacing process) with its linear approximation. The linear approximation gives the possibility easier and faster to determine the relationships between the input factors and the quality criterion. This created conditions for ignoring the subjective factor and for optimizing and automating the studied technological process.