Stability Criteria of Interval Time-Varying Delay Systems and Their Application

The stability for a class of uncertain linear systems with interval time-varying delays is studied. Based on the delay-dividing approach, the delay interval is partitioned into two subintervals. By constructing an appropriate Lyapunov-Krasovskii functional and using the convex combination method and the improved integral inequality, the delay-dependent stability criteria with less conservation are derived. Finally, some numerical examples are given to show the effectiveness and superiority of the proposed method.

Laplace Transform Collocation Method for Solving Hyperbolic Telegraph Equation

This article presents a new numerical scheme to approximate the solution of one-dimensional telegraph equations. With the use of Laplace transform technique, a new form of trial function from the original equation is obtained. The unknown coefficients in the trial functions are determined using collocation method. The efficiency of the new scheme is demonstrated with examples and the approximations are in excellent agreement with the analytical solutions. This method produced better approximations than the ones produced with the standard weighted residual methods.

Modelling of the Deformation Diffusion Areas on a Para-Aramid Fabric with B-Spline Curves

The geometrical modelling of the planar energy diffusion behaviors of the deformations on a para-aramid fabric has been performed. In the application process of the study, in the experimental period, drop test with bullets of different weights has been applied. The B-spline curve-generating technique has been used in the study. This is an efficient method for geometrical modelling of the deformation diffusion areas formed after the drop test. Proper control points have been chosen to be able to draw the borders of the diffusion areas on the fabric which is deformed, and then the De Casteljau and De Boor algorithms have been used. The Holditch area calculation according to the beams taken at certain fixed lengths has been performed for the B-spline border curve obtained as a closed form. After the calculations, it has been determined that the diffusion area where the bullet with pointed end was dropped on a para-aramid fabric is bigger and the diffusion area where the bullet with rounded end was dropped is smaller when compared with the areas where other bullets with different ends were dropped.

Transient Free Convective MHD Flow Past an Exponentially Accelerated Vertical Porous Plate with Variable Temperature through a Porous Medium

This paper is concerned with analytical solution of one-dimensional unsteady laminar boundary layer MHD flow of a viscous incompressible fluid past an exponentially accelerated infinite vertical plate in presence of transverse magnetic field. The vertical plate and the medium of flow are considered to be porous. The fluid is assumed to be optically thin and the magnetic Reynolds number is considered small enough to neglect the induced hydromagnetic effects. The governing boundary layer equations are first converted to dimensionless form and then solved by Laplace transform technique. Numerical values of transient velocity, temperature, skin friction, and Nusselt number are illustrated and are presented in graphs for various sets of physical parametric values, namely, Grashof number, accelerating parameter, suction parameter, permeability parameter, radiation parameter, magnetic parameter, and time. It is found that the velocity decreases with increases of the suction parameter for both cases of cooling and heating of the porous plate whereas skin friction increases with increase of suction parameter.

A New Iterative Numerical Continuation Technique for Approximating the Solutions of Scalar Nonlinear Equations

The present study concerns the development of a new iterative method applied to a numerical continuation procedure for parameterized scalar nonlinear equations. Combining both a modified Newton’s technique and a stationary-type numerical procedure, the proposed method is able to provide suitable approximate solutions associated with scalar nonlinear equations. A numerical analysis of predictive capabilities of this new iterative algorithm is addressed, assessed, and discussed on some specific examples.

Unsteady Natural Convection Flow past an Infinite Cylinder with Thermal and Mass Stratification

This paper presents an analytical solution of unsteady one-dimensional free convection flow past an infinite vertical circular cylinder in a stratified fluid medium. The dimensionless coupled linear governing partial differential equations are solved by Laplace transform technique for unit Prandtl number and Schmidt number. Effects of various physical parameters are presented with graphs. Numerical values of boundary layer thickness for different parameters are presented in table. Due to the effects of thermal and mass stratifications, the velocity, temperature, and skin friction, Nusselt number shows oscillatory behaviour at smaller times and then reaches steady state at larger times.

On the Extension of Sarrus’ Rule to n×n (n>3) Matrices: Development of New Method for the Computation of the Determinant of 4×4 Matrix

The determinant of a matrix is very powerful tool that helps in establishing properties of matrices. Indisputably, its importance in various engineering and applied science problems has made it a mathematical area of increasing significance. From developed and existing methods of finding determinant of a matrix, basketweave method/Sarrus’ rule has been shown to be the simplest, easiest, very fast, accurate, and straightforward method for the computation of the determinant of 3 × 3 matrices. However, its gross limitation is that this method/rule does not work for matrices larger than 3 × 3 and this fact is well established in literatures. Therefore, the state-of-the-art methods for finding the determinants of 4 × 4 matrix and larger matrices are predominantly founded on non-basketweave method/non-Sarrus’ rule. In this work, extension of the simple, easy, accurate, and straightforward approach to the determinant of larger matrices is presented. The paper presents the developments of new method with different schemes based on the basketweave method/Sarrus’ rule for the computation of the determinant of 4 × 4. The potency of the new method is revealed in generalization of the basketweave method/non-Sarrus’ rule for the computation of the determinant of n×n (n>3) matrices. The new method is very efficient, very consistence for handy calculations, highly accurate, and fastest compared to other existing methods.

Various Fixed Point Theorems in Complex Valued b-Metric Spaces

We prove some common fixed point results for a pair of mappings which satisfy generalized contractive conditions with rational expressions having point-dependent control functions as coefficients in complex valued b-metric spaces. The results of this paper generalize and extend the several known results in complex valued b-metric spaces. Finally, examples are provided to verify the effectiveness and to usability of our main results.

An Efficient and Straightforward Numerical Technique Coupled to Classical Newton’s Method for Enhancing the Accuracy of Approximate Solutions Associated with Scalar Nonlinear Equations

This study concerns the development of a straightforward numerical technique associated with Classical Newton’s Method for providing a more accurate approximate solution of scalar nonlinear equations. The proposed procedure is based on some practical geometric rules and requires the knowledge of the local slope of the curve representing the considered nonlinear function. Therefore, this new technique uses, only as input data, the first-order derivative of the nonlinear equation in question. The relevance of this numerical procedure is tested, evaluated, and discussed through some examples.

Reflection of Plane Waves in Generalized Thermoelastic Half Space under the Action of Uniform Magnetic Field

Reflection of longitudinal displacement waves in a generalized thermoelastic half space under the action of uniform magnetic field has been investigated. The magnetic field is applied in such a direction that the problem can be considered as a two-dimensional one. The discussion is based on the three theories of generalized thermoelasticity: Lord-Shulman (L-S), Green-Lindsay (G-L), and Green-Naghdi (G-N) with energy dissipation. We compute the possible wave velocities for different models. Amplitude ratios have been presented. The effects of magnetic field on various subjects of interest are discussed and shown graphically.