ON THE STABILITY OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC DIFFERENTIAL EQUATIONS

In this paper,we address the stability of periodic solutions of piecewise smooth periodic differential equations.By studying the Poincarémap,we give a sufficient condition to judge the stability of a periodic solution.We also present examples of some applications.

Self-Triggered Set Stabilization of Boolean Control Networks and Its Applications

Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.

A new model of flow over stretching(shrinking)and porous sheet with its numerical solutions

The viscous fluid flow and heat transfer over a stretching(shrinking)and porous sheets of nonuniform thickness are investigated in this paper.The modeled problem is presented by utilizing the stretching(shrinking)and porous velocities and variable thickness of the sheet and they are combined in a relation.Consequently,the new problem reproduces the different available forms of flow motion and heat transfer maintained over a stretching(shrinking)and porous sheet of variable thickness in one go.As a result,the governing equations are embedded in several parameters which can be transformed into classical cases of stretched(shrunk)flows over porous sheets.A set of general,unusual and new variables is formed to simplify the governing partial differential equations and boundary conditions.The final equations are compared with the classical models to get the validity of the current simulations and they are exactly matched with each other for different choices of parameters of the current problem when their values are properly adjusted and manipulated.Moreover,we have recovered the classical results for special and appropriate values of the parameters(δ_(1),δ_(2),δ_(3),c,and B).The individual and combined effects of all inputs from the boundary are seen on flow and heat transfer properties with the help of a numerical method and the results are compared with classical solutions in special cases.It is noteworthy that the problem describes and enhances the behavior of all field quantities in view of the governing parameters.Numerical result shows that the dual solutions can be found for different possible values of the shrinking parameter.A stability analysis is accomplished and apprehended in order to establish a criterion for the determinations of linearly stable and physically compatible solutions.The significant features and diversity of the modeled equations are scrutinized by recovering the previous problems of fluid flow and heat transfer from a uniformly heated sheet of variable(uniform)thickness with variable(uniform)stretching/shrinking and injection/suction velocities.

Development of Morus alba Reinforced Poly-Lactic Acid with Elevated Mechanical and Thermal Properties

This research investigates the mechanical and thermal properties of Morus alba combined with polylactic acid in comparison with other natural fibers. The study uses three different fiber and PLA compositions - 20%, 30%, and 40% respectively - to produce composite materials. In addition, another composite with the same fiber volume is treated with a 4% NaOH solution to improve mechanical properties. The composites are processed by twin-screw extrusion, granulation, and injection molding. Tensile strength measurements of raw fibers and NaOH-treated fibers were carried out using a single-fiber tensile test with a gauge length of 40 mm. It was observed that the NaOH surface treatment increases the resistance against tensile loading and exhibited improved properties for raw fiber strands. The diameter of the fibers was measured using optical microscopy. During this research, flexural tests, impact tests, differential scanning calorimetry (DSC), and heat deflection temperature measurements (HDT) were conducted to evaluate the mechanical and thermal properties of the developed composite samples. The results indicate that the mechanical properties of NaOH-treated Morus alba-reinforced polylactic acid outperform both virgin PLA samples and untreated Morus alba samples.

A Study of Traveling Wave Structures and Numerical Investigation of Two-Dimensional Riemann Problems with Their Stability and Accuracy

The Riemann wave system has a fundamental role in describing waves in various nonlinear natural phenomena,for instance,tsunamis in the oceans.This paper focuses on executing the generalized exponential rational function approach and some numerical methods to obtain a distinct range of traveling wave structures and numerical results of the two-dimensional Riemann problems.The stability of obtained traveling wave solutions is analyzed by satisfying the constraint conditions of the Hamiltonian system.Numerical simulations are investigated via the finite difference method to verify the accuracy of the obtained results.To extract the approximation solutions to the underlying problem,some ODE solvers in FORTRAN software are applied,and outcomes are shown graphically.The stability and accuracy of the numerical schemes using Fourier’s stabilitymethod and error analysis,respectively,to increase the reassurance are investigated.A comparison between the analytical and numerical results is obtained and graphically provided.The proposed methods are effective and practical to be applied for solving more partial differential equations(PDEs).

Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

We study nonhomogeneous systems of linear conformable fractional differential equations with pure delay.By using new conformable delayed matrix functions and the method of variation,we obtain a representation of their solutions.As an application,we derive a finite time stability result using the representation of solutions and a norm estimation of the conformable delayedmatrix functions.The obtained results are new,and they extend and improve some existing ones.Finally,an example is presented to illustrate the validity of our theoretical results.

THE NONLINEAR STABILITY OF TRAVELLING WAVE SOLUTIONS FOR A REACTING FLOW MODEL WITH SOURCE TERM

In this paper, author considers a 3 x 3 system for a reacting flow model propesed by [9]. Since this model has source term, it can be considered as a relaxation approximation to 2 x 2 systems of conservation laws, which include the well-known p-system. From this viewpoint, the author establishes the global existence and the nonlinear stability of travelling wave solutions by L-2 energy method.

THE GLOBAL L^2 STABILITY OF SOLUTIONS TO THREE DIMENSIONAL MHD EQUATIONS

In this paper, we mainly study the global L2 stability for large solutions to the MHD equations in three-dimensional bounded or unbounded domains. Under suitable conditions of the large solutions, it is shown that the large solutions are stable. And we obtain the equivalent condition of this stability condition. Moreover, the global existence and the stability of two-dimensional MHD equations under three-dimensional perturbations are also established.

Stability Test of Ampicillin Sodium Solutions in the Accufuser^(■) Elastomeric Infusion Device Using HPLC-UV Method

The stabilities of two kinds of solutions (30 mg/mL) of Ampicillin sodium in 0.9% NaCl in water (NS, normal saline) and in sterile water (SW) in the intravenous elastomeric infusion device (Accufuser&#174) were evaluated based on recommended solutions and storage periods. The injectable NS- and SW-Ampicillin solutions in the Accufuser&#174 device were stored and evaluated at controlled temperature (room temperature, 25℃ ± 2℃ and cold temperature, 4℃ ± 2℃) during 7 days. Effects of the periods of storage (from 0 to 7 days) and the temperatures of storage (RT and CT) on the physico-chemical appearances and concentrations of active compounds were determined. The visual clarity, pH, and concentrations of Ampicillin were determined by stability-indicating high-performance liquid chromatography (HPLC)-ultraviolet (UV) detection. The results showed that the amount of Ampicillin in studied solutions gradually decreased with time. The Ampicillin in NS, which was stored in CT, was relatively stable, retaining 94% of its original amount up to 7 days. The solution that showed least stability was Ampicillin in SW, which was stored in RT, retaining 80% of its original amount. Generally, solutions that were stored in CT were more stable than the solutions that were stored in RT. No significant changes in physical appearance or color of the solutions were observed during the study. Particles were not detected in any solution samples. In summary, two kinds of solutions of Ampicillin sodium, in NS and SW, showed different chemical stabilities with time in intravenous infusion device without any significant physical changes and retained about 94% vs 89% and 83% vs 80% of initial concentrations after 7 days in CT and RT, respectively. We suggest that 30 mg/mL of Ampicillin sodium in NS solution in an Accufuser&#174 infusion device which is stored in CT can be applicable for 7 days in clinical situations.

Asymptotic stability of solutions to the nonisentropic hydrodynamic model for semiconductors

In this paper, the asymptotic stability of smooth solutions to the multidimensional nonisentropic hydrodynamic model for semiconductors is established, under the assumption that the initial data are a small perturbation of the stationary solutions for the thermal equilibrium state, whose proofs mainly depend on the basic energy methods.

Stability Criteria of Solutions for Stochastic Set Differential Equations

The existence and uniqueness results on solutions of set stochastic differential equation were studied in [1]. In this paper, we present the stability criteria for solutions of stochastic set differential equation.

Existence and Exponential Stability of the Anti-Periodic Solutions for a Class of Impulsive CohenGrossberg Neural Networks with Mixed Delays

In this paper,we study the anti-periodic solutions for a class of impulsive Cohen-Grossberg neural networks with mixed delays.By using analysis techniques,some sufficient conditions are obtained which guarantee the existence and global exponential stability of the anti-periodic solutions.The criteria extend and improve some earlier results.Moreover,we give an examples to illustrate our main results.

THE EXISTENCE AND STABILITY OF STATIONARY SOLUTIONS OF THE INFLOW PROBLEM FOR FULL COMPRESSIBLE NAVIER-STOKES-POISSON SYSTEM

In this paper,we consider an inflow problem for the non-isentropic Navier-StokesPoisson system in a half line(0,∞).For the general gas including ideal polytropic gas,we first give some results for the existence of the stationary solution with the aid of center manifold theory on a 4×4 system of autonomous ordinary differential equations.We also show the time asymptotic stability of the stationary solutions with small strength under smallness assumptions on the initial perturbations by using an elementary energy method.

EXISTENCE AND STABILITY OF PERIODIC AND ALMOST PERIODIC SOLUTIONS TO THE BOUSSINESQ SYSTEM IN UNBOUNDED DOMAINS

In this paper we investigate the existence and stability of periodic solutions(on a half-line R_(+))and almost periodic solutions on the whole line time-axis R to the Boussinesq system on several classes of unbounded domains of R^(n) in the framework of interpolation spaces.For the linear Boussinesq system we combine the L^(p)—L^(q)-smoothing estimates and interpolation functors to prove the existence of bounded mild solutions.Then,we prove the existence of periodic solutions by invoking Massera’s principle.We also prove the existence of almost periodic solutions.Then we use the results of the linear Boussinesq system to establish the existence,uniqueness and stability of the small periodic and almost periodic solutions to the Boussinesq system using fixed point arguments and interpolation spaces.Our results cover and extend the previous ones obtained in[13,34,38].

Exponential Stability of Weak Solutions to Linear Thernioviscoelastic Systems

This paper is concerned with the exponential stability of weak solutions to a linear one-dimensional thermoviscoelastic system with clamped boundary conditions. This system defines a C0-semigroup {S（t）}t≥0 on the space L^2（0, 1） × C^1 （0,1） × H^1（0, 1）, which processes the property of the exponential stability.

GLOBAL STABILITY OF LARGE SOLUTIONS TO THE 3D MAGNETIC BéNARD PROBLEM

In this paper,we consider the 3D magnetic Bénard problem.More precisely,we prove that the large solutions are stable under certain conditions.And we obtain the equivalent condition with respect to this stability condition.Finally,we also establish the stability of 2 D magnetic Bénard problem under 3D perturbations.

Existence and Nonlinear Stability of Stationary Solutions to the Viscous Two-Phase Flow Model in a Half Line

The outflow problem for the viscous two-phase flow model in a half line is investigated in the present paper.The existence and uniqueness of the stationary solution is shown for both supersonic state and sonic state at spatial far field,and the nonlinear time stability of the stationary solution is also established in the weighted Sobolev space with either the exponential time decay rate for supersonic flow or the algebraic time decay rate for sonic flow.

Exact Solutions of Discrete Complex Cubic Ginzburg-Landau Equation and Their Linear Stability

The discrete complex cubic Ginzburg-Landau equation is an important model to describe a number of physical systems such as Taylor and frustrated vortices in hydrodynamics and semiconductor laser arrays in optics. In this paper, the exact solutions of the discrete complex cubic Ginzburg-Landau equation are derived using homogeneous balance principle and the GI/G-expansion method, and the linear stability of exact solutions is discussed.

Effect of the Formulation of Sodium Activation Solutions on the Setting Time of Metakaolin Based Geopolymers

Geopolymer materials today represent innovative products,used frequently as a substitute for cementitious traditional materials.They are obtained by the action of an alkaline activation solution(composed of mainly of silicon dioxide(SiO2)and sodium hydroxide(NaOH)and water)on a powder natural or synthetic aluminosilicates.In this work,we seek to highlight the effect of the percentage of sodium dioxide firstly,on the evolution of the viscosity of the alkali-activated solution and secondly,on the evolution of the viscosity of geopolymeric solution.Another aspect of this work is the determination of the effect of this percentage on the kinetics that characterize the start of the percolation phenomenon(transition from the fresh state to the hardened state).At last result concerns the impact of temperature on this transition.This contribution consolidates the control protocols for the formulation of geopolymers and allows the optimization of the processes of their exploitation.

Multiple solutions and stability of the steady transonic small-disturbance equation

Numerical solutions of the steady transonic small-disturbance（TSD） potential equation are computed using the conservative Murman-Cole scheme. Multiple solutions are discovered and mapped out for the Mach number range at zero angle of attack and the angle of attack range at Mach number 0.85 for the NACA 0012 airfoil. We present a linear stability analysis method by directly assembling and evaluating the Jacobian matrix of the nonlinear finite-difference equation of the TSD equation. The stability of all the discovered multiple solutions are then determined by the proposed eigen analysis. The relation of stability to convergence of the iterative method for solving the TSD equation is discussed. Computations and the stability analysis demonstrate the possibility of eliminating the multiple solutions and stabilizing the remaining unique solution by adding a sufficiently long splitter plate downstream the airfoil trailing edge. Finally, instability of the solution of the TSD equation is shown to be closely connected to the onset of transonic buffet by comparing with experimental data.