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.

Influence of dissolved oxygen content on oxidative stability of linked polymer solution

The influence of dissolved oxygen content on the oxidative stability of a linked polymer solution (LPS) was studied by micro-filtration, dynamic light scattering and viscosity measurements. The results showed that at the same temperature, the degree of the oxidative degradation of the LPS increased and the rapidity of the oxidative degradation was accelerated with the increase of the dissolved oxygen content. Consequently, the size of linked polymer coils (LPCs) of the LPS became small, and the plugging capability of the LPS decreased. At a fixed content of dissolved oxygen, with increasing degradation temperature, almost the same results were observed, namely, an increased degree of oxidative degradation, accelerated rapidity of the oxidative degradation and decreased plugging capacity, with decreased oxidative stability of LPS. At 90 °C, in the presence of oxygen, LPS lost its plugging capability after having been degraded for a period of time. But at 40 °C, LPS with low dissolved oxygen content could be stable for a long time. The decreased plugging ability of LPS after oxidative degradation is mainly caused by the decreased size and number of the LPCs due to the breaking of hydrolyzed polyacrylamide (HPAM) molecule segments and the structural changing of HPAM molecules.

Existence of asymptotically almost periodic solutions and stability properties for functional difference equations

For functional difference equations with unbounded delay,we characterized the existence of totally stable and asymptotically almost periodic solution by using stability properties of a bounded solution in a certain limiting equation.

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.

Long-term stability of gentamicin sulfate-ethylenediaminetetraacetic acid disodium salt (EDTA-Na_2) solution for catheter locks

A lock solution composed of gentamicin sulfate(5 mg/mL) and ethylenediaminetetraacetic acid disodium salt(EDTA-Na2, 30 mg/mL) could fully eradicate in vivo bacterial biofilms in totally implantable venous access ports(TIVAP). In this study, fabrication, conditioning and sterilization processes of antimicrobial lock solution(ALS) were detailed and completed by a stability study. Stability of ALS was conducted for12 months in vial(25 °C 7 2 °C, 60% 7 5% relative humidity(RH), and at 40 °C 7 2 °C, RH 75% 7 5%)and for 24 h and 72 h in TIVAP(40 °C 7 2 °C, RH 75% 7 5%). A stability indicating HPLC assay with UV detection for simultaneous quantification of gentamicin sulfate and EDTA-Na2 was developed. ALS was assayed by ion-pairing high performance liquid chromatography(HPLC) needing gentamicin derivatization, EDTA-Na2 metallocomplexation of samples and gradient mobile phase. HPLC methods to separate four gentamicin components and EDTA-Na2 were validated. Efficiency of sterility procedure and conditioning of ALS was confirmed by bacterial endotoxins and sterility tests. Physicochemical stability of ALS was determined by visual inspection, osmolality, pH, and sub-visible particle counting. Results confirmed that the stability of ALS in vials was maintained for 12 months and 24 h and 72 h in TIVAP.

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.

Upper Bound Solution of Soil Slope Stability under Coupling Effect of Rainfall and Earthquake

Based on the limit analysis upper bound method,a new model of soil slope collapse has been proposed which consists of two rigid block zones and a plastic shear zone.Soil slope was induced failure by coupling effect of rainfall and earthquake,and these blocks were also incorporated horizontal earthquake force and vertical gravitate.The velocities and forces were analyzed in three blocks,and the expression of velocity discontinuities was obtained by the principle of incompressibility.The external force work for the blocks,the internal energy of the plastic shear zone and the velocity discontinuous were solved.The present stability ratios are compared to the prevenient research,which shows the superiority of the mechanism and rationality of the analysis.The critical height of the soil slope can provide theoretical basis for slope support and design.

Stability of Global Solution to Boltzmann-Enskog Equation with External Force

In the presence of external forces depending only on the time and space variables, the Boltzmann-Enskog equation formally conserves only the mass of the . system, and its entropy functional is also nonincreasing. Corresponding to this type of equation, we first give some hypotheses of its bicharacteristic equations and then get some results about the stablity of its global solution with the help of two new Lyapunov functionals： one is to describe interactions between particles with different velocities and the other is to measure the L1 distance between two mild solutions. The former Lyapunov functional yields the time-asymptotic convergence of global classical solutions to the collision free motion while the latter is applied into the veri-fication of the L1 stability of global mild solutions to the Boltzmann-Enskog equation for a moderately or highly dense gas in the influence of external forces.

Analysis of Bifurcation and Stability on Solutions of a Lotka-Volterra Ecological System with Cubic Functional Responses and Diffusion

This paper deals with a Lotka-Volterra ecological competition system with cubic functional responses and diffusion. We consider the stability of semitrivial solutions by using spectrum analysis. Taking the growth rate as a bifurcation parameter and using the bifurcation theory, we discuss the existence and stability of the bifurcating solutions which emanate from the semi-trivial solutions.

Three-dimensional MHD flow over a shrinking sheet: Analytical solution and stability analysis

The magnetohydrodynamic（MHD） steady and unsteady axisymmetric flows of a viscous fluid over a two-dimensional shrinking sheet are addressed. The mathematical analysis is carried out in the presence of a large magnetic field. The steady state problem results in a singular perturbation problem having an infinite domain singularity. The secular term appearing in the solution is removed and a two-term uniformly valid solution is derived using the Lindstedt–Poincaré technique. This asymptotic solution is validated by comparing it with the numerical solution. The solution for the unsteady problem is also presented analytically in the asymptotic limit of large magnetic field. The results of velocity profile and skin friction are shown graphically to explore the physical features of the flow field. The stability analysis of the unsteady flow is made to validate the asymptotic solution.

Existence and Exponential Stability of Almost Periodic Solution for Hopfield Neural Network Equations with Almost Periodic Imput

By constructing Liapunov functions and building a new inequality, we obtain two kinds of sufficient conditions for the existence and global exponential stability of almost periodic solution for a Hopfield-type neural networks subject to almost periodic external stimuli. Irt this paper, we assume that the network parameters vary almost periodically with time and we incorporate variable delays in the processing part of the network architectures.

Stability and Approximate Analytical Periodic Solution of a Structurally Orthotropic Stringer Shell

Combined with real engineering, we mainly study the stability of the equilibrium state at the coordinate center of an orthotropic stringer shell system, and the approximate analytic periodic motion is presented around the studied equilibrium state. In addition the rationality of the obtained results is verified by numerical simulation. Furthermore we found that there are actually only four kinds of phase portrait of this type of shell.

Variational Solution of Coral Reef Stability Due to Horizontal Wave Loading

This paper proposes a theoretical method that can be used in calculating the stability of coral reefs or artificial islands.In this work,we employ the variational limiting equilibrium procedure to theoretically determine the slope stability of coral reefs covered with hard reef shells as a result of horizontal wave loads.A reasonable functional is proposed and its extremum is calculated based on the conservation of energy.Then,we deduce the stability factor Ns of coral reefs under combined vertical self-gravity and horizontal wave loads,which is consistent with the published results.We compare some classic examples of homogeneous slopes without hard shells in order to analyze the accuracy of results generated by this variational procedure.The variational results are accurate and reliable according to the results of a series of detailed calculations and comparisons.Simultaneously,some other influence parameters on the reef stability,including the top-layer tensile strength of coral reef,the amplitude of wave loading,and the tensile crack,are calculated and discussed in detail.The analysis results reveal that the existence of a hard reef shell could enhance the stability of reef slope and that there is a nonlinear relationship between the stability factor Ns,the shear strength,and the thickness Ds of the covered coral reef shell.Furthermore,the emergence of top-layer tensile cracks on the coral reefs reduces their stability,and the action of horizontal wave loads greatly decreases the stability of coral reefs.Thus,the hard shell strength and its thickness Ds,surface tensile crack,and wave loading require more careful attention in the field of practical engineering.

Existence and exponential stability of almost-periodic solutions for MAM neural network with distributed delays on time scales

This paper is concerned with multidirectional associative memory neural network with distributed delays on almost-periodic time scales.Some sufficient conditions on the existence,uniqueness and the global exponential stability of almost-periodic solutions are established.An example is presented to illustrate the feasibility and effectiveness of the obtained results.

Stability of calcium silicate in basic solution

Mixture of CaO and SiO 2 was sintered at 1 200 or 1 400 ℃ according to the mole ratio of CaO/SiO 2 of 1 or 2, and then calcium silicate was leached in pure caustic or soda solution. The results indicated that calcium silicate exists much more stably in caustic solution than that in soda solution, and CaO·SiO 2 is more stable than β 2CaO·SiO 2 whether in caustic solution or in soda solution. The increase of sintering temperature favored the stability of calcium silicate in the leaching process. When β 2CaO·SiO 2 was leached in soda solution, the increase of leaching temperature and time resulted in decomposing of more calcium silicate. And when β 2CaO·SiO 2 was leached in caustic solution at high temperature, much 2CaO·SiO 2·H 2O but little CaO·SiO 2·H 2O appeared in slag.

Global Exponential Stability of Almost Periodic Solution of Cellular Neural Networks with Time-Varying Delays

In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays （CNNVDs） is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improved and extended in this letter and one example is given to illustrate the effectiveness of the new results.

STABILITY OF SUBHARMONIC SOLUTIONS OF FIRST-ORDER HAMILTONIAN SYSTEMS WITH ANISOTROPIC GROWTH

Using the dual Morse index theory, we study the stability of subharmonic solutions of first-order autonomous Hamiltonian systems with anisotropic growth, that is, we obtain a sequence of elliptic subharmonic solutions(that is, all its Floquet multipliers lying on the unit circle on the complex plane C).

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.

Exact solutions and linear stability analysis for two-dimensional Ablowitz Ladik equation

The Ablowitz-Ladik equation is a very important model in nonlinear mathematical physics. In this paper, the hyper- bolic function solitary wave solutions, the trigonometric function periodic wave solutions, and the rational wave solutions with more arbitrary parameters of two-dimensional Ablowitz-Ladik equation are derived by using the （GI/G）-expansion method, and the effects of the parameters （including the coupling constant and other parameters） on the linear stability of the exact solutions are analysed and numerically simulated.

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.