The Laplacian energy of random graphs

Gutman {\it et al.} introduced the concepts of energy \En(G) and Laplacian energy \EnL(G) for a simple graph $G$, and furthermore, they proposed a conjecture that for every graph $G$, \En(G) is not more than \EnL(G). Unfortunately, the conjecture turns out to be incorrect since Liu {\it et al.} and Stevanovi\'c {\it et al.} constructed counterexamples. However, So {\it et al.} verified the conjecture for bipartite graphs. In the present paper, we obtain, for a random graph, the lower and upper bounds of the Laplacian energy, and show that the conjecture is true for almost all graphs.Comment: 14 page

Hopf bifurcation control for a class of delay differential systems with discrete-time delayed feedback controller

This paper is concerned with asymptotical stabilization for a class of delay differential equations, which undergo Hopf bifurcation at equilibrium as delay increasing. Two types of controllers, continuous-time and discrete-time delay feedback controllers, are presented. Although discrete-time control problems have been discussed by several authors, to the best of our knowledge, so few controllers relate to both delay and sampling period, and the method of Hopf bifurcation has not been seen. Here, we first give a range of control parameter which ensures the asymptotical stability of equilibrium for the continuous time controlled system. And then, for the discrete-time controller we also obtain an efficient control interval provided that the sampling period is sufficiently small. Meanwhile, we try our best to estimate a well bound on sampling period and get a more complete conclusion. Finally, the theoretical results are applied to a physiological system to illustrate the effectiveness of the two controllers

Stability and Boundedness of Stochastic Volterra Integrodifferential Equations with Infinite Delay

We make the first attempt to discuss stability and boundedness of solutions to stochastic Volterra integrodifferential equations with infinite delay (IDSVIDEs). By the Lyapunov-Krasovskii functional approach, we get kinds of sufficient criteria for stability and boundedness of solutions to IDSVIDEs. The main innovation here is that stochastic systems with infinite delay can retain stability and boundedness of corresponding deterministic systems under some conditions

Study on the damping reduction of the safe-belt constraint system of low gravity center cable-stayed bridge

The structural system with better seismic performance is one of the key to the seismic design of cable-stayed bridges. The research shows that the internal force response of floating system is small and the displacement response is large, and the seismic response of the hinged system is the opposite. However, the tower bottom moment of the fix hinged cable-bridge could be less than it of the floating system actually, because the inertia force of the girder in the hinge system would be transmitted to the tower through the connection of tower and girder. In the light of these characteristics, a new low-gravity cable-stayed bridge seismic structure system, the safe-belt constraint system, is proposed in this paper, and the seismic response characteristics are studied by ANSYS. In addition, the effect of safe-belt parameters on the vibration reduction effect of the belt system cable-stayed bridge is analyzed

Simplified calculation method for transverse seismic response of aqueducts considering fluid-structure interaction

Aqueduct is the key structure in water conveyance engineering, which may be damaged during earthquake. Although numerous water conveyance designs have been built, the current state of researches on aqueduct aseismic design is inadequate. In this paper, based on the fluid-structure interaction dynamics and response spectra analysis, a simplified analysis method was proposed to evaluate the transverse seismic response of aqueducts, and the simplified calculating results were compared with the results of the nonlinear finite element calculation of fluid-structure interaction and experimental results. The results showed that the simplified analysis method put forward in this paper could be used to evaluate the transverse seismic response of aqueducts. In the condition that the pier height is less than 40 m, the first-order lateral vibration mode of the aqueduct has a higher model contribution rate; the simplified calculation method can achieve extremely high accuracy. The simplified calculation precision decreases as the height increases when the pier height exceeds 40 m

Global exponential stability for coupled systems of neutral delay differential equations

In this paper, a novel class of neutral delay differential equations (NDDEs) is presented. By using the Razumikhin method and Kirchhoff's matrix tree theorem in graph theory, the global exponential stability for such NDDEs is investigated. By constructing an appropriate Lyapunov function, two different kinds of sufficient criteria which ensure the global exponential stability of NDDEs are derived in the form of Lyapunov functions and coefficients of NDDEs, respectively. A numerical example is provided to demonstrate the effectiveness of the theoretical results