Estimates on the first two buckling eigenvalues on spherical domains

In this paper, we study the first two eigenvalues of the buckling problem on spherical domains. We obtain an estimate on the second eigenvalue in terms of the first eigenvalue, which improves one recent result obtained by Wang-Xia in [7].Comment: This article has been submitted for publication on 2009-04-2

Stabilisation of highly non-linear continuous-time hybrid stochastic differential delay equations by discrete-time feedback control

In this study, the authors consider how to use discrete-time state feedback to stabilise hybrid stochastic differential delay equations. The coefficients of these stochastic differential delay equations do not satisfy the conventional linear growth conditions, but are highly non-linear. Using the Lyapunov functional method, they show that a discrete feedback controller, which depends on the states of the discrete-time observations, can be designed to make the solutions of such controlled hybrid stochastic differential delay equations asymptotically stable and exponentially stable. The upper bound of the discrete observation interval τ is also given in this study. Finally, a numerical example is given to illustrate the proposed theory

Boundedness and stability of highly nonlinear neutral stochastic systems with multiple delays

This paper reports the boundedness and stability of highly nonlinear hybrid neutral stochastic differential delay equations (NSDDEs) with multiple delays. Without imposing linear growth condition, the boundedness and exponential stability of the exact solution are investigated by Lyapunov functional method. In particular, using the M-matrix technique, the mean square exponential stability is obtained. Finally, three examples are presented to verify our results

Stability equivalence between the stochastic dierential delay equations driven by G-Brownian motion and the Euler-Maruyama method

Consider a stochastic differential delay equation driven by G-Brownian motion (G-SDDE) dx(t) = f(x(t), x(t − τ))dt + g(x(t), x(t − τ))dB(t) + h(x(t), x(t − τ))dhBi(t). Under the global Lipschitz condition for the G-SDDE, we show that the G-SDDE is exponentially stable in mean square if and only if for sufficiently small step size, the Euler-Maruyama (EM) method is exponentially stable in mean square. Thus, we can carry out careful numerical simulations to investigate the exponential stability of the underlying G-SDDE in practice, in the absence of an appropriate Lyapunov function. A numerical example is provided to illustrate our results

A highly sensitive mean-reverting process in finance and the Euler-Maruyama approximations

Empirical studies show that the most successful continuous-time models of the short term rate in capturing the dynamics are those that allow the volatility of interestchanges to be highly sensitive to the level of the rate. However, from the mathematics, the high sensitivity to the level implies that the coeffcients do not satisfy the lineargrowth condition, so we can not examine its properties by traditional techniques. This paper overcomes the mathematical difculties due to the nonlinear growth and examines its analytical properties and the convergence of numerical solutions in probability. The convergence result can be used to justify the method within Monte-Carlo simulations that compute the expected payoff of financial products. For illustration, we apply our results compute the value of a bond with interest rate given by the highly sensitive mean-reverting process as well as the value of a single barrier call option with the asset price governed by this process

Adaptive fuzzy sliding mode algorithm-based decentralised control for a permanent magnet spherical actuator

<p>The dynamic model of multi-degree-of-freedom permanent magnet (PM) spherical actuators is multivariate and nonlinear due to strong inter-axis couplings, which affects the trajectory tracking performance of the system. In this paper, a decentralised control strategy based on adaptive fuzzy sliding mode (AFSM) algorithm is developed for a PM spherical actuator to enhance its trajectory tracking performance. In this algorithm, the coupling terms are separated as subsystems from the entire system. The AFSM algorithm is applied in such a way that the fuzzy logic systems are used to approximate the subsystem with uncertainties. A sliding mode term is introduced to compensate for the effect of coupling terms and fuzzy approximation error. The stability of the proposed method is guaranteed by choosing the appropriate Lyapunov function. Both simulation and experimental results show that the proposed control algorithm can effectively handle various uncertainties and inter-axis couplings, and improve the trajectory tracking precision of the spherical actuator.</p

Outcomes in Human Immunodeficiency Virus Infected Recipients of Heart and Lung Transplants

Background: With the advent of combined antiretroviral therapy (cART), growing evidence has shown human immunodeficiency virus (HIV) may no longer be an absolute contraindication for solid organ transplantation. This study compares outcomes of heart transplantations between HIV‐positive and HIV‐negative recipients using SRTR transplant registry data. Methods: Patient survival, overall graft survival and death‐censored graft survival were compared between HIV‐positive and HIV‐negative recipients. Multivariate Cox regression and Cox regression with a disease risk score (DRS) methodology were used to estimate the adjusted hazard ratios among heart transplant recipients (HTRs). Results: In total, 35 HTRs with HIV+ status were identified. No significant differences were found in patient survival (88% vs 77%; P = 0.1493), overall graft survival (85% vs 76%; P = 0.2758), and death‐censored graft survival (91% vs 91%; P = 0.9871) between HIV‐positive and HIV‐negative HTRs in 5‐year follow‐up. No significant differences were found after adjusting for confounders. Conclusions: This study supports the use of heart transplant procedures in selected HIV‐positive patients. This study suggests that HIV‐positive status is not a contraindication for life‐saving heart transplant as there were no differences in graft, patient survival

Stabilization of hybrid stochastic differential equations by delay feedback control based on discrete-time observations

Response lags are necessary for most physical systems. For the sake of saving time and costs, the main aim of this paper is to design the feedback control term based on the response lags varying in a certain interval and the discrete-time observations of both the system states and the Markovian states to stabilize the controlled hybrid systems. The control principles are established, which permit the control function only depends on the partial information of the states and the modes. The upper bound on the sum of the upper bound Τ̅ of response lags, and the duration Ƭ between two consecutive observations is obtained. Some examples and numerical experiments are given to illustrate our theory