Generalized age-dependent model for estimation of mean survival time in the presence of two competing risks

The paper is motivated towards developing a generalized probability model describing the longevity of a system exposed to paired risks R₁ and R₂ which are dependent. The bivariate exponential model of Freund (1961) with failure times X and Y under risks R₁ and R₂ with a time-independent hazard rate set-up has been generalized by incorporating an additional age factor, t, as a variable. The hazard rates due to R₁ and R₂ have been changed from a to α(t) = αt^α?1, and from β to β(f) = βt^β?1 where α,β > 0 which are Weibull hazard functions for α,β > 1. Further conditions are imposed such that α is changed to α' when R₂ is off and β is changed to β' when R₁ is off. The trivariate distribution of Freund so generalized has again been doubly truncated in the range a  t  b, for a, b > 0; and the conditional distribution of X and Y given t has been used to study the role of the component's age in the context of the system's survival under paired dependent risks in the finite age range.     

Design of H ∞ control of neural networks with time-varying delays

This paper deals with the H _∞ control problem of neural networks with time-varying delays. The system under consideration is subject to time-varying delays and various activation functions. Based on constructing some suitable Lyapunov–Krasovskii functionals, we establish new sufficient conditions for H _∞ control for two cases of time-varying delays: (1) the delays are differentiable and have an upper bound of the delay-derivatives and (2) the delays are bounded but not necessary to be differentiable. The derived conditions are formulated in terms of linear matrix inequalities, which allow simultaneous computation of two bounds that characterize the exponential stability rate of the solution. Numerical examples are given to illustrate the effectiveness of our results.

     

Phase-equilibria investigation of the Dy-Mo-Si ternary system at 1173 K (900 °C)

The phase equilibria of the Dy-Mo-Si ternary system at 1173 K (900 °C) was experimentally determined in the entire concentration range by using x-ray powder diffraction (XRPD), scanning electron microscope equipped with energy dispersive spectrometer (SEM-EDS), and differential scanning calorimetry (DSC). The results show that there are 13 single-phase regions, 24 two-phase regions, and 12 three-phase regions in the studied isothermal section. Nine binary compounds, i.e., α-MoSi₂, Mo₅Si₃, Mo₃Si, α-DySi₂, β-DySi_1.67, Dy₃Si₄, DySi, Dy₅Si₄, and Dy₅Si₃ and one ternary compound Dy₂Mo₃Si₄ were confirmed to exist at this temperature. The highest solubilities of Dy in Mo₃Si and Mo in β-DySi_1.67 are both determined to be less than 1 at.%. While the solubilities of Dy in (Mo), Mo₅Si₃, and α-MoSi₂ and Mo in (α-Dy), α-DySi₂, Dy₃Si₄, DySi, Dy₅Si₄, and Dy₅Si₃ and Si in (α-Dy) and (Mo) are about 1–6.8 at.%. Combining both DSC analysis and XRPD results, it is concluded that the polymorphic transformation of α-DySi₂↔β-DySi₂ does not occur in the range of 573 K (300 °C) to 1323 K (1050 °C). DySi₂ phase exists as α-DySi₂ within the temperature range. β-DySi₂ is a metastable phase that exists in higher temperatures.     

Memoryless H ∞ controller design for switched non-linear systems with mixed time-varying delays

This article deals with the H _∞ control problem for a class of switched non-linear systems with mixed time-varying delays. The novel features here are that the system in consideration is non-linear perturbation with discrete and distributed delays, the time-varying delay is also involved in the observation output, and the controllers to be designed satisfy some exponential stability constraints on the closed-loop poles. By using Lyapunov–Razumikhin functional approach, new sufficient conditions for the H _∞ control with exponential stability constraint are derived in terms of the solution of Riccati-type equations. The approach allows for simultaneous computation of the two bounds that characterise the stability rate of the solution.     

Thermodynamic description of the Al-Li-Zn system

The Al-Li-Zn system was critically assessed using the CALPHAD technique. The solution phases (liquid, bcc, fcc and hcp) were described by the substitutional solution model. The compounds Al₂Li₃ and Al₄Li₉ in the Al-Li system had homogeneity ranges of Zn and were treated as (Al,Zn)₂Li₃ and (Al,Zn)₄Li₉ in the Al-Li-Zn system, respectively. The compounds αLi₂Zn₃, βLi₂Zn₃, αLi₂Zn₅, βLi₂Zn₅ and αLiZn₄ in the Li-Zn system had no solubility of the third component Al in the Al-Li-Zn system. A two-sublattice model (Al,Li,Zn)_0.2(Al,Li,Zn)_0.8 was applied to describe the compound βLiZn₄ in the Al-Li-Zn system in order to cope with the order-disorder transition between hexagonal close-packed solution (hcp-A3) and βLiZn₄ with the Mg-type structure. The ternary compound τ₂ with a NaTl-type structure (B32) had the same structure with the compounds AlLi in the binary Al-Li system and LiZn in the binary Li-Zn system. In the present work, the three compounds AlLi, LiZn and τ₂ were treated as one phase by a two-sublattice model (Al,Li,Zn)_0.5(Al,Li,Zn)_0.5 in order to cope with the order-disorder transition between B32(AlLi, LiZn and τ₂) and body-centered cubic solid solution (bcc-A2). The ternary intermetallic compounds τ₁ and τ₃ in the Al-Li-Zn system were treated as the formula Li(Al,Zn)₂ and (AlLi,Zn)Zn₃, respectively. A set of self-consistent thermodynamic parameters describing the Gibbs energy of each individual phase as a function of composition and temperature in the Al-Li-Zn system was obtained.     

Thermodynamic assessment of the Eu–Pb and Lu–Pb systems

The thermodynamic assessment of the Eu–Pb and Lu–Pb binary systems has been carried out by using the Calculation of Phase Diagrams (CALPHAD) method based on the available literature data including the phase equilibria and thermodynamic properties. The Gibbs free energies of the liquid, bcc, fcc and hcp phases were described by the subregular solution model with Redlich–Kister formula, and those of the intermetallic compounds (Eu₂Pb, Eu₅Pb₃, βEuPb, αEuPb, EuPb₃, Lu₅Pb₃, βLu₅Pb₄, αLu₅Pb₄, Lu₆Pb₅, and LuPb₂) in the binary systems were described by the two-sublattice model. A consistent set of the thermodynamic parameters leading to a reasonable agreement between the calculated results and literature data was obtained.     

Globally exponential stability and stabilization of interconnected Markovian jump system with mode-dependent delays

This paper focuses on the problems of globally exponential stability and stabilization with H_∞ performance for a class of interconnected Markovian jump system with mode-dependent delays in interconnection. By constructing a Lyapunov-Krasovskii functional, delay-range-dependent globally mean-square exponential stability conditions are established in terms of linear matrix inequalities. Based on the obtained conditions, state feedback control utilizing global state information and state feedback control utilizing global state information of decentralised observers are developed to render the closed-loop interconnected Markovian jump time-delay system globally exponential stable with H_∞ performance. Numerical simulation of a power system, composed of three coupled machines, is used to illustrate the effectiveness of the obtained results.     

Thermodynamic modeling of the yttrium–oxygen system

The updated thermodynamic evaluation of the yttrium–oxygen (Y–O) system is presented. Thermodynamic model parameters of all phases, i.e., liquid, α$\alpha$-Y, β$\beta$-Y, α$\alpha$- Y ₂O₃ and β$\beta$- Y ₂O₃, have been derived by the least-squares minimization procedure using Thermo-Calc^®software. The backward compatibility of the refined parameters with experimental data has been demonstrated by calculation of phase and property diagrams.     

Teleoperation in the presence of varying time delays and sandwich linearity in actuators

In this paper, a novel control scheme is proposed to guarantee global asymptotic stability of bilateral teleoperation systems that are subjected to time-varying time delays in their communication channel and sandwich linearity in their actuators. This extends prior art concerning control of nonlinear bilateral teleoperation systems under time-varying time delays to the case where the local and the remote robots’ control signals pass through saturation or similar nonlinearities that belong to a class of systems we name sandwich linear systems. Our proposed controller is similar to the proportional plus damping (P+D) controller with the difference that it takes into account the actuator saturation at the outset of control design and alters the proportional term by passing it through a nonlinear function; thus, we call the proposed method as nonlinear proportional plus damping (nP+D). The asymptotic stability of the closed-loop system is established using a Lyapunov–Krasovskii functional under conditions on the controller parameters, the actuator saturation characteristics, and the maximum values of the time-varying time delays. To show the effectiveness of the proposed method, it is simulated on a variable-delay teleoperation system comprising a pair of planar 2-DOF robots subjected to actuator saturation. Furthermore, the controller is experimentally validated on a pair of 3-DOF PHANToM Premium 1.5A robots, which have limited actuation capacity, that form a teleoperation system with a varying-delay communication channel.     

Robust stability of uncertain impulsive control systems with time-varying delay

In this paper, we are concerned with the robust stability problem of an uncertain impulsive control system with time-varying delay. By employing the formula for the variation of parameters and estimating the Cauchy matrix, several criteria on robust exponential stability are derived and the exponential convergence rate is estimated. Based on $P$-norm and $P$-measure of matrix, it is seen that our sufficient conditions are less restrictive than the ones in the earlier publication. Some numerical examples and simulations are given to illustrate the theoretical results and to show that the criteria can be applied to stabilize the unstable continuous system with time delays and uncertainties by utilizing impulsive control.     

Exponential stability of delayed bidirectional associative memory neural networks with reaction diffusion terms

This article considers a class of delayed bi-directional associative memory (BAM) neural networks with reaction diffusion terms and delays. We obtain some simple criteria ensuring the existence and uniqueness of the equilibrium and its global exponential stability by applying homeomorphism mapping, constructing a new Lyapunov functional and inequality techniques. These criteria are independent of delays and posses infinitely adjustable real parameters, which improve and extend some recent results [J. Cao and M. Dong, “Exponential stability of delayed bidirectional associative memory networks”, Appl. Math. Comput., 135, pp. 105–112, 2003; J. Cao and L. Wang, “Exponential stability and periodic oscillatory solution in BAM networks with delays”, IEEE Trans. Neural Networ., 13, pp. 457–463, 2002; Q. Song and J. Cao, “Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction-diffusion terms”, Chaos Soliton. Fract., 23, pp. 421–430, 2005.] and have an important instructional significance in the designs and applications of bidirectional associative memory neural networks.     

An example for the switching delay feedback stabilization of an infinite dimensional system: The boundary stabilization of a string

For vibrating systems, a delay in the application of a feedback control may destroy the stabilizing effect of the control. In this paper we consider a vibrating string that is fixed at one end and stabilized with a boundary feedback with delay at the other end.We show that certain delays in the boundary feedback preserve the exponential stability of the system. In particular, we show that the system is exponentially stable with delays freely switching between the values 4L/c and 8L/c, where L is the length of the string and c is the wave speed.     

Robust H∞ control for networked systems with transmission delays and successive packet dropouts under stochastic sampling

This paper is concerned with the H_∞ performance analysis for networked control systems with transmission delays and successive packet dropouts under stochastic sampling. The parameter uncertainties are time‐varying norm‐bounded and appear in both the state and input matrices. If packet loss is considered the same as time delay, when models the networked control systems with successive packet dropouts and delays as ordinary linear system with input‐delay approach, due to sampling period is stochastic, then the delay caused by packet losses is a stochastic variable, which leads to difficulties in the stability analysis of the considered system. However, if we can transform the system with stochastic delay into a continuous system with stochastic parameter, we can solve the problem. In this paper, by assuming that the network packet loss rate and employing the information of probabilistic distribution of the time delays, the stochastic sampling system is transformed into a continuous‐time model with stochastic variable, which satisfies a Bernoulli distribution. By linear matrix inequality approach, sufficient conditions are obtained, which guarantee the robust mean‐square exponential stability of the system with an H_∞ performance. What's more, an H_∞ controller design procedure is then proposed, and a less conservative result is obtained by taking the probability into consideration. Finally, a numerical simulation example is employed to show the effectiveness of the obtained results. Copyright © 2016 John Wiley & Sons, Ltd.     

Thermodynamic modeling of B–Mo–Nb ternary system with modified B–Nb description

Based on a critical evaluation of the literature data, the B–Mo–Nb ternary system has been assessed by means of the CALPHAD (CALculation of PHAse Diagrams) technique. There is no ternary compound reported in this system. According to their crystal structures, the substitutional solution is adopted to model the ternary liquid, and the sublattice models are used to describe the Mo₂B, αMoB, (Mo,Nb)B, (Mo,Nb)B₂, Mo₂B₅, MoB₄, Nb₃B₂, Nb₅B₆, Nb₃B₄, Nb₂B₃, (Mo,Nb) and (B) phases. The modeling covers the whole composition and temperature ranges. Due to the same crystal structure, the sublattice model of the NbB phase in the B–Nb binary system is adjusted as (Me,Va)_0.5(B,Va)_0.5, in order to be consistent with the βMoB phase in the B–Mo binary system. The obtained thermodynamic parameters of the B–Mo–Nb system are demonstrated to be self-consistent and reasonable by adequately comparing the calculated and reported thermodynamic information and phase diagram. Based on the present thermodynamic parameters, the liquidus projection and reaction scheme of B–Mo–Nb system are presented.     

Thermodynamic assessments of the Bi-Lu and Lu-Sb systems

The phase diagrams and thermodynamic properties in the Bi-Lu and Lu-Sb binary systems have been assessed by using the CALPHAD (Calculation of Phase Diagrams) method on the basis of experimental data including the thermodynamic properties and phase equilibria. The Gibbs free energies of the liquid, hexagonal close-packed (hcp) and rhombohedral phases were described by the substitutional solution model, and the intermetallic compounds (Bi₂Lu, BiLu, Bi₃Lu₅, Lu₃Sb, Lu₅Sb₃, αLuSb, βLuSb and LuSb₂ phases) were treated as stoichiometric compounds. The thermodynamic parameters of the Bi-Lu and Lu-Sb binary systems were obtained, and agreement between the calculated results and experimental data was obtained for each binary system.     

Thermodynamic optimization of the Gd–Pb system using random solution and associate models

The Gd–Pb system was critically modeled by means of the CALPHAD technique on the basis of experimental data in the literature. Given the asymmetric shape of the liquidus in the Gd–Pb phase diagram, the associate model for the liquid phase was tested and compared with the substitutional solution model. The results of the optimization show that a better agreement with the available experimental data is obtained by means of the associate model than the substitutional solution model. The solution phases (liquid, bcc, fcc, hcp) were treated with the Redlich–Kister equation. The intermetallic compounds Gd₅Pb₃, αGd₅Pb₄, βGd₅Pb₄, Gd₁₁Pb₁₀, Gd₆Pb₇, GdPb₂, GdPb₃ were treated as stoichiometric compounds. Two sets of self-consistent thermodynamic parameters of the Gd–Pb system were obtained.     

Modelling the &Vdot;O2 kinetic response to heavy intensity exercise in children

The purpose of this study was to apply a series of mathematical models in order to investigate the nature of the kinetic response to heavy intensity exercise with children and identify a suitable model with which to estimate parameters of the response. Sixty two children (35 male, 27 female aged 10?–?15 years) completed four transitions from baseline pedalling to 40% of the difference between their previously determined anaerobic threshold and peak [Vdot]O₂ on an electronically braked cycle ergometer. Initially three models were fitted to the averaged response profiles following the end of phase 1, and their residuals compared; 1, a single exponential with a delay term; 2, an exponential and linear term with independent delays; and 3, a double exponential with independent delays. Up to 95% of the response profiles were better fitted by either model 2 or 3 (p?<?0.05), and model 3 was a statistically better fit (p?<?0.05) than model 2 in 77% of cases. Residual inspection confirmed the superior fit by model 3. A fourth model which consisted of a single exponential with a delay term was fitted within the phase 2 fitting window. Estimated parameters (A₁ and τ₁), using model 4 were not significantly different from model 3, and model 4 was identified as the model of choice due to the wide confidence intervals in τ₂ and A₂ using model 3. It was concluded that the nature of the response to heavy intensity exercise in children is similar to that previously reported with adults and that the response should be modelled accordingly.     

A thermodynamic modeling of the Pd-Ti system

The thermodynamic properties of the Pd-Ti system were optimized using the CALPHAD (CALculation of PHAse Diagram) technique. The solution phases, liquid, bcc, fcc and hcp, were described by the substitutional-solution model. Both compounds Pd₂Ti and PdTi₂ with tetragonal MoSi₂-type structure were treated as one phase with the formula (Pd,Ti)₂(Pd,Ti) by a two-sublattice model. The intermetallic compounds Pd₃Ti, Pd₃Ti₂, and PdTi₃ were treated as stoichiometric compounds. The intermetallic compound αPdTi, which had a homogeneity range, was treated as the formula (Pd,Ti)(Pd,Ti) by a two-sublattice model. A two-sublattice model (Pd,Ti)_0.5(Pd,Ti)_0.5 was applied to describe the compound βPdTi in order to cope with the order-disorder transition between βPdTi with CsCl-type structure (B2) and body-centered cubic solution (A2) in the Pd-Ti system. A set of self-consistent thermodynamic parameters was obtained.     

Experimental phase diagram study of the TiAl-rich part of the Ti–Al–Ni ternary system

Phase equilibria of the TiAl-rich part of the Ti–Al–Ni ternary system have been studied experimentally by scanning electron microscopy and electron probe micro-analysis of heat-treated alloys. Partial isothermal sections involving the liquid, β-Ti, α-Ti, α₂-Ti₃Al, γ-TiAl and τ₃-Al₃NiTi₂ phases were constructed between 1623 and 1273 K. Eight three-phase regions of the L + β + α, L + α + γ, L + β + γ, β + α + γ, L + β + τ₃, β + γ + τ₃, β + α₂ + τ₃ and α₂ + γ + τ₃ were derived. Extrapolations of these tie-triangles indicate the occurrence of three transition-type reactions; L + α = β + γ at around 1593 K, L + γ = β + τ₃ at around 1553 K, and β + γ = α + τ₃ at around 1393 K. The Ni solid solubility in the α and α₂ phase is extremely low, less than 1 at.% in all studied temperature ranges.     

H∞ Output Feedback Control for Stochastic Systems with Mode-dependent Time-varying Delays and Markovian Jump Parameters

This paper deals with the H∞ control problems of Markovian jump systems with mode-dependent time delays. First, considering the mode-dependent time delays, a different delay-dependent H∞ performance condition for Markovian jump systems is proposed by constructing an improved Lyapunov-Krasovskii function. Based on this new H∞ disturbance attenuation criterion, a full-order dynamic output feedback controller that ensures the exponential mean-square stability and a prescribed H∞ performance level for the resulting closed-loop system is designed. Illustrative numerical examples are provided to demonstrate the effectiveness of the proposed approach.