Stochastic comparison of processes generated by random interruptions of monotone functions and related results

Many stochastic processes considered in applied probability models, and, in particular, in reliability theory, are processes of the following form: Shocks occur according to some point process, and each shock causes the process to have a random jump. Between shocks the process increases or decreases in some deterministic fashion. In this paper we study processes for which the rate of increase or decrease between shocks depends only on the height of the process. For such processes we find conditions under which the processes can be stochastically compared. We also study 'hybrid' processes in which periods of increase and periods of decrease alternate. A further result yields a stochastic comparison of processes that start with a random jump, rather than processes in which there is at the beginning some random delay time before the first jump.     

Photochlorination of Stearic Acid Adsorbed on Alumina

Stearic acid adsorbed on alumina as a dense monomolecular layer was photochlorinated in the dry solid state. The results show that over 90% of the chlorination was on the ω and ω-1 positions and 8.5% on ω-2. No chlorination was detected on the other positions. This establishes the assumption that in a dense monomolecular layer only the terminal groups are exposed to chemical reaction.     

Robust minimum variance filtering

This paper deals with the robust minimum variance filtering problem for linear systems subject to norm-bounded parameter uncertainty in both the state and the output matrices of the state-space model. The problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty. Two methods for designing robust filters are investigated. The first one deals with constant parameter uncertainty and focuses on the design of steady-state filters that yield an upper bound to the worst-case asymptotic error variance. This bound depends on an upper bound for the power spectrum density of a signal at a specific point in the system, and it can be made tighter if a tight bound on the latter power spectrum can be obtained. The second method allows for time-varying parameter uncertainty and for general time-varying systems and is more systematic. We develop filters with an optimized upper bound for the error variance for both finite and infinite horizon filtering problems     

A frequency domain approach to the problems ofH∞-minimum error state estimation anddeconvolution

The properties of the minimum H_∞-norm filtering estimation error are investigated, and the relation between the optimal estimator and the equalizing solution to the standard H _∞-minimization problem is discussed. The optimal estimation method is applied in the multivariable deconvolution problem. A simple deconvolution filter of minimum order which minimizes the H _∞-norm of the deconvolution error is obtained. The proposed methods of optimal estimation and deconvolution are useful in cases where the statistics of the disturbance and the noise signals is not completely known, or in cases where it is required to minimize the maximum singular value of the estimation, or the deconvolution, error problem     

Two-stage opening switch for inductive energy storage systems

A two-stage opening switch comprising of a vacuum switch as the first stage and a high voltage fuse in series with a silicon controlled rectifier (SCR) as the second stage is presented. The switch offers low resistance of 20 μΩ during charge intervals of several hundred milliseconds, controlled time to opening, minimal fuse size, and a relatively fast opening of 0.25-0.7 ms. It serves as a closing switch as well. In a series of experiments, the current of 30-40 kA was commutated routinely from a 0.13 mH inductor into a resistive load at a voltage of 3000 V. Various quenching media were examined. The liquids were found to yield maximum inductively generated voltage and transfer efficiency. A strong correlation exists between the fuse performance and the pressure generated in the fuse. This dependence is used as a guideline in fuse design. It was found that a 2-3 ms fuse conduction time suffices for the recovery of the vacuum switch. A PSpice circuit simulation using an action-dependent fuse model is in good agreement with experimental results. A semi-empirical fuse model based on electron-ion recombination mechanism of the fuse resistance change is proposed. This model is integrated into PSpice circuit simulation. The calculations are in fairly good agreement with experimental results     

Frequency effects in a pancake coil

An aluminum pancake coil is designed to amplify pulsed power in the range of 100-MW to a 100-mΩ electro-thermal load. For the tradeoff between the coil energy density limit and energy discharge efficiency, the frequency dependence of its current and magnetic field distributions is calculated in the range of DC to 1 kHz. Near DC magnetic field measurements are compared to the calculated results. Energy efficiency of about 85% has been measured for the discharge of 1.6 kA from the coil to a linear resistive load in the range of 40-400 mΩ     

Phytoplankton-mediated redox cycle of iron in the epilimnion of Lake Kinneret

The biological-mediated redox cycle of Fe was studied in the epilimnion of Lake Kinneret (Sea of Galilee), a mesotrophic lake in Israel. Multi-annual lake water sampling and incubation experiments were carried out to study Fe(III) reduction by natural phytoplankton populations and their possible role in inhibiting Fe(II) oxidation. The reduction characteristics of the dinoflagellate Peridinium gatunense, the dominant lake alga, were further examined in the laboratory. The steady-state concentration of Fe(II) calculated from the assessed reduction and oxidation rates was compared with Fe(II) measured in the lake in order to evaluate the significance of these processes to the lake Fe redox cycle. Nanomolar concentrations of Fe(II) were measured in the oxygenated, high pH, upper water layer of the lake throughout the year. Reduction rates of Fe by natural phytoplankton assemblages ranged between 0.1 and 10 nM/h. The highest reduction rates, determined in dinoflagellate-dominated lake waters, coincided with the highest concentrations of Fe(II) measured simultaneously in the lake. Iron(II) oxidation rates calculated from the measured lake Fe(II) and the obtained reduction rates were significantly slower than published abiotic Fe(II) oxidation rates. Indeed, Fe(II) oxidation rates measured in algal-enriched lake water were 30-fold slowerthan Fe(II) oxidation rates in natural water, demonstrating the potential for Fe(II) stabilization by the lake phytoplankton.     

New conditions for delay-derivative-dependent stability

Two recent Lyapunov-based methods have significantly improved the stability analysis of time-delay systems: the delay-fractioning approach of Gouaisbaut and Peaucelle (2006) for systems with constant delays and the convex analysis of systems with time-varying delays of Park and Ko (2007). In this paper we develop a convex optimization approach to stability analysis of linear systems with interval time-varying delay by using the delay partitioning-based Lyapunov–Krasovskii Functionals (LKFs). Novel LKFs are introduced with matrices that depend on the time delays. These functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives.     

Mixed H∞/H2 design of digital phase‐locked loops with polytopic‐type uncertainties

A robust H_∞ control method is applied to the design of loop filters for digital phase locked loop carrier phase tracking. The proposed method successfully copes with large S‐curve slope uncertainty and with a significant decision delay in the closed‐loop that may stem from the decoder and/or the equalizer there. The design problem is transformed into a state‐feedback control problem where phase and gain‐margins should be guaranteed in spite of the uncertainty. Of all the loop filters that achieve the required margins the one that minimizes an upper‐bound on the effect of the phase and the measurement noise signals is derived. Copyright © 2002 John Wiley & Sons, Ltd.