Bayesian analysis of M/Er/1 and M/H_k/1 queues

This paper describes Bayesian inference and prediction for some M/G/1 queueing models. Cases when the service distribution is Erlang, hyperexponential and hyperexponential with a random number of components are considered. Monte Carlo and Markov chain Monte Carlo methods are used for estimation of quantities of interest assuming the queue is in equilibrium. This revised version was published online in June 2006 with corrections to the Cover Date.     

Thermal slip boundary conditions in vibrational nonequilibrium flows

This paper deals with new thermal jump boundary conditions at the wall in polyatomic gas flows. The calculations and results especially concern vibrational nonequilibrium conditions when the dissociation effects may be neglected. First the usual conditions are briefly described. Then the boundary conditions proposed in the paper are justified on the basis of previous experimental results and by developing direct heat flux calculations at the wall. Analytical expressions and numerical values of the various fluxes are presented.     

Isomorphism of lattices of recursively enumerable sets

Let , and for , let be the lattice of subsets of which are recursively enumerable relative to the ``oracle' . Let be , where is the ideal of finite subsets of . It is established that for any , is effectively isomorphic to if and only if , where is the Turing jump of . A consequence is that if , then . A second consequence is that can be effectively embedded into preserving least and greatest elements if and only if .

     

Effect of pressure on the conductivities of HCl and KCl in water at 0°C

The electrical conductivities of hydrochloric acid and potassium chloride in water have been measured in the concentration range of 3×10 ^–4 –10 ^–3 moles-dm ^–3 at 0°C up to 3500 bar. The limiting molar conductance (₀) for HCl increases with increasing pressure, while ₀(KCl) has a maximum around 1700 bar. The excess conductance of hydrogen ion [ ₀ ^E =₀(HCl)–₀(KCl)] increases with increasing pressure. Its pressure dependence indicates that the reorientation of water molecules, which is the rate-determining step in the proton jump, becomes faster at higher pressure. This anomaly is attributed to the distortion with pressure of the hydrogen bonds in water.     

A predictive model for pressure fluctuations on sloping channels using support vector machine

In this study, support vector machine (SVM) is proposed as a new predictive model for pressure fluctuations beneath free jump occurring on sloping channels. The proposed model reproduces the pressure fluctuation intensity C′_p in terms of normalized flow and channel section characteristics. The model variables were derived from dimensional analysis. The proposed model is calibrated and validated by using a wide range of experimental data. The SVM predicted C′_p with a correlation of coefficient (CC) of 0.989 and a root mean square error (RMSE) of 0.004. Also, linear and nonlinear regression analyses are applied on the same experimental data set, and the SVM model is compared to the equations obtained from these regression analyses. CC, RMSE and average absolute deviation (D_i) are used in the evaluation of performance of each model. The SVM model predicted the measured pressure fluctuations better than conventional regression equations. The results of this study reveal that the proposed SVM model can be effectively used in predicting the pressure fluctuation beneath free jump. Copyright © 2010 John Wiley & Sons, Ltd.     

A capacitively coupled temperature‐jump arrangement for high‐resolution biomolecular NMR

A simple design for performing rapid temperature jumps within a high‐resolution nuclear magnetic resonance (NMR) setting is presented and exemplified. The design is based on mounting, around a conventional NMR glass tube, an inductive radiofrequency (RF) irradiation coil that is suitably tuned by a resonant circuit and is driven by one of the NMR's console high‐power RF amplifiers. The electric fields generated by this coil's thin metal strips can lead to a fast and efficient heating of the sample, amounting to temperature jumps of ≈ 20 °C in well within a second—particularly in the presence of lossy dielectric media like those provided by physiological buffers. Moreover, when wound around a 4‐mm NMR tube, the resulting device fits a conventional 5‐mm inverse probe and is wholly compatible with the field homogeneities and sensitivities expected for high‐resolution biomolecular NMR conditions. The performance characteristics of this new system were tested using saline solutions, as well as on a lyotropic liquid crystal capable of undergoing nematic → isotropic transitions in the neighborhood of ambient temperature. These settings were then incorporated into the performance of a new kind of single‐scan 2D NMR spectroscopy acquisition, correlating the anisotropic and isotropic patterns elicited by solutes dissolved in such liquid‐crystalline systems, before and after a sudden temperature jump occurring during an intervening mixing period. Copyright © 2010 John Wiley & Sons, Ltd.     

Small time convergence of subordinators with regularly or slowly varying canonical measure

We consider subordinators $X_{\alpha }={\left(X_{\alpha }\left(t\right)\right)}_{t\ge 0}$ in the domain of attraction at 0 of a stable subordinator ${\left(S_{\alpha }\left(t\right)\right)}_{t\ge 0}$ (where $\alpha \in (0,1)$); thus, with the property that ${\overline{\Pi }}_{\alpha }$, the tail function of the canonical measure of $X_{\alpha }$, is regularly varying of index $?\alpha \in (?1,0)$ as $x\downarrow 0$. We also analyse the boundary case, $\alpha =0$, when ${\overline{\Pi }}_{\alpha }$ is slowly varying at 0. When $\alpha \in (0,1)$, we show that ${\left(t{\overline{\Pi }}_{\alpha }\left(X_{\alpha }\left(t\right)\right)\right)}^{?1}$ converges in distribution, as $t\downarrow 0$, to the random variable ${\left(S_{\alpha }\left(1\right)\right)}^{\alpha }$. This latter random variable, as a function of $\alpha$, converges in distribution as $\alpha \downarrow 0$ to the inverse of an exponential random variable. We prove these convergences, also generalised to functional versions (convergence in $\mathbb{D}[0,1]$), and to trimmed versions, whereby a fixed number of its largest jumps up to a specified time are subtracted from the process. The $\alpha =0$ case produces convergence to an extremal process constructed from ordered jumps of a Cauchy subordinator. Our results generalise random walk and stable process results of Darling, Cressie, Kasahara, Kotani and Watanabe.     

Normal polytopes: Between discrete,continuous, and random

The first three sections of this survey represent an updated and much expanded version of the abstract of my talk at FPSAC'2010: new results are incorporated and several concrete conjectures on the interactions between the three perspectives on normal polytopes in the title are proposed. The last section outlines new challenges in general convex polytopes, motivated by the study of normal polytopes.     

Robust ℋ∞ tracking control for uncertain Markovian jumping systems with interval time‐varying delay

In this article, the problem of robust tracking control for a class of uncertain Markovian jump systems with interval time‐varying delay is investigated. Based on an augmented Lyapunov–Krasovskii functional with triple integral term, partitioning the delay's lower bound and reciprocally convex approach, delay‐dependent conditions for the existence of desired controller are achieved. Meanwhile, stability criteria for delayed Markovian jump systems are also provided with less conservativeness and less matrix variables than some recent results. Finally, two simulation examples are given to illustrate the effectiveness of the proposed design method. © 2014 Wiley Periodicals, Inc. Complexity 21: 355–366, 2015