The M/M/c with critical jobs

We consider theM/M/c queue, where customers transfer to a critical state when their queueing (sojourn) time exceeds a random time. Lower and upper bounds for the distribution of the number of critical jobs are derived from two modifications of the original system. The two modified systems can be efficiently solved. Numerical calculations indicate the power of the approach.     

Adaptive discretization of convex multistage stochastic programs

We propose a new scenario tree reduction algorithm for multistage stochastic programs, which integrates the reduction of a scenario tree into the solution process of the stochastic program. This allows to construct a scenario tree that is highly adapted on the optimization problem. The algorithm starts with a rough approximation of the original tree and locally refines this approximation as long as necessary. Promising numerical results for scenario tree reductions in the settings of portfolio management and power management with uncertain load are presented.     

The Mössbauer spectrum of synthetic hureaulite: Fe5 2+(H2O)4(PO4H)2(PO4)2

The crystal structure of synthetic ferrous hureaulite, Fe₅ ²⁺ (H₂O)₄(PO₄H)₂(PO₄)₂, was refined from single-crystal X-ray data. It is monoclinic, space group C2/c, with a=17.487(4), b=9.017(2), c=9.338(2) Å, β=96.27(3)°, V=1463.6(6) Å³, Z=4 and D _calc=3.327 g/cm³. This end member of the hureaulite series was crystallized under distinctly acidic conditions, by a method that gives perfect crystals, large enough for X-ray single crystal studies. The main feature of the hureaulite structure is that it has an equal number of normal (PO₄)³⁺ and acid (PO₄H)²⁺ tetradentate groups. These are centered on Fe²⁺ atoms and share corners with edge-linked octahedra, forming pentamer units. The five Fe²⁺ atoms are distributed on three distinct sites in these units. This can be directly observed in the Mössbauer spectrum at 295 K, which contains three doublets whose relative intensities correspond to the 1:2:2 distributions of crystallographic sites.     

Algorithms for separable nonlinear least squares with application to modelling time-resolved spectra

The multiexponential analysis problem of fitting kinetic models to time-resolved spectra is often solved using gradient-based algorithms that treat the spectral parameters as conditionally linear. We make a comparison of the two most-applied such algorithms, alternating least squares and variable projection. A numerical study examines computational efficiency and linear approximation standard error estimates. A new derivation of the Fisher information matrix under the full Golub-Pereyra gradient allows a numerical comparison of parameter precision under variable projection variants. Under the criteria of efficiency, quality of standard error estimates and parameter precision, we conclude that the Kaufman variable projection technique performs well, while techniques based on alternating least squares have significant disadvantages for application in the problem domain.     

Local convergence of the (exact and inexact) iterative aggregation method for linear systems and Markov operators

Summary. The iterative aggregation method for the solution of linear systems is extended in several directions: to operators on Banach spaces; to the method with inexact correction, i.e., to methods where the (inner) linear system is in turn solved iteratively; and to the problem of finding stationary distributions of Markov operators. Local convergence is shown in all cases. Convergence results apply to the particular case of stochastic matrices. Moreover, an argument is given which suggests why the iterative aggregation method works so well for nearly uncoupled Markov chains, as well as for Markov chains with other zero-nonzero structures. Received May 25, 1991/Revised version received February 23, 1994     

Aggregation/Disaggregation Iterative Methods Applied to Leontev Systems and Markov Chains

The paper surveys some recent results on iterative aggregation/disaggregation methods (IAD) for computing stationary probability vectors of stochastic matrices and solutions of Leontev linear systems. A particular attention is paid to fast IAD methods.     

Basicity Limits of Neutral Organic Superbases

The potential limits of superbasicity achievable with different families of neutral bases by expanding the molecular framework are explored using DFT computations. A number of different core structures of non‐ionic organosuperbases are considered (such as phosphazenes, guanidinophosphazenes, guanidino phosphorus ylides). A simple model for describing the dependence of basicity on the extent of the molecular framework is proposed, validated, and used for quantitatively predicting the ultimate basicities of different compound families and the rates of substituent effect saturation. Some of the considered bases (guanidino phosphorus carbenes) are expected to reach gas‐phase basicity around 370 kcal mol^?1, thus being the most basic neutral bases ever reported. Also, the classical substituted alkylphosphazenes were predicted to reach pK_a values of around 50 in acetonitrile, which is significantly higher than previously expected.     

Boron as a Powerful Reductant: Synthesis of a Stable Boron‐Centered Radical‐Anion Radical‐Cation Pair

Despite the fundamental importance of radical‐anion radical‐cation pairs in single‐electron transfer (SET) reactions, such species are still very rare and transient in nature. Since diborenes have highly electron‐rich B? B double bonds, which makes them strong neutral reductants, we envisaged a possible realization of a boron‐centered radical‐anion radical‐cation pair by SET from a diborene to a borole species, which are known to form stable radical anions upon one‐electron reduction. However, since the reduction potentials of all know diborenes (E_1/2=?1.05/?1.55 V) were not sufficiently negative to reduce MesBC₄Ph₄ (E_1/2=?1.69 V), a suitable diborene, IiPr?(iPr)B?B(iPr)?IiPr, was tailor‐made to comply with these requirements. With a halfwave potential of E_1/2=?1.95 V, this diborene ranks amongst the most powerful neutral organic reductants known and readily reacted with MesBC₄Ph₄ by SET to afford a stable boron‐centered radical‐anion radical‐cation pair.     

Tutorial review on validation of liquid chromatography–mass spectrometry methods: Part I

This is the part I of a tutorial review intending to give an overview of the state of the art of method validation in liquid chromatography mass spectrometry (LC–MS) and discuss specific issues that arise with MS (and MS/MS) detection in LC (as opposed to the “conventional” detectors). The Part I briefly introduces the principles of operation of LC–MS (emphasizing the aspects important from the validation point of view, in particular the ionization process and ionization suppression/enhancement); reviews the main validation guideline documents and discusses in detail the following performance parameters: selectivity/specificity/identity, ruggedness/robustness, limit of detection, limit of quantification, decision limit and detection capability. With every method performance characteristic its essence and terminology are addressed, the current status of treating it is reviewed and recommendations are given, how to determine it, specifically in the case of LC–MS methods.