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.     

A Novel Alkaloid from Aspidosperma pyricollum (Apocynaceae) and Complete 1H and 13C Chemical Shift Assignments

A novel natural product indole, alkaloid, named rel‐pyricolluminol ( 1 ), was isolated from Aspidosperma pyricollum Müll .Arg . together with six known metabolites sitsirikine ( 2 ), aparicin ( 3 ), ulein ( 4 ), stemmadenine ( 5 ), lupeol ( 6 ), and (3β)‐sitoster‐3‐yl β‐D ‐glucopyranoside ( 7 ). These compounds were characterized on the basis of their spectral data, mainly 1D‐ (¹H,¹³C‐DEPTQ) and 2D‐NMR (¹H,¹H‐COSY, NOESY, HSQC, and HMBC), and mass spectra (EI‐MS and HR‐ES‐MS), involving also comparison with data from the literature.     

Application of enriched stable 196Hg isotope for monitoring the stability of total mercury in water samples

A novel tool for the investigation of stability of total mercury in water samples is presented. The study focuses on the application of enriched ¹⁹⁶Hg stable isotopic reagent for the stability studies. Natural abundance of ¹⁹⁶Hg in water samples is only 0.15%. Thus, the use of the ¹⁹⁶Hg isotope spike represents a major advantage, when it can be assumed that all the measured isotope is the same as is accurately added by the analyst, and the change in its mass concentration can be followed simply and reliably. Tests were carried out with industrial waste water and two type of the natural water. Cold vapour (CV) inductively coupled plasma mass spectrometer (ICP-MS) technique was applied for the mercury measurements. Monitoring was continued for approximately 100 days. It is commonly advised that the measurement for total mercury in water samples should be carried out within 14 days. In this study the samples were observed to be stable for more than three months, if they were stored at a temperature of 4–6°C. The results of this stability study were in line with the guidance presented in EPA standard 1631. However, the samples were noticed to be stable for a much longer time than is presented in the standard method ISO 17852.     

Ansa‐Bridged Bis(benzene) Titanium Complexes

Taking advantage of an improved synthesis of [Ti(η⁶‐C₆H₆)₂], we report here the first examples of ansa‐bridged bis(benzene) titanium complexes. Deprotonation of [Ti(η⁶‐C₆H₆)₂] with nBuLi in the presence of N,N,N′,N′′,N′′‐pentamethyldiethylenetriamine (pmdta) leads to the corresponding 1,1′‐dilithio salt [Ti(η⁶‐C₆H₅Li)₂] ? pmdta that enables the preparation of the first one‐ and two‐atom‐bridged complexes by simple salt metathesis. The ansa complexes were fully characterized (NMR spectroscopy, UV/Vis spectroscopy, elemental analysis, and X‐ray crystallography) and further studied electrochemically and computationally. Moreover, [Ti(η⁶‐C₆H₆)₂] is found to react with the Lewis base 1,3‐dimethylimidazole‐2‐ylidene (IMe) to give the bent sandwich complex [Ti(η⁶‐C₆H₆)₂(IMe)].     

Ansa‐Complexes of [Mn(η5‐C5H5)(η6‐C6H6)]: Preparation,Characterization, and Reactivity of [n]Manganoarenophanes (n=1, 2, 3)

We report the synthesis of [n]manganoarenophanes (n=1, 2) featuring boron, silicon, germanium, and tin as ansa‐bridging elements. Their preparation was achieved by salt‐elimination reactions of the dilithiated precursor [Mn(η⁵‐C₅H₄Li)(η⁶‐C₆H₅Li)]?pmdta (pmdta=N,N,N′,N′,N′′‐pentamethyldiethylenetriamine) with corresponding element dichlorides. Besides characterization by multinuclear NMR spectroscopy and elemental analysis, the identity of two single‐atom‐bridged derivatives, [Mn(η⁵‐C₅H₄)(η⁶‐C₆H₅)SntBu₂] and [Mn(η⁵‐C₅H₄)(η⁶‐C₆H₅)SiPh₂], could also be determined by X‐ray structural analysis. We investigated for the first time the reactivity of these ansa‐cyclopentadienyl–benzene manganese compounds. The reaction of the distannyl‐bridged complex [Mn(η⁵‐C₅H₄)(η⁶‐C₆H₅)Sn₂tBu₄] with elemental sulfur was shown to proceed through the expected oxidative addition of the Sn?Sn bond to give a triatomic ansa‐bridge. The investigation of the ring‐opening polymerization (ROP) capability of [Mn(η⁵‐C₅H₄)(η⁶‐C₆H₅)SntBu₂] with [Pt(PEt₃)₃] showed that an unexpected, unselective insertion into the C_ipso?Sn bonds of [Mn(η⁵‐C₅H₄)(η⁶‐C₆H₅)SntBu₂] had occurred.