A moment problem associated to rational Szegő functions

Leta ₁,...,a _p be distinct points in the finite complex plane ?, such that |a _j|>1,j=1,..., p and let \(b_j = 1/\bar \alpha _j ,\) j=1,..., p. Let μ₀, μ _π ^(j) , ν _π ^(j) j=1,..., p;n=1, 2,... be given complex numbers. We consider the following moment problem. Find a distribution ψ on [?π, π], with infinitely many points of increase, such that $$\begin{array}{l} \int_{ - \pi }^\pi {d\psi (\theta ) = \mu _0 ,} \\ \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - a_j )^n }} = \mu _n^{(j)} ,} \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - b_j )^n }} = v_n^{(j)} ,} j = 1,...,p;n = 1,2,.... \\ \end{array}$$ It will be shown that this problem has a unique solution if the moments generate a positive-definite Hermitian inner product on the linear space of rational functions with no poles in the extended complex plane ?^* outside {a ₁,...,a _p,b ₁,...,b _p}.     

Optimal allocation of replicas in parallel tempering simulations

We have studied the efficiency of parallel tempering simulations for a variety of systems including a coarse-grained protein, an atomistic model polypeptide, and the Lennard-Jones fluid. A scheme is proposed for the optimal allocation of temperatures in these simulations. The method is compared to the existing empirical approaches used for this purpose. Accuracy associated with the computed thermodynamic quantities such as specific heat is also computed and their dependence on the trial-exchange acceptance rate is reported.     

Palladium-catalyzed cascade reaction of alpha,beta-unsaturated sulfones with aryl iodides

Unlike traditionally used acyclic 1,2-disubstituted alkenes, the reaction of alpha,beta-unsaturated phenyl sulfones with aryl iodides under Heck reaction conditions (Pd(OAc)(2) as catalyst, Ag(2)CO(3) as base in DMF at 120 (0)C) takes place mainly by a cascade process, involving one unit of the alkene and three units of the aryl iodide, to afford a substituted 9-phenylsulfonyl-9,10-dihydrophenanthrene. The dominant formation of this 3:1 coupling product, instead of the Heck trisubstituted olefin, shows that aromatic C-H bond activation processes can compete with the usually fast syn beta-hydrogen elimination step in the Heck arylation of an acyclic olefin. The structural scope of this palladium-catalyzed cascade arylation of alpha,beta-unsaturated sulfones has proved to be wide with regard to substitution at the beta-position (alkyl, aryl, or alkenyl substitution), substitution at the sulfone unit (alkyl or phenyl sulfones), and configuration at the CdoublebondC bond (trans or cis). Moreover, although less favored than in the case of the arylation of alpha,beta-unsaturated sulfones, similarly substituted 9,10-dihydrophenanthrenes have also been obtained in the case of alpha,beta-unsaturated phosphine oxides and alpha,beta-unsaturated phosphonate esters. A Pd(0)-Pd(II)-Pd(IV) mechanistic pathway involving the successive formation of highly electrophilic sigma-alkylpalladium intermediates and palladacycles is proposed for this multicomponent arylation.     

Development of a liquid chromatography/tandem mass spectrometry assay for the quantification of PM00104, a novel antineoplastic agent, in mouse, rat, dog, and human plasma

A rapid and sensitive liquid chromatography/tandem mass spectrometry (LC/MS/MS) assay was developed and validated to quantify a novel antineoplastic agent, PM00104, in mouse, rat, dog, and human plasma. The method was validated to demonstrate the specificity, limit of quantification (LOQ), accuracy, and precision of measurements. The calibration range for PM00104 was established using PM00104 standards from 0.01-5.0 ng/mL in blank plasma. The selected reaction monitoring (SRM), based on the m/z 692.2 --> 218.2 transition, was specific for PM00104, and that based on the m/z 697.2 --> 218.2 transition was specific for PM00104 ((13)C(2),(2)H(3)) (the internal standard, IS); no endogenous materials interfered with the analysis of PM00104 and IS from blank plasma. The assay was linear over the concentration range 0.01-5.0 ng/mL. The correlation coefficients for the calibration curves ranged from 0.9981-0.9999. The mean intra-day and inter-day accuracies for all calibration standards (n = 8) ranged from 97-105% (< or =5% bias) in human plasma, and the mean inter-day precision for all calibration standards was less than 8.5%. The mean intra- and inter-day assay accuracy for all quality control (QC) replicates in human plasma (n = 9), determined at each QC level throughout the validated runs, ranged from 96-112% (< or =12% bias) and from 102-105% (< or =5% bias), respectively. The mean intra- and inter-day assay precision was less than 15.0 and 11.8% for all QC levels, respectively. For the QC samples prepared in animal species plasma, the %CV values of the assays ranged from 1.8-8.8% in mouse plasma, from 3.7-13.8% in rat plasma, and from 3.0-7.2% in dog plasma. The assay accuracies ranged from 92-102% (< or =8% bias) for all QC levels prepared in mouse plasma; ranged from 93-106% (< or =7% bias) in rat plasma; and ranged from 95-114% (< or =14% bias) in dog plasma. The assay has been used to support preclinical pharmacokinetic and toxicokinetic studies and is currently used to measure PM00104 plasma concentrations to support clinical trials.     

Finite primitive groups and edge-transitive hypergraphs

We determine all finite primitive groups that are automorphism groups of edge-transitive hypergraphs. This gives an answer to a problem proposed by Babai and Cameron.