Synthesis of pentacyclic 13-azadibenzo[a,de]anthracenes via anionic cascade ring closure

Bromine-lithium exchange using tert-butyllithium at -78 degrees C initiates a cascade process whereby either xanthone derivatives or pentacyclic 13-azadibenzo[a,de]anthracenes are produced in high yields. The reaction proceeds via a sequential intramolecular trapping of organolithium intermediates.     

Direct astatination of a tumour-binding protein, human epidermal growth factor, using nido-carborane as a prosthetic group

We have investigated a method for direct astatine labeling of proteins. Binding sites for astatine were created by coupling of a nido-carborane derivative to a protein, the human epidermal growth factor (hEGF), using two different conjugation methods - by glutaraldehyde cross-linking or by introduction of sulfohydryl groups by Traut's reagent with subsequent linking of ANC-1 with m-maleimidobenzoyl-N-hydroxysulfosuccinimide ester. The conjugates were astatinated using the Chloramine-T method in high yield. The best labeling was obtained by the glutaraldehyde conjugate with an average yield of 68±9%. In vitro stability tests indicated that the glutaraldehyde conjugated label was as stable as hEGF labeled with astatobenzoate.     

Development of a chiral non-aqueous capillary electrophoretic system using the partial filling technique with UV and mass spectrometric detection

A chiral non-aqueous CE system with UV and mass spectrometric detection has been developed. The enantioseparation was promoted by diastereomeric complex (ion-pair) formation between the amines (e.g. salbutamol, atenolol) and the chiral selector, (-)-2,3:4,6-di-O-isopropylidene-2-keto-L-gulonic acid [(-)-DIKGA]. Different solvent mixtures were studied, as well as different concentrations of (-)-DIKGA and ammonium acetate in the background electrolyte. A partial filling technique was developed with a selector plug composed of (-)-DIKGA and ammonium acetate in a solvent mixture of methanol and 2-propanol. The separated enantiomers of pronethalol were detected by a Q-TOF MS system equipped with a sheath-flow electrospray ionization interface.     

A littlewood-paley inequality for the Carleson operator

The Carleson operator is closely related to the maximal partial sum operator for Fourier series. We study generalizations of this operator in one and several variables.     

Asymmetric equilibria in dynamic two-sided matching markets with independent preferences

A fundamental fact in two-sided matching is that if a market allows several stable outcomes, then one is optimal for all men in the sense that no man would prefer another stable outcome. We study a related phenomenon of asymmetric equilibria in a dynamic market where agents enter and search for a mate for at most n rounds before exiting again. Assuming independent preferences, we find that this game has multiple equilibria, some of which are highly asymmetric between sexes. We also investigate how the set of equilibria depends on a sex difference in the outside option of not being mated at all.     

Multivariate design

In multivariate data analysis such as principal components analysis (PCA) and projections to latent structures (PLS), it is essential that the training set systems (objects) are selected to provide data with substantial information for model parametrization, and to represent properly any future situations where the multilvariate model is used for predictions. In the framework of multivariate projections (PCA, SIMCA and PLS), elementary concepts of statistical design (fractional factorials and composite designs) can be used with the latent variables (PC or PLS scores) as design variables. The plan of action thus becomes: (1) problem formulation (specify aim and model, make a conceptual division of the investigated system into subsystems); (2) collection of multivariate data for each type of subsystems; (3) estimation of the practical dimensionality of the data for each type of subsystems by PC or PLS analysis; (4) use of the PC or PLS scores (t) as design variables in the combination of subsystems to systems in the training set; (5) measurement of responses (Y); (6) analysis of data by PCA or PLS; (7) interpretation of results with possible feedback to steps 1, 2 or 3. The procedures are illustrated by two problems: a structure/activity relationship for a family of peptides, and optimization of an organic synthesis with respect to system variables (solvent, substrate, co-reactant_) and process variables (temperature, reactant concentrations).     

Haar-like expansions and boundedness of a Riesz operator on a solvable Lie group

Consider the group of affine transformations of the line. Denote by X and Y the right-invariant vector fields corresponding to the s and t directions, respectively, and let We prove that the first-order Riesz operator is of weak type (1, 1) with respect to left Haar measure. This operator is therefore also bounded on . Our results provide answers, in a particular instance, to the open question of the boundedness of Riesz operators on Lie groups of exponential growth. The main parts of the proof concern the behaviour of the kernel of the operator at infinity, and exploit cancellation. A key technique is to use expansion with respect to scales of Haar-like functions. Received March 16, 1998; in final form June 22, 1998