On the n-Coupling Problem

In this paper we obtain based on an idea of M. Knott and C. S. Smith (1994, Linear Algebra Appl.199, 363–371) characterizations of solutions of three-coupling problems by reduction to the construction of optimal couplings of each of the variables to the sum. In the case of normal distributions this leads to a complete solution. Under a technical condition this idea also works for general distributions and one obtains explicit results. We extend these results to the n-coupling problem and derive a characterization of optimal n-couplings by several 2-coupling problems. This leads to some constructive existence results for Monge solutions.     

Design and synthesis of cyclic RGD pentapeptoids by consecutive Ugi reactions

A new strategy for the synthesis of cyclic peptoids was developed. The approach is based on the use of consecutive Ugi reactions for the assembly of the acyclic peptoid and for the ring closure. Cyclopentapeptoid analogues of the RGD peptides were designed and synthesized using this methodology. The results confirm the versatility and efficiency of the method for the preparation of cyclic oligopeptoids.     

On the Method of Optimal Portfolio Choice by Cost-Efficiency

We develop the method of optimal portfolio choice based on the concept of cost-efficiency in two directions. First, instead of specifying a payoff distribution in an unique way, we allow customer-defined constraints and preferences for the choice of a distributional form of the payoff distribution. This leads to a class of possible payoff distributions. We determine upper and lower bounds for the corresponding strategies in stochastic order and describe related upper and lower price bounds for the induced class of cost-efficient payoffs. While the results for the cost-efficient payoff given so far in the literature in the context of Lévy models are based on the Esscher pricing measure we use as alternative the method of empirical pricing measures. This method is well established in the literature and leads to more precise pricing of options and their cost-efficient counterparts. We show in some examples for real market data that this choice is numerically feasible and leads to more precise prices for the cost-efficient payoffs and for values of the efficiency loss.     

Alkaloids from Papaver coreanum

The alkaloid pattern of the endemic plant Papaver coreanum Nakai (Papaveraceae) was determined for the first time. Eight alkaloids could be identified by LC/ESI-MS/MS and high-resolution mass spectrometry. Among them, protopine and allocryptopine represent the main components. Besides norsanguinarine, sanguinarine, dihydrosanguinarine, oxysanguinarine, lincangenine, and cryptopine, some other trace alkaloids were found whose structures remain unknown.     

Deuterated dimethyl sulfoxide as a good NMR solvent for the characterization of alkali metal cyclopentadienides, amides, alkoxides and phenoxides

A series of alkali metal cyclopentadienides, amides, alkoxides and phenoxides was characterized using NMR spectroscopy in deuterated dimethyl sulfoxide. Deuterated dimethyl sulfoxide showed very good stability and solubility for these compounds. Very nice and well resolved spectra were obtained for most compounds tested. The low cost of the solvent makes it possible to use it for the routine characterization of these alkali salts as the ligands in organometallic synthesis.