Stability of the intersection of solution sets of semi-infinite systems

Many mathematical programming models arising in practice present a block structure in their constraint systems. Consequently, the feasibility of these problems depends on whether the intersection of the solution sets of each of those blocks is empty or not. The existence theorems allow to decide when the intersection of non-empty sets in the Euclidean space, which are the solution sets of systems of (possibly infinite) inequalities, is empty or not. In those situations where the data (i.e., the constraints) can be affected by some kind of perturbations, the problem consists of determining whether the relative position of the sets is preserved by sufficiently small perturbations or not. This paper focuses on the stability of the non-empty (empty) intersection of the solutions of some given systems, which can be seen as the images of set-valued mappings. We give sufficient conditions for the stability, and necessary ones as well; in particular we consider (semi-infinite) convex systems and also linear systems. In this last case we discuss the distance to ill-posedness.     

Catalytic asymmetric hydrosilylation of acetophenone with new chiral thiourea ligands containing the (S)-α-phenylethyl group

New chiral thioureas 1–8 containing 1,2-ethylendiamine or trans-1,2-diaminocyclohexane as the carbon skeleton, and containing an (S)-α-phenylethyl group have been prepared (79–98% yield). Thioureas 1–8 were used as ligands for the zinc-based catalyzed asymmetric hydrosilylation of acetophenone with polymethylhydrosiloxane (PMHS). The best result was achieved with monothiourea 1 (up to 75% ee), in toluene and a catalyst load of 5 mol %.     

Pricing life insurance under stochastic mortality via the instantaneous Sharpe ratio

We develop a pricing rule for life insurance under stochastic mortality in an incomplete market by assuming that the insurance company requires compensation for its risk in the form of a pre-specified instantaneous Sharpe ratio. Our valuation formula satisfies a number of desirable properties, many of which it shares with the standard deviation premium principle. The major result of the paper is that the price per contract solves a linear partial differential equation as the number of contracts approaches infinity. One can represent the limiting price as an expectation with respect to an equivalent martingale measure. Via this representation, one can interpret the instantaneous Sharpe ratio as a market price of mortality risk. Another important result is that if the hazard rate is stochastic, then the risk-adjusted premium is greater than the net premium, even as the number of contracts approaches infinity. Thus, the price reflects the fact that systematic mortality risk cannot be eliminated by selling more life insurance policies. We present a numerical example to illustrate our results, along with the corresponding algorithms.     

New Approach to Mechanism of Action of Paclitaxel by Means of BioArena Studies

JPC – Journal of Planar Chromatography – Modern TLC - The accumulation of hydrogen peroxide (H2O2) is an early and crucial step in paclitaxel-induced cancer cell death before commitment...     

Isolation of Some Antimicrobial Compounds of Red Wine by OPLC Flowing Eluent Wall Technique

The first results of the combination of BioArena and OPLC with flowing eluent wall technique (FEW) show an especially attractive solution of the detection of antimicrobial activity and compound isolation based on peak collection. Because of the different separation mechanisms applied for on-line FEW–OPLC isolation of red wine constituents and for further off-line OPLC investigation of fractions, the combined system yields high selectivity.     

Fatty acid derived phosphorus‐containing polyesters via acyclic diene metathesis polymerization

The acyclic diene metathesis (ADMET) polymerization of a phosphorus‐containing α,ω‐diene prepared from a plant oil derived building block is reported. Different ruthenium based metathesis catalysts and conditions were tested to optimize the ADMET polymerization of this monomer. Undecylenyl undecenoate was used as fully renewable comonomer to obtain polyesters with different phosphorus contents and to increase the renewable content of the final polymers. Copolymerization caused marked variations in the molecular weights leading to polyesters from 6 to 38 KDa. The effect of the ADMET polymerization temperature in the thermal properties of the copolymers was studied and their thermal degradation and flame retardant properties were evaluated. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 5760–5771, 2009     

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