Axiomatic Quantum Mechanics and Completeness

The standard axiomatization of quantum mechanics (QM) is not fully explicit about the role of the time-parameter. Especially, the time reference within the probability algorithm (the Born Rule, BR) is unclear. From a probability principle P1 and a second principle P2 affording a most natural way to make BR precise, a logical conflict with the standard expression for the completeness of QM can be derived. Rejecting P1 is implausible. Rejecting P2 leads to unphysical results and to a conflict with a generalization of P2, a principle P3. All three principles are shown to be without alternative. It is thus shown that the standard expression of QM completeness must be revised. An absolutely explicit form of the axioms is provided, including a precise form of the projection postulate. An appropriate expression for QM completeness, reflecting the restrictions of the Gleason and Kochen-Specker theorems is proposed.     

Guanidiniocarbonylpyrrole–Aryl Derivatives: Structure Tuning for Spectrophotometric Recognition of Specific DNA and RNA Sequences and for Antiproliferative Activity

We present a systematic study of different guanidiniocarbonylpyrrole‐aryl derivatives designed to interact with DNA or RNA both through intercalation of an aromatic moiety into the base stack of the nucleotide and through groove binding of a guanidiniocarbonylpyrrole cation. We varied 1) the size of the aromatic ring (benzene, naphthalene, pyrene and acridine), 2) the length and flexibility of the linker connecting the two binding groups, and 3) the total number of positive charges present at different pH values. The compounds and their interactions with DNA and RNA were studied by UV/Vis, fluorescence and CD spectroscopy. Antiproliferative activities against human tumour cell lines were also determined. Our studies show that efficient interaction with, for example, DNA requires a significantly large aromatic ring (pyrene) connected through a flexible linker to the pyrrole moiety. However, a positive charge, as in 12 , is also needed. Compound 12 allows for base‐pair‐selective recognition of ds‐DNA at physiological pH values. The antiproliferative activities of these compounds correlate with their binding affinities towards DNA, suggesting that their biological effects are most probably due to DNA binding.     

Design for Minimum Stress Concentration by Finite Elements and Linear Programming

The problem of design for minimum stress concentration is highly nonlinear and must be solved iteratively. Each iteration (redesign) involves three steps: an analysis of the stresses for a design, a sensitivity analysis corresponding to possible changes in this design, and the decision of redesign. For stress analysis, the FEM is a unified approach which is applied in the present paper to axisymmetric solids that are also subjected to nonaxisymmetric loads. The decision of redesign is a linear programming problem and can thus be solved with the Simplex algorithm. The introduction of move-limits to the formulation is of major importance. The optimization approach is described in general, but most of the paper concentrates on a specific example and shows optimum shapes of a shoulder fillet in a stepped bar. Loads are bending, tension, or torsion, and the stress concentrations are considerably reduced.