What Is a Quantum-Mechanical “Weak Value” the Value of?

A so called “weak value” of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM paradoxes (e.g., the so called Three-Box Paradox and Hardy’s Paradox). This requires the weak value to be interpreted as a bona fide property of the system considered, a par with entities like operator mean values and eigenvalues. I question such an interpretation; it has no support in the basic axioms of quantum mechanics and it leads to unreasonable results in concrete situations.     

Absorption Statistics in Linear Dichroism

Attention is called to an artifact in linear dichroism (LD), so called absorption statistics, which leads to reduced LD intensity in regions of high absorption. The reduction factor is larger than that governing the corresponding reduction in absorption, when LD is measured by using a Legrand-Grosjean circular dichroism spectrophotometer. In the case of infinite fibres at perfect order it coincides with the absorption statistical reduction factor of optical activity. The artifact was observed for β-carothene solubilized in lecithin liposomes oriented at flow.     

Membrane characterization and solute diffusion in porous composite nanocellulose membranes for hemodialysis

The membrane and solute diffusion properties of Cladophora cellulose and polypyrrole (PPy) functionalized Cladophora cellulose were analyzed to investigate the feasibility of using electroactive membranes in hemodialysis. The membranes were characterized with scanning electron microscopy, ζ-potentiometry, He-pycnometry, N₂ gas adsorption, and Hg porosimetry. The diffusion properties across the studied membranes for three model uremic toxins, i.e. creatinine, vitamin B12 and bovine serum albumin, were also analyzed. The characterization work revealed that the studied membranes present an open structure of weakly negatively charged nanofibers with an average pore size of 21 and 53 nm for pristine cellulose and PPy-Cladophora cellulose, respectively. The results showed that the diffusion of uremic toxins across the PPy-Cladophora cellulose membrane was faster than through pure cellulose membrane, which was related to the higher porosity and larger average pore size of the former. Since it was found that the average pore size of the membranes was larger than the hydrodynamic radius of the studied model solutes, it was concluded that these types of membranes are favorable to expand the Mw spectrum of uremic toxins to also include conditions associated with accumulation of large pathologic proteins during hemodialysis. The large average pore size of the composite membrane could also be exploited to ensure high-fluxes of solutes through the membrane while simultaneously extracting ions by an externally applied electric current.     

A semiempirical MO study of the electronic structure and excited states of the Tris(2,2′-bipyridyl)Iron(II) and Tris(glyoxal-Bis-N-methylimine)iron(II)Ions

A semi-empirical SCF-MO method, the PEEL method, has been applied in an investigation of the electronic structure and excited states of two iron compounds, [Fe(II)-(GMI)₃]⁺⁺ and [Fe(II)-(bipy)₃]⁺⁺.The electronic absorption spectra have been recorded. The calculations show that it is necessary to account for the trigonal distortion and the covalency in order to explain these spectra quantitatively. Mössbauer measurements have also been performed. The calculated electronic population of the iron is in accord with Mössbauer isomer shift data, indicating that a realistic electron distribution has been obtained by the PEEL method.

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Zusammenfassung Eine semiempirische SCF-MO-Methode, die PEEL-Methode, wurde zur Untersuchung der Elektronenstruktur sowie von angeregten Zuständen der beiden Eisenverbindungen [Fe(II)-(GMI)₃]⁺⁺ und [Fe(II)-(bipy)₃]⁺⁺ angewendet.Die elektronischen Absorptionsspektren wurden aufgenommen. Die Berechnungen zeigen, daß die trigonale Verzerrung und die Kovalenz berücksichtigt werden müssen, um die Spektren quantitativ zu erklären. Mössbauer-Messungen wurden ebenfalls durchgeführt. Die berechnete Elektronenverteilung am Eisenatom ist in Übereinstimmung mit den Daten der Isomerenverschiebung der Mössbauer-Messungen, wodurch gezeigt wird, daß mit der PEEL-Methode eine realistische Elektronen-Verteilung erhalten wurde.

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Résumé Une méthode SCF-MO semi-empirique, la méthode PEEL, a été appliquée à une étude de la structure électronique et des états excités de deux composés ferreux: [Fe(II)-(bipy)₃]⁺⁺ et [Fe(II)-(GMI)₃]⁺⁺. Les spectres d'absorption électronique ont été enregistrés. Les calculs montrent qu'il est nécessaire de rendre compte de la distorsion trigonale et de la covalence pour expliquer ces spectres quantitativement.Des mesures de l'effet Mössbauer ont aussi été effectuées. La population électronique calculée du fer est en bon accord avec les données sur le déplacement isomérique de Mössbauer, ce qui indique que la méthode PEEL fournit une distribution électronique réaliste.

     

Khachiyan's linear programming algorithm

L. G. Khachiyan's polynomial time algorithm for determining whether a system of linear inequalities is satisfiable is presented together with a proof of its validity. The algorithm can be used to solve linear programs in polynomial time.