Extending shelling orders and a hierarchy of functions of unimodal simple polytopes

Let P be a simplicial d-polytope with n facets ((d − 1)-dimensional faces) in R^d. A shelling of P is an ordering of the facets of P such that the intersection of each facet F with the union of all facets that precede it the ordering is a nonempty union of (d − 2)-faces of F. The following open question was raised by Tverberg and is recorded in [4]. Suppose for some k < n, there is an ordering of k of the facets of P so that the intersection of each of these facets with the union of all of the facets that precede it in the ordering is a nonempty union of (d − 2)-faces. Can this initial “segment” be extended to a shelling of all the facets? This question is open even in the case that P is the dual of the d-dimensional hypercube. The question in this case has resurfaced several times since G. Danaraj and V. Klee (1978) in a variety of forms. It is related to the hierarchies of completely unimodal pseudo-Boolean functions studied in P.L. Hammer et al. (1988), the author (1988) and D. Wiedemann (1986). (A pseudo-Boolean function is a function mapping the vertices of the d-dimensional hypercube into the reals). In this paper, the hierarchies are compared and combined. This hierarchy is then extended to general simple polytopes, and the relationship to the above open question is explained.     

Quadrupole ion trap mass spectrometry of fullerenes

The fullerenes C₆₀ and C₇₀ can be ionized by desorption from a liquid matrix upon bombardment by Cs⁺ ions of 7 keV kinetic energy. The resulting radical cations, when activated in the ion trap by collisions with Xe target, in the presence of helium, undergo extensive dissociation by loss of multiple C₂ units. Large internal energies are deposited into these molecular ions and the dissociation efficiency is in excess of 60%.     

Fast, long-range electron-transfer reactions of a "blue" copper protein coupled non-covalently to an electrode through a stilbenyl thiolate monolayer

A self-assembled monolayer (SAM), formed by the insitu saponification of a stilbenyl thioacetate on a gold electrode, yields fast electron transfer (ET)(the exchange rate at zero driving force exceeds 1600 s-1) with adsorbed molecules of the blue copper protein, azurin, over a distance exceeding 15 angstroms .     

The rotational Zeeman effect in Trans-crotonaldehyde

The rotational Zeeman spectrum of trans-crotonaldehyde has been assigned using a Fourier transform microwave spectrometer. Using the experimental molecular g values and magnetic susceptibility anisotropies, we obtain the molecular quadrupole moments (in units of 10^-26 esu) of Q_aa = -7.5 ± 1.6, Q_bb = 12.1 ± 2.0, and Q_cc = -4.6 ± 2.7. Several additional molecular quantities are also determined.     

Determination of (R)- and (S)-ketoprofen in human plasma by liquid chromatography/tandem mass spectrometry following automated solid-phase extraction in the 96-well format

A sensitive and selective method was developed for the determination of (R)-ketoprofen ((R)-kt) and (S)-ketoprofen ((S)-kt) in human plasma using chiral liquid chromatography/tandem mass spectrometry (LC/MS/MS). Plasma samples spiked with stable-isotope-labeled [(13)C(1), (2)H(3)]-(R and S)-ketoprofen, for use as the internal standards, were prepared for analysis using automated solid-phase extraction (SPE) in the 96-well microtiter format. The enantiomers were separated on an (R)-1-naphthylglycine and 3,5-dinitrobenzoic acid (Chirex 3005) 250x2.0 mm i.d. analytical column, equipped with a 30x2.0 mm i.d. guard column using isocratic mobile phase conditions. The (R)- and (S)-kt levels were quantifiable from 0.05 to 2500 ng ml(-1) by constructing two separate curves from calibration standards covering the same range. The first curve ranged from 0.05 to 100 and the second from 100 to 2500 ng ml(-1). A concentration of 0.05 ng ml(-1) of either enantiomer was easily detected using a 1 ml plasma sample volume. The average method accuracy, evaluated at four levels over an extended period, was better than +/-3% over the entire range. The precision for the same set of quality control samples ranged from 4.0 to 7.0 % RSD (n = 24). The method was applied to the evaluation of pharmacokinetic parameters in human plasma obtained from volunteers who received 25 mg of kt by peroral administration of Actron caplets or by topical administration of Oruvail gel.     

3,4-Disubstituted polyalkylthiophenes for high-performance thin-film transistors and photovoltaics

We demonstrate that poly(3,4-dialkylterthiophenes) (P34ATs) have comparable transistor mobilities (0.17 cm(2) V(-1) s(-1)) and greater environmental stability (less degradation of on/off ratio) than regioregular poly(3-alkylthiophenes) (P3ATs). Unlike poly(3-hexylthiophene) (P3HT), P34ATs do not show a strong and distinct π-π stacking in X-ray diffraction. This suggests that a strong π-π stacking is not always necessary for high charge-carrier mobility and that other potential polymer packing motifs in addition to the edge-on structure (π-π stacking direction parallel to the substrate) can lead to a high carrier mobility. The high charge-carrier mobilities of the hexyl and octyl-substituted P34AT produce power conversion efficiencies of 4.2% in polymer:fullerene bulk heterojunction photovoltaic devices. An enhanced open-circuit voltage (0.716-0.771 eV) in P34AT solar cells relative to P3HT due to increased ionization potentials was observed.     

A Layered Hybrid Perovskite Solar‐Cell Absorber with Enhanced Moisture Stability

Two‐dimensional hybrid perovskites are used as absorbers in solar cells. Our first‐generation devices containing (PEA)₂(MA)₂[Pb₃I₁₀] ( 1 ; PEA=C₆H₅(CH₂)₂NH₃⁺, MA=CH₃NH₃⁺) show an open‐circuit voltage of 1.18 V and a power conversion efficiency of 4.73 %. The layered structure allows for high‐quality films to be deposited through spin coating and high‐temperature annealing is not required for device fabrication. The 3D perovskite (MA)[PbI₃] ( 2 ) has recently been identified as a promising absorber for solar cells. However, its instability to moisture requires anhydrous processing and operating conditions. Films of 1 are more moisture resistant than films of 2 and devices containing 1 can be fabricated under ambient humidity levels. The larger bandgap of the 2D structure is also suitable as the higher bandgap absorber in a dual‐absorber tandem device. Compared to 2 , the layered perovskite structure may offer greater tunability at the molecular level for material optimization.     

Regioselectivity in the palladium-catalyzed addition of carbon nucleophiles to carbocyclic derivatives.

The regioselectivity of Pd-catalyzed malonate additions and arylations to cycloalkenyl esters can be predicted by completing a stereochemical analysis of the Pd-pi-allyl complex. The Pd-catalyzed malonate additions which have the greatest degree of regioselectivity are in which substituents have a steric influence in blocking the incoming nucleophile. Cyclopentenyl substrates displayed lower regioselectivity than the cyclohexyl counterparts presumably due to increased planarity of the system. Arylations using tin and hypervalent silicon reagents were compared.