Deducing the multidimensional Szemerédi theorem from an infinitary removal lemma

We offer a new proof of the Furstenberg-Katznelson multiple recurrence theorem for several commuting probability-preserving transformations T ₁, T ₂, …, T _d : ℤ ↷ (X, ∑, μ) ([6]), and so, via the Furstenberg correspondence principle introduced in [5], a new proof of the multi-dimensional Szemerédi Theorem. We bypass the careful manipulation of certain towers of factors of a probability-preserving system that underlies the Furstenberg-Katznelson analysis, instead modifying an approach recently developed in [1] to pass to a large extension of our original system in which this analysis greatly simplifies. The proof is then completed using an adaptation of arguments developed by Tao in [13] for his study of an infinitary analog of the hypergraph removal lemma. In a sense, this addresses the difficulty, highlighted by Tao, of establishing a direct connection between his infinitary, probabilistic approach to the hypergraph removal lemma and the infinitary, ergodic-theoretic approach to Szemerédi’s Theorem set in motion by Furstenberg [5].     

Complementary control by additives of the kinetics of amorphous CaCO3 mineralization at an organic interface: in-situ synchrotron x-ray observations

The kinetics of biomimetic mineralization at a fatty acid monolayer interface have been measured in situ by synchrotron x-ray reflectivity. The formation of biologically relevant amorphous calcium carbonate films is affected by soluble macromolecules, supersaturation rate of change, and Mg cations. We find that these solution conditions influence mineral film formation in a complementary fashion. Poly(sodium acrylate) extends the lifetime of metastable amorphous calcium carbonate, solution saturation controls the mineral film growth rate, and Mg cations create a longer induction time. This is the first quantification of potentially competitive biomineralization mechanisms that addresses nucleation and growth of the amorphous mineral phases, which are important in biomineralization.     

Pricing and advertisement in a manufacturer–retailer supply chain

We use a game theoretical approach to study pricing and advertisement decisions in a manufacturer–retailer supply chain when price discounts are offered by both the manufacturer and retailer. When the manufacturer is the leader of the game, we obtained Stackelberg equilibrium with manufacturer’s local allowance, national brand name investment, manufacturer’s preferred price discount, retailer’s price discount, and local advertising expense. For the special case of two-stage equilibrium when the manufacturer’s price discount is exogenous, we found that the retailer is willing to increase local advertising expense if the manufacturer increases local advertising allowance and provides deeper price discount, or if the manufacturer decreases its brand name investment. When both the manufacturer and retailer have power, Nash equilibrium in a competition game is obtained. The comparison between the Nash equilibrium and Stackelberg equilibrium shows that the manufacturer always prefers Stackelberg equilibrium, but there is no definitive conclusion for the retailer. The bargaining power can be used to determine the profit sharing between the manufacturer and the retailer. Once the profit sharing is determined, we suggest a simple contract to help the manufacturer and retailer obtain their desired profit sharing.     

Intense geodesic acousticlike modes driven by suprathermal ions in a tokamak plasma

Intense axisymmetric oscillations driven by suprathermal ions injected in the direction counter to the toroidal plasma current are observed in the DIII-D tokamak. The modes appear at nearly half the ideal geodesic acoustic mode frequency, in plasmas with comparable electron and ion temperatures and elevated magnetic safety factor (q_{min}>or=2). Strong bursting and frequency chirping are observed, concomitant with large (10%-15%) drops in the neutron emission. Large electron density fluctuations (n[over ]_{e}/n_{e} approximately 1.5%) are observed with no detectable electron temperature fluctuations, confirming a dominant compressional contribution to the pressure perturbation as predicted by kinetic theory. The observed mode frequency is consistent with a recent theoretical prediction for the energetic-particle-driven geodesic acoustic mode.     

Ruthenium (II) complexes bearing thioether-appended α-iminopyridine ligands: Arene precursors permit access to κ2-N,N and κ3-N,N,S complexes

Herein we report the preparation of a series of Ru(II) complexes featuring α-iminopyridine ligands bearing thioether functionality (NNS^R, where R = Me, CH₂Ph, Ph). Metallation using [(p-cymene)RuCl]₂ permits access to Ru complexes with a κ²-N,N donor set in which the thioether moiety remains uncoordinated. In the presence of a strong field ligand such as acetonitrile or triphenylphosphine, the p-cymene moiety is displaced, and the ligand adopts a κ³-N,N,S binding mode. These complexes are characterized using a combination of solution and solid state methods, including the crystal structure of [(NNS^Me)Ru (NCMe)₂Cl]Cl. The κ²-N,N-Ru(II) complexes are shown to serve as efficient precatalysts for the oxidation of sec-phenethyl alcohol at modest loadings (alcohol: Ru = 20:1), using a variety of external oxidants and solvents. The complex bearing an S-Ph donor was found to be the most active oxidation catalyst of those surveyed, suggesting that the thioether donor plays an active role in the catalytic cycle.     

Evolved Gas Analysis‐Mass Spectrometry to Identify the Earliest Organic Binder in Aegean Style Wall Paintings

An organic binder was identified in the painted fragments from the Canaanite palace of Tel Kabri, Israel. Recently dated to the late 18th century B.C.E. by ¹⁴C, Tel Kabri is the most ancient of the Eastern Mediterranean sites in which Aegean style paintings have been found. The application of pigments was suspected to be using an organic binding medium, particularly for the Egyptian Blue pigment. Samples of blue paint were examined using evolved gas analysis‐mass spectrometry (EGA‐MS) in order to overcome the analytical challenges imposed by highly degraded aged proteinaceous materials. Egg was identified as the binder based on the presence of hexadecanonitrile and octadecanonitrile, confirming the use of a secco painting technique. Lysozyme C from Gallus gallus was detected by proteomics analysis, confirming the presence of egg. To our knowledge, this is the earliest use of egg as a binder in Aegean style wall paintings.     

Improved Miniaturized Linear Ion Trap Mass Spectrometer Using Lithographically Patterned Plates and Tapered Ejection Slit

We present a new two-plate linear ion trap mass spectrometer that overcomes both performance-based and miniaturization-related issues with prior designs. Borosilicate glass substrates are patterned with aluminum electrodes on one side and wire-bonded to printed circuit boards. Ions are trapped in the space between two such plates. Tapered ejection slits in each glass plate eliminate issues with charge build-up within the ejection slit and with blocking of ions that are ejected at off-nominal angles. The tapered slit allows miniaturization of the trap features (electrode size, slit width) needed for further reduction of trap size while allowing the use of substrates that are still thick enough to provide ruggedness during handling, assembly, and in-field applications. Plate spacing was optimized during operation using a motorized translation stage. A scan rate of 2300 Th/s with a sample mixture of toluene and deuterated toluene (D8) and xylenes (a mixture of o-, m-, p-) showed narrowest peak widths of 0.33 Th (FWHM).

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A formal total synthesis of platencin

The readily available and enantiomerically pure trienes 12 undergo a thermally induced intramolecular Diels-Alder reaction to give the corresponding mixture of compounds 13 and 14. This mixture has been elaborated to an advanced intermediate associated with Nicolaou's recently reported total synthesis of the natural enantiomeric form of the antibiotic platencin (2).