Generic boundary behaviour of Taylor series in Hardy and Bergman spaces

We establish a general identity between the Mahler measures \(\mathrm {m}(Q_k(x,y))\) and \(\mathrm {m}(P_k(x,y))\) of two polynomial families, where \(Q_k(x,y)=0\) and \(P_k(x,y)=0\) are generically hyperelliptic and elliptic curves, respectively.     

Investigating the molecular mechanisms of in-plane mechanochemistry on cantilever arrays

Free-standing cantilevers, which directly translate specific biochemical reactions into micromechanical motion, have recently attracted much attention as label-free biosensors and micro/nano robotic devices. To exploit this mechanochemical sensing technology, it is essential to develop a fundamental understanding of the origins of surface stress. Here we report a detailed study into the molecular basis of stress generation in aqueous environments focusing on the pH titration of model mercaptohexadecanoic acid self-assembled monolayers (SAMs), using in situ reference cantilevers coated with nonionizable hexadecanethiol SAMs. Semiautomated data analysis and a statistical model were developed to quantify cyclic deprotonation/protonation reactions on multiple arrays. In-plane force titrations were found to have the sensitivity to detect ionic hydrogen bond formation between protonated and nonprotonated carboxylic acid groups in the proximity of the surface pK1/2, which generated a mean tensile differential surface stress of +1.2 +/- 0.3 mN/m at pH 6.0, corresponding to 1 pN attractive force between two adjacent MHA molecules. Conversely, the magnitude of compressive differential surface stress was found to increase progressively with pH >/= 7.0, reaching a maximum of -14.5 +/- 0.5 mN/m at pH 9.0, attributed to enhanced electrostatic repulsion between deprotonated carboxylic acid groups. However, striking differences were observed in the micromechanical responses to different ionic strength and ion species present in the aqueous environment, highlighting the critical role of counter- and co-ions on surface stress. Our findings provide fundamental insights into the molecular mechanisms of in-plane mechanochemistry, which may be exploited for biosensing and nanoactuation applications.     

Advantages of synthesizing trans-1,2-cyclohexanediol in a continuous flow microreactor over a standard glass apparatus

Comparison is made between the preparation of trans-1,2-cyclohexanediol in standard glassware (conventional batch production) and in a microreactor (continuous flow production). The reaction sequence involved two exothermic steps where the standard procedure demands slow reagent addition and careful temperature control. In the microreactor, the reaction could be carried out safely with up to 3 times higher reagent concentration. Synthetic benefits were a faster reaction rate and a higher purity product free of colored impurities (a feature of the batch procedure).     

Structural Changes and Activation of Cellulose by Caustic Soda Solution with Urea

Investigations on the activation of cellulose by mixed solutions of caustic soda and urea are reported. The structural effects of those solutions on various dissolving pulps are studied by ¹³C-CP/MAS-NMR spectroscopy. In a series of steeping lyes, the concentration of NaOH was varied in a range from 0% to 8% and the urea-concentration in a range from 15% to 40% at ambient temperature and −25 °C. Using solely the single NaOH or urea solutions in the concentration ranges given above, no or only minor structural changes were found. In contrast to that, the cellulose I structure was partially or completely destroyed by using the bicomponent solution with urea added to caustic soda. The structural effect of the bicomponent solutions is comparable with the effect of solely caustic soda solutions of approx. 10% to 18% NaOH. However, the ¹³C-CP/MAS-NMR-spectra from the bicomponent pretreated samples indicate a structure different from the usual ordered structures of sodium cellulose I or II, namely a special urea-NaOH-cellulose complex. The results show that for cellulose activation the NaOH concentration of the caustic soda can be remarkably reduced by adding urea. The improved activating effect of an optimized caustic soda solution with added urea was proved to be useful for the synthesis of cellulose carbamate.     

M2Ga6Te10 (M: Li,Na): Two New Non‐metallic Filled β‐Manganese Phases – X‐ray and NMR Studies

Two new non‐metallic filled β‐manganese phases M₂Ga₆Te₁₀ (M: Li, Na) are obtained as black, homogeneous, microcristalline samples as well as single crystals by direct reaction of the elements. According to the single crystal structure determinations both compounds crystallize in space group R32 (No. 155, Z = 2) with the lattice constants: a = 1436.9(2), c = 1759.0(4) pm (T = 180 K, Li₂Ga₆Te₁₀) and a = 1458(1) pm, c = 1776.1(4) pm (T = 290 K, Na₂Ga₆Te₁₀). Their structures are characterized by tetrahedral close packings of Te^2–, corresponding to the arrangement of Mn atoms in β‐Mn. While Ga³⁺ ions are distributed in an ordered way over 12% of the tetrahedral holes, the M⁺ ions occupy all distorted octahedral (“metaprismatic”) holes. As the Li⁺ ions are too small they occupy off‐center positions inside the metaprisms. Positions with the strongest off‐centering can only be refined on the basis of a split model. MAS‐NMR measurements, including multiple quantum NMR, allowed the two different crystallographic M⁺ sites to be distinguished unambigously by separate ⁷Li and ²³Na signals, respectively. The assignment of the NMR signals was supported by measurements of samples in which Li⁺ was partly substituted by larger cations (Sn²⁺, Pb²⁺).     

Proton formation in 2+1 resonance enhanced multiphoton excitation of HCl and HBr via (Omega=0) Rydberg and ion-pair states

Molecular beam cooled HCl was state selected by two-photon excitation of the V (1) summation operator(0(+)) [v=9,11-13,15], E (1) summation operator(0(+)) [v=0], and g (3) summation operator(-)(0(+)) [v=0] states through either the Q(0) or Q(1) lines of the respective (1,3) summation operator(0(+))<--<--X (1) summation operator(0(+)) transition. Similarly, HBr was excited to the V (1) summation operator(0(+)) [v=m+3, m+5-m+8], E (1) summation operator(0(+)) [v=0], and H (1) summation operator(0(+)) [v=0] states through the Q(0) or Q(1) lines. Following absorption of a third photon, protons were formed by three different mechanisms and detected using velocity map imaging. (1) H(*)(n=2) was formed in coincidence with (2)P(i) halogen atoms and subsequently ionized. For HCl, photodissociation into H(*)(n=2)+Cl((2)P(12)) was dominant over the formation of Cl((2)P(32)) and was attributed to parallel excitation of the repulsive [(2) (2)Pi4llambda] superexcited (Omega=0) states. For HBr, the Br((2)P(32))Br((2)P(12)) ratio decreases with increasing excitation energy. This indicates that both the [(3) (2)Pi(12)5llambda] and the [B (2) summation operator5llambda] superexcited (Omega=0) states contribute to the formation of H(*)(n=2). (2) For selected intermediate states HCl was found to dissociate into the H(+)+Cl(-) ion pair with over 20% relative yield. A mechanism is proposed by which a bound [A (2) summation operatornlsigma] (1) summation operator(0(+)) superexcited state acts as a gateway state to dissociation into the ion pair. (3) For all intermediate states, protons were formed by dissociation of HX(+)[v(+)] following a parallel, DeltaOmega=0, excitation. The quantum yield for the dissociation process was obtained using previously reported photoionization efficiency data and was found to peak at v(+)=6-7 for HCl and v(+)=12 for HBr. This is consistent with excitation of the repulsive A(2) summation operator(12) and (2) (2)Pi states of HCl(+), and the (3) (2)Pi state of HBr(+). Rotational alignment of the Omega=0(+) intermediate states is evident from the angular distribution of the excited H(*)(n=2) photofragments. This effect has been observed previously and was used here to verify the reliability of the measured spatial anisotropy parameters.     

Zwitterionic 1-phosphonioalkyl dithiophosphinates

The title compounds (and, in part, their seleno analogs) result from the oxidation of an ylidylphosphine and also from the addition of ylides to a perthiophosphonic anhydride. They can be deprotonated and alkylated to give anions or cations, respectively. The reaction with phenacyl bromide opens a way to 1,3,2-oxathiaphosphole sulfides. © 1998 John Wiley & Sons, Inc. Heteroatom Chem 9:433–437, 1998     

Upper- and lower-bound Hylleraas–CI calculations for the nonrelativistic Po states of the 4He isotope

Extensive Hylleraas–CI calculations for the lowest P^o states of ⁴He were performed. The dependence of the variational energy values E_κ on the mass parameter κ given by κ=m/m is discussed. Furthermore, lower bounds to E_κ were calculated using variance minimization. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 25–30, 1998     

N,N-Dimethylcarbamato-Komplexe von Kupfer und Zink

N,N -Dimethylcarbamato Complexes of Copper and Zinc Reactions of the 1 : 1 adduct of dimethylamine and carbon dioxide (dimcarb) with metallic copper and zinc, respectively, are reported. Dimcarb gives with copper in the presence of oxygen the N,N-dimethylcarbamato copper(II) complex [Cu(O₂CNMe₂)₂(HNMe₂)₂] ( 1 ). Zinc spontaneously dissolves in a dimcarb-acetonitrile mixture under generation of hydrogen and giving (H₂NMe₂)[Zn₂(O₂CNMe₂)₅] · MeCN ( 3 ). The rate of this reaction is strongly depending on the purity of the metal, high purity zinc doesn't react. But 3 can be prepared from it by electrosynthesis. The crystal structures of 1 and 3 were determined by X-ray analysis. In 1 the copper atom has a distorted octahedral coordination sphere in which the two carbamate ligands are chelating. In the homoleptic complex anion of 3 two zinc atoms are bridged by three carbamate ligands whereas the other two carbamate ligands are coordinated monodentately.