Products of mixed covering arrays of strength two

A covering array CA(N;t,k, v is an N × k array such that every N × t subarray contains all t‐tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used to generate software test suites to cover all t‐sets of component interactions. The particular case when t = 2 (pairwise coverage) has been extensively studied, both to develop combinatorial constructions and to provide effective algorithmic search techniques. In this paper, a simple “cut‐and‐paste” construction is extended to covering arrays in which different columns (factors) admit different numbers of symbols (values); in the process an improved recursive construction for covering arrays with t = 2 is derived. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 124–138, 2006     

Compact complex homogeneous manifolds with large automorphism groups

Let X be a compact complex homogeneous manifold and let Aut(X) be the complex Lie group of holomorphic automorphisms of X. It is well-known that the dimension of Aut(X) is bounded by an integer that depends only on n=dim X. Moreover, if X is K?hler then dimAut (X)≤n(n+2) with equality only when X is complex projective space. In this article examples of non-K?hler compact complex homogeneous manifolds X are given that demonstrate dimAut(X) can depend exponentially on n. Let X be a connected compact complex manifold of dimension n. The group of holomorphic automorphisms of X, Aut(X), is a complex Lie group [3]. For a fixed n>1, the dimension of Aut(X) can be arbitrarily large compared to n. Simple examples are provided by the Hirzebruch surfaces F _m , m∈N, for which dimAut(F _m )=m+5, see, e.g. [2, Example 2.4.2]. If X is homogeneous, that is, any point of X can be mapped to any other point of X under a holomorphic automorphism, then the dimension of the automorphism group of X is bounded by an integer that depends only on n, see [1, 2, 6]. The estimate given in [2, Theorem 3.8.2] is roughly dimAut(X)≤(n+2) ⁿ . For many classes of manifolds, however, the dimension of the automorphism group never exceeds n(n+2). For example, it follows directly from the classification given by Borel and Remmert [4], that if X is a compact homogeneous K?hler manifold, then dimAut(X)≤n(n+2) with equality only when X is complex projective space P ⁿ . It is an old question raised by Remmert, see [2, p. 99], [6], whether this same bound applies to all compact complex homogeneous manifolds. In this note we show that this is not the case by constructing non-K?hler compact complex homogeneous manifolds whose automorphism group has a dimension that depends exponentially on n. The simplest case among these examples has n=3m+1 and dimAut(X)=3m+3 ^m , so the above conjectured bound is exceeded when n≥19. These manifolds have the structure of non-trivial fiber bundles over products of flag manifolds with parallelizable fibers given as the quotient of a solvable group by a discrete subgroup. They are constructed using the original ideas of Otte [6, 7] and are surprisingly similar to examples found there. Generally, a product of manifolds does not result in an automorphism group with a large dimension relative to n. Nevertheless, products are used in an essential way in the construction given here, and it is perhaps this feature that caused such examples to be previously overlooked. Oblatum 13-X-97 & 24-X-1997     

Manifolds with almost nonnegative curvature operator and principal bundles

We study closed manifolds with almost nonnegative curvature operator (ANCO) and derive necessary and/or sufficient conditions for the total spaces of principal bundles over (A)NCO manifolds to admit ANCO connection metrics. In particular, we provide first examples of closed simply connected ANCO manifolds which do not admit metrics with nonnegative curvature operator.     

Synthesis of α-fluoro-α,β-unsaturated esters monitored by 1D and 2D benchtop NMR spectroscopy

For optimization and control of pharmaceutically and industrially important reactions, chemical information is required in real time. Instrument size, handling, and operation costs are important criteria to be considered when choosing a suitable analytical method apart from sensitivity and resolution. This present study explores the use of a robust and compact nuclear magnetic resonance (NMR) spectrometer to monitor the stereo-selective formation of α-fluoro-α,β-unsaturated esters from α-fluoro-β-keto esters via deprotonation and deacylation in real time. These compounds are precursors of various pharmaceutically active substances. The real-time study revealed the deprotonation and deacylation steps of the reaction. The reaction was studied at temperatures ranging from 293 to 333 K by interleaved one-dimensional ¹H and ¹⁹F and two-dimensional ¹H–¹H COSY experiments. The kinetic rate constants were evaluated using a pseudo first-order kinetic model. The activation energies for the deprotonation and deacylation steps were determined to 28 ± 2 and 63.5 ± 8 kJ/mol, respectively. This showed that the deprotonation step is fast compared with the deacylation step and that the deacylation step determines the rate of the overall reaction. The reaction was repeated three times at 293 K to monitor the repeatability and stability of the system. The compact NMR spectrometer provided detailed information on the mechanism and kinetics of the reaction, which is essential for optimizing the synthetic routes for stepwise syntheses of pharmaceutically active substances.     

Catalytic enantioselective allyl- and crotylboration of aldehydes using chiral diol x SnCl4 complexes. optimization, substrate scope and mechanistic investigations

We report a novel class of C2-symmetric chiral diols derived from the hydrobenzoin skeleton. The combination of these diols with SnCl4 under Yamamoto's concept of Lewis acid assisted Br?nsted acidity (LBA catalysis) leads to high levels of asymmetric induction in the allylboration of aldehydes by commercially available allylboronic acid pinacol ester 1a. The corresponding homoallylic alcohol products of synthetically useful aliphatic aldehydes are obtained in excellent yields with up to 98:2 er. This combined acid manifold is also efficient in catalyzing the diastereo- and enantioselective crotylboration of aldehydes, thus providing the propionate units in >95:5 dr and up to 98:2 er. The X-ray crystal structure of the optimal diol x SnCl4 complex, Vivol (4m) x SnCl4, unambiguously shows the Br?nsted acidic character of this LBA catalyst and its highly dissymmetrical environment. Further controls have ruled out a possible boron trans-esterification mechanism with the chiral diol and point to LBA catalyst-derived activation of the pinacol allylic boronates 1. Due to slow dissociation of the diol x SnCl4 complex, a small excess of diol is required in order to suppress a competing racemic cycle catalyzed by free SnCl4.     

The putative Diels-Alderase macrophomate synthase is an efficient aldolase

We find that the putative Diels-Alderase macrophomate synthase (MPS) catalyzes the addition of pyruvate enolate, generated by decarboxylation of oxaloacetate, to a variety of aldehydes. Alkyl, aryl, and heteroaryl aldehydes are accepted as substrates, providing gamma-hydroxy-alpha-ketoacids in 35-95% yield with modest levels of stereochemical control. These aldol products, which are difficult to synthesize by other methods, are formed with efficiency comparable to that of macrophomate. Our results thus provide evidence that a two-step Michael-aldol pathway is a plausible alternative to the postulated [4 + 2] cycloaddition in the MPS-catalyzed addition of pyruvate enolate to 2-pyrones. They are also relevant to understanding the divergent evolution of type II pyruvate aldolases.     

Construction of subphthalocyanine-porphyrin and subphthalocyanine-phthalocyanine heterodyads through axial coordination

The treatment of boron(III) subphthalocyanine chloride (SPcCl) with 3- or 4-hydroxypyridine in the presence of pyridine in toluene gave the corresponding boron(III) subphthalocyanine pyridinolates SPc(3-OPy) ( 1) or SPc(4-OPy) ( 2). Having a pyridyl group, these compounds could axially complex with a series of zinc(II) and ruthenium(II) porphyrins and phthalocyanines to form the corresponding subphthalocyanine-porphyrin and subphthalocyanine-phthalocyanine heterodyads. As revealed by UV-vis spectroscopy, the ground-state interaction between the two chromophores in these dyads is insignificant. The complexation processes were also studied by (1)H NMR and fluorescence spectroscopic methods, which confirmed the 1:1 binding stoichiometry. The association constants, as determined by fluorescence titration, were generally higher for the ruthenium(II) tetrapyrroles [(2.5-4.7) x 10 (4) M (-1)] than for the zinc(II) counterparts [(0.3-1.8) x 10 (4) M (-1)]. The molecular structures of the two pyridyl subphthalocyanines 1 and 2, together with three novel subphthalocyanine-porphyrin heterodyads, were also determined by X-ray diffraction analyses.     

Facile preparation of fluorovinylene aryl ether telechelic polymers with dual functionality for thermal chain extension and tandem crosslinking

New fluorovinylene aromatic ether polymers, possessing dual reactivity, have been successfully prepared via the step-growth polymerization of commercial bis(trifluorovinyl) aromatic ethers and bisphenols.     

Studies of the inner reorganization energies of the cation radicals of 1,4-bis(dimethylamino)benzene, 9,10-bis(dimethylamino)anthracene, and 3,6-bis(dimethylamino)durene by photoelectron spectroscopy and reinterpretation of the mechanism of the electrochemical oxidation of the parent diamines

The inner reorganization energy of the cation radical of 1,4-bis(dimethylamino)benzene, 1, has been determined to be 0.72 +/- 0.02 eV by means of gas-phase photoelectron spectroscopy (PES). PES studies of 9,10-bis(dimethylamino)anthracene, 2, and 3,6-bis(dimethylamino)durene, 3, demonstrate that their reorganization energies are smaller than that of 1. The effect of lowering the inner reorganization energy on the rate constant for an electrochemical electron-transfer reaction is to increase the electron-transfer rate constant, k(s). However, voltammetric studies of the two-electron oxidation of 2 and 3 indicate that the values of k(s) for each step are smaller than those for 1, in contradistinction to the measured differences in reorganization energies. The voltammetric studies of 2 and 3 were reinterpreted according to a mechanism in which each step of oxidation was written as a two-step process, electron transfer with a small inner reorganization energy plus a chemical step of structural change. The agreement of simulations according to this mechanism with the experimental data was excellent. The new reaction scheme eliminated some suspicious features previously obtained with an analysis where electron transfer and structural change were considered to be concerted. In particular, all electron-transfer coefficients (alpha) were close to one-half, whereas the earlier treatment produced values of alpha much larger or smaller than one-half.     

Amperometric detection of simple alcohols in aqueous solutions by application of a triple-pulse potential waveform at platinum electrodes

Application of a triple-pulse waveform is described for the anodic detection of methanol, ethanol, and ethylene glycol. The execution of the waveform incorporates the cleaning and reactivation of the platinum electrode, by alternate anodic and cathodic polarization, with measurement of the faradaic signal for the analyte at the reduced electrode surface. Some results for formic acid are also presented. The waveform is completed within approximately 2 s and the faradaic signal exhibits no decay with time as would be the case for amperometric detection at a constant applied potential. Calibration curves made by plotting —1/I vs. 1/C are linear. This is consistent with a reaction mechanism in which the analyte is adsorbed prior to anodic detection. The technique is applicable for detection in chromatographic and flow-injection systems.