Chiral discrimination of β‐3‐homo‐amino acids using the kinetic method

Chiral discrimination of seven enantiomeric pairs of β‐3‐homo‐amino acids was studied by using the kinetic method and trimeric metal‐bound complexes, with natural and unnatural α‐amino acids as chiral reference compounds and divalent metal ions (Cu²⁺ and Ni²⁺) as the center ions. The β‐3‐homo‐amino acids were selected for this study because, first of all, chiral discrimination of β‐amino acids has not been extensively studied by mass spectrometry. Moreover, these β‐3‐homo‐amino acids studied have different aromatic side chains. Thus, the emphasis was to study the effect of the side chain (electron density of the phenyl ring, as well as the difference between phenyl and benzyl side chains) for the chiral discrimination. The results showed that by the proper choice of a metal ion and a chiral reference compound, all seven enantiomeric pairs of β‐3‐homo‐amino acids could be differentiated. Moreover, it was noted that the β‐3‐homo‐amino acids with benzyl side chains provided higher enantioselectivity than the corresponding phenyl ones. However, increasing or decreasing the electron density of the aromatic ring by different substituents in both the phenyl and benzyl side chains had practically no role for chiral discrimination of β‐3‐homo‐amino acids studied. When copper was used as the central metal, the phenyl side chain containing reference molecules (S)‐2‐amino‐2‐phenylacetic acid (L ‐Phg) and (S)‐2‐amino‐2‐(4‐hydroxyphenyl)‐acetic acid (L ‐4′‐OHPhg) gave rise to an additional copper‐reduced dimeric fragment ion, [Cu^I(ref)(A)]⁺. The inclusion of this ion improved noticeably the enantioselectivity values obtained. Copyright © 2010 John Wiley & Sons, Ltd.     

High-performance liquid chromatographic enantioseparation of β-amino acids using a long-tethered (+)-(18-crown-6)-2,3,11,12-tetracarboxylic acid-based chiral stationary phase

Reversed-phase high-performance liquid chromatographic methods were developed for the separation of enantiomers of eleven unnatural β²-amino acids on a new chiral stationary phase, using the 11-methylene-unit spacer of aminoundecylsilica gel for the bonding of (+)-(18-crown-6)-2,3,11,12-tetracarboxylic acid as selector. The nature and concentration of the acidic and organic modifiers, the pH, the mobile phase composition, and the structures of the analytes substantially influenced the retention and resolution. Separations were carried out at constant mobile phase compositions in the temperature range 7–40 °C and the changes in enthalpy, Δ(ΔH°), entropy, Δ(ΔS°), and free energy, Δ(ΔG°) were calculated. The elution sequence was determined in some cases: the S enantiomers eluted before the R enantiomers.     

On double sine and cosine transforms,Lipschitz and Zygmund classes

We consider complex-valued functions f ∈ L 1 (R+2),where R +:= [0,∞),and prove sufficient conditions under which the double sine Fourier transform f ss and the double cosine Fourier transform f cc belong to one of the two-dimensional Lipschitz classes Lip(α,β) for some 0 α,β≤ 1;or to one of the Zygmund classes Zyg(α,β) for some 0 α,β≤ 2.These sufficient conditions are best possible in the sense that they are also necessary for nonnegative-valued functions f ∈ L 1 (R+2).     

Single-pass high-harmonic generation at 20.8 MHz repetition rate

We report on single-pass high-harmonic generation (HHG) with amplified driving laser pulses at a repetition rate of 20.8?MHz. An Yb:YAG Innoslab amplifier system provides 35?fs pulses with 20?W average power at 1030?nm after external pulse compression. Following tight focusing into a xenon gas jet, we observe the generation of high-harmonic radiation of up to the seventeenth order. Our results show that state-of-the-art amplifier systems have become a promising alternative to cavity-assisted HHG for applications that require high repetition rates, such as frequency comb spectroscopy in the extreme UV.     

A new enzymatic strategy for the preparation of (2R,3S)-3-phenylisoserine: a key intermediate for the Taxol side chain

Burkholderia cepacia lipase PS-IM catalysed the hydrolysis of racemic ethyl 3-amino-3-phenyl-2-hydroxypropionate with excellent enantioselectivity (E >200), when the reaction was performed with added H₂O as a nucleophile, in iPr₂O, at 50 °C. The hydrolysis of the less reactive enantiomeric ethyl 3-amino-3-phenyl-2-hydroxypropionate with 18% HCl afforded the corresponding enantiomerically pure (2R,3S)-3-amino-3-phenyl-2-hydroxypropionic acid hydrochloride, a key intermediate for the Taxol side chain.     

Triangular summability of two-dimensional Fourier transforms

We consider the triangular summability of two-dimensional Fourier transforms, and show that the maximal operator of the triangular-??-means of a tempered distribution is bounded from H _p (?²) to L _p (?²) for all 2/(2 + ??) < p ?? ??; consequently, it is of weak type (1,1), where 0 < ?? ?? 1 is depending only on ??. As a consequence, we obtain that the triangular-??-means of a function f ?? L ₁(?²) converge to f a.e. Norm convergence is also considered, and similar results are shown for the conjugate functions. Some special cases of the triangular-??-summation are considered, such as the Weierstrass, Picar, Bessel, Fejér, de la Vallée-Poussin, Rogosinski, and Riesz summations.     

Complex Hadamard matrices and equiangular tight frames

In this paper, we give a new construction of parametric families of complex Hadamard matrices of square orders, and connect them to equiangular tight frames. The results presented here generalize some of the recent ideas of Bodmann et al. [3] and extend the list of known equiangular tight frames. In particular, a (36, 21)-frame coming from a nontrivial cube root signature matrix is obtained for the first time.     

Duality results and inequalities with respect to Hardy spaces containing function sequences

With the help of two-parameter martingales and strong martingales Hardy spaces consisting of adapted function sequences are considered. The Hardy spaces generated by the square and by the conditional square functions and their dual spaces are investigated. An inequality due to Stein and Lepingle is extended to two parameters.This research was supported by the Hungarian Scientific Research Funds No. 2085 and No. 74189 as well as by DAAD, the lattest with a stay at the Ludwig-Maximilians-Universität in München.     

Side-chain chlorination of methylquinolines

Methylquinolines 1–4 were chlorinated by heating with phosphorus pentachloride in chlorobenzenes to side-chain halogen derivatives 5–14 . Methyl groups of compounds 1–4 can be chlorinated to chloromethyl, dichloromethyl or trichloromethyl groups depending on their positions and the reaction conditions.