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-accuracy theoretical study on the thermochemistry of several formaldehyde derivatives

In the case of several formaldehyde derivatives, with importance in atmospheric and combustion chemistry, the currently available thermochemical values suffer from considerably large uncertainties. In this study a high-accuracy theoretical model chemistry has been used to provide accurate thermochemical data including heats of formation at 0 and 298 K and standard molar entropies at 298 K for CF(2)O, FCO, HFCO, HClCO, FClCO, HOCO, and NH(2)CO. For most of the thermochemical quantities studied here, this investigation delivers the best available estimate.     

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.     

Weakly separative weakly commutative semigroups

A semigroup S is called a weakly commutative semigroup if, for every a,b∈S, there is a positive integer n such that (ab) ⁿ ∈Sa∩bS. A semigroup S is called archimedean if, for every a,b∈S, there are positive integers m and n such that a ⁿ ∈SbS and b ^m ∈SaS. It is known that every weakly commutative semigroup is a semilattice of weakly commutative archimedean semigroups. A semigroup S is called a weakly separative semigroup if, for every a,b∈S, the assumption a ²=ab=b ² implies a=b. In this paper we show that a weakly commutative semigroup is weakly separative if and only if its archimedean components are weakly cancellative. This result is a generalization of Theorem 4.16 of Clifford and Preston (The Algebraic Theory of Semigroups, Am. Math. Soc., Providence, 1961).     

Linear groups as right multiplication groups of quasifields

For quasifields, the concept of parastrophy is slightly weaker than isotopy. Parastrophic quasifields yield isomorphic translation planes but not conversely. We investigate the right multiplication groups of finite quasifields. We classify all quasifields having an exceptional finite transitive linear group as right multiplication group. The classification is up to parastrophy, which turns out to be the same as up to the isomorphism of the corresponding translation planes.     

3-Nets realizing a group in a projective plane

In a projective plane $\mathit{PG}(2,\mathbb{K})$ defined over an algebraically closed field $\mathbb{K}$ of characteristic 0, we give a complete classification of 3-nets realizing a finite group. An infinite family, due to Yuzvinsky (Compos. Math. 140:1614–1624, 2004), arises from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky (Adv. Math. 219:672–688, 2008), comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family. Urzúa’s 3-nets (Adv. Geom. 10:287–310, 2010) realizing the quaternion group of order 8 are the unique sporadic examples. If p is larger than the order of the group, the above classification holds in characteristic p>0 apart from three possible exceptions $\rm{Alt}_{4}$ , $\rm{Sym}_{4}$ , and $\rm{Alt}_{5}$ . Motivation for the study of finite 3-nets in the complex plane comes from the study of complex line arrangements and from resonance theory; see (Falk and Yuzvinsky in Compos. Math. 143:1069–1088, 2007; Miguel and Buzunáriz in Graphs Comb. 25:469–488, 2009; Pereira and Yuzvinsky in Adv. Math. 219:672–688, 2008; Yuzvinsky in Compos. Math. 140:1614–1624, 2004; Yuzvinsky in Proc. Am. Math. Soc. 137:1641–1648, 2009).