Triads, Flocks of Conics and Q -(5,q)

We show that if an ovoid of Q (4,q),q even, admits a flock of conics then that flock must be linear. It follows that an ovoid of PG (3,q),q even, which admits a flock of conics must be an elliptic quadric. This latter result is used to give a characterisation of the classical example Q ^-(5,q) among the generalized quadrangles T ₃( ), where is an ovoid of PG (3q) and q is even, in terms of the geometric configuration of the centres of certain triads.     

Groups with infinitely many types of fixed subgroups

It is a theorem of Shor that ifG is a word-hyperbolic group, then up to isomrphism, only finitely many groups appear as fixed subgroups of automorphisms ofG. We give an example of a groupG acting freely and cocompactly on a CAT(0) square complex such that infinitely many non-isomorphic groups appear as fixed subgroups of automorphisms ofG. Consequently, Shor’s finiteness result does not hold if the negative curvature condition is relaxed to either biautomaticity or nonpositive curvature. D. T. Wise was supported by grants from FCAR and NSERC.     

Free group representations from vector-valued multiplicative functions,I

Let Γ denote a noncommutative free group and let Ω stand for its boundary. We construct a large class of unitary representations of Γ. This class contains many previously studied representations, and is closed under several natural operations. Each of the constructed representations is in fact a representation of Γ ⋉_λ C(Ω). We prove here that each of them is irreducible as a representation of Γ ⋉_λ C(Ω). Actually, as will be shown in further work, each of them is irreducible as a representation of Γ, or is the direct sum of exactly two irreducible, inequivalent Γ-representations. This research was supported by the Italian CNR.     

Isoperimetric inequalities for nilpotent groups

We prove that every finitely generated nilpotent group of class c admits a polynomial isoperimetric function of degree c + 1 and a linear upper bound on its filling length function.     

Synthesis of SnO2−x nanoparticles tuned between 0 x 1 in a premixed low pressure H2/O2/Ar flame

The transition from tin monoxide to tin dioxide is investigated by doping a low pressure premixed H₂/O₂/Ar flame with dilute concentrations of tetramethyl tin (TMT) Sn(CH₃)₄. The H₂/O₂ ratio was varied between 1.97 and 0.97; the reactor pressure was set to 30 mbar. The inlet gas velocity was kept constant and the precursor concentration was varied between 200 and 700 ppm. Mean particle diameters between 3 nm d_p 7 nm were measured using a particle mass spectrometer (PMS), while X-ray diffraction (XRD) and transmission electron microscope (TEM) analysis revealed information on crystal structure as well as morphology of the synthesized oxides. A gray SnO film was observed in the reactor at low oxygen concentrations, while for higher oxygen concentrations light yellow sub-stoichiometric tin oxides and white SnO₂ were obtained. Further analysis of the sub-stoichiometric oxides, using atomic electron spectroscopy AES revealed that SnO_2−x (0.2 x 0.6) was obtained. Furthermore, electrical characterization of all materials, deposited on interdigital capacitors, showed a decrease in the conductivity of the nanoparticles with increasing oxidation (decreasing x).     

Oganoboron compounds : XVIII. Chlorodiualkylaminophenylboranes

The synthesis and properties of a series of chlorodialkylaminophenylboranes, PhB(NR₂)CL, are reported and their ¹H and ¹³C NMR spectra discussed     

Carbodiimide-Driven Dimerization and Self-Assembly of Artificial,Ribose-Based Amphiphiles

The aqueous self-assembly of amphiphiles into aggregates such as micelles and vesicles has been widely investigated over the past decades with applications ranging from materials science to drug delivery. The combination of characteristic properties of nucleic acids and amphiphiles is of substantial interest to mimic biological self-organization and compartmentalization. Herein, we present ribose- and ribonucleotide-based amphiphiles and investigate their self-assembly as well as their fundamental reactivity. We found that various types of aggregates are formed, ranging in size from nanometers to micrometers and all amphiphiles exhibit aggregation-induced emission (AIE) in solution as well as in the solid state. We also observed that the addition of 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC) leads to rapid and selective dimerization of the amphiphiles into pyrophosphates, which decreases the critical aggregation concentration (CAC) by a factor of 25 when compared to the monomers. Since the propensity for amphiphile dimerization is correlated with their tendency to self-assemble, our results may be relevant for the formation of rudimentary compartments under prebiotic conditions.     

Synthesis of 13C and 2H Labeled Vinyl Pyruvate and Hyperpolarization of Pyruvate

The hyperpolarization of nuclear spins has enabled unique applications in chemistry, biophysics, and particularly metabolic imaging. Parahydrogen-induced polarization (PHIP) offers a fast and cost-efficient way of hyperpolarization. Nevertheless, PHIP lags behind dynamic nuclear polarization (DNP), which is already being evaluated in clinical studies. This shortcoming is mainly due to problems in the synthesis of the corresponding PHIP precursor molecules. The most widely used DNP tracer in clinical studies, particularly for the detection of prostate cancer, is 1-¹³C-pyruvate. The ideal derivative for PHIP is the deuterated vinyl ester because the spin physics allows for 100 % polarization. Unfortunately, there is no efficient synthesis for vinyl esters of β-ketocarboxylic acids in general and pyruvate in particular. Here, we present an efficient new method for the preparation of vinyl esters, including ¹³C labeled, fully deuterated vinyl pyruvate using a palladium-catalyzed procedure. Using 50 % enriched parahydrogen and mild reaction conditions, a ¹³C polarization of 12 % was readily achieved; 36 % are expected with 100 % pH₂. Higher polarization values can be potentially achieved with optimized reaction conditions.