Prime specialization in genus 0

For a prime polynomial , a classical conjecture predicts how often has prime values. For a finite field and a prime polynomial , the natural analogue of this conjecture (a prediction for how often takes prime values on ) is not generally true when is a polynomial in ( the characteristic of ). The explanation rests on a new global obstruction which can be measured by an appropriate average of the nonzero Möbius values as varies. We prove the surprising fact that this ``Möbius average,' which can be defined without reference to any conjectures, has a periodic behavior governed by the geometry of the plane curve .

The periodic Möbius average behavior implies in specific examples that a polynomial in does not take prime values as often as analogies with suggest, and it leads to a modified conjecture for how often prime values occur.

     

Expedient generation of patterned surface aldehydes by microfluidic oxidation for chemoselective immobilization of ligands and cells

An expedient and inexpensive method to generate patterned aldehydes on self-assembled monolayers (SAMs) of alkanethiolates on gold with control of density for subsequent chemoselective immobilization from commercially available starting materials has been developed. Utilizing microfluidic cassettes, primary alcohol oxidation of tetra(ethylene glycol) undecane thiol and 11-mercapto-1-undecanol SAMs was performed directly on the surface generating patterned aldehyde groups with pyridinium chlorochromate. The precise density of surface aldehydes generated can be controlled and characterized by electrochemistry. For biological applications, fibroblast cells were seeded on patterned surfaces presenting biospecifc cell adhesive (Arg-Glyc-Asp) RGD peptides.     

Poly(D,L-lactide-co-glycolide) dispersions containing pluronics: from particle preparation to temperature-triggered aggregation

In this work the preparation mechanism, properties and temperature-triggered aggregation of poly(D, L-lactide- co-glycolide) (PLGA) dispersions are investigated. The dispersions were prepared by interfacial deposition in aqueous solution containing Pluronic L62 (EO(6)PO(30)EO(6)) or F127NF (EO(101)PO(56)EO(101)), where EO and PO are ethylene oxide and propylene oxide, respectively. PLGA dispersions were also prepared in the absence of added Pluronic for comparison. The PLGA particles were characterized using SEM, photon correlation spectroscopy and electrophoretic mobility measurements. It was found that the hydrodynamic diameter (d) increased with PLGA concentration used in the organic solvent phase ( C PLGA(o) ). The value for d was proportional to C(PLGA)(o) (1/3). The value for d increased upon addition of 0.04 M NaNO(3) which demonstrated the importance of electrostatic interactions during particle formation. Electrophoretic mobility measurements were conducted as a function of pH and the data used to estimate the Pluronic layer thicknesses on the PLGA particles. The layer thickness was greatest for the PLGA particles prepared in the presence of Pluronic F127NF. PLGA dispersions containing Pluronic L62 exhibited temperature-triggered aggregation in the presence of 0.15 M NaNO(3). It was found that the critical temperature for dispersion aggregation (T(crit)) was comparable to the cloud point temperature ( T(cp)) for the parent Pluronic L62 solution. Conditions were established for achieving temperature-triggered aggregation at body temperature for PLGA particle/Pluronic L62 dispersions under physiological ionic strength and pH conditions. The PLGA/Pluronic L62 mixtures studied may have potential for use as injectable biodegradable implants for controlled release applications.     

Microfluidic etching and oxime-based tailoring of biodegradable polyketoesters

A straightforward, flexible, and inexpensive method to etch biodegradable poly(1,2,6-hexanetriol alpha-ketoglutarate) films is reported. Microfluidic delivery of the etchant, a solution of NaOH, can create micron-scale channels through local hydrolysis of the polyester film. In addition, the presence of a ketone in the repeat unit allows for prior or post chemoselective modifications, enabling the design of functionalized microchannels. Delivery of oxyamine tethered ligands react with ketone groups on the polyketoester to generate covalent oxime linkages. By thermally sealing an etched film to a second flat surface, poly(1,2,6-hexanetriol alpha-ketoglutarate) can be used to create biodegradable microfluidic devices. In order to determine the versatility of the microfluidic etch technique, poly(epsilon-caprolactone) was etched with acetone. This strategy provides a facile method for the direct patterning of biodegradable materials, both through etching and chemoselective ligand immobilization.     

High‐temperature catalysts for the production of α‐olefins based on iron(II) and iron(III) tridentate bis(imino)pyridine complexes modified by nitrilo group

Series of Fe(II) and Fe(III) tridentate bis(imino)pyridine complexes without nitrilo groups 2–6 and with nitrilo groups 7–13 were synthesized. According to X‐ray analysis, the introduction of nitrilo groups in para‐ and ortho‐positions tends to result in shorter axial Fe? N bonds. Both types of complexes, 2–6 and 9–13 , afforded very productive catalysts for the production of α‐olefins with higher K values and better linearity of Schultz–Flory distribution α‐olefins than the parent methyl substituted Fe(II) complex 1 . Noticeably, the complexes functionalized with a para‐nitrilo group 9–13 tend to make α‐olefins with higher K values of the Schultz–Flory distribution, more ideal distributions, and less of the heavier insoluble fractions of α‐olefins than corresponding nonsymmetrically substituted complexes without para‐nitrilo groups 2–6 . Statistically significant correlations were obtained between % solids of total α‐olefins and the blocked solid angle fraction in the +z hemisphere ( = 51.3%, p = 0.012) and between catalyst productivity and total blocked solid angle fraction ( = 43.5%, p = 0.023). The modest values of show that, while steric effects are significant, they are not the sole factor determining catalyst performance. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 585–611, 2008     

The elusive structure of CrCl(2): a combined computational and gas-phase electron-diffraction study

Chromium dichloride poses a challenge to the structural chemist. Its different forms of aggregation and association display all well-known structural distortions induced by vibronic interactions. The monomeric molecule has a Renner-Teller distorted bent geometry, the crystal exhibits strong Jahn-Teller distortion, and the oligomers have slightly distorted four-membered-ring structures due to the pseudo-Jahn-Teller effect. In this paper we report on the low-energy structures of the monomer and its clusters, Cr(2)Cl(4), Cr(3)Cl(6), and Cr(4)Cl(8), from unrestricted Kohn-Sham (broken-symmetry) density functional calculations. CrCl(2) was also investigated at higher level, including coupled-cluster and state-average CASSCF computations. The global minima of the gas-phase clusters consist of two-dimensional, antiferromagnetically coupled chains of CrCl(2) units forming four-membered, doubly bridged Cr(2)Cl(2) rings, closely resembling the solid-state structure of alpha-CrCl(2). Each Cr atom in these chains has spin quantum number S=2. This suggests that the CrCl(2) nucleation starts very early on the structural chain motif found in the solid. There is only a very small change in energy from the antiferromagnetically to the ferromagnetically coupled Cr atoms, which indicates little spin-coupling between the metal centers. There is an approximately constant change in energy, about 50 kcal mol(-1), with every new CrCl(2) unit during cluster formation. Information about the structure of these clusters was used in the re-analysis of high-temperature electron-diffraction data. The vapor at 1170 K contained about 77 % monomeric molecules, 19 % dimers, and a small amount of trimers. Monomeric CrCl(2) was found to be bent with a bond angle of 149(10) degrees, in good agreement with our computations, which resulted in a Renner-Teller distortion of the lowest-energy (5)Pi(g) electronic state into the bent (5)B(2) ground state. The vibrational spectrum of chromium dichloride is discussed and the thermodynamics of cluster formation from 1000-2000 K is examined.     

1,4-dicyanobenzene as a scaffold for the preparation of bimetallic actinide complexes exhibiting metal-metal communication

Reaction of two equivalents of [(C(5)Me(4)Et)(2)U(CH(3))(Cl)] (6) or [(C(5)Me(5))(2)Th(CH(3))(Br)] (7) with 1,4-dicyanobenzene leads to the formation of the novel 1,4-phenylenediketimide-bridged bimetallic organoactinide complexes [{(C(5)Me(4)Et)(2)(Cl)U}(2)(mu-{N==C(CH(3))-C(6)H(4)-(CH(3))C==N})] (8) and [{(C(5)Me(5))(2)(Br)Th}(2)(mu-{N==C(CH(3))-C(6)H(4)- (CH(3))C==N})] (9), respectively. These complexes were structurally characterized by single-crystal X-ray diffraction and NMR spectroscopy. Metal-metal interactions in these isovalent bimetallic systems were assessed by means of cyclic voltammetry, UV-visible/NIR absorption spectroscopy, and variable-temperature magnetic susceptibility. Although evidence for magnetic coupling between metal centers in the bimetallic U(IV)/U(IV) (5f(2)-5f(2)) complex is ambiguous, the complex displays appreciable electronic communication between the metal centers through the pi system of the dianionic diketimide bridging ligand, as judged by voltammetry. The transition intensities of the f-f bands for the bimetallic U(IV)/U(IV) system decrease substantially compared to the related monometallic ketimide chloride complex, [(C(5)Me(5))(2)U(Cl){-N==C(CH(3))-(3,4,5-F(3)-C(6)H(2))}] (11). Also reported herein are new synthetic routes to the actinide starting materials [(C(5)Me(4)Et)(2)U(CH(3))(Cl)] (6) and [(C(5)Me(5))(2)Th(CH(3))(Br)] (7) in addition to the syntheses and structures of the monometallic uranium complexes [(C(5)Me(4)Et)(2)UCl(2)] (3), [(C(5)Me(4)Et)(2)U(CH(3))(2)] (4), [(C(5)Me(4)Et)(2)U{-N==C(CH(3))-C(6)H(4)-C==N}(2)] (10), and 11.     

Human urinary metabolite profile of tea polyphenols analyzed by liquid chromatography/electrospray ionization tandem mass spectrometry with data-dependent acquisition

Tea is rich in polyphenols and has a variety of biological activities. In order to better understand the biological effects of tea constituents on human health, markers for their exposure and their metabolic fates are needed. Previously, we have characterized several catechin metabolites in the blood and urine, but more information on the metabolite profile of tea polyphenols is needed. In the present study, the human urinary metabolite profile of tea polyphenols was investigated using liquid chromatography/electrospray ionization tandem mass spectrometry with data-dependent acquisition. With data-dependent MS/MS analysis by collecting the MS2 and MS3 spectra of the most intense ions in the sample, we identified more than twenty metabolites of tea polyphenols from human urine samples. (-)-Epigallocatechin (EGC) glucuronide, methylated EGC glucuronide, methylated EGC sulfate, (-)-epicatechin (EC) glucruronide, EC sulfate, methylated EC sulfate, as well as the glucuronide and sulfate metabolites of the ring-fission metabolites of tea catechins, 5-(3',4',5'-trihydroxyphenyl)-gamma-valerolactone (M4), 5-(3',4'-dihydroxyphenyl)-gamma-valerolactone (M6) and 5-(3',5'-dihydroxyphenyl)-gamma-valerolactone (M6'), were the major human urinary metabolites of tea polyphenols. To our knowledge, this is the first report of the direct simultaneous analysis of the human urinary metabolite profile of tea polyphenols using single sample analysis. This method can also be used for thorough investigations of the metabolite profiles of many other dietary constituents.     

Ion mobility augments the utility of mass spectrometry in the identification of human hemoglobin variants

The global dispersion of hemoglobin variants through population migration has precipitated a need for their identification. A particularly effective mass spectrometry (MS)-based procedure involves analysis of the intact globin chains in diluted blood to detect the variant through mass anomalies, followed by location of the variant amino acid residue by direct analysis of the enzymatically digested globins. Here we demonstrate the use of ion mobility separation in combination with this MS procedure to reduce mass spectral complexity. In one example, the doubly charged tryptic peptide from a low abundance variant (4%) occurred at the same m/z value as a singly and a doubly charged interfering ion. In another example, the singly charged tryptic peptide from an alpha-chain variant (26%) occurred at the same m/z value as a doubly charged interfering ion. Ion mobility was used to separate the variant ions from the interfering ions, thus allowing the variant peptides to be observed and sequenced by tandem mass spectrometry.     

The synthesis of azadirachtin: a potent insect antifeedant

We describe in full the first synthesis of the potent insect antifeedant azadirachtin through a highly convergent approach. An O-alkylation reaction is used to unite decalin ketone and propargylic mesylate fragments, after which a Claisen rearrangement constructs the central C8-C14 bond in a stereoselective fashion. The allene which results from this sequence then enables a second critical carbon-carbon bond forming event whereby the [3.2.1] bicyclic system, present in the natural product, is generated via a 5-exo-radical cyclisation process. Finally, using knowledge gained through our early studies into the reactivity of the natural product, a series of carefully designed steps completes the synthesis of this challenging molecule.