Analogue of the degree conjecture over function fields

Under a certain assumption, similar to Manin's conjecture, we prove an upper bound on the degree of modular parametrizations of elliptic curves by Drinfeld modular curves, which is the function field analogue of the conjectured bound over the rational numbers.

     

Oligonucleotide Analogues with Integrated Bases and Backbone. Part 14

The self‐complementary tetrameric propargyl triols 8, 14, 18 , and 21 were synthesized to investigate the duplex formation of self‐complementary, ethynylene‐linked UUAA, AAUU, UAUA, and AUAU analogues with integrated bases and backbone (ONIBs). The linear synthesis is based on repetitive Sonogashira couplings and C‐desilylations (34–72% yield), starting from the monomeric propargyl alcohols 9 and 15 and the iodinated nucleosides 3, 7, 11 , and 13 . Strongly persistent intramolecular H‐bonds from the propargylic OH groups to N(3) of the adenosine units prevent the gg‐type orientation of the ethynyl groups at C(5′). As such, an orientation is required for the formation of cyclic duplexes, this H‐bond prevents the formation of duplexes connected by all four base pairs. However, the central units of the UAUA and AAUU analogues 18 and 14 associate in CDCl₃/(D₆)DMSO 10 : 1 to form a cyclic duplex characterized by reverse Hoogsteen base pairing. The UUAA tetramer 8 forms a cyclic UU homoduplex, while the AUAU tetramer 21 forms only linear associates. Duplex formation of the O‐silylated UUAA and AAUU tetramers is no longer prevented. The self‐complementary UUAA tetramer 22 forms Watson–Crick‐ and Hoogsteen‐type base‐paired cyclic duplexes more readily than the sequence‐isomeric AAUU tetramer 23 , further illustrating the sequence selectivity of duplex formation.     

Molar volumes and ion pairing of lithium halides in alcohols

The concentration dependence of the apparent molar volumes of lithium halides (and electrolytes in general) in alcohols (and solvents permitting association in general) is, in the first instance, due to changes in the degree of association and to the inherent difference between the apparent molar volumes of the ions and of the ion pairs. Previous publications on the molar volumes of electrolytes in organic solvents, disregarding altogether ion pairing, appear to be incorrect. Data from the literature for lithium chloride and lithium bromide in normal primary alcohols and several branched alcohols from C₁ to C₈ and data from our laboratory for lithium halides in 1-hexanol and 2-ethyl-1-hexanol served for the determination of φ _V and φ _E . Electrical and structural contributions to the values of these functions for the ions and for the ion pairs are discussed.     

Fractional Power Series and Pairings on Drinfeld Modules

Let be an algebraically closed field containing which is complete with respect to an absolute value . We prove that under suitable constraints on the coefficients, the series converges to a surjective, open, continuous -linear homomorphism whose kernel is locally compact. We characterize the locally compact sub--vector spaces of which occur as kernels of such series, and describe the extent to which determines the series. We develop a theory of Newton polygons for these series which lets us compute the Haar measure of the set of zeros of of a given valuation, given the valuations of the coefficients. The ``adjoint' series converges everywhere if and only if does, and in this case there is a natural bilinear pairing

which exhibits as the Pontryagin dual of . Many of these results extend to non-linear fractional power series. We apply these results to construct a Drinfeld module analogue of the Weil pairing, and to describe the topological module structure of the kernel of the adjoint exponential of a Drinfeld module.

     

Unusual ion pairs and their relationship to acid ionization

Osmotic and activity coefficients, determined from isopiestic measurements, are presented for aqueous solutions of eight tetramethylguanidinium salts. It is proposed that both hydronium and tetramethylguanidinium ions are capable of forming stable ion pairs with many anions by means of bridged hydrogens forming six-membered rings and that these ion pairs are stable in rather dilute aqueous solutions.     

Effects of Strong Ion‐Pairing on the Electrochemical Reduction of Cyclooctatetraene in Tetrahydrofuran in the Presence of Lithium Ion. Peak Coalescence Does Not Imply Potential Inversion

The first study of the voltammetric reduction of cyclooctatetraene (COT) in tetrahydrofuran (THF) in the presence of lithium ion is reported. A single wave is observed at ?2.23 V vs. Ag/0.1 M AgNO₃. Density functional calculations have been carried out on a variety of COT/Li/THF species in order to clarify the nature and role of ion pairing in this system. The dominant species in solution are the COT/Li/(THF)₂ anion radical and the COT/Li₂/(THF)₄ dianion. Computer simulations have been carried out to further understand the effects of ion pairing on the reduction. The simulations show that coalescence of two waves into one can occur in the presence of strong ion pairing even when the second reduction potential is negative of the first.     

Ion Association in Lanthanide Chloride Solutions

A better understanding of the solution chemistry of the lanthanide (Ln) salts in water would have wide ranging implications in materials processing, waste management, element tracing, medicine and many more fields. This is particularly true for minerals processing, given governmental concerns about lanthanide security of supply and the drive to identify environmentally sustainable processing routes. Despite much effort, even in simple systems, the mechanisms and thermodynamics of Ln^III association with small anions remain unclear. In the present study, molecular dynamics (MD), using a newly developed force field, provide new insights into LnCl₃(aq) solutions. The force field accurately reproduces the structure and dynamics of Nd³⁺, Gd³⁺ and Er³⁺ in water when compared to calculations using density functional theory (DFT). Adaptive-bias MD simulations show that the mechanisms for ion pairing change from dissociative to associative exchange depending upon cation size. Thermodynamics of association reveal that whereas ion pairing is favourable, the equilibrium distribution of species at low concentration is dominated by weakly bound solvent-shared and solvent-separated ion pairs, rather than contact ion pairs, reconciling a number of contrasting observations of Ln^III–Cl association in the literature. In addition, we show that the thermodynamic stabilities of a range of inner sphere and outer sphere coordination complexes are comparable and that the kinetics of anion binding to cations may control solution speciation distributions beyond ion pairs. The techniques adopted in this work provide a framework with which to investigate more complex solution chemistries of cations in water.     

Conductance of tetraalkylammonium salts in 2-butanone from −45 to 25°C

Interactions of three types of tetraalkylammonium cations (tetrapropyltetrabutyl-and tri-isoamylbutyl- ammonium) with perchlorate and tetraphenylborate anions were studied by the conductivity method in 2-butanone from –45°C to 25°C. Conductance data obtained for diluted solutions (5×10^–5 – 2×10^–3 mol-dm^–3) were used to calculate the limiting molar conductivities and associationconstants. The conductance equation of Fuoss-Hsia including the Chen term and the chemical model assumption were applied. Limiting ion conductivities were calculated assuming equal limiting conductivities of the i-Am₃BuN⁺ and BPh ₄ ^– ions at all temperatures. Gibbs energies and entropies of ion pair formation, calculated from the dependence of association constants on temperature, are presented including the contributions due to short-range forces.     

Artificial Genetic Sets Composed of Size‐Expanded Base Pairs

We describe in this Minireview the synthesis, properties, and applications of artificial genetic sets built from base pairs that are larger than the natural Watson–Crick architecture. Such designed systems are being explored by several research groups to investigate basic chemical questions regarding the functions of the genetic information storage systems and thus of the origin and evolution of life. For example, is the terrestrial DNA structure the only viable one, or can other architectures function as well? Working outside the constraints of purine–pyrimidine geometry provides more chemical flexibility in design, and the added size confers useful properties such as high binding affinity and helix stability as well as fluorescence. These features are useful for the investigation of fundamental biochemical questions as well as in the development of new biotechnological, biomedical, and nanostructural tools and methods.