Frobenius distributions of elliptic curves in short intervals on average

The Ramanujan Journal - For an elliptic curve $$E/{\mathbb {Q}}$$ , let $$a_p$$ denote the trace of its Frobenius endomorphism over $${\mathbb {F}}_p$$ , where p is a prime of good reduction for E....     

Zero cycles on conic fibrations and a conjecture of Bloch

Let X be a smooth projective surface over a number field k. Let (CH₀(X)) denote the Chow group of zero-cyles modulo rational equivalence on X. Let CH₀(X) be the subgroup of CH ₀(X) consisting of classes which vanish when going over to an arbitrary completion of k. Bloch put forward a conjecture asserting that this group is isomorphic to the Tate-Shafarevich group of a certain Galois module atttached to X. In this paper, we disprove this general conjecture. We produce a conic bundle X over an elliptic curve, for which the group (CH₀(X) is not zero, but the Galois-theoretic Tate-Shafarevich group vanishes.     

A predictive model for impact response of viscoelastic polymers in drop tests

We show for the first time that a classical Hookean viscoelastic constitutive law for rubbery materials can predict the impact forces and deflections measured with a commercial drop tester when a mass, or tup with a flat impacting surface is dropped onto a flat pad of commercial impact-absorbing rubber. The viscoelastic properties of the rubber, namely the relaxation times and strengths, are obtained by a standard rheological linear-oscillatory test, and the equation of momentum transfer is then solved, using these measured parameters, assuming a uniaxial deflection of the pad during the impact. Good agreement between measured and predicted forces and deflections is obtained for a series of various drop heights, tup masses, impact areas, and pad thicknesses, as long as the deflection of the pad relative to its thickness is small or modest (<50% or so), and as long as the area of the pad is less than or equal to that of the tup. When the pad area is greater than the tup, forces are higher than predicted, unless an empirical factor is introduced to account for the nonuniaxial stretching of the ring of material that extends outside of the impact area. These results imply that the impact-absorbing properties of a rubbery polymeric material can be assessed by simply examining the material's linear viscoelastic spectrum.     

Versatile new uranyl(VI) dihalide complexes supported by tunable organic amide ligands

A series of uranyl(VI) dihalide complexes UO2X2L2 (X = Cl, Br) supported by organic amide ligands (L = R'C(O)NR2; R' = i-Pr; R = i-Pr, i-Bu, s-Bu) offers the versatile combination of facile synthesis using benchtop methods, air-stable crystalline solids obtained in high yield, high solubility in common organic solvents and tunable steric/electronic properties.     

Synthesis of erythrinin A,a naturally occurring pyranoisoflavone

Erythrinin A ($\text{10}$) has been synthesised by the oxidative rearrangement of dihydropyranochalcone $\text{1}$ with thallium(III) nitrate (TTN) in trimethyl orthoformate (TMOF) to the dimethyl acetal $\text{2}$, followed by cyclisation to $\text{3}$, demethylation to $\text{6}$ and dehydrogenation. Compound $\text{10}$ could also be obtained from chalcone $\text{4}$ on similar rearrangement followed by cyclisation, demethoxymethylation and dehydrogenation. In another route, chalcone $\text{7}$ was oxidatively rearranged with TTN in TMOF, to $\text{8}$ which on treatment with HCl yielded $\text{10}$.     

Aqueous-phase ion solvation and the selectivity of anion exchange resins for monovalent ions

This research examines and quantifies the influence of ion solvation parameters on the affinity of monovalent anions for strong-base anion resins. A data set comprising resin selectivity coefficients and solvation parameters from the literature is statistically analyzed using correlation and multiple regression techniques. The affinity of monovalent anions for the resin phase correlated well to ionic radii. Solvation parameters such as the hydration number, and entropy, enthalpy and free energy of hydration are also strongly correlated to selectivity. Using the stepwise regression procedure on subsets of independent variables, the entropy of hydration, which characterizes the structure-influencing nature of ions in solution, is incorporated as the sole parameter in the predictive model for resin selectivity. The data are best correlated by the exponential form of the regression equation, and the physical meaning of the correlation is shown to be reasonable. A simple rule for categorizing ions as structure-makers and structure-breakers is proposed, and the results are consistent with conventional classifications.     

Supramolecular porphyrin-fullerene via 'two-point' binding strategy: axial-coordination and cation-crown ether complexation

A highly stable porphyrin-fullerene conjugate with defined distance and orientation, was formed using a newly developed 'two-point' binding strategy involving axial-coordination and cation-crown ether complexation; photochemical studies performed in benzonitrile revealed efficient charge separation and slow charge-recombination in the supramolecular complex.     

Backbone cleavages of [M - H](-) anions of peptides. Cyclisation of citropin 1 peptides involving reactions between the C-terminal [CONH](-) residue and backbone amide carbonyl groups. A new type of beta cleavage: a joint experimental and theoretical study

This paper reports the study of backbone cleavages in the collision-induced negative-ion mass spectra of the [M - H](-) anions of some synthetic modifications of the bioactive amphibian peptide citropin 1 (GLFDVIKKVASVIGGL-NH(2)). The peptides chosen for study contain no amino acid residues which could effect facile side-chain cleavage, i.e. Ser (-CH(2)O, side-chain cleavage) and Asp (-H(2)O) are replaced by Ala or Lys. We expected that such peptides should exhibit standard and pronounced peaks due to alpha cleavage ions (and to a lesser extent beta cleavage ions) in their collision-induced negative-ion spectra. This expectation was realised, but the spectra also contained peaks formed by a new series of cleavage anions. These are produced following cyclisation of the C-terminal CONH(-) moiety at carbonyl functions of amide groups along the peptide backbone; effectively transferring the NH of the C-terminal CONH(-) group to other amino acid residues. We have called the product anions of these processes beta' ions, in order to distinguish them from standard beta ions. Some beta' ions also fragment directly to some other beta' ions of smaller mass. The reaction coordinates of alpha,beta and beta' backbone processes have been calculated at the HF/6-31G*//AM1 level theory for simple model systems. The initial cyclisation step of the beta' sequence is barrierless and exothermic. Subsequent steps have a maximum barrier of +40 kcal mol(-1), with the overall reaction being endothermic by some 30 kcal mol(-1) at the level of theory used. These calculations take no account of the complexity of the conformationally flexible peptide system, and it is surprising that each of the two reacting centres can 'find' each other in such a large system.     

Electron depleted bis(methylene)cyclobutenes: sulfinyl and sulfonyl substitution

Double [2,3] sigmatropic rearrangements of bis(propargyl sulfenates) to bis(allenic sulfoxides) and of bis(propargyl sulfinates) to bis(allenic sulfones) are shown to be a convenient and effective method for the preparation of conjugated diallene systems bearing two electron withdrawing trihalomethyl sulfoxide or sulfone substituents either on C-1 and C-6, or on C-3 and C-4. Such substituents are further shown to facilitate cyclization to bis(methylene)cyclobutenes, and to stabilize the latter. The electron withdrawing group substitution on the exocyclic methylene extremities proved more effective than similar substitution on the endocyclic double bond.     

Macromolecular crystallography research at Trombay

Neutron diffraction studies of hydrogen positions in small molecules of biological interest at Trombay have provided valuable information that has been used in protein and enzyme structure model-building and in developing hydrogen bond potential functions. The new R-5 reactor is expected to provide higher neutron fluxes and also make possible smallangle neutron scattering studies of large biomolecules and bio-aggregates. In the last few years infrastructure facilities have also been established for macromolecular x-ray crystallography research. Meanwhile, the refinement of carbonic hydrases’ and lysozyme structures have been carried out and interesting results obtained on protein dynamics and structure-function relationships. Some interesting presynaptic toxin phospholipases have also been taken up for study.