Equivariant Birch-Swinnerton-Dyer Conjecture for the Base Change of Elliptic Curves: An Example

Let E be an elliptic curve defined over Q and let K/Q be a finite Galois extension with Galois group G. The equivariant Birch-Swinnerton-Dyer conjecture for h(1)(E x(Q) K)(1) viewed as amotive over Q with coefficients in Q[G] relates the twisted L-values associated with E with the arithmetic invariants of the same. In this paper I prescribe an approach to verify this conjecture for a given data. Using this approach, we verify the conjecture for an elliptic curve of conductor 11 and an S-3-extension of Q.

A thermal molecular migration in the solid-state - structures of isomeric 5-amino-4-(2,6-dichlorophenyl)-1-(2-nitrophenyl)-1h-1,2,3-triazole (yellow form i) and 4-(2,6-dichlorophenyl)-5-(2-nitroanilino)-2h-1,2,3-triazole (red form-ii), c14h9cl2n5o2

Yellow form (I): Mr= 350.09, monoclinic, P2Jn, Z--4, a=9.525(1), b=14.762(1), c= 11.268(1),/t, fl= 107.82 (1) o , V= 1508.3 A 3 , Din(flotation in aqueous KI)= 1.539 (2), D x= 1.541 (2) g cm -3, #(Cu Ka, 2 = 1.5418 A) = 40.58 cm -~, F(000) = 712, T= 293 K, R = 8.8% for 2054 significant refections. Red form (II): Mr= 350.09, triclinic, Pi, Z=2, a=9.796(2), b= 10.750 (2), c= 7.421 (1)A, a= 95.29 (2), fl= 0108-2701/84/111901-05501.50 70.18 (1), y = 92-.76 (2) °, V= 731.9 A 3, Din(flotation in KI) = 1.585 (3), D x = 1.588 (3) g cm -3, ~t(Cu Ka, 2 = 1.5418/~) = 40.58 cm -1, F(000) = 356, T=293 K, R = 5.8% for 1866 significant reflections. There are no unusual bond distances or angles. The triazole and two phenyl rings are planar. On the basis of packing considerations the possibility of intermolecular interactions playing a role in the reactivity of the starting material is ruled out.

Facile synthesis of large area porous Cu2O as super hydrophobic yellow-red phosphors

By employing a thermal oxidation strategy, we have grown large area porous Cu2O from Cu foil. CuO nanorods are grown by heating Cu which were in turn heated in an argon atmosphere to obtain a porous Cu2O layer. The porous Cu2O layer is superhydrophobic and exhibits red luminescence. In contrast, Cu2O obtained by direct heating, is hydrophobic and exhibits yellow luminescence. Two more luminescence bands are observed in addition to red and yellow luminescence, corresponding to the recombination of free and bound excitons. Over all, the porous Cu2O obtained from Cu via CuO nanorods, can serve as a superhydrophobic luminescence/phosphor material.

Exfoliated graphite/titanium dioxide nanocomposites for photodegradation of eosin yellow

An improved photocatalyst consisting of a nanocomposite of exfoliated graphite and titanium dioxide (EG-TiO2) was prepared. SEM and TEM micrographs showed that the spherical TiO2 nanoparticles were evenly distributed on the surface of the EG sheets. A four times photocatalytic enhancement was observed for this floating nanocomposite compared to TiO2 and EG alone for the degradation of eosin yellow. For all the materials, the reactions followed first order kinetics where for EG-TiO2, the rate constant was much higher than for EG and TiO2 under visible light irradiation. The enhanced photocatalytic activity of EG-TiO2 was ascribed to the capability of graphitic layers to accept and transport electrons from the excited TiO2, promoting charge separation. This indicates that carbon, a cheap and abundant material, can be a good candidate as an electron attracting reservoir for photocatalytic organic pollutant degradation. (C) 2014 Elsevier B.V. All rights reserved.

A Comparative Assessment of Hand Preference in Captive Red Howler Monkeys, Alouatta seniculus and Yellow-Breasted Capuchin Monkeys, Sapajus xanthosternos

There are two major theories that attempt to explain hand preference in non-human primates-the `task complexity' theory and the `postural origins' theory. In the present study, we proposed a third hypothesis to explain the evolutionary origin of hand preference in non-human primates, stating that it could have evolved owing to structural and functional adaptations to feeding, which we refer to as the `niche structure' hypothesis. We attempted to explore this hypothesis by comparing hand preference across species that differ in the feeding ecology and niche structure: red howler monkeys, Alouatta seniculus and yellow-breasted capuchin monkeys, Sapajus xanthosternos. The red howler monkeys used the mouth to obtain food more frequently than the yellow-breasted capuchin monkeys. The red howler monkeys almost never reached for food presented on the opposite side of a wire mesh or inside a portable container, whereas the yellow-breasted capuchin monkeys reached for food presented in all four spatial arrangements (scattered, on the opposite side of a wire mesh, inside a suspended container, and inside a portable container). In contrast to the red howler monkeys that almost never acquired bipedal and clinging posture, the yellow-breasted capuchin monkeys acquired all five body postures (sitting, bipedal, tripedal, clinging, and hanging). Although there was no difference between the proportion of the red howler monkeys and the yellow-breasted capuchin monkeys that preferentially used one hand, the yellow-breasted capuchin monkeys exhibited an overall weaker hand preference than the red howler monkeys. Differences in hand preference diminished with the increasing complexity of the reaching-for-food tasks, i.e., the relatively more complex tasks were perceived as equally complex by both the red howler monkeys and the yellow-breasted capuchin monkeys. These findings suggest that species-specific differences in feeding ecology and niche structure can influence the perception of the complexity of the task and, consequently, hand preference.

Li2MnO3: a rare red-coloured manganese(IV) oxide exhibiting tunable red-yellow-green emission

An experimental assessment of Li2MnO3 has been conducted, in conjunction with related Mn(IV) oxides, to investigate its red colour and photoluminescence. Optical absorption spectra revealed strong band gap absorption, with a sharp edge at similar to 610 nm and a transparent region between similar to 610 and similar to 650 nm, giving rise to the red colour of this compound. Octahedral Mn(IV) ligand field transitions have been observed in the excitation spectra of Li2MnO3, corresponding both to Mn(IV) at ideal sites and displaced in Li sites in the rock salt-based layered structure of Li2MnO3. Optical excitation at ligand field transition energies produces tunable emission in the red-yellow-green region, rendering Li2MnO3 a unique Mn(IV) oxide. The honeycomb-ordered LiMn6] units in its structure are probably the origin of both the absorption and the photoluminescent properties of Li2MnO3.

Yellow-red luminescence in ZnO nanoparticles synthesized from zinc acetylacetonate phenanthroline

ZnO powders/thin films/coatings when excited by a suitable excitation source, usually yield green luminescence in the visible wavelength range along with characteristic ultra-violet emission. We report yellow-red emission from ZnO nanoparticles synthesized within 5 min of microwave irradiation by using zinc acetylacetonate phenanthroline as the starting precursor material. The emission is strongly dependent on the typical structure of the starting precursor for ZnO synthesis, where one phenanthroline moiety is attached with zinc acetylacetonate hydrate complex. These ZnO nanoparticles could be potentially suitable phosphor for white light generation when excited by a blue laser. In contrast, the ZnO nanoparticles obtained from zinc acetylacetonate by similar method yield weak green emission. (C) 2015 Elsevier B.V. All rights reserved.

Synthesis of novel poly[(2,5-dimethoxy-p-phenylene)vinylene] precursors having two eliminatable groups: An approach for the control of conjugation length

Poly[(2,5-dimethoxy-p-phenylene)vinylene] (DMPPV) of varying conjugation length was synthesized by selective elimination of organic soluble precursor polymers that contained two eliminatable groups, namely, methoxy and acetate groups. These precursor copolymers were in turn synthesized by competitive nucleophilic substitution of the sulfonium polyelectrolyte precursor (generated by the standard Wessling route) using methanol and sodium acetate in acetic acid. The composition of the precursor copolymer, in terms of the relative amounts of methoxy and acetate groups, was controlled by varying the composition of the reaction mixture during nucleophilic substitution. Thermal elimination of these precursor copolymers at 250 degrees C, yielded partially conjugated polymers, whose color varied from light yellow to deep red. FT-IR studies confirmed that, while essentially all the acetate groups were eliminated, the methoxy groups were intact and caused the interruption in conjugation. Preliminary photoluminescence studies of the partially eliminated DMPPV samples showed a gradual shift in the emission maximum from 498 to 598 nm with increasing conjugation lengths, suggesting that the color of LED devices fabricated from such polymers can, in principle, be fine-tuned.

Studies in metal-ammonia reduction-5: Reduction and reductive methylation of some naphthoic acids

Birch reductio and reductive methylations of some substituted naphtholic acids have been examined. The factors influencing the mechanism of reduction process have been discussed. Some of the reduced naphthoic acids are useful synthons for synthesis.

Thermodynamic properties of Pb2PtO4 and PbPt2O4 and phase equilibria in the system Pb–Pt–O

The compounds Pb2PtO4 and PbPt2O4 were synthesized from an intimate mixture of yellow PbO and Pt metal powders by heating under pure oxygen gas at 973 K for periods up to 600 ks with intermediate grinding and recompacting. Both compounds were found to decompose on heating in pure oxygen to PbO and Pt, apparently in conflict with the requirements for equilibrium phase relations in the ternary system Pb–Pt–O. The oxygen chemical potential corresponding to the three-phase mixtures, Pb2PtO4 + PbO + Pt and PbPt2O4 + PbO + Pt were measured as a function of temperature using solid-state electrochemical cells incorporating yttria-stabilized zirconia as the solid electrolyte and pure oxygen gas at 0.1 MPa pressure as the reference electrode. The standard Gibbs free energies of formation of the ternary oxides were derived from the measurements. Analysis of the results indicated that the equilibrium involving three condensed phases Pb2PtO4 + PbO + Pt is metastable. Under equilibrium conditions, Pb2PtO4 should have decomposed to a mixture of PbO and PbPt2O4. Measurement of the oxygen potential corresponding to this equilibrium decomposition as a function of temperature indicated that decomposition temperature in pure oxygen is 1014(±2) K. This was further confirmed by direct determination of phase relations in the ternary Pb–Pt–O by equilibrating several compositions at 1023 K for periods up to 850 ks and phase identification of quenched samples using X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS). Only one ternary oxide PbPt2O4 was stable at 1023 K under equilibrium conditions. Alloys and intermetallic compounds along the Pb–Pt binary were in equilibrium with PbO.

Studies in metal-ammonia reduction. Part 4. Reduction and reductive methylation of 7-methoxy-3,4-dihydrophenanthren-1(2H)-one and 7-methoxy-1,2-dihydrophenanthren-4(3H)-one

Birch reduction and reductive methylations of the title compounds have been investigated. 7-Methoxy-3,4-dihydrophenanthren-1(2H)-one (2) yields the cis-3,4,9,10,11,12-hexahydro-derivative (15) while the 7-methoxy-1,2-dihydrophenanthren-4(3H)-one (5) is reduced to the corresponding 1,2,9,10-tetrahydro-derivative (7). The factors influencing the mechanism of the reduction process have been discussed. The reductive methylation products of the ketone (2) are useful substrates in the synthesis of 9-methyl steroids.

Strategies of synthesis of aromatic polyketides using cyclohexa-1,4-and-1,3-dienes in Alder Rickett reactions

Cyclohexa-1, 4-dienes with appropriate substituents, obtained by birch reduction of the substituted benzene, react directly with derivatives of propiolic ester or aldchyde to yield aromatic polyketides. The following compounds have been synthesized; mycophenolic acid, nidulol methyl other, the root growth hormone 3, 5-dihydroxy-2-formyl-4-mythyl-benzoic acid, antibiotic DB 2073, the macrocyclic lactones lasiodiplodin and dihydrozearalenone and the biphenyl derivatives alternario and altenusin. Polyketide anthraquinones can be made from naphthoquinone precursors.

Studies on an enzyme reacting with isoniazid fromMycobacterium tuberculosis H37Rv

Mycobacterium tuberculosis H37Rv possesses an enzyme (referred to as ‘Y enzyme’) which catalyses in the presence of INH and NAD, the formation of a product, which turns yellow on acidification. The requirements for the reaction, such as enzyme concentration, INH concentration, etc., have been standardized. The substrate specificity of the enzyme with respect to INH and NAD has been determined. The reaction is specific for the INH-sensitive strain and is totally absent in INH-resistant strains. Furthermore, the ‘Y enzyme’ shows some characteristic features of a peroxidase in its requirement for oxygen and sensitivity to inhibition by various reagents. The requirements of this enzyme which is involved in the action of isoniazid inM. tuberculosis H37Rv is described for the first time.

Condensed phase reactions in solid propellants

The paper investigates the cause for the difference between differential scanning calorimetric results and mass spectrometric studies on polystyrene (PS) ammonium perchlorate (AP) propellants as related to the method of preparation of the propellant and the difference in experimental conditions by the use of mass spectrometry. Sufficient time is given for the product sublimates to interact with each other and attain equilibrium. It is shown that the propellant decomposition is a nonadditive phenomenon and that even a physical mixture of AP and PS does not yield additive decomposition products of its components. Results on the identification of a yellow compound containing chlorine in the bulk of the propellant suggest a condensed phase reaction. The occurrence of the reaction in the porous condensed phase of the propellant may explain the larger exothermicity of the propellant compared to the additive heats of decomposition of its components.