Equidistribution of Heegner points and ternary quadratic forms

We prove new equidistribution results for Galois orbits of Heegner points with respect to single reduction maps at inert primes. The arguments are based on two different techniques: primitive representations of integers by quadratic forms and distribution relations for Heegner points. Our results generalize an equidistribution result with respect to a single reduction map established by Cornut and Vatsal in the sense that we allow both the fundamental discriminant and the conductor to grow. Moreover, for fixed fundamental discriminant and variable conductor, we deduce an effective surjectivity theorem for the reduction map from Heegner points to supersingular points at a fixed inert prime. Our results are applicable to the setting considered by Kolyvagin in the construction of the Heegner points Euler system.     

Spin structure of antiprotonic helium in a magnetic field

The spin structure of the (37,35) energy level of antiprotonic helium-4 in permanent homogenous external magnetic field has been calculated in first order of perturbation theory. For weak magnetic fields the effect is observed as an additional broadening of the spectral lines. For magnetic fields of the order of kG and higher, the magnetic and hyperfine interactions become comparable to each other, and the hyperfine spectrum is rearranged.     

Spongipyran synthetic studies. Evolution of a scalable total synthesis of (+)-spongistatin 1

Three syntheses of the architecturally complex, cytotoxic marine macrolide (+)-spongistatin 1 (1) are reported. Highlights of the first-generation synthesis include: use of a dithiane multicomponent linchpin coupling tactic for construction of the AB and CD spiroketals, and their union via a highly selective Evans boron-mediated aldol reaction en route to an ABCD aldehyde; introduction of the C(44)-C(51) side chain via a Lewis acid-mediated ring opening of a glucal epoxide with an allylstannane to assemble the EF subunit; and final fragment union via Wittig coupling of the ABCD and EF subunits to form the C(28)-C(29) olefin, followed by regioselective Yamaguchi macrolactonization and global deprotection. The second- and third-generation syntheses, designed with the goal of accessing 1 g of (+)-spongistatin 1 (1), maintain both the first-generation strategy for the ABCD aldehyde and final fragment union, while incorporating two more efficient approaches for construction of the EF Wittig salt. The latter combine the original chelation-controlled dithiane union of the E- and F-ring progenitors with application of a highly efficient cyanohydrin alkylation to append the F-ring side chain, in conjunction with two independent tactics to access the F-ring pyran. The first F-ring synthesis showcases a Petasis-Ferrier union/rearrangement protocol to access tetrahydropyrans, permitting the preparation of 750 mg of the EF Wittig salt, which in turn was converted to 80 mg of (+)-spongistatin 1, while the second F-ring strategy, incorporates an organocatalytic aldol reaction as the key construct, permitting completion of 1.009 g of totally synthetic (+)-spongistatin 1 (1). A brief analysis of the three syntheses alongside our earlier synthesis of (+)-spongistatin 2 is also presented.     

The photocatalytic degradation of 17α-ethynylestradiol by pure and carbon nanotubes modified TiO<Subscript>2</Subscript> under UVC illumination

Commercial product Degussa TiO2 P25, sol-gel produced TiO₂ and TiO₂ modified by carbon nanotubes addition (5% of the TiO₂ mass) are tested as photocatalysts for the degradation of endocrine disrupting compound 17α-ethynylestradiol (1 μM aqueous solution). The molecular and crystal structure, phase composition, crystallite size, specific surface area, pore average diameter, their area and volume distribution, morphology, IR and UV/Vis spectra of the catalysts are characterized. HPLC is used for estrogen analysis. The sorption ability and photocatalytic activity (measured by degradation rate constant and percentage of the pollutant conversion) of the catalysts under UV (17 W, emission maximum at 254 nm) irradiation is determined. Full destruction of the pollutant is reached after 30 min irradiation in presence of Degussa P25. The performance of some of the catalysts is compared with literature data for their activity under 365 nm-illumination.      

Synthesis, X-ray structural analysis, and cytotoxic activity of some new androstane d-homo lactone derivatives

A series of d-homo lactones 4?C10 from dehydroepiandrosterone 1 via 16-hydroximino derivatives 2 and 3 were synthesized. The d-homo lactone 4 was transformed by the Oppenauer oxidation to obtain compound 5. The (Z)-2-hydroxymethylene-4-en-3-one compound 6, was obtained through reaction of 4-en-3-one compound 5 with ethyl formate and sodium hydride. The epoxides 8 and 9 were prepared from compound 7 by oxidation with m-chloroperbenzoic acid. Compound 10 was obtained by treating epoxides 8 and 9 with chromium(VI)-oxide. The structure of compounds 6 and 10 were confirmed by X-ray structural analysis. These derivatives were screened for antitumor activity against three tumor cell lines (human breast adenocarcinoma ER+, MCF-7, human breast adenocarcinoma ER?, MDA-MB-231, prostate cancer AR?, PC-3), and one human non-tumor cell line, MRC-5. Compounds 4, 7, 8, and 10 exhibited significant antitumor activity against MDA-MB-231 cells, while compound 5 showed strong cytotoxicity against MDA-MB-231. No compounds displayed toxicity against MRC-5 cells.     

Comparative chemical composition and antioxidant activity of Calamintha nepeta (L.) Savi subsp. glandulosa (Req.) Nyman and Calamintha grandiflora (L.) Moench (Labiatae)

The two studied Calamintha species showed different polyphenolic content and sterol composition. Calamintha grandiflora possessed twice the polyphenolic content of Calamintha nepeta subsp. glandulosa, while the latter contained a higher number of sterols. Among them, stigmast-5-en-3β-ol was found to be the major constituent. The methanolic extract of C. grandiflora was more potent than the C. nepeta subsp. glandulosa methanolic extract in a DPPH assay, while the activity of the C. grandiflora EtOAc fraction was weaker than its C. nepeta subsp. glandulosa counterpart. Fractions of C. nepeta subsp. glandulosa showed higher activity using a β-carotene bleaching test. The petrol ether fraction of C. grandiflora showed significant inhibition of NO production.     

High-precision calculation of the hyperfine structure of the HD+ ion

High-precision laser spectroscopy of ultracold hydrogen molecular ions has the potential of improving the precision of the electron-to-proton mass ratio. An accurate knowledge of the spin structure of the transition is required in order to permit precise comparison with experimental transition frequencies. We calculate with a relative accuracy of the order of O(alpha2) the hyperfine splitting of the rovibrational states of HD+ with orbital momentum L相似文献