On the Constructive Inverse Problem in Differential Galois Theory#

We give sufficient conditions for a differential equation to have a given semisimple group as its Galois group. For any group G with G ⁰ = G ₁ · ··· · G _r , where each G _i is a simple group of type A_?, C_?, D_?, E₆, or E₇, we construct a differential equation over C(x) having Galois group G.     

Intra‐strain Variability in the Effects of Temperature on UV‐B Sensitivity of Cyanobacteria

Stratospheric ozone depletion is mostly marked over the Antarctic and to a lesser extent over the Arctic, though recent reports have revealed that this also occurs at lower latitudes. Continued depletion of ozone in the lower stratosphere allows more UVR to reach the Earth's surface. Furthermore, it is projected that surface water temperatures will increase by between 0.2 and 2.0°C by the year 2060 and this will directly or indirectly influence algal growth. The interactions between environmental factors are complicated by the existence of different strains (ecotypes) of the same species that may respond differently. To understand the interactive effects of temperature and UV‐B on two strains of Anabaena circinalis, we investigated the damaging effects of UV‐B on cell numbers and photosynthetic characteristics and also examined the effect of temperature on the capacity of cells to recover from such stress. Both strains of A. circinalis responded differently in terms of survival, photosynthetic characteristics and recovery with interactions between temperature and UV‐B. This could be due to the variations in strain‐specific photoreactive mechanisms. This needs to be explored further including more strains and species before definitive conclusions can be reached about effects of global change on cyanobacteria generally.     

Stereoinversion of Unactivated Alcohols by Tethered Sulfonamides

The direct, catalytic substitution of unactivated alcohols remains an undeveloped area of organic synthesis. Moreover, catalytic activation of this difficult electrophile with predictable stereo‐outcomes presents an even more formidable challenge. Described herein is a simple iron‐based catalyst system which provides the mild, direct conversion of secondary and tertiary alcohols to sulfonamides. Starting from enantioenriched alcohols, the intramolecular variant proceeds with stereoinversion to produce enantioenriched 2‐ and 2,2‐subsituted pyrrolidines and indolines, without prior derivatization of the alcohol or solvolytic conditions.     

Ultrahigh-temperature regenerated gratings in boron-codoped germanosilicate optical fiber using 193 nm

Regenerated gratings seeded by type I gratings in boron-codoped germanosilicate optical fiber written with 193 nm are shown to withstand temperatures beyond 1000 degrees C.     

Maximum of the Characteristic Polynomial for a Random Permutation Matrix

Let P_N be a uniform random N × N permutation matrix and let χ_N(z) = det(zI_N − P_N) denote its characteristic polynomial. We prove a law of large numbers for the maximum modulus of χ_N on the unit circle, specifically, with probability tending to 1 as N → ∞ , for a numerical constant x₀ ≈ 0.652 . The main idea of the proof is to uncover a logarithmic correlation structure for the distribution of (the logarithm of) χ_N , viewed as a random field on the circle, and to adapt a well-known second-moment argument for the maximum of the branching random walk. Unlike the well-studied CUE field in which P_N is replaced with a Haar unitary, the distribution of χ_N(e^2πit) is sensitive to Diophantine properties of the point t . To deal with this we borrow tools from the Hardy-Littlewood circle method. © 2020 Wiley Periodicals LLC     

Mechanism from isotope effects

Abstract Isotope effects represent perhaps one of the most versatile tools available to investigators interested in the determination of reaction mechanism, particularly in the case of the mechanistic enzymologist. Interpretation of isotope effect data is somewhat more difficult for enzyme reactions, since the chemical or isotope-dependent step(s) is(are) normally not solely rate-limiting as they are for non-enzyme-catalyzed reactions. One can, however, take advantage of rate-limitation by multiple steps in an enzyme-catalyzed reaction to obtain information on a number of aspects of mechanism. In this paper, simple theory for the application of isotope effects to reaction mechanism is developed, and applied to organic reactions and those catalyzed by enzymes. Techniques used to measure isotope effects depend somewhat on the isotope used, that is radioisotope vs. stable isotope, or hydrogen isotope vs. heavier atoms. Techniques to be discussed include competitive and noncompetitive (or internal discrimination) measurements. In enzymecatalyzed reactions, information can be obtained on the order of addition of reactants and release of products, and this will be illustrated using the 6-phosphogluconate and alcohol dehydrogenase reactions. The use of multiple isotope effects can be used to distinguish between stepwise and concerted reactions, and this will be illustrated with the formate and glucose 6-phosphate dehydrogenase and malic enzyme reactions.     

Crystal structures of two isomeric oximes. (EE)-2-methyl-3-phenyl-3-thiocyanatopropenaldoxime and (Z)-5-methyl-6-phenyl-1,3-thiazin-2-one oxime

The crystal structure of two isomeric oximes, C₁₁N₁₀N₂OS have been studied by X-ray diffraction. The open-chain thiocyanato derivative is somewhat'less dense and crystallizes with the orthorhombic space group Pbcn;a,b,c=18.718(1), 10.601(3), 11.528(1) Å,Z=8. The heterocyclic isomer occurs as pseudo-orthorhombic (Cmma)twinned crystals of space group P2₁/n, a, b, c, =12.11(1), 7.46(1), 12.12(1) Å, 100.09(1)^o,Z=4. Twinning occurs as a result of the near-equality of the monoclinica andc cell constants.     

Synthesis, spectroscopy, and X-ray structures of fac-(CO)3(dppe)MnSC(S)H, fac-(CO)3(dppe)ReSC(S)H, fac-(CO)3(dppp)ReSC(S)H, and fac-(CO)3(dppb)ReSC(S)H

The monodentate dithioformato complexes, fac-(CO)₃(dppe)MnSC(S)H (1), fac- (CO)₃(dppe)ReSC(S)H (2), fac-(CO)₃(dppp)ReSC(S)H (3), and fac-(CO)₃ (dppb)ReSC(S)H (4), where dppe is 1,2-bis(diphenylphosphino)ethane, dppp is 1,3-bis(diphenylphosphino)propane, and dppb is 1,4-bis(diphenylphosphino)butane, were synthesized from the treatment of the corresponding hydrides, fac-(CO)₃ (P-P)MSC(S)H with CS₂. Compounds 1–4 crystallize in the monoclinic crystal system: for 1, space group = P2₁/c, a = 15.3139(3) Å, b = 9.7297(4) Å, c = 19.0991(6) Å, = 105.928(1), V = 2736.5 ų, Z = 4; for 2, space group = P2₁/c, a = 15.6395(8) Å, b = 9.8182(5) Å, c = 19.4153(11) Å, = 106.741(1), V = 2854.9(3) ų, Z = 4; for 3, space group = P2₁/n, a = 11.3570(10) Å, b = 19.465(2) Å, c = 15.5702(14) Å, = 104.776(2), V = 3328.3(5) ų, Z = 4; and for 4, space group = C2/c, a = 32.078(2) Å, b = 10.4741(6) Å, c = 19.0608(9) Å, = 94.315(2), V = 6386.1(6) ų, Z = 8.     

Flavylium chromophores as species markers for dragon's blood resins from Dracaena and Daemonorops trees

A simple and rapid liquid chromatographic method with diode-array UV-vis spectrophotometric detection has been developed for the authentication of dragon's blood resins from Dracaena and Daemonorops trees. Using this method it was discovered that the flavylium chromophores, which contribute to the red colour of these resins, differ among the species and could be used as markers to differentiate among species. A study of parameters, such as time of extraction, proportion of MeOH and pH, was undertaken to optimise the extraction of the flavyliums. This method was then used to make extracts from samples of dragon's blood resin obtained from material of known provenance. From the samples analysed 7,6-dihydroxy-5-methoxyflavylium (dracorhodin), 7,4'-dihydroxy-5-methoxyflavylium (dracoflavylium) and 7,4'-dihydroxyflavylium were selected as species markers for Daemonorops spp., Dracaena draco and Dracaena cinnabari, respectively. The chromatograms from these samples were used to build an HPLC-DAD database. The ability to discriminate among species of dragon's blood using the single marker compounds was compared with a principal components analysis of the chromatograms in the HPLC-DAD database. The results from the HPLC-DAD method based on the presence of these flavylium markers was unequivocal. The HPLC-DAD method was subsequently applied to 37 samples of dragon blood resins from the historical samples in the Economic Botany Collection, Royal Botanic Gardens, Kew. The method identified anomalies in how samples in this collection had been labelled. It is clear that the method can be used to evaluate the provenance of samples used in different areas of cultural heritage. It also could be used to monitor the trade of endangered species of dragon's blood and the species being used in complex formulations of traditional Chinese medicine.