Computing automorphisms of abelian number fields

Let be an abelian number field of degree . Most algorithms for computing the lattice of subfields of require the computation of all the conjugates of . This is usually achieved by factoring the minimal polynomial of over . In practice, the existing algorithms for factoring polynomials over algebraic number fields can handle only problems of moderate size. In this paper we describe a fast probabilistic algorithm for computing the conjugates of , which is based on -adic techniques. Given and a rational prime which does not divide the discriminant of , the algorithm computes the Frobenius automorphism of in time polynomial in the size of and in the size of . By repeatedly applying the algorithm to randomly chosen primes it is possible to compute all the conjugates of .

     

Sequence and phosphorylation level determination of two donkey β‐caseins by mass spectrometry

Two coeluting components, with experimentally measured M_r values of 25529 and 24606 Da, were identified by reversed‐phase high‐performance liquid chromatography (RP‐HPLC) and mass spectrometric analysis in the dephosphorylated casein fraction of a milk sample collected from an individual donkey belonging to the Ragusano breed of the east of Sicily. By coupling enzymatic digestions, matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry (MALDI‐TOF MS) and RP‐HPLC/nano‐electrospray ionization tandem mass spectrometry (nESI‐MS/MS) analysis, the two proteins were identified as donkey β‐CNs and their sequences characterized completely, using the two known β‐CNs from mare as references. The two donkey β‐CNs, showing a mass difference of 923 Da, differ by the presence of the domain E²⁷SITHINK³⁴ in the full‐length component (M_r 25529 Da). In comparison with the mare's β‐CNs used as reference, they present nine amino acid substitutions: L→S³⁷, R→H⁵², S→N⁸¹, P→V⁸⁴, L→V⁹¹, R→Q²⁰³, P→L/I²⁰⁶, L→F²¹⁰ and A→P²¹⁹. Together, these substitutions account for the increase of 18 Da in the M_r of the donkey β‐CNs with respect to the counterparts from the mare. The molecular mass determination by ESI‐MS for the phosphorylated proteins showed that the full‐length component was composed of highly multi‐phosphorylated isoforms with five to seven phosphate groups. By analogy with the homologous mare's β‐CNs, the full‐length (226 amino acids) β‐CN was termed variant A, whereas the shorter (218 amino acids) β‐CN was termed variant A^Δ5. Copyright © 2009 John Wiley & Sons, Ltd.     

Carbon-13 NMR characterisation of carboxyl derivatives of 1-ureidopyrroles

1-Ureido-5-methyl-2,3-dicarbethoxypyrrole under acidic conditions afforded different partially hydrolyzed or decarboxylated products. It has been possible to characterize two isomeric monoethyl esters of dicarboxylic acids of 1-ureidopyrroles by proton gated decoupled carbon-13 nmr spectra on the basis of multiplicities of the carbonyl carbons resonances.     

Mononuclear heterocyclic rearrangement. Note I. Kinetic study of the rearrangement of the phenylhydrazone of 3-benzoyl-5-phenyl-1,2,4-oxadiazole into 2,5-diphenyl-4-benzoylamino-1,2,3-triazole

The rates of the mononuclear heterocyclic rearrangement of the phenylhydrazone of 3-benzoyl-5-phenyl-1,2,4-oxadiazole (1) into 2,5-diphenyl-4-benzoylamino-1,2,3-triazole (II) have heen measured in dioxane/water (50:50, v:v) in the range of pS⁺ 3.8–12.2 at various temperatures and the activation parameters determined. On the basis of the results obtained, we present evidence for the occurrence of two different types of reaction: the first, base-catalyzed; the second, pS⁺ -independent. In the base-catalyzed range the catalysis is of the general type.     

Multielemental,Nutritional, and Proteomic Characterization of Different Lupinus spp. Genotypes: A Source of Nutrients for Dietary Use

Among grain pulses, lupins have recently gained considerable interest for a number of attractive nutritional attributes relating to their high protein and dietary fiber and negligible starch contents. The seeds of Lupinus albus (cv. Multitalia and Luxor, and the Modica ecotype); L. luteus (cv. Dukat, Mister, and Taper); and L. angustifolius (cv. Sonet) analyzed in this study were deposited within the germplasm collection of the Research Centre for Cereal and Industrial Crops of Acireale and were sowed in East Sicily in 2013/14. The collected seeds were analyzed for their multielemental micro- and macronutrient profiles, resulting in a wide variability between genotypes. Lupin seed flour samples were subjected to a defatting process using supercritical CO₂, with oil yields dependent on the species and genotype. We determined the fatty acid profile and tocopherol content of the lupin oil samples, finding that the total saturated fatty acid quantities of different samples were very close, and the total tocopherol content was about 1500.00 µg/g FW. The proteomic analysis of the defatted lupin seed flours showed substantial equivalence between the cultivars of the same species of Lupinus albus and L. luteus. Moreover, the L. angustifolius proteome map showed the presence of additional spots in comparison to L. albus, corresponding to α-conglutins. Lupin, in addition to being a good source of mineral elements, also contributes vitamin E and, thanks to the very high content of gamma-tocopherols, demonstrates powerful antioxidant activity.     

The crystal and molecular structure of the tetraethylammonium salt of tetrahydridopentadecacarbonyltetrarhenate(2−) in two crystallographic forms

The structure of the title compound, (NEt₄)₂[H₄Re₄(CO)₁₅], is reported in two crystallographic modifications, I and II. Both forms axe monoclinic and the cell constants are as follows: I, a 11.355(2), b 21.204(4), c 17.416(3) Å, β 94.15(2)°, space group P2₁/c; II, a 21.831(4), b 17.584(3), c 11.446(2) Å, β 96.02(2)°, space group P2₁,/n. Two sets of 3042 (I) and 2870 (II) independent diffraction intensities, collected by counter methods, were used for the solution and refinement of the two structures. The final conventional R factors have values 5.5% (I) and 6.3% (II), respectively. The crystal packings are compared, showing different conformations of the (NEt₄)⁺ cations. The anions contain a tetrametal cluster formed by an isosceles triangle plus an apically bound metal atom; the carbonyl groups are all terminally bonded to the rhenium atoms. Some differences, present both in the metal atom clusters and in the carbonyl dispositions, are discussed and compared with a third, previously reported, crystallographic modification of the same compound.     

Isoperimetric inequalities for an ergodic stochastic control problem

In this paper we deal with blow-up solutions to an elliptic equation with a nonlinear gradient term. The problem under consideration can be seen as the ergodic limit of a stochastic control problem with state constraints. It is well known that it has a solution only when a parameter which appears in the equation assumes a particular value known as ergodic constant. For such a constant many properties similar to those of an eigenvalue hold true. We show that a Faber–Krahn inequality can be stated for the ergodic constant and that for the corresponding solution a comparison result in terms of the solution to a symmetrized problem can be proved.