Twists of genus three curves over finite fields

In this article we recall how to describe the twists of a curve over a finite field and we show how to compute the number of rational points on such a twist by methods of linear algebra. We illustrate this in the case of plane quartic curves with at least 16 automorphisms. In particular we treat the twists of the Dyck–Fermat and Klein quartics. Our methods show how in special cases non-Abelian cohomology can be explicitly computed. They also show how questions which appear difficult from a function field perspective can be resolved by using the theory of the Jacobian variety.     

Sol–gel routes for microporous zirconia and titania membranes

Zirconia and titania nanoparticle sols were prepared, using either ligand-based precursor stabilization or acid stabilization routes. These sols were used to prepare microporous coatings on γ-alumina substrates. The acetylacetonate-based particles have very small hydrodynamic diameters (1–2 nm), which lead to sol intrusion into the supports. As a result no appropriate membrane layer was formed. A microemulsion-based zirconia sol leads to a membrane that was selective in pervaporation dehydration of a water/n-butanol mixture. An optimized membrane showed stable separation performance for 120 days with a high selectivity toward water. Permporometry and gas permeation results on a titania membrane based on an acid-stabilized sol not only show microporosity, but also a significant contribution from defect flow.     

Asymptotic Tail Probabilities of Sums of Dependent Subexponential Random Variables

In this paper we study the asymptotic behavior of the tail probabilities of sums of dependent and real-valued random variables whose distributions are assumed to be subexponential and not necessarily of dominated variation. We propose two general dependence assumptions under which the asymptotic behavior of the tail probabilities of the sums is the same as that in the independent case. In particular, the two dependence assumptions are satisfied by multivariate Farlie-Gumbel-Morgenstern distributions.     

Implicit a posteriori error estimates for the Maxwell equations

An implicit a posteriori error estimation technique is presented and analyzed for the numerical solution of the time-harmonic Maxwell equations using Nédélec edge elements. For this purpose we define a weak formulation for the error on each element and provide an efficient and accurate numerical solution technique to solve the error equations locally. We investigate the well-posedness of the error equations and also consider the related eigenvalue problem for cubic elements. Numerical results for both smooth and non-smooth problems, including a problem with reentrant corners, show that an accurate prediction is obtained for the local error, and in particular the error distribution, which provides essential information to control an adaptation process. The error estimation technique is also compared with existing methods and provides significantly sharper estimates for a number of reported test cases.

     

The electronic structure of dinuclear transition-metal complexes containing metal—metal interactions: II. He(I) and He(II) photoelectron spectra of hexacarbonyldi-irondisulfur and related complexes

The He(I) and He(II) photoelectron spectra of a series of Fe₂(CO)₆LL¹-type complexes (L = L¹ = S, (i-propyl)S; L,L¹ = t-but of an all-electron, ab initio SCF MO calculation on Fe₂(CO)₆S₂ and of extended CNDO calculations on related molecules. Assignments given ar He(I)/He(II) intensity differences, and on comparison with related molecules.The coordination of the bridging ligands to the metal centres and the nature of the metal—metal interactions are discussed.     

Vesicular catalysis of an S(N)2 reaction: toward understanding the influence of glycolipids on reactions proceeding at the interface of biological membranes

The kinetics of the S(N)2 reaction of a series of aromatic alkylsulfonates with water and bromide ions in membrane mimetic media have been investigated. These media include vesicles formed from only synthetic amphiphiles, vesicles composed only of phospholipids and mixtures of these components. Special focus is placed on the influence of the addition of n-dodecyl-beta-glucoside as a mimic for glycolipids. The kinetic data have been analyzed by using the pseudophase model for bimolecular reactions. Contrary to previous results on a base-catalyzed E2 reaction (Org. Biomol. Chem. 2004, 2, 1789-1799), the presence of n-dodecyl-beta-glucoside at the vesicular surface does not lead to large rate accelerations for the S(N)2 reaction. In fact, when present at 50 mol % (i.e., the additive covers 34% of the vesicular surface) these glycolipid mimics appear not to affect the bimolecular rate constants, but they only decrease the local water concentration by about 40%. The reactivity of water at the surface of vesicles that are formed from cationic amphiphiles appears to be increased about 10-fold relative to the reactivity of water in the bulk liquid, whereas in zwitterionic vesicles the reactivity is comparable to that in bulk water. The obtained rate constants are also compared to micellar rate constants.     

Direct-temperature mass spectrometric detection of volatile terpenoids and natural terpenoid polymersin fresh and artificially aged resins

Electron impact (EI) ionization and ammonia chemical ionization (NH(3)/CI) direct-temperature mass spectrometry (DTMS) was used to characterize five natural terpenoid resins: dammar, mastic, colophony, Manila copal and sandarac. Compositional differences were highlighted by the identification of low molecular mass compounds, ranging from di- to triterpenoids, and polymeric components, based on polycadinene and polycommunic acid. Photo-ageing processes occurring under accelerated indoor and outdoor exposure conditions were also investigated. NH(3)/CI and tetramethylammonium hydroxide EI were applied to increase the sensitivity towards highly oxidized molecules. Oxidation and cross-linking reactions were found to affect mostly triterpenoid resins and diterpenoid abietane and pimarane molecules. Oxidation proceeds through a radical mechanism, generally starting from conjugated double bonds. Oxygen atoms are incorporated in the terpenoid structures in the form of alcohols, ketones and carboxylic acids. Oxidized cadinene oligomers released by pyrolytic degradation of the polycadinene fraction of dammar were detected even in unaged samples. Evidence is given indicating the occurrence of cleavages in the cross-linked polycommunic structure of aged sandarac and Manila copal. Bond scissions produce oligomeric fragments based on the communic acid structure and sufficiently volatile to be desorbed at low temperature in DTMS measurements.     

Oxidative electrochemical switching in dithienylcyclopentenes, Part 2: effect of substitution and asymmetry on the efficiency and direction of molecular switching and redox stability

The electrochemical and spectroelectrochemical properties of a series of C5-substituted dithienylhexahydro- and dithienylhexafluorocyclopentenes are reported. The effect of substitution at C5 of the thienyl moiety on the redox properties is quite dramatic, in contrast to the effect on their photochemical properties. The efficiency of electrochemical switching is dependent both on the central cyclopentene unit and on the nature of the substituents, whereby electron-donating moieties favour oxidative electrochemical ring-closure and vice versa. Asymmetrically substituted dithienylcyclopentenes were investigated to explore the ring-closure process in more detail. The results indicate that electrochemically induced ring-closure occurs via the monocation of the open form. In the presence of electroactive groups at C5 of the thienyl ring (e.g., methoxyphenyl) initial oxidation of these groups is followed by intermolecular electron transfer, which drives ring-closure of the open forms.     

Isomer separation of hyperbranched polyesteramides with gas-phase H/D exchange and a novel MS(n) approach: DoDIP

Two approaches are introduced that provide information about the isomeric composition of hyperbranched polyesteramides. The first approach is based on a novel tandem mass spectrometric (MS(n)) approach that allows the study of different types of isomeric structures by a separation based on their difference in appearance energy. The method is called DoDIP: dissociation of depleted ion populations. A first MS/MS step is used to fragment isomers with relatively low appearance energy. The isomers with higher appearance energy are fragmented in a second MS/MS step of higher energy. The second approach is based on gas-phase H/D exchange experiments that result in a bimodal isotopic distribution for oligomers X(n)D(n+1) of which one distribution corresponds to a type of isomeric structure that exhibits H/D exchange behaviour and the other to an isomeric structure that does not exhibit H/D exchange behaviour. X is a difunctional anhydride of phthalic acid (P), 1,2-cyclohexanedicarboxylic acid (C), succinic acid (S) or glutaric acid (G). D in X(n)D(n+1) is a trifunctional diisopropanolamine and n the degree of polymerization. The type of isomeric structure that does not exhibit H/D exchange behaviour has a non-alternating monomer sequence that contains an amine bond with a relatively high proton affinity. The other isomeric structure that does exhibit H/D exchange behaviour has an alternating monomer sequence containing only amide and ester bonds with relatively low proton affinity. Oligomer structures were confirmed with additional MS(2) experiments after H/D exchange. H/D exchange experiments on the fragments obtained after MS(2) of the parent ion show that next to previously postulated mechanisms for the cleavage of the ester and amide bond another reaction pathway must be operational. A new mechanism is introduced to explain the H/D exchange behaviour of the fragments that requires a cleavage of the amide bonds only. Two types of fragments are formed by this mechanism. One type is protonated due to the cleavage of the amide bond whereas the other type has an oxazolonium ion structure due to the loss of an additional H(2)O.     

Tetrakis­[1‐(3‐chloro­propyl)‐1,2,4‐tri­azole‐κN4]­bis­(tetrafluoroborato‐κF)copper(II)

In the title complex, [Cu(BF₄)₂(1tpc)₄] [1tpc is 1‐(3‐chloro­propyl)‐1,2,4‐triazole, C₅H₈ClN₃], the copper(II) centres reside in a tetragonally distorted octahedral coordination environment. Four 1tpc ligands are coordinated to the metal atom via the N4 atom of the triazole rings in a square‐planar arrangement, with Cu—N bond lengths in the range 2.002 (2)–2.019 (2) Å. Two tetra­fluoro­borate anions, in the axial positions above and below the square plane, are weakly coordinated to the copper(II) centre, with Cu—F distances of 2.4009 (18) and 2.5096 (18) Å.