Higher order invariants in extended supergravity

On-shell linearized extended supergravity is presented in superspace for all N. The formalism is then used in the construction of higher order invariants which may serve as counterterm lagrangians. It is shown that three-loop counterterms exist for N ? 3 and (N ? 1)-loop counterterms for N ? 4. In the full non-linear theory, the presence of a global non-compact symmetry group for N ? 4 does not allow a simple extension of the (N ? 1)-loop term, but N-loop counterterms may be constructed.     

The supercurrent in five dimensions

The supercurrent multiplet is constructed for N=2 and 4 extended supersymmetries in five dimensions. The corresponding supergravity multiplets are also exhibited and have 40 + 40 and 128 + 128 components, respectively.     

UV-photoemission at constant wavevector component k6: Application to copper

Angle-resolved energy distribution curves of photoelectrons obtained at constant wavevector component k₆ have been presented for the surface of Cu(111). The main observed transitions can be interpreted as due to direct interband transitions between the APW initial states and free-electron-like final states which are calculated simply in one-dimension along k_⊥ lines parallel to the surface normal.     

Enhanced protein adsorption due to charge regulation

When a protein molecule approaches a charged surface, its protonation state can undergo dramatic changes due to the imposed electric potential. This has a large impact on adsorption strengths that may be enhanced by several kT. Using mesoscopic simulation techniques as well as analytical theories, we have investigated this regulation mechanism and demonstrate how it is influenced by salt concentration and solution pH. Using hisactophilin as a test case, we show how the binding to a lipid membrane is governed by small changes in pH and that this is intimately coupled to the charge regulation mechanism.     

Artificial glycosyl phosphorylases

alpha- and beta-Cyclodextrin 6(A),6(D)-diacids (1 and 2), beta-cyclodextrin-6-monoacid (14), beta-cyclodextrin 6(A),6(D)-di-O-sulfate (16) and beta-cyclodextrin-6-heptasulfate (19) were synthesised. Acids 1, 2 and 14 were made from perbenzylated alpha- or beta-cyclodextrin, by diisobutylaluminum hydride (DIBAL)-promoted debenzylation, oxidation and deprotection. Addition of molecular sieves was found to improve the debenzylation reaction. Sulfates 16 and 19 were made by sulfation of the appropriately partially protected derivatives and deprotection. Catalysis of 4-nitrophenyl glycoside cleavage by these cyclodextrin derivatives was studied. Compounds 1, 2 and 16 were found to catalyse the reaction, with the catalysis following Michaelis-Menten kinetics and depending first order on the phosphate concentration. In a phosphate buffer (0.5 M, 59 degrees C, pH 8.0), K(M) varied from 2-10 mM and the k(cat)/k(uncat) ratio from 80-1000 depending on the stereochemistry of the substrate and the catalyst, with 2 being the best catalyst and with the sulfated 16 also displaying catalytic ability. The monoacid 14 and the heptasulfate 19 were not catalytic.     

Numerical Approximation for a White Noise Driven SPDE with Locally Bounded Drift

A numerical scheme for a stochastic partial differential equation of heat equation type is considered where the drift is locally bounded and the dispersion may be state dependent. Uniform convergence in probability is obtained. Roger Pettersson: Partially supported by the EU grant ref. ERBF MRX CT96 0057A.     

Non-regular simplicial matroids

Let (ks) denote the set of all k-element-subsets of a finite set S. A k-simplical matroid on a subset E of (ks) is a binary matroid the circuit of which are simplicial complexes {X1,…Xm} ? E with boundary 0 (mod 2). The k-simplical matroid on (ks) is called the full simplicial matroid Gk(S). The polygon matroid on the edges of a finite graph is 2-simplicial. Polygon-matroids and their duals are regular. The dual of Gk(S) is Gn?k(S) if the cardinnlity of S is n. More details on simplicial matroids can be found in [3, Chapter 6] and also in [4, pp. 180–181].Welsh asked if every simplicial matroid is regular. We prove that this is not the case, for all full k-simplicial matroids Gk(S) with 3?k?n?3 are non-regular (n is the cardinality of S). This result has also been proved σy R. Cordovil and M. Las Vergnas recently. Their proof is different from our proof, which is somewhat shorter.     

A desarguesian theorem for algebraic combinatorial geometries

The points of an algebraic combinatorial geometry are equivalence classes of transcendentals over a fieldk; two transcendentals represent the same point when they are algebraically dependent overk. The points of an algebraically closed field of transcendence degree two (three) overk are the lines (resp. planes) of the geometry. We give a necessary and sufficient condition for two coplanar lines to meet in a point (Theorem 1) and prove the converse of Desargues’ theorem for these geometries (Theorem 2). A corollary: the “non-Desargues” matroid is non-algebraic. The proofs depend on five properties (or postulates). The fifth of these is a deep property first proved by Ingleton and Main [3] in their paper showing that the Vámos matroid is non-algebraic.     

Detection of laser induced dielectric breakdown in water using a laser doppler vibrometer

This study is focused on exploring the feasibility of an all-optic surface scanning method in determining the size and position of a submerged, laser generated, optoacoustic (OA) source. The optoacoustic effect in this case was generated when the absorption of a short electromagnetic pulse in matter caused a dielectric breakdown, a plasma emission flash and a subsequent acoustic wave. In the experiment, a laser pulse with λ = 1064 nm and 12 ns pulse length was aimed at a volume of deionized water. When the laser beam was focused by a f = 16 mm lens, a single dielectric breakdown spot occurred. When a f = 40 mm was used several breakdowns in a row were induced. The breakdowns were photographed using a double shutter camera. The acoustic wave generated by the dielectric breakdowns were detected at a point on the water surface using a laser Doppler vibrometer (LDV). First, the LDV signal was used to calculate the speed of sound with an accuracy of 10 m/s. Secondly, the location and length of the dielectric breakdown was calculated with an accuracy of 1 mm. The calculated position matched the breakdown location recorded by a camera. The results show that it is possible to use LDV surface measurements from a single spot to determine both the position and length of the OA source as well as the speed of sound in the medium. Furthermore, the LDV measurements also show a secondary peak that originates from the OA source. To unravel the origin and properties of this interesting feature, further investigations are necessary