Dimensions and Lyapunov exponents from exchange rate series

Detecting the presence of deterministic chaos in economic time series is an important problem that may be solved by measuring the largest Lyapunov exponent. In this paper we present estimates of the largest Lyapunov exponent in daily data for the Swedish Krona vs Deutsche Mark, ECU, U.S. Dollar and Yen exchange rates. In order to estimate the dimension of the systems producing these exchange rate series, we also present estimates of the correlation dimension. We found indications of deterministic chaos in all exchange rate series. However, the estimates for the largest Lyapunov exponents are not reliable, except in the Swedish Krona-ECU case, because of the limited number of data points. In the Swedish Krona-ECU case, we found indications of a low-order chaotic dynamical system.     

Schwartz spaces and compact holomorphic mappings

LetE be a locally convex space. We investigate under which conditions onE it is true that every holomorphic mapping fromE intoc ₀ is compact. We show that Schwartzity ofE is a sufficient condition and also a necessary condition ifE is quasi-normable.     

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.     

Stationary inverted Lyman populations and free-free and bound-free emission of lower-energy state hydride ion formed by an exothermic catalytic reaction of atomic hydrogen and certain group I catalysts

Rb⁺ to Rb²⁺ and 2K⁺ to K + K²⁺ each provide a reaction with a net enthalpy equal to the potential energy of atomic hydrogen. The presence of these gaseous ions with thermally dissociated hydrogen formed a plasma having strong VUV emission with a stationary inverted Lyman population. Significant Balmer α line broadening of 18 and 9 eV was observed from a rt-plasma of hydrogen with KNO₃, and RbNO₃, respectively, compared to 3 eV from a hydrogen microwave plasma. The reaction was exothermic since excess power of about 20 mW/cc was measured by Calvet calorimetry. We propose an energetic catalytic reaction involving a resonance energy transfer between hydrogen atoms and Rb⁺ or 2K⁺ to form a very stable novel hydride ion. Its predicted binding energy of 3.0471 eV with the fine structure was observed at 4071 Å, and its predicted bound-free hyperfine structure lines matched those observed for about 40 lines to within.01 percent. Characteristic emission from each catalyst was observed. This catalytic reaction may pump a CW HI laser.