An almost sure invariance principle for stationary ergodic sequences of Banach space valued random variables

Summary In this paper we establish an almost sure invariance principle with an error termo((t log logt)^1/2) (ast) for partial sums of stationary ergodic martingale difference sequences taking values in a real separable Banach space. As partial sums of weakly dependent random variables can often be well approximated by martingales, this result also leads to almost sure invariance principles for a wide class of stationary ergodic sequences such as ø-mixing and -mixing sequences and functionals of such sequences. Compared with previous related work for vector valued random variables (starting with an article by Kuelbs and Philipp [27]), the present approach leads to a unification of the theory (at least for stationary sequences), moment conditions required by earlier authors are relaxed (only second order weak moments are needed), and our proofs are easier in that we do not employ estimates of the rate of convergence in the central limit theorem but merely the central limit theorem itself.     

Otpically illuminated dielectric interfaces as high-speed far-infrared modulators

A new device for the gigahertz modulation of far-infrared radiation is analytically and numerically analyzed. It consists of a thin layer of a high-mobility, direct-bandgap semiconductor, such as GaAs, in which a high-density electron-hole plasma is rapidly created and destroyed, thereby rapidly changing the free-carrier reflectivity of the active layer. Illumination by a high-power, near-infrared laser diode array generates the plasma through intrinsic photoconduction. It is shown that this device acis primarily as an amplitude modulator, and that its efficiency increases sharply with increasing far-IR frequency, in contrast to a Schottky diode, which acts primarily as a phase modulator, and whose efficiency falls off sharply with far-IR frequency. The breakeven frequency lies at about 1.5 THz, depending slightly on the assumed device parameters. The relative advantage of the new device increases rapidly with increasing far-infrared frequency. At an operating frequency of 2.5 THz (119 m), for example, a 1 GHz modulation bandwidth may be achieved with a single-sideband conversion loss of only-21 db, versus a Schottky's loss of-39 db, assuming a laser diode power of 1 W, which is readily available from recently developed laser diode arrays.     

Extension of the measuring range of balances

The basic principle of comparing the sample mass with the mass of a reference body in equilibrium gives the equal-armed beam balance a unique accuracy. Main parameters characterising the suitability of the instrument are measuring range, resolution and relative sensitivity (resolution/maximum load). The historical development of the values of these parameters achieved depended strongly on the practical need in those times. Technically unfavourable scales of the oldest Egyptian dynasties (~3000 BC) could resolve mass differences of 1 g and had a relative sensitivity of at least 10^–3. More sophisticated instruments from the 18^th Dynasty (~1567–1320 BC) achieved a relative sensitivity of 10^–4 independent of the size of the instrument. In 350 BC Aristotle clarified the theory of the lever and at about 250 BC Archimedes used the balance for density determinations of solids. The masterpiece of a hydrological balance was Al Chazini’s 'Balance of Wisdom’ built about 1120. Its relative sensitivity was 2⋅10^–5. Real progress took place when scientists like Lavoisier (1743–1794) founded modern chemistry. At the end of the 19^th century metrological balances reached a relative sensitivity of 10^–9 with a maximum load of several kilogrammes. That seems to be the high end of sensitivity of the classical mechanical beam balance with knife edges. Improvements took place by electrodynamic compensation (Emich, Gast). In 1909 Ehrenhaft and Millikan could weigh particles of 10^–15 g by means of electrostatic suspension. In 1957 Sauerbrey invented the oscillating quartz crystal balance. By observing the frequency shift of oscillating carbon nanotubes or of silica nanorods, masses or mass changes in the attogram or zeptogram have been observed recently.     

General application of jäntti's method for the fast calculation of sorption equilibrium

On the basis of a molecular model for adsorption kinetics Jäntti introduced a method to calculate equilibriums shortly after a change of the pressure of the sorptive gas. In the present paper we show that this method is useful in many more situations than those intended originally.     

Studium und Anwendung eines neuen Komplexes von Kupfer mit Salicylsäure

Microchimica Acta - Eine empfindliche spektrophotometrische Methode zur Bestimmung von Kupfer mit Salicyls~iure wurde beschrieben (Molarextinktion ε = 2,4 · 9 105). Die nachweisbaren...     

3,7-Dioxaazelaamides as Ionophores for Lithium Ion Selective Liquid Membrane Electrodes

Lipophilic neutral carriers were synthesized which show Li⁺/Na⁺ selectivities of up to ca. 80 in highly lipophilic liquid membranes. The sensor membranes exhibit improved response times and increased lifetimes as compared to systems described earlier. They allow reliable measurements of Li⁺ in blood serum within the clinical concentration range. A 1:1 Li⁺/ionophore complex of one representative (N,N,N′,N′-tetracyclohexyl-5,5-dimethyl-3,7-dioxaazelaamide) has been prepared, and its structure was elucidated by X-ray analysis.     

Comments on surface structure analysis by water and nitrogen adsorption

Specific surface area and pore size distribution are determined usually from adsorption isotherms at low temperatures using nitrogen or noble gases. These are not absolute parameters and the measuring methods are fraught with serious difficulties. General problems of sorption measurements and recent developments are discussed. To obtain information for practical purposes these measurements need to be supplemented by investigations of the sorbate/sorbent system used in practice. Results of the measurement of nitrogen and water vapour adsorption on different materials are compared. This revised version was published online in July 2006 with corrections to the Cover Date.     

The average a posteriori error of numerical methods

Summary The definition of the average error of numerical methods (by example of a quadrature formula to approximateS(f)= f d on a function classF) is difficult, because on many important setsF there is no natural probability measure in the sense of an equidistribution. We define the average a posteriori error of an approximation by an averaging process over the set of possible information, which is used by (in the example of a quadrature formula,N(F)={(f(a ₁), ...,f/fF} is the set of posible information). This approach has the practical advantage that the averaging process is related only to finite dimensional sets and uses only the usual Lebesgue measure. As an application of the theory I consider the numerical integration of functions of the classF={f:[0,1]/f(x)–f(y)||x–y|}. For arbitrary (fixed) knotsa _i we determine the optimal coefficientsc _i for the approximation and compute the resulting average error. The latter is minimal for the knots . (It is well known that the maximal error is minimal for the knotsa _i .) Then the adaptive methods for the same problem and methods for seeking the maximum of a Lipschitz function are considered. While adaptive methods are not better when considering the maximal error (this is valid for our examples as well as for many others) this is in general not the case with the average error.     

Solution- and bound-state conformational study of N,N',N"-triacetyl chitotriose and other analogous potential inhibitors of hevamine: application of trNOESY and STD NMR spectroscopy

The solution-state conformations of N,N',N"-triacetyl chitotriose (1) and other potential chitinase inhibitors 2-4 were studied using a combination of NMR spectroscopy (NOESY) and molecular mechanics calculations. Determination solely of the global energy minimum conformation was found to be insufficient for an agreement with the NMR results. An appropriate consistency between the NMR experimental data and theoretical calculations was only reached by assessing the structures as population-weighted average conformers based on Boltzmann distributions derived from the calculated relative energies. Analogies, but also particular differences, between the synthetic compounds 2-4 and the naturally-occurring N,N',N"-triacetyl chitotriose were found. Furthermore, the conformation of compounds 1 and 2 when bound to hevamine was also studied using transferred NOESY experiments and the binding process was found to impart a level of conformational restriction on the ligands. The preferred conformation as determined for 1 in the bound state to hevamine belonged to one of the conformational families found for the compound when free in solution, although full characterisation of the bound-state conformations was impeded due to severe signal overlap. Saturation transfer difference NMR experiments were also employed to analyse the binding epitopes of the bound compounds. We thus determined that it is mainly the acetyl amido groups of the trisaccharide and the heterocyclic moiety which are in close contact with hevamine.