New classes of self-similar symmetric stable random fields

We construct two new classes of symmetric stable self-similar random fields with stationary increments, one of the moving average type, the other of the harmonizable type. The fields are defined through an integral representation whose kernel involves a norm on ⁿ . We examine how the choice of the norm affects the finite-dimensional distributions. We also study the processes which are obtained by projecting the random fields on a one-dimensional subspace. We compare these projection processes with each other and with other well-known self-similar processes and we characterize their asymptotic dependence structure.The research was done at Boston University while the first author was on leave from the Hugo Steinhaus Center, Poland. The second author was partially supported by the ONR Grant N00014-90-J-1287 at Boston University and by a grant of the United States-Israel Binational Science Foundation.     

Convergence of integrated processes of arbitrary Hermite rank

Summary Let {X(s), –<s<} be a normalized stationary Gaussian process with a long-range correlation. The weak limit in C[0,1] of the integrated process , is investigated. Here d(x) = x ^H L(x) with <H<1 and L(x) is a slowly varying function at infinity. The function G satisfies EG(X(s))=0, EG ² (X(s))< and has arbitrary Hermite rank m1. (The Hermite rank of G is the index of the first non-zero coefficient in the expansion of G in Hermite polynomials.) It is shown thatZ _x (t) converges for all m1 to some process ¯Z _m (t) that depends essentially on m. The limiting process ¯Z _m (t) is characterized through various representations involving multiple Itô integrals. These representations are all equivalent in the finite-dimensional distributions sense. The processes ¯Z _m (t) are non-Gaussian when m2. They are self-similar, that is,¯Z _m (at) and a ^H ¯Z _m (t) have the same finite-dimensional distributions for all a>0.Research supported by the National Science Foundation grants MCS 77-03543 and ENG 78-11454.This paper contains results closely connected to those of the paper by Dobrushin and Major, Z. Wahrscheinlichkeitstheorie verw. Gebiete 50, 27–52 (1979). The investigations were done independently and at about the same time. Different methods were usedDedicated to Professor Leopold Schmetterer on occasion of his 60th Birthday     

High-speed simultaneous ion-exclusion/cation-exchange chromatography of anions and cations on a weakly acidic cation-exchange resin column

The simultaneous ion-exclusion/cation-exchange separation column packed with a polymethacrylate-based weakly acidic cation-exchange resin of 3 microm particle size was used to achieve the simultaneous high-speed separation of anions and cations (Cl(-), NO3(-), SO4(2-), Na(+), K(+), NH4(+), Ca(2+) and Mg(2+)) commonly found in environmental samples. The high-speed simultaneous separation is based on a combination of the ion-exclusion mechanism for the anions and the cation-exchange mechanism for cations. The complete separation of the anions and cations was achieved in 5 min by elution with 15 mM tartaric acid-2.5 mM 18-crown-6 at a flow-rate of 1.5 ml/min. Detection limits at S/N=3 ranged from 0.36 to 0.68 microM for anions and 0.63-0.99 microM for cations. This method has been applied to the simultaneous determination of anions and cations in several environmental waters with satisfactory results.     

Molecular dynamics simulations of osmosis and reverse osmosis in solutions

Computer simulation studies using the method of molecular dynamics have been carried out to investigate osmosis and reverse osmosis in solutions separated by semi-permeable membranes. The method has been used to study the dynamic approach to equilibrium in such systems from their initial nonequilibrium state. In addition density profiles of both the solute and solvent molecules have been investigated, especially near the walls for adsorption effects. Finally the diffusion coefficients and osmotic pressure have also been measured.Our results show both osmosis and reverse osmosis, as well as a smooth transition between the two when either the solution concentration is changed, or the density (pressure) difference between the solvent and solution compartments is varied. We believe this new method can be used to improve our understanding of these two important phenomena at the molecular level.     

Electron transfer networks

In this paper, we study electron transfer networks. These are generalisations of electron transport chains, and consist of a set of substrates which can exist in reduced and oxidised forms. The reduced forms can transfer electrons to the oxidised forms, and there are some electron inflow and outflow processes. We show that under mild assumptions, such systems can have only very simple behaviour, with a single globally stable equilibrium. To prove this we show that the Jacobian of the system has negative logarithmic norm in an appropriate norm. From this result, uniqueness and global stability of any equilibrium follows. The results extend, with only minor modifications, to binary interconversion networks, where the only allowed reactions are interconversions between substrates, and inflow/outflow processes.      

On Spinning Particles

There exist classical systems whose canonical quantization yields relativistic wave equations. As a constructive proof, the classical mechanics of a translating-rotating five-frame is considered. Its quantization yields the Dirac, Weyl, Klein-Gordon, Maxwell-Proca, and higher spin equations, together with a rotational mass spectrum for the states predicted.     

Zeolite-fiber integrated optical chemical sensors for detection of dissolved organics in water

MFI zeolite coated optical fiber sensors have been developed for in situ detection of dissolved organics in water. The sensors operate by monitoring the optical reflectivity changes caused by the selective adsorption of organic molecules, i.e., 2-propanol or pentanoic acid in this study, from aqueous solutions in the zeolitic pores. Reversible and monotonic sensor signals were observed in response to the variation of 2-propanol concentration in water with fast response. However, the sensor exhibited a much slower response to pentanoic acid than to 2-propanol. It was also found that substitution of Si by Al in the MFI framework increased the adsorption of pentanoic acid that resulted in enhanced sensor responses.     

Solution conformation of d(C(4)ACAC(4)TGT)(2); an intramolecularly folded i-motif from the insulin minisatellite

A 28-mer sequence taken from the insulin minisatellite is shown, through NMR and UV thermal melting studies, to form an intramolecular i-motif with two ACA and one TGT loop that persists to near neutral pH and room temperature.     

Mössbauer study of illitic clays containing iron-rich impurities

The iron mineralogy of nineteen illitic clays from eastern Bavaria was studied by Mössbauer spectroscopy and X-ray powder diffraction. Mössbauer spectra of the <2 μm fraction were taken at RT, 120 K and 4.2 K. The clays contain both paramagnetic Fe³⁺ and Fe²⁺. Superparamagnetic oxides are frequently present. The Fe²⁺ quadrupole splitting and the ratio of Fe³⁺ at 4.2 K to Fe²⁺ at 120 K are correlated and define two groups distinguished by their mineral content. The samples were heated systematically for 48 h up to 1250°C in steps of 50°C. One clay which is rich in chlorite and Fe(II) was studied in detail after firing in air and following a reduction for 3 h at 800°C with charcoal. The transformations of the mineral phases with temperature as shown by X-ray diffraction are also evident in the Mössbauer spectra.