Kinetics of the light-driven aqueous autoxidation of sulfur(IV) in the absence and presence of iron(II)

The photochemical autoxidation of aqueous, acidic sulfur(IV) solutions was studied in the absence and presence of iron(II) by a newly introduced technique using a diode-array spectrophotometer, in which the same light source is used to drive and detect the reaction. Based on detailed kinetic and stoichiometric data sets, a non-chain mechanism is proposed for the autoxidation of sulfur(IV). In this mechanism, excited hydrated sulfur dioxide, *H2O.SO2, first reacts with O2 to form peroxomonosulfate ion, HSO5-, which rapidly oxidizes another H2O.SO2 to give hydrogensulfate ion as a final product. In the presence of iron(II), the formation of iron(III) was detected, which can be interpreted through the simultaneous contribution of two additional pathways: some of the HSO5- formed oxidizes iron(II) instead of sulfur(iv), and *H2O.SO2 also reacts directly with iron(II) to yield iron(III). This mechanism provides a sufficient quantitative interpretation of all experimental observations.     

Alkane isomers: presence in petroleum ether and complexity

The presence and absence of alkane isomers in petroleum and petroleum derivatives depend on the complexity of these structures. It was assumed that the more complex the structure is the less probable it is that that the molecule can be detected in any petroleum derivative. Complexity is a vague concept, which has not been defined in quantitative terms yet, and therefore there is no experimental method, which could be used to determine 'complexity'. Mass spectrometry and infrared spectroscopy in combination with gas chromatography were used to identify the various structural isomers of alkanes in petroleum ether. The isomers were categorised in quantitative terms by using topological indices and linear discriminant analysis. It was found that alkanes possessing a more complex, highly branched structure are less probable to be detected in petroleum ether than isomers with a simpler backbone structure. It was proposed that the experimental 'measure' of the complexity of isomer(i) should be proportional to 1/C(i), where C(i), denotes the concentration of isomer(i) in a (primary) petroleum derivative.     

Ordering transition and demixing of a binary mixture of thick and thin rodlike molecules in the presence of an external field

The effect of an external field (electric/magnetic) on the phase behavior of the binary mixture of very long thick and thin rodlike particles is studied. Both the thick and thin particles possess positive but different susceptibility anisotropics (Delta alpha). The difference in the extent of interaction between the external field and the two species is varied by means of a coupling parameter (l = Delta alpha(thick)/Delta alpha(thin)). Isotropic-nematic phase transition and demixing phase transitions taking place both in the isotropic and nematic phases are examined as a function of field strength on the level of the second virial theory of Onsager in the range of 0 < l <1. The approximate sixth order Legendre polynomial expansion method is used to represent the excluded volume interaction between the rodlike particles. It is found that the isotropic phase becomes weakly nematic (paranematic) in the presence of external field and the field orients both components in the direction of the field even if the field does not have direct interaction with the thick component (l = 0). Analytical expressions are derived for the external field induced order parameters and birefringence. The increasing field destabilizes both types of demixing transitions (isotropic-isotropic and nematic-nematic) and the paranematic-nematic phase transition. Moreover it induces closed loop immiscibility, and upper and lower critical points terminating the paranematic-nematic phase coexistence may occur for low values of the coupling parameter. It is interesting that while the phase boundaries of the paranematic-paranematic demixing and the paranematic-nematic transitions are very sensitive to the value of the coupling parameter at low pressures, the paranematic-nematic and nematic-nematic phase boundaries are practically independent of the coupling parameter at high pressures.     

An application of index forms in cryptography

We investigate the possibility of using index forms as basic ingredients of cryptographically important functions. We suggest the use of a hash function based on index forms and we prove some important properties of the suggested function. The research was supported in part by the Hungarian Academy of Sciences, by grants T048791 and K67580 of the Hungarian NFSR, by the National Office for Research and Technology and by the grant JP-26/2006.     

Rate of Convergence of Space Time Approximations for Stochastic Evolution Equations

Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered. Under some regularity condition assumed for the solution, the rates of convergence of various numerical approximations are estimated under strong monotonicity and Lipschitz conditions. The abstract setting involves general consistency conditions and is then applied to a class of quasilinear stochastic PDEs of parabolic type. The research of the second named author is partially supported by the research project BMF2003-01345.     

Application of external micro-spectrophotometric detection to improve sensitivity on microchips

The goal of this work was to increase the sensitivity of a UV–Vis spectrophotometer by decreasing the background noise and lengthening the optical path. A microphotometer has been modified to precisely select very small parts of a microfluidic channel pattern of a chip and to measure light absorbance on a magnified area of the selected part of the channel. The viability of combining a projection microscope and a spectrophotometer for external absorbance measurements on disposable PDMS chips was studied. Besides the external direct detection above a microfluidic channel, the optical pathlength was lengthened by detecting in the region of the perpendicular exit port. Increasing the cross-sectional area of the zone of irradiation improved the signal-to-noise ratio and the limits of detection (LOD).     

Sites are Separable in Garnets with ALCHEMI

 It is shown in this paper that – in contrast to the accepted belief in the literature – it is possible to determine if a minority component is located on the dodecahedral, octahedral or tetrahedral sites in a garnet single crystal. Previous literature regarded the dodecahedral sites indistinguishable form the tetrahedral sites. Our prediction about the separability is based upon dynamical Bloch-wave calculations and proved experimentally in a transmission electron microscope (TEM) on two different natural garnets (almandine and grossular). The crystallographic positions of the minority components are determined in an ALCHEMI experiment that makes use of the channeling of electrons in special directions of a single-crystal sample.     

Fixed Point and Equilibrium Theorems in Pseudoconvex and Related Spaces

Convexity spaces defined in the paper are generated by families of continuous functions. Without imposing any explicitly stated linear structure on the spaces, Browder's, Brouwer's and Kakutani's fixed point theorems are proved and used for deriving generalized Fan inequalities and two-function minimax theorems. The existence of Nash equilibria in noncooperative games is also established under more general conditions than known before. The convexity spaces studied in the paper allow for unusual (generalized) convex sets and functions.     

Detecting Embedded Networks in LP Using GUB Structures and Independent Set Algorithms

In this paper, we present an alternative multi-stage generalized upper bounds (GUB) based approach for detecting an embedded pure network structure in an LP problem. In order to identify a GUB structure, we use two different approaches; the first is based on the notion of Markowitz merit count and the second exploits independent sets in the corresponding graphs. Our computational experiments show that the multi-stage GUB algorithm based on these approaches performs favourably when compared with other well known algorithms.