Bounds for the Distance Between Nearby Jordan and Kronecker Structures in a Closure Hierarchy

Computing the fine-canonical-structure elements of matrices and matrix pencils are ill-posed problems. Therefore, besides knowing the canonical structure of a matrix or a matrix pencil, it is equally important to know what are the nearby canonical structures that explain the behavior under small perturbations. Qualitative strata information is provided by our StratiGraph tool. Here, we present lower and upper bounds for the distance between Jordan and Kronecker structures in a closure hierarchy of an orbit or bundle stratification. This quantitative information is of importance in applications, e.g., distance to more degenerate systems (uncontrollability). Our upper bounds are based on staircase regularizing perturbations. The lower bounds are of EckartYoung type and are derived from a matrix representation of the tangent space of the orbit of a matrix or a matrix pencil. Computational results illustrate the use of the bounds. Bibliography: 42 titles.     

Oscillatory instabilities of standing waves in one-dimensional nonlinear lattices

In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of analyticity versus wave amplitude is observed. As a consequence of the discreteness, oscillatory linear instabilities, persisting for arbitrarily small amplitude in infinite lattices, appear for all wave numbers Q not equal 0,pi. Incommensurate analytic SWs with |Q|>pi/2 may however appear as "quasistable," as their instability growth rate is of higher order.     

Theoretical investigation of high pressure phases of carbon dioxide

The recent discovery of a new solid phase of carbon dioxide ( CO2-V) has made it apparent that the properties of this vital chemical species are drastically altered under high pressure conditions. The reported transition at around 40 GPa from the Cmca phase ( CO2-III), which is a molecular solid, into the novel phase, which was observed to be quartzlike, clearly suggests a dramatic change of the chemical, electronic, and structural properties. We here present a theoretical analysis of the implications of this metamorphosis. At even higher pressures, we predict the existence of a very hard phase of the stishovite type.     

A fast simple hot-wire method of determining the mean velocity vector of complex three-dimensional flows

A fast and simple method of determining the mean velocity vector of complex three-dimensional flow fields is outlined. Straight and slanted single hot-wires are rotated in two perpendicular planes. This method increases the angular resolution, which is of importance in flow situations where one of the velocity components dominates and the other changes rapidly from one point to another. The method was calibrated in a wind tunnel and assessed in the internal flow field at the outlet of a fan in a defroster channel. It is shown that the hot-wire method yields good agreement with corresponding flow visualizations determined using a textile thread, and an integration of the measured mean flow yields a flow rate which agrees within a few percent with corresponding direct measurements on an orifice plate.     

Fluoride determination with a micro flow-calorimeter

Fluoride is determined by an integration technique with a flow calorimeter. All samples are absorbed on an anion-exchange resin before being brought into the calorimetric system. The reaction between hydrofluoric add and sodium hydroxide is used in the determinations. The method is applied to samples with between 7 mug and 5 mg of fluoride. The confidence limit is +/-2-5 mug for small samples and +/-25 mug for large samples. The enthalpy of the reaction H(+) + F(-) --> HF((aq)) was found to be 13.77 +/- 0.08 kJ mole .     

Testing shelled corn for aflatoxin, Part III: evaluating the performance of aflatoxin sampling plans

The effects of changes in sample size and/or sample acceptance level on the performance of aflatoxin sampling plans for shelled corn were investigated. Six sampling plans were evaluated for a range of sample sizes and sample acceptance levels. For a given sample size, decreasing the sample acceptance level decreases the percentage of lots accepted while increasing the percentage of lots rejected at all aflatoxin concentrations, and decreases the average aflatoxin concentration in lots accepted and lots rejected. For a given sample size where the sample acceptance level decreases relative to a fixed regulatory guideline, the number of false positives increases and the number of false negatives decreases. For a given sample size where the sample acceptance level increases relative to a fixed regulatory guideline, the number of false positives decreases and the number of false negatives increases. For a given sample acceptance level, increasing the sample size increases the percentage of lots accepted at concentrations below the regulatory guideline while increasing the percentage of lots rejected at concentrations above the regulatory guideline, and decreases the average aflatoxin concentration in the lots accepted while increasing the average aflatoxin concentration in the rejected lots. For a given sample acceptance level that equals the regulatory guideline, increasing the sample size decreases misclassification of lots, both false positives and false negatives.     

Structural and mechanistic look at the orthoplatination of aryl oximes by dichlorobis(sulfoxide or sulfide)platinum(II) complexes

Structural and mechanistic aspects of orthoplatination of acetophenone and benzaldehyde oximes by the platinum(II) sulfoxide and sulfide complexes [PtCl(2)L(2)] (2, L = SOMe(2) (a), rac-SOMePh (b), R-SOMe(C(6)H(4)Me-4) (c), and SMe(2) (d)) to afford the corresponding platinacycles cis-(C,S)-[Pt(II)(C(6)H(3)-2-CR'=NOH-5-R)Cl(L)] (3, R, R' = H, Me) have been investigated. The reaction of acetophenone oxime with sulfoxide complex 2a in methanol solvent occurs noticeably faster than with sulfide complex 2d due to the fact that the sulfoxide is a much better platinum(II) leaving ligand than the sulfide. Evidence is presented that the orthoplatination is a multistep process. The formation of unreactive dichlorobis(N-oxime)platinum(II) cations accounts for the rate retardation by excess acetophenone oxime and suggests the importance of pseudocoordinatively unsaturated species for the C-H bond activation by Pt(II). A comparative X-ray structural study of dimethyl sulfoxide platinacycle 3b (R = R' = Me) and its sulfide analogue 3e (R = H, R' = Me), as well as of SOMePh complex 3c (R = H, R' = Me), indicated that they are structurally similar and a sulfur ligand is coordinated in the cis position with respect to the sigma-bound phenyl carbon. The differences concern the Pt-S bond distance, which is notably longer in the sulfide complex 3e (2.2677(11) A) as compared to that in sulfoxide complexes 3b (2.201(2)-2.215(2) A) and 3c (2.2196(12) A). Whereas the metal plane is practically a plane of symmetry in 3b due to the H-bonding between the sulfoxide oxygen and the proton at carbon ortho to the Pt-C bond, an S-bonded methyl of SOMePh and SMe(2) is basically in the platinum(II) plane in complexes 3c and 3e, respectively. There are intra- and intermolecular hydrogen bond networks in complex 3b. An interesting structural feature of complex 3c is that the two independent molecules in the asymmetric unit of the crystal reveal an extremely short Pt-Pt contact of 3.337 A.     

Time-resolved and steady-state fluorescence spectroscopic studies of the human lens with comparison to argpyrimidine,pentosidine and 3-OH-kynurenine

The intrinsic fluorescence from the human lens on excitation in the UV region, referred to as blue lens autofluorescence, increases with age or in the presence of diabetes. The present study reveals that the relative contribution of compounds responsible for the blue autofluorescence appears to be a constant with age. Three potential candidates for the blue fluorescence were also studied with respect to fluorescence spectroscopic properties. These were argpyrimidine and pentosidine, both advanced glycation end products, and 3-hydroxykynurenine (3-OH-kynurenine), a photooxidative derivative of tryptophan. It was shown that the spectral properties of argpyrimidine and pentosidine are compatible with the observed blue fluorescence of the human lens, whereas the fluorescence from 3-OH-kynurenine is negligible.     

Redox-switchable direction of photoinduced electron transfer in an Ru(bpy)3(2+)-viologen dyad

Quenching of the 3MLCT excited state of [Ru(bpy)3]2+ (bpy=bipyridine) by the reduction products (MV*+ and MV0) of methyl viologen (MV2+) was studied by a combination of electrochemistry with laser flash photolysis or femtosecond pump-probe spectroscopy. Both for the bimolecular reactions and for the reactions in an Ru(bpy)3(2+)-MVn+ dyad, quenching by MV*+ and MV0 is reductive and gives the reduced ruthenium complex [Ru(bpy)3]+, in contrast to the oxidative quenching by MV2+. Rate constants of quenching (kq), and thermal charge recombination (krec) and cage escape yields (phi(ce)) were determined for the bimolecular reactions, and rates of forward (kf) and backward (kb) electron transfer in the dyad were measured for quenching by MV2+, MV*+, and MV0. The reactions in the dyad are very rapid, with values up to kf = 1.3 x 10(12) s(-1) for *Ru(bpy)3(2+)-MV*+. In addition, a long-lived (tau = 15 ps) vibrationally excited state of MV*+ with a characteristically structured absorption spectrum was detected; this was generated by direct excitation of the MV*+ moiety both at 460 and 600 nm. The results show that the direction of photoinduced electron transfer in a Ru(bpy)3-MV molecule can be switched by an externally applied bias.