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.     

(e, 3e) test on e-e correlations in helium

The angular variations of the five-fold differential cross section obtained by using different wave functions of helium are compared with experimental data. It is found that in the coplanar geometry two kinematical arrangements, (i) equal energy sharing between the two ejected electrons with one of them ejected along the momentum transfer direction and the other along varying direction and (ii) the Bethe ridge condition with fixed sum of ejected electron energies and varying angle between them, are very sensitive to e-e correlations contained in the target wave function. This comparison has been used to show that open-shell class of wave functions better incorporate e-e correlations than the closed-shell class.     

Selective enzyme amplification of NAD/NADH using coimmobilized glycerol dehydrogenase and diaphorase with amperometric detection

A flow system for substrate recycling of NAD⁺/NADH was set up with an enzyme reactor containing coimmobilized glycerol dehydrogenase (GDH) and diaphorase. The product from the diaphorase catalysis, hexacyanoferrate(II), aws detected amperometrically at a glassy carbon electrode. The amplification factor was 150 for a reactor volume of 100 μ l at a flow-rate of 0.5 ml/min. With a stopped flow of four minutes, the signal increased another 88 times, resulting in a signal amplification of 13 300 times. Equations are derived for the amplification factor and used for a discussion of the optimization of amplification systems. The K_m for GDH with glycerol as a substrate was found to be 5 × 10⁻³ M at pH 8.0. GDH from Cellulomonas sp. was purified on a gel filtration column and the purified enzyme showed a specificity toward NAD⁺, compared to NADP⁺, that was higher than 99.9%. Due to the NAD⁺ specificity of the purified GDH, the enzyme amplification system reported here could be used in detection systems for enzyme immunoassays when using alkaline phosphatase as a label and NADP⁺ as a substrate. The stability of immobilized GDH and diaphorase is several orders of magnitude better than that of alcohol dehydrogenase, which is the enzyme commonly used for NAD⁺-specific detection in these applications.     

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.     

Molecular orientation of thiol-derivatized tetraphenylporphyrin on gold studied by XPS and NEXAFS

Tetraphenylporphyrins bearing four linkers consisting of thioacetyl-functionalized carbon chains were immobilized on a gold surface via thiolate-gold bonds using two different preparation routes. The structure of these molecular layers was characterized in detail with synchrotron radiation based core-level spectroscopy, X-ray photoelectron spectroscopy (XPS) and near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. The results show that the geometry of the molecular layers and the number of linkers that bind to the gold surface depends on the preparation schemes. The deprotection of the linkers through removal of the terminal acetyl group before the molecular adsorption (deprotected systems) resulted in porphyrins bound to the gold surface with on the average three linkers, their normal axis being tilted ∼38° with respect to the surface normal. On the other hand, porphyrin layers prepared directly with the acetyl group still in place on the linkers (protected systems) are made of molecules bound to the gold surface via two linkers on the average. The resulting orientation is more upright, with the normal axis of the porphyrin plane tilted ∼50° with respect to the surface normal. Moreover, NEXAFS measurements revealed that the acetyl deprotected porphyrin layers have a higher degree of ordering than the protected systems.     

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 .