Synchronization through system interconnections

An interconnection strategy with built-in adaptive controllersis presented which achieves synchronization of scalar linearsystems: the closed-loop network forces all outputs to followthe same signal asymptotically while maintaining the open-loopcharacteristics. In the design of the output feedback controllers,no knowledge of system parameters is assumed, but each systemmust have the same poles and be high-gain-stable. The proofof the main theorem relies critically on derived systems-theoreticresults and the special system topology as a network of interconnectedsystems. The topology is explained by first solving the simplerproblem of signal synchronization.     

Kinetics of Hydrogen Peroxide Decomposition in Guaiacol Solution, Catalyzed by Hexacyanoferrate(II)

The kinetics of hydrogen peroxide decomposition in a guaiacol solution, catalyzed by potassium hexacyanoferrate(II), were studied. The reaction mainly follows the pathway of guaiacol hydroxylation. The reaction order is 1 with respect to H₂O₂, 0.5 with respect to hexacyanoferrate, and from 0.4 to 0 with respect to guaiacol (the latter parameter decreases with increasing guaiacol concentration). The apparent activation energy is 105 kJ mol^{- 1}. A kinetic scheme of the process was proposed. An expression consistent with the experiment was obtained for the rate of hydrogen peroxide decomposition in the presence of guaiacol, catalyzed by hexacyanoferrate(II).     

An implicit characteristic-flux-averaging method for the euler equations for real gases

A formulation of an implicit characteristic-flux-averaging method for the unsteady Euler equations with real gas effects is presented. Incorporation of a real gas into a general equation of state is achieved by considering the pressure as a function of density and specific internal energy. The Ricmann solver as well as the flux-split algorithm are modified by introducing the pressure derivatives with respect to density and internal energy. Expressions for calculating the values of the flow variables for a real gas at the cell faces are derived. The Jacobian matrices and the eigenvectors are defined for a general equation of state. The solution of the system of equations is obtained by using a mesh-sequencing method for acceleration of the convergence. Finally, a test case for a simple form of equation of state displays the differences from the corresponding solution for an ideal gas.     

Interference inspection of the aspherical components of an objective for nanolithography

Methods and schemes to inspect the EUV mirror shape are developed on the basis of a point diffraction interferometer with computer processing of interferograms. A measurement accuracy to within 0.001 of a wavelength in the visual range is achieved.     

Kinetics and mechanism of the formation of poly[(1,1,3,3-tetramethyldisiloxanyl)ethylene] and poly(methyldecylsiloxane) by hydrosilylation

The kinetics of the formation of poly(carbosiloxane), as well as of alkyl-substituted poly(siloxane), by Karstedt's catalyst catalyzed hydrosilylation were investigated. Linear poly(carbosiloxane), poly[(1,1,3,3-tetramethyldisiloxanyl)ethylene], (PTMDSE), was obtained by hydrosilylation of 1,3-divinyltetramethyldisiloxane (DVTMDS) and 1,1,3,3-tetramethyldisiloxane (TMDS), while alkyl-substituted poly(siloxane), poly(methyldecylsiloxane), (PMDS), was synthesized by hydrosilylation of poly(methylhydrosiloxane) (PMHS) and 1-decene. To investigate the kinetics of PTMDSE formation, two series of experiments were performed at reaction temperatures ranging from 25 to 56 °C and with catalyst concentrations ranging from 7.0 × 10⁻⁶ to 3.1 × 10⁻⁵ mol Pt/mol CHCH₂. A series of experiments was performed at reaction temperatures ranging from 28 to 48 °C, with catalyst concentrations of 7.0 ×10⁻⁶ mol of Pt per mol of CHCH₂, when kinetics of PMDS formation was investigated. All reactions were carried out in bulk, with equimolar amounts of the reacting Si H and CHCH₂ groups. The course of the reactions was monitored by following the disappearance of the Si H bands using quantitative infrared spectroscopy. The results obtained showed typical first order kinetics for the PTMDSE formation, consistent with the proposed reaction mechanism. In the case of PMDS an induction period occurred at lower reaction temperatures, but disappeared at 44 °C and the rate of Si H conversion also started to follow the first-order kinetics. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2246–2258, 2007     

Realization of graphs in a subspace of bounded height

A realization of graphs with vertices of bounded branching in a subspace of bounded depth is considered. A volume order inside of which an arbitrary graph can be realized is determined.