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.     

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.     

New Heat-Resistant Polyimidates Derived from Bisphenols and Mono- and Dicarboxylic Acid Imidoyl Chlorides

New polyimidates were prepared from bisphenols and mono- and dicarboxylic acid imidoyl chlorides. The structures of the polymers were determined, and their physicochemical, chemical, and thermal properties were studied. The possibility of preparing film and compression materials with good mechanical characteristics from these polymers was examined.     

Monomial ideals

In this paper, we study the numeric characteristics (the Hilbert function and graded Betti numbers) of monomial ideals in the polynomial ring and in the exterior algebra. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 30, Algebra, 2005.     

Finite element method in the solution of the Euler and Navier-Stokes equations for internal flow

Finite element solutions of the Euler and Navier-Stokes equations are presented, using a simple dissipation model. The discretization is based on the weak-Galerkin weighted residual method and equal interpolation functions for all the unknowns are permitted. The nonlinearity is iterated upon using a Newton method and at each iteration the linear algebraic system is solved by a direct solver with all unknowns fully coupled. Results are presented for two-dimensional transonic inviscid flows and two- and three-dimensional incompressible viscous flows. Convergence of the algorithm is shown to be quadratic, reaching machine accuracy in very few iterations. The inviscid results demonstrate the existence of nonunique numerical solutions to the steady Euler equations.     

Interpretation of the polyelectrolyte and antipolyelectrolyte effects of poly(N‐vinylimidazole‐co‐sodium styrenesulfonate) hydrogels

Hydrogels of N‐vinylimidazole (VI) and sodium styrenesulfonate (SSS) were synthesized in aqueous solution by radical crosslinking copolymerization with N,N′‐methylene‐bis(acrylamide) as crosslinker. Swelling in several saline solutions was measured for hydrogel samples synthesized with different comonomer concentrations (C_T = 10, 25, or 40%) and with SSS mole fractions covering a broad range (f_SSS = 0–0.7), while the crosslinker ratio was 2 wt % in all cases. The degree of swelling in aqueous solution with a specific ionic strength (μ), plotted versus the SSS composition of the feed, shows a minimum for any set of samples synthesized with a fixed C_T. The dependence of swelling on μ shows both polyelectrolyte (f_SSS beyond the minimum) and antipolyelectrolyte behaviors (in the low f_SSS limit). It was found that the nonGaussian factor of the crosslinking density and the polymer‐solvent interaction parameter increase with f_SSS for any C_T. Moreover, in the low f_SSS limit, the osmotic swelling pressure is governed not only by the ionic contribution, but also by the polymer‐solvent mixing and, the concentration of mobile counterions inside the gel is not proportional to the net fixed charge but to the addition of cationic and anionic side groups, what discards the formation of ionic pairs. The antipolyelectrolyte effect is interpreted as due to the increasing protonation of VI as μ goes up. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1683–1693, 2007