A partition relation for partially ordered sets

We introduce a partition relation which is an alternate for measuring how badly the ordinary partition relation fails, we develop its corresponding partition calculus and we determine its status for various typical partially ordered sets.     

Nonlinear Galerkin methods and mixed finite elements: two-grid algorithms for the Navier-Stokes equations

Summary. A nonlinear Galerkin method using mixed finite elements is presented for the two-dimensional incompressible Navier-Stokes equations. The scheme is based on two finite element spaces and for the approximation of the velocity, defined respectively on one coarse grid with grid size and one fine grid with grid size and one finite element space for the approximation of the pressure. Nonlinearity and time dependence are both treated on the coarse space. We prove that the difference between the new nonlinear Galerkin method and the standard Galerkin solution is of the order of $H^2$, both in velocity ( and pressure norm). We also discuss a penalized version of our algorithm which enjoys similar properties. Received October 5, 1993 / Revised version received November 29, 1993     

Cyclometalated Iridium(III) Complexes Containing Semicarbazone Ligands: Synthesis,Characterization, Photophysical and Biological Studies

The synthesis, crystal structure, photophysical properties, and biological activity of the novel bis‐cyclometalated complexes [Ir(ptpy)₂(vnsc)] ( 2 ) and [Ir(ptpy)₂(acsc)] ( 3 ) [ptpy = 2‐(p‐tolyl)pyridinato, vnsc = vanillin semicarbazone, acsc = acetone semicarbazone] are described. The new compounds were prepared by the reaction of [{Ir(μ‐Cl)(ptpy)₂}₂] ( 1 ) with the corresponding semicarbazone ligands under basic conditions. The molecular structure of compound 3 was confirmed by a single‐crystal X‐ray diffraction study. The complex crystallized from chloroform as a mono‐ solvate in the orthorhombic space group Pcab with eight molecules in the unit cell.     

Approximate inertial manifolds for reaction-diffusion equations in high space dimension

The concept of approximate inertial manifolds was introduced by Foiaset al. (1987) in the case of the two-dimensional Navier-Stokes equations. These manifolds are finite dimensional smooth manifolds such that the orbits enter a very thin neighborhood of the manifold after a transient time; this concept replaces the one of inertial manifold when either an inertial manifold does not exist or its existence is not known. Our aim in this paper is to prove that approximate inertial manifolds exist for reaction-diffusion equations in high space dimension by opposition with exact inertial manifolds whose existence has only been proved in low dimension and for which nonexistence results have been obtained in space dimensionn=4.     

Interaction between inner and outer layer in drag-reduced turbulent flows

Effects of wall-based skin-friction drag reduction strategies on the statistical properties of large-scale motions in moderate Reynolds number turbulent flows have been investigated by exploiting Direct Numerical Simulation of turbulent channels. To educe large scales, a new efficient parallel distributed memory algorithm has been implemented which delivers data-driven modes of increasing characteristic lengthscales: the Fast and Adaptive Bidimensional Empirical Mode Decomposition (FABEMD). The influence of wall-based skin friction reduction on large scales is studied by comparing single point statistics, such as r.m.s. fluctuations, and two-point statistics, as cross-correlation functions in controlled and uncontrolled channel flow fields at constant friction Reynolds number. The traditional way of observing large-scale footprinting at the wall, as cross-correlation of the streamwise velocity components at different wall distances, has been found to be unreliable when comparing drag-reduced flows, due to the arbitrary choice of a reference plane in the logarithmic layer. A more sound way of observing the footprinting via the correlation of the streamwise velocity with the friction velocity is addressed and shows an increase of the footprinting in drag-reduced flows. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)