Zur Berechnung des Dampf—Flüssigkeits-Gleichgewichtes in ternären flüssigen Systemen

A simple method for predicting ternary vapor—liquid equilibria is presented and experimentally verified. The method is based on the solution of algebraic equations derived by the integration of the differential equations characterizing the dependence of the equilibrium properties of the ternary system on the state variables with the assumption that the partial derivates enter as constants. The values of the partial derivates are approximately evaluated from the binary experimental data.     

Pressure beneath a Stokes wave

We investigate the pressure within an irrotational fluid in a periodic, steady, two‐dimensional gravity wave above a flat bed. We prove that the pressure in the fluid strictly decreases horizontally away from the crest line. Furthermore, the pressure strictly increases with depth. We also investigate the effect of an underlying current on the paths of the particles. © 2009 Wiley Periodicals, Inc.     

On Double Stratonovich Fractional Integrals and Some Strong and Weak Approximations

Abstract

Double Stratonovich integrals with respect to the odd part and even part of the fractional Brownian motion are constructed. The first and the second moments of such integrals are explicitly identified. As application of double Stratonovich integrals a strong law of large numbers for efBm and ofBm is derived.

Riemann–Stieltjes integral approximations to double Stratonovich fractional integrals are also considered. The strong convergence (almost surely and mean square) is obtained for approximations based on explicit series expansions of the fractional Brownian processes. The weak convergence is derived for approximations by processes with absolutely continuous paths which converge weakly to the considered fractional Brownian processes. The above-mentioned convergences are obtained for deterministic integrands which are given by bimeasures.     

Aggregation Behavior of a Six‐Membered Cyclic Frustrated Phosphane/Borane Lewis Pair: Formation of a Supramolecular Cyclooctameric Macrocyclic Ring System

A new six‐membered cyclic frustrated phosphane/borane Lewis pair was liberated from its HB(C₆F₅)₂ adduct by treatment with vinylcyclohexane. The system is an active frustrated Lewis pair that undergoes cycloaddition reactions with suitable π reagents and it splits dihydrogen. At room temperature in solution the new compound is a monomer, however, in the crystal and in solution at low temperature it aggregates to a thermodynamically favoured supramolecular macrocyclic cyclooctamer.     

Preparation of the Borane (Fmes)BH2 and its Utilization in the FLP Reduction of Carbon Monoxide and Carbon Dioxide

Treatment of 1,3,5‐tris(trifluoromethyl)benzene with n‐BuLi, followed by H₃B?SMe₂ and subsequent hydride removal gave the (Fmes)BH₂ reagent, which was isolated as a SMe₂ stabilized monomer or a ligand free (μ‐H)₂‐bridged dimer. Reaction with Mes₂P(vinyl) gave the respective ethylene‐bridged P/B(Fmes)H FLP. It reduced carbon monoxide to the formyl stage and carbon dioxide to the formaldehyde oxidation state. Most new compounds were characterized by X‐ray diffraction.     

Multi‐Component Synthesis of Rare 1,3‐Dihydro‐1,3‐azaborinine Derivatives: Application of a Bora‐Nazarov Type Reaction

The twofold hydroboration products of (Fmes)BH₂?SMe₂ with a series of alkynes (2‐butyne, arylethynes) react with two molar equiv of 2,6‐dimethylphenyl isocyanide (CN‐Xyl) at 80 °C to give rare examples of 1,3‐azaborinine derivatives. A mechanistic study revealed a reaction course involving insertion of one isonitrile followed by a bora‐Nazarov type ring‐closure reaction and subsequent isonitrile insertion to give the respective 1,3‐dihydro‐1,3‐azaborinines 5 .     

On‐Surface Reactive Planarization of Pt(II) Complexes

A series of Pt(II) complexes with tetradentate luminophores has been designed, synthesized, and deposited on coinage metal surfaces with the aim to produce highly planar self‐assembled monolayers. Low‐temperature scanning tunneling microscopy (STM) and density functional theory (DFT) calculations reveal a significant initial nonplanarity for all complexes. A subsequent metal‐catalyzed separation of the nonplanar moiety at the bridging unit via the scission of a C?N bond is observed, leaving behind a largely planar core complex. The activation barrier of this bond scission process is found to depend strongly on the chemical nature of both bridging group and coordination plane, and to increase from Cu(111) through Ag(111) to Au(111).     

Collapse of the electron gas to two dimensions in density functional theory

Local and semilocal density functional approximations for the exchange-correlation energy fail badly in the zero-thickness limit of a quasi-two-dimensional electron gas, where the density variation is rapid almost everywhere. Here we show that a fully nonlocal fifth-rung functional, the inhomogeneous Singwi-Tosi-Land-Sj?lander (STLS) approach, which employs both occupied and unoccupied Kohn-Sham orbitals, recovers the true two-dimensional STLS limit and appears to be remarkably accurate for any thickness of the slab (and thus for the dimensional crossover). We also show that this good behavior is only partly due to the use of the full exact exchange energy.     

Nonlinear Multigrid Methods for Numerical Solution of the Variably Saturated Flow Equation in Two Space Dimensions

The need of accurate and efficient numerical schemes to solve Richards’ equation is well recognized. This study is carried out to examine the numerical performances of the nonlinear multigrid method for numerical solving of the two-dimensional Richards’ equation modeling water flow in variably saturated porous media. The numerical approach is based on an implicit, second-order accurate time discretization combined with a vertex centered finite volume method for spatial discretization. The test problems simulate infiltration of water in 2D saturated–unsaturated soils with hydraulic properties described by van Genuchten–Mualem models. The numerical results obtained are compared with those provided by the modified Picard–preconditioned conjugated gradient (Krylov subspace) approach.