New phosphonium salts based on 3-(diphenylphosphino)propanoic and ω-haloalkanoic acids

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Generalized Derivatives for Solutions of Parametric Ordinary Differential Equations with Non-differentiable Right-Hand Sides

Sensitivity analysis provides useful information for equation-solving, optimization, and post-optimality analysis. However, obtaining useful sensitivity information for systems with nonsmooth dynamic systems embedded is a challenging task. In this article, for any locally Lipschitz continuous mapping between finite-dimensional Euclidean spaces, Nesterov’s lexicographic derivatives are shown to be elements of the plenary hull of the (Clarke) generalized Jacobian whenever they exist. It is argued that in applications, and in several established results in nonsmooth analysis, elements of the plenary hull of the generalized Jacobian of a locally Lipschitz continuous function are no less useful than elements of the generalized Jacobian itself. Directional derivatives and lexicographic derivatives of solutions of parametric ordinary differential equation (ODE) systems are expressed as the unique solutions of corresponding ODE systems, under Carathéodory-style assumptions. Hence, the scope of numerical methods for nonsmooth equation-solving and local optimization is extended to systems with nonsmooth parametric ODEs embedded.     

Experimental investigation of flow and heat transfer in rectangular cross-sectioned duct with baffles mounted on the bottom surface with different inclination angles

In this study, steady-state forced convection heat transfer and pressure drop characteristics in a horizontal rectangular cross-sectioned duct, baffles mounted on the bottom surface with different inclination angles were investigated experimentally in the Reynolds number range from 1 × 10³ to 1 × 10⁴. The study was performed under turbulent flow conditions. Effects of different baffle inclination angles on flow and heat transfer were studied. Results are also presented in terms of thermal enhancement factor. It is observed that increasing in baffle inclination angle enhances the heat transfer and causes an increase in pressure drop in the duct.     

Integrating methods for the analysis of oxide scales on high-temperature alloys using GDOS and EPMA

Summary The oxidation of Ni-based alloys leads to multiphase oxide scales with an inhomogeneous microstructure. By introducing an integrating method for EPMA it was possible to find a common basis with GDOS depth profiles for the chemical characterization of such layers. At first it was necessary to quantify the GDOS intensity profiles; thus the comparison of relative mass fractions supplied by both methods was successful. Generally it was found a substantial agreement also with quantitative SNMS profiles.     

Une remarque sur les Gδ-denses

Sans résuméThe first author is supported by the Scientific and Technical Research Council of Turkey, T.B.A.G-Ç2     

Integrated-plane photoelastic method—Application of photoelastic isodynes

It has been shown by Pindera and Mazurkiewicz that a new type of scattered-light modulation in the plane of a two-dimensional photoelastic object can be obtained when the stationary integrated photoelastic method developed by Pindera and Straka is applied in a scanning mode and when the transfer function of the photoelastic system satisfies certain conditions. The new type of light modulation, called field of isodynes by the authors, carries information on stress components normal to the direction of propagation of primary beam, and on corresponding total-force component. The points where this stress component is equal to zero can be easily determined. The classical scattered-light modulation along a chosen line represents a cross section of a corresponding isodynes field. It is shown that these features of the method of isodynes make it possible to easily determine the distribution and values of normal stress components at any arbitrary rectilinear cross section, and to check immediately the accuracy of measurements. The experimental determination of contact stresses and contact regions using the method of isodynes is especially simple and elegant.     

(Liquid + liquid) equilibria of binary systems containing hyperbranched polymer Boltorn® H2004 – Experimental study and modelling in terms of lattice-cluster theory

(Liquid + liquid) phase equilibria (LLE) of binary mixtures containing hyperbranched polymer Boltorn® H2004 and n-alkanes (n-hexane, n-heptane, n-octane, and n-decane) were studied over the temperature range from about (260 up to 360) K. The polymer is partially miscible with n-alkanes and the solubility decreases with an increase of the chain length of the solvent. Corresponding LLE phase diagrams including spinodal and binodal (liquid + liquid) coexistence curves were calculated in terms of the statistical mechanics – based on the lattice-cluster theory, based only on the upper critical solution temperature, and the polymer chain architecture. The results show semi-qualitative agreement of predicted and experimental equilibrium compositions and temperatures. Boltorn® H2004 reveals complete miscibility in the liquid phase with alcohols (C₁–C₈), aromatic hydrocarbons (benzene, toluene, and thiophene), and ethers (methyl tetra-butyl ether, ethyl tetra-butyl ether, and tetrahydrofurane).     

Covalent stabilization: a sturdy molecular square from reversible metal-ion-directed self-assembly

Supramolecular self-assembly using weak interactions under quasi-equilibrium conditions has provided easy access to very complex but often quite fragile molecules. We now show how a labile structure obtained from reversible transition-metal-directed self-assembly of rods and connectors serves as a template that can be converted into a sturdy structure of identical topology and similar geometry. The process consists of Cu(I)-catalyzed replacement of all rods or connectors terminated with pyridines for analogues terminated with ethynyls, converting dative N→Pt(+) bonds into covalent C-Pt bonds. The procedure combines the facility and high yield of reversible self-assembly with the robustness of covalent synthesis.