Subgradient Method for Convex Feasibility on Riemannian Manifolds

In this paper, a subgradient type algorithm for solving convex feasibility problem on Riemannian manifold is proposed and analysed. The sequence generated by the algorithm converges to a solution of the problem, provided the sectional curvature of the manifold is non-negative. Moreover, assuming a Slater type qualification condition, we analyse a variant of the first algorithm, which generates a sequence with finite convergence property, i.e., a feasible point is obtained after a finite number of iterations. Some examples motivating the application of the algorithm for feasibility problems, nonconvex in the usual sense, are considered.     

Structure,chemistry and stereochemistry of rastevione,a sequiterpenoid from the genus stevia

The structure and relative stereochemistry of rastevione (1a), the main constituent of the roots of S. serrata and S. rhombifolia, were deduced from chemical transformations combined with spectral data and by a single crystal X-ray diffraction study of rastevione acetate (1b). Chemical correlation of a rastevione derivative with a molecule thought to have structure IVb, suggests the structures of several previously described longipinene and longipinane derivatives, should be revised. The behaviour of longipinane-7α,8β,9β-triol-l-one in the presence of periodic acid was studied, and the structure of the reaction product established from deuterium labeling experiments showed the 7α,8β diol split.     

A material model for cementitious composite materials with an exterior point Eshelby microcrack initiation criterion

A micromechanical model for cementitious composite materials is described in which microcrack initiation, in the interfacial transition zone between aggregate particles and cement matrix, is governed by an exterior-point Eshelby solution. The model assumes a two-phase elastic composite, derived from an Eshelby solution and the Mori–Tanaka homogenization method, to which circular microcracks are added. A multi-component rough crack contact model is employed to simulate normal and shear behaviour of rough microcrack surfaces. The development of the microcrack initiation criterion and the rules adopted for microcrack evolution are a particular focus of the paper. Finally, it is shown, on the basis of several numerical simulations, that the model captures key characteristics of the behaviour of cementitious composites such as concrete.     

Numerical simulation of transpiration cooling through porous material

Transpiration cooling using ceramic matrix composite materials is an innovative concept for cooling rocket thrust chambers. The coolant (air) is driven through the porous material by a pressure difference between the coolant reservoir and the turbulent hot gas flow. The effectiveness of such cooling strategies relies on a proper choice of the involved process parameters such as injection pressure, blowing ratios, and material structure parameters, to name only a few. In view of the limited experimental access to the subtle processes occurring at the interface between hot gas flow and porous medium, reliable and accurate simulations become an increasingly important design tool. In order to facilitate such numerical simulations for a carbon/carbon material mounted in the side wall of a hot gas channel that are able to capture a spatially varying interplay between the hot gas flow and the coolant at the interface, we formulate a model for the porous medium flow of Darcy–Forchheimer type. A finite‐element solver for the corresponding porous medium flow is presented and coupled with a finite‐volume solver for the compressible Reynolds‐averaged Navier–Stokes equations. The two‐dimensional and three‐dimensional results at Mach number Ma = 0.5 and hot gas temperature T_HG=540 K for different blowing ratios are compared with experimental data. Copyright © 2014 John Wiley & Sons, Ltd.     

A Duality Theory for a Class of Generalized Fractional Programs

In generalized fractional programming, one seeks to minimize the maximum of a finite number of ratios. Such programs are, in general, nonconvex and consequently are difficult to solve. Here, we consider a particular case in which the ratio is the quotient of a quadratic form and a positive concave function. The dual of such a problem is constructed and a numerical example is given.     

Application of Atmospheric Solids Analysis Probe Mass Spectrometry (ASAP-MS) in Petroleomics: Analysis of Condensed Aromatics Standards,Crude Oil,and Paraffinic Fraction

Atmospheric solids analysis probe mass spectrometry (ASAP-MS) is a powerful tool for analysis of solid and liquid samples. It is an excellent alternative for crude oil analysis without any sample preparation step. Here, ASAP-MS in positive ion mode, ASAP(+)-MS, has been optimized for analysis of condensed aromatics (CA) standards, crude oil, and paraffinic fraction samples using a Synapt G2-S HDMS. Initially, two methodologies were used to access the chemical composition of samples: (1) using a temperature gradient varying from 150 to 600 °C at a heating rate of 150 °C min^–1, and (2) with constant temperature of 300 and 400 °C. ASAP(+)-MS ionized many compounds with a typical petroleum profile, showing a greater signals range of m/z 250–1300 and 200–1400 for crude oil and paraffin samples, respectively. Such performance, mainly related to the detection of high molecular weight compounds (>1000 Da), is superior to that of other traditional ionization sources, such as ESI, APCI, DART, and DESI. Additionally, the CA standards were identified in both forms: radicals, [M]^+?, and protonated cations, [M + H]⁺, with minimum fragmentation. Therefore, ASAP was more efficient in accessing the chemical composition of nonpolar and polar compounds. It is promising in its application with ultrahigh resolution MS instruments, such as FT-ICR MS and Orbitrap, since molecular formulas with greater resolution and mass accuracy (<1 ppm) would be assigned.

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On the universal behavior of some thermodynamic properties along the whole liquid-vapor coexistence curve

When thermodynamic properties of a pure substance are transformed to reduced form by using both critical- and triple-point values, the corresponding experimental data along the whole liquid-vapor coexistence curve can be correlated with a very simple analytical expression that interpolates between the behavior near the triple and the critical points. The leading terms of this expression contain only two parameters: the critical exponent and the slope at the triple point. For a given thermodynamic property, the critical exponent has a universal character but the slope at the triple point can vary significantly from one substance to another. However, for certain thermodynamic properties including the difference of coexisting densities, the enthalpy of vaporization, and the surface tension of the saturated liquid, one finds that the slope at the triple point also has a nearly universal value for a wide class of fluids. These thermodynamic properties thus show a corresponding apparently universal behavior along the whole coexistence curve.     

Tellurium/lithium exchange reactions in the synthesis of spiroketals and 1,6-dioxygenated systems

1,4-C,O-dianions have been generated through concomitant acid/base and tellurium/lithium exchange reactions. The di-lithium salts were transmetallated with cerium chloride to the corresponding di-cerium salts and subsequently reacted with lactones and carboxylic acid anhydrides to yield the respective spiroketals. The di-lithium entities were also converted into the corresponding cyanocuprates that add in a 1,4-manner to 2-cyclohexen-1-one to form 1,6-dioxygenated compounds.