Random Version of the Theorems of the Alternative

Three theorems of the alternative for abstract linear inequality systems which depend on random parameter are produced in infinite dimensions.     

Blends of carbon blacks and multiwall carbon nanotubes as reinforcing fillers for hydrocarbon rubbers

The reinforcement of a styrene‐butadiene rubber (SBR) by single fillers—carbon black (CB) or multiwall carbon nanotubes (MWNTs)—or by mixtures of CB and MWNTs, is investigated. The morphologies, mechanical and electrical properties of the composites, are analyzed. A significant improvement in the tensile properties is observed for samples containing a dual phase. Using atomic force (AFM) and transmission electron (TEM) microscopies, we demonstrate that the double loading improves the dispersion of the nanotubes in SBR. Electrical measurements show lower resistivity and a lower percolation threshhold for composites containing blends of fillers, which provides further evidence of better dispersion. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci 46: 1939–1951, 2008     

Analysis of an industrial component commonality problem

We discuss a case study of an industrial production-marketing coordination problem involving component commonality. For the product line considered, the strategic goal of the company is to move from the current low volume market to a high volume market. The marketing department believes that this can be achieved by substantially lowering the end products’ prices. However, this requires a product redesign to lower production costs in order to maintain profit margins. The redesign decision involves grouping end products into families. All products within one family use the same version of some components. This paper fits in the stream of recent literature on component commonality where the focus has shifted from inventory cost savings to production and development cost savings. Further, we consider both costs and revenues, leading to a profit maximization approach. The price elasticity of demand determines the relationship between the price level and number of units sold. Consequently, we integrate information from different functional areas such as production, marketing and accounting. We formulate the problem as a net-present-value investment decision. We propose a mixed integer nonlinear optimization model to find the optimal commonality decision. The recommendation based on our analysis has been implemented in the company. In addition, the application allows us to experimentally validate some claims made in the literature and obtain managerial insights into the trade-offs.     

Isotopic characteristics of the Garonne River and its tributaries

The Garonne is the largest river in the south‐west of France, and its drainage basin stretches between the Pyrénées and the Massif Central mountains. Until now, no water stable isotope study has been performed on the whole Garonne river basin which is composed of different geological substrata, and where the water resources are limited during the dry summer period. This study focuses on the Garonne river and its tributaries from the Pyrénées foothill upstream to its confluence with the Lot River downstream. The aim of the study is to determine the origins of the surface waters using their chemical and stable isotopic compositions (¹⁸O, D and ¹³C), to better understand their circulation within the drainage basin and to assess the anthropogenic influences. The Garonne displays a specific ¹⁸O seasonal effect, and keeps its Pyrénean characteristics until its confluence with the Tarn River. The difference in the dissolved inorganic carbon (DIC) comes mainly from the change in lithology between the Pyrénées and the Massif Central mountains. Agriculture activity is only detected in the small tributaries. Copyright © 2009 John Wiley & Sons, Ltd.     

Scalarization of vector optimization problems

In this paper, we investigate the scalar representation of vector optimization problems in close connection with monotonic functions. We show that it is possible to construct linear, convex, and quasiconvex representations for linear, convex, and quasiconvex vector problems, respectively. Moreover, for finding all the optimal solutions of a vector problem, it suffices to solve certain scalar representations only. The question of the continuous dependence of the solution set upon the initial vector problems and monotonic functions is also discussed.The author is grateful to the two referees for many valuable comments and suggestions which led to major imporvements of the paper.     

Porous polycrystals built up by uniformly and axisymmetrically oriented needles: homogenization of elastic propertiesPolycristaux poreux constitués d'aiguilles orientées de façon uniforme ou axisymétrique : homogénéisation des propriétés élastiques

Porous polycrystal-type microstructures built up of needle-like platelets or sheets are characteristic for a number of biological and man-made materials. Herein, we consider (i) uniform, (ii) axisymmetrical orientation distribution of linear elastic, isotropic as well as anisotropic needles. Axisymmetrical needle orientation requires derivation of the Hill tensor for arbitrarily oriented ellipsoidal inclusions with one axis tending towards infinity, embedded in a transversely isotropic matrix; therefore, Laws' integral expression of the Hill tensor is evaluated employing the theory of rational functions. For a porosity lower 0.4, the elastic properties of the polycrystal with uniformly oriented needles are quasi-identical to those of a polycrystal with solid spheres. However, as opposed to the sphere-based model, the needle-based model does not predict a percolation threshold. As regards axisymmetrical orientation distribution of needles, two effects are remarkable: Firstly, the sharper the cone of orientations the higher the anisotropy of the polycrystal. Secondly, for a given cone, the anisotropy increases with the porosity. Estimates for the polycrystal stiffness are hardly influenced by the anisotropy of the bone mineral needles. Our results also confirm the very high degree of orientation randomness of crystals building up mineral foams in bone tissues. To cite this article: A. Fritsch et al., C. R. Mecanique 334 (2006).     

On a Volume‐Constrained Variational Problem

. Existence of minimizers for a volume-constrained energy $ E(u) := \int_{\Omega} W(\nabla u)\, dx Existence of minimizers for a volume-constrained energy E(u) : = ò_W W(?u) dx E(u) := \int_{\Omega} W(\nabla u)\, dx where L^N({u = z_i}) = a_i, i = 1, ?, P, {\cal L}^N(\{u = z_i\}) = \alpha_i, i = 1, \ldots, P, is proved for the case in which z_iz_i are extremal points of a compact, convex set in \Bbb R^d\Bbb R^d and under suitable assumptions on a class of quasiconvex energy densities W. Optimality properties are studied in the scalar-valued problem where d=1d=1, P=2P=2, W(x)=|x|²W(\xi)=|\xi|^2, and the &-limit as the sum of the measures of the 2 phases tends to \L(W)\L(\Omega) is identified. Minimizers are fully characterized when N=1N=1, and candidates for solutions are studied for the circle and the square in the plane.     

In situ investigations of vault paintings in the Antwerp cathedral

X-ray fluorescence spectroscopy (XRF) and Raman spectroscopy have been used to examine 15th century mediaeval and 16th century renaissance vault paintings in the Our Lady's Cathedral (Antwerp, Belgium) in view of their restoration. The use of mobile instruments made it possible to work totally non-destructively. This complementary approach yields information on the elemental (XRF) and on the molecular composition (Raman) of the pigments. For the 15th century vault painting the pigments lead–tin yellow (Pb₂SnO₄), lead white (2PbCO₃·Pb(OH)₂), vermilion (HgS), massicot (PbO) and azurite (2CuCO₃·Cu(OH)₂) could be identified. The pigments used for the 16th century vault painting could be identified as red lead (Pb₃O₄), hematite (Fe₂O₃), lead white (2PbCO₃·Pb(OH)₂) and azurite (2CuCO₃·Cu(OH)₂). For both paintings the presence of the strong Raman scatterer calcite (CaCO₃) resulted in a difficult identification of the pigments by Raman spectroscopy. The presence of gypsum (CaSO₄·2H₂O) on the mediaeval vault painting probably indicates that degradation took place.