Representing orders on the plane by translating convex figures

Given a finite collection of disjoint, convex figures on the plane, is it possible to assign to each a single direction of motion so that this collection of figures may be separated, through an arbitrary large distance, by translating each figure one at a time, along its assigned direction? We present a computational model for this separability problem based on the theory of ordered sets.     

Constructing greedy linear extensions by interchanging chains

A natural way to prove that a particular linear extension of an ordered set is ‘optimal’ with respect to the ‘jump number’ is to transform this linear extension ‘canonically’ into one that is ‘optimal’. We treat a ‘greedy chain interchange’ transformation which has applications to ordered sets for which each ‘greedy’ linear extension is ‘optimal’.     

Contact Elements on Fibered Manifolds

For every product preserving bundle functor T ^μ on fibered manifolds, we describe the underlying functor of any order (r, s, q), s ≥ r ≤ q. We define the bundle K_k,l^r,s,q YK_{k,l}^{r,s,q} Y of (k, l)-dimensional contact elements of the order (r, s, q) on a fibered manifold Y and we characterize its elements geometrically. Then we study the bundle of general contact elements of type μ. We also determine all natural transformations of K_k,l^r,s,q YK_{k,l}^{r,s,q} Y into itself and of T( K_k,l^r,s,q Y )T\left( {K_{k,l}^{r,s,q} Y} \right) into itself and we find all natural operators lifting projectable vector fields and horizontal one-forms from Y to K_k,l^r,s,q YK_{k,l}^{r,s,q} Y .     

Infinitesimal Hecke algebras

In this Note, we define infinitesimal analogues of the Iwahori–Hecke algebras associated with finite Coxeter groups. These are reductive Lie algebras for which we announce several decomposition results. These decompositions yield irreducibility results for representations of the corresponding (pure) generalized braid groups deduced from Hecke algebra representations through tensor constructions. To cite this article: I. Marin, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Electronic transport in Mo/Ni superlattices

An experimental relationship between superconductivity, magnetism and localization is explored in short-wavelength (14Å ? ? ? 40Å) sputtered Mo/Ni superlattices. A crossover to a superconducting state is observed for ? < 9Å consistent with the observed paramagnetic behavior when the Ni strata are four atomic layers thick, or less. All samples show localization effects at helium temperatures and non-superconducting samples develop an unusual resistance plateau below T ? 0.5K.     

A general theory of surrogate dual and perturbational extended surrogate dual optimization problems

For the optimization problem (P) α = inf h(G), where G ≠ Ø is a subset of a locally convex space $\text{F}\text{and}\text{h: F →}\text{R}\text{?}$, we introduce and study two general concepts of dual problems, encompassing the classical surrogate dual problem. The first one involves only a family of surrogate constraints sets Δ_{G, Φ} ? F (Φ ∈ W), where W ? R^X, X being a locally convex space. The second one uses a perturbation functional $\text{?: F × X →}\text{R}\text{?}$ and a family of sets $\text{}\text{?}\text{gD}{}_{\mathrm{(F,x0),\Phi }}\text{? F × X (Φ ∈ W)}$, where W ? R^X. We give duality theorems, introduce Lagrangians, and show some relations between these problems and the dual problems to (P) defined with the aid of a perturbation and a concept of conjugation of functionals.     

Structure and mechanical properties of talc‐filled blends of polypropylene and styrenic block copolymers

The structure–property relationships of isotactic polypropylene (iPP)/styrenic block copolymer blends filled with talc were examined by optical and scanning electron microscopy, wide‐angle X‐ray diffraction, and tensile‐ and impact strength measurements. The composites were analyzed as a function of the poly(styrene‐b‐ethylene‐co‐propylene) diblock copolymer (SEP) and the poly(styrene‐b‐butadiene‐b‐styrene) triblock copolymer (SBS) content in the range from 0 to 20 vol % as elastomeric components and with 12 vol % of aminosilane surface‐treated talc as a filler. Talc crystals incorporated in the iPP matrix accommodated mostly plane‐parallel to the surface of the samples and strongly affected the crystallization process of the iPP matrix. The SBS block copolymer disoriented plane‐parallel talc crystals more significantly than the SEP block copolymer. The mechanical properties depended on the final phase morphology of the investigated iPP blends and composites and supermolecular structure of the iPP matrix because of the interactivity between their components. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1255–1264, 2004     

Metal-support interactions in systems palladium deposited on oxidized tungsten surfaces

The morphology of the palladium (Pd) overlayers on oxidized tungsten (W) tips has been studied by Field Emission Microscopy (FEM). The effect of thermal treatment on the interaction of Pd with the support and chemisorption of CO on variously treated Pd-containing samples has been investigated. The results are discussed in relation to complementary macroscopic experiments by synchrotron radiation excited photoelectron spectroscopy (SRPES) and thermally programmed desorption (TPD) of carbon monoxide (CO) on a polycrystalline W foil. A distinct influence of support pre-oxidation on the Pd layer growth has been demonstrated. Two types of oxidized supports have been used: tungsten with oxygen pre-adsorbed at room temperature (RT) and then heated to 700 K (WO_x/W (RT) system) and tungsten oxidized at 1300 K (WO_x/W (1300 K) system) in situ. The surface of WO_x/W (1300 K) sample is fully oxidized in contrast to WO_x/W (RT), where the presence of un-oxidized patches has been demonstrated by SRPES measurements. A Pd layer grows on the WO_x/W (RT) surface mostly on the densely populated planes (1 1 0) and (2 1 1) of the W tip. Heating of this system up to 700 K results in disaggregation of the original Pd layer. Pd clusters on the tungsten tip oxidized at 1300 K are localized on the atomically rough (1 1 1) plane. The observed differences in CO adsorption on the aforementioned types of investigated samples can be attributed to differences in the chemical nature of their surfaces.