Weighted allocation rules for standard fixed tree games

In this paper we consider standard fixed tree games, for which each vertex unequal to the root is inhabited by exactly one player. We present two weighted allocation rules, the weighted down-home allocation and the weighted neighbour-home allocation, both inspired by the painting story in Maschler et al. (1995) . We show, in a constructive way, that the core equals both the set of weighted down-home allocations and the set of weighted neighbour allocations. Since every weighted down-home allocation specifies a weighted Shapley value (Kalai and Samet (1988)) in a natural way, and vice versa, our results provide an alternative proof of the fact that the core of a standard fixed tree game equals the set of weighted Shapley values. The class of weighted neighbour allocations is a generalization of the nucleolus, in the sense that the latter is in this class as the special member where players have all equal weights.     

Adjustable cavity for host-guest recognition in cofacial bis-porphyrinic tweezer

The synthesis of a cofacial bis-porphyrinic tweezer bearing a tris-anthracenic spacer is reported. Its behavior as host has been evidenced as well as the ability of its cavity to adjust to guests of various sizes.     

A supramolecular cup-and-ball C60-porphyrin conjugate system

In addition to the ammonium-crown ether recognition, pi-stacking interactions between the C60 sphere and the porphyrin moiety have been evidenced in a supramolecular complex obtained from a porphyrin-crown ether conjugate and a fullerene derivative bearing an ammonium unit.     

Donor-substituted peralkynylated "radiaannulenes": novel all-carbon macrocycles with an intense intramolecular charge-transfer

A novel class of planar, highly conjugated all-carbon macrocycles, which we christened "radiaannulenes", have been prepared based on acetylenic scaffolding using tetraethynylethene (TEE) building blocks; these structures are powerful electron acceptors and, upon peripheral substitution with electron-donating N,N-dialkylanilino groups, display intense intramolecular charge-transfer.     

Cover Picture

The cover picture shows how thrombosis occurs in the deep veins of the lower limbs. Stasis, which results from slow and turbulent blood flow, combined with hypercoagulation, caused, for example, by a surgical procedure, may result in thrombus formation. The synthetic sulfated pentasaccharide shown in part is a potent antithrombotic compound that exerts its effect by activation of the plasma protein antithrombin III. Conformationally locked monosaccharides have now been synthesized to demonstrate that L-iduronic acid, one part of the pentasaccharide, must adopt an unusual distorted conformation to activate antithrombin III. Such conformational effects might be relevant in explaining the unique biological properties of glycosaminoglycans that contain L-iduronic acid. In the background of the picture, a flight of vampire bats is attracted by the pentasaccharide. Vampire was the name given to South American blood-sucking bats (Latin name: desmodus rotundus) in 1761 by the French naturalist Georges Louis Leclerc Comte de Buffon (1707-1788). These bats are known to attack cattle and, very rarely, sleeping human beings. Although their saliva has been shown to contain an anticoagulant compound, they would also be happy to benefit from the pentasaccharide mentioned above, to suck the blood out of the vein more easily. More details about this compound which would be helpful to vampire bats are reported by Petitou, Sina? et al. on p. 1670 ff.     

Equitable resolvable coverings

In an earlier article, Willem H. Haemers has determined the minimum number of parallel classes in a resolvable 2‐(qk,k,1) covering for all k ≥ 2 and q = 2 or 3. Here, we complete the case q = 4, by construction of the desired coverings using the method of simulated annealing. Secondly, we look at equitable resolvable 2‐(qk,k,1) coverings. These are resolvable coverings which have the additional property that every pair of points is covered at most twice. We show that these coverings satisfy k < 2q ? , and we give several examples. In one of these examples, k > q. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 113–123, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10024     

Initial stages of oxidation of Cu(1 1 1)

Several surface analysis techniques were combined to study the initial stages of oxidation of Cu(1 1 1) surfaces exposed to O₂ at low pressure (<5 × 10⁻⁶ mbar) and room temperature. Scanning tunneling microscopy (STM) results show that the reactivity is governed by the restructuring of the Cu(1 1 1) surface. On the terraces, oxygen dissociative adsorption leads to the formation of isolated O adatoms and clusters weakly bound to the surface. The O adatoms are located in the fcc threefold hollow sites of the unrestructured terraces. Friedel oscillations with an amplitude lower than 5 pm have been measured around the adatoms. At step edges, surface restructuring is initiated and leads to the nucleation and growth of a two-dimensional disordered layer of oxide precursor. The electronic structure of this oxide layer is characterised by a band gap measured by scanning tunneling spectroscopy to be ∼1.5 eV wide. The growth of the oxide islands progresses by consumption of the upper metal terraces to form triangular indents. The extraction of the Cu atoms at this interface generates a preferential orientation of the interface along the close-packed directions of the metal. A second growth front corresponds to the step edges of the oxide islands and progresses above the lower metal terraces. This is where the excess Cu atoms extracted at the first growth front are incorporated. STM shows that the growing disordered oxide layer consists of units of hexagonal structure with a first nearest neighbour distance characteristic of a relaxed Cu-Cu distance (∼0.3 nm), consistent with local Cu₂O(1 1 1)-like elements. Exposure at 300 °C is necessary to form an ordered two-dimensional layer of oxide precursor. It forms the so-called “29” superstructure assigned to a periodic distorted Cu₂O(1 1 1)-like structure.     

Calibration and evaluation of optical systems for full-field strain measurement

The design and testing of a reference material for the calibration of optical systems for strain measurement is described, together with the design and testing of a standardized test material that allows the evaluation and assessment of fitness for purpose of the most sophisticated optical system for strain measurement. A classification system for the steps in the measurement process is also proposed and allows the development of a unified approach to diagnostic testing of components or sub-systems in an optical system for strain measurement based on any optical technique. The results described arise from a European study known as SPOTS whose objectives were to begin to fill the gap caused by a lack of standards.     

A New Approach to the {\ast} -Genvalue Equation

We show that the eigenvalues and eigenfunctions of the star-genvalue equation can be completely expressed in terms of the corresponding eigenvalue problem for the quantum Hamiltonian. Our methods make use of a Weyl-type representation of the star-product and of the properties of the cross-Wigner transform, which appears as an intertwining operator.