On the determinateness of semi-infinite bimatrix games

In this paper it is shown that every 2 × ∞ bimatrix game is weakly determined. For the proof of this fact we introduce ?-optimal andk-guaranteeing points for a convex set in IR ^m and a labeling technique which is typical for 2 × ∞ bimatrix games.     

Linear production with transport of products,resources and technology

This paper considers linear production situations with a finite number of production facilities, each with its own production technology and market prices. The economic agents control resources at the different facilities. Transport of resources, products and technology is restricted. Sufficient conditions for the corresponding TU-game to be balanced are discussed. In this we extend the results of Owen (1975), Granot (1986) and Curiel, Derks, and Tijs (1989). An example is presented in some detail.This research is sponsored by the Foundation for the Promotion of Research in Economic Sciences, which is part of the Dutch Organization for Scientific Research (NWO).     

Chemical analysis of sulfur species in geothermal waters

Analytical methods have been developed to determine sulfur species concentrations in natural geothermal waters using Reagent-Free™ Ion Chromatography (RF™-IC), titrations and spectrophotometry. The sulfur species include SO₄²⁻, S₂O₃²⁻, and ∑S²⁻ with additional determination of SO₃²⁻ and S_xO₆²⁻ that remains somewhat semiquantitative. The observed workable limits of detections were ≤0.5 μM depending on sample matrix and the analytical detection limits were 0.1 μM. Due to changes in sulfur species concentrations upon storage, on-site analyses of natural water samples were preferred. Alternatively, the samples may be stabilized on resin for later elution and analysis in the laboratory. The analytical method further allowed simultaneous determination of other anions including F⁻, Cl⁻, dissolved inorganic carbon (DIC) and NO₃⁻ without sample preservation or stabilization. The power of the newly developed methods relies in routine analysis of sulfur speciation of importance in natural waters using techniques and facilities available in most laboratories doing water sample analysis. The new methods were successfully applied for the determination of sulfur species concentrations in samples of natural and synthetic waters.     

Stochastic Arithmetic in Multiprecision

Floating-point arithmetic precision is limited in length the IEEE single (respectively double) precision format is 32-bit (respectively 64-bit) long. Extended precision formats can be up to 128-bit long. However some problems require a longer floating-point format, because of round-off errors. Such problems are usually solved in arbitrary precision, but round-off errors still occur and must be controlled. Interval arithmetic has been implemented in arbitrary precision, for instance in the MPFI library. Interval arithmetic provides guaranteed results, but it is not well suited for the validation of huge applications. The CADNA library estimates round-off error propagation using stochastic arithmetic. CADNA has enabled the numerical validation of real-life applications, but it can be used in single precision or in double precision only. In this paper, we present a library called SAM (Stochastic Arithmetic in Multiprecision). It is a multiprecision extension of the classic CADNA library. In SAM (as in CADNA), the arithmetic and relational operators are overloaded in order to be able to deal with stochastic numbers. As a consequence, the use of SAM in a scientific code needs only few modifications. This new library SAM makes it possible to dynamically control the numerical methods used and more particularly to determine the optimal number of iterations in an iterative process. We present some applications of SAM in the numerical validation of chaotic systems modeled by the logistic map.     

Structure and impact resistance of short carbon fiber reinforced polyamide 6 composites

Short carbon fiber (CF) reinforced polyamide 6 (PA6) composites were prepared by homogenization of the components in a twin-screw extruder and by injection molding. Fiber content was varied between 0 and 16 vol%, while specimens were injection molded at rates between 2.0 and 22.6 cm/s. Average fiber length and orientation were measured to characterize structure. Average fiber length decreased with increasing fiber content and processing rate. The observed structure is contradictory to those reported in the literature for short glass fiber reinforced composites. Fibers were oriented randomly relative to the mold fill direction in the skin layer, while they were oriented parallel to this direction in the middle of the specimen. The thickness of the skin decreased with increasing injection rate and decreasing fiber content. Although instrumented impact testing indicated brittle failure at all combinations of the variables, the strain energy release rate could not be determined by the usual technique using varying notch depths because of the different properties of the skin and the core. Also, the mechanism of failure seems to be different in the two layers. A minimum appears in the fracture toughness and impact resistance at low fiber contents, indicating that fibers might promote fracture initiation at such compositions. Fiber length changed in a narrow range in the studied composites; thus, properties are determined mainly by orientation. As a consequence, both increased fiber content and injection rate lead to an increase of stiffness and toughness.     

Convex multi-choice games: Characterizations and monotonic allocation schemes

This paper focuses on new characterizations of convex multi-choice games using the notions of exactness and superadditivity. Furthermore, level-increase monotonic allocation schemes (limas) on the class of convex multi-choice games are introduced and studied. It turns out that each element of the Weber set of such a game is extendable to a limas, and the (total) Shapley value for multi-choice games generates a limas for each convex multi-choice game.     

Cooperative interval games: a survey

The (re)distribution of collective gains and costs is a central question for individuals and organizations contemplating cooperation under uncertainty. The theory of cooperative interval games provides a new game theoretical angle and suitable tools for answering this question. This survey aims to briefly present the state-of-the-art in this young field of research, discusses how the model of cooperative interval games extends the cooperative game theory literature, and reviews its existing and potential applications in economic and operations research situations with interval data.     

Preferential Siting of Aluminum Heteroatoms in the Zeolite Catalyst Al‐SSZ‐70

The adsorption and reaction properties of heterogeneous zeolite catalysts (e.g. for catalytic cracking of petroleum, partial oxidation of natural gas) depend strongly on the types and distributions of Al heteroatoms in the aluminosilicate frameworks. The origins of these properties have been challenging to discern, owing in part to the structural complexity of aluminosilicate zeolites. Herein, combined solid‐state NMR and synchrotron X‐ray powder diffraction analyses show the Al atoms locate preferentially in certain framework sites in the zeolite catalyst Al‐SSZ‐70. Through‐covalent‐bond 2D ²⁷Al{²⁹Si} J‐correlation NMR spectra allow distinct framework Al sites to be identified and their relative occupancies quantified. The analyses show that 94 % of the Al atoms are located at the surfaces of the large‐pore interlayer channels of Al‐SSZ‐70, while only 6 % are in the sub‐nm intralayer channels. The selective siting of Al atoms accounts for the reaction properties of catalysts derived from SSZ‐70.     

A study on Fe+ centers in NaCl crystals

An ESR study on Fe⁺ centers in NaCl at sites with various symmetries is presented. Such centers, with axial, octahedral or orthorhombic symmetry, can be observed below 32 K, in crystals freshly quenched at RT, before irradiating at 77 K. On warming to 180 K the conversion of Fe⁺ (orthorhombic) to Fe⁺ (axial) occurs. A second conversion of Fe⁺ (axial) to Fe⁺ (octahedral) takes place at 220 K. Both conversions are due to the tendency of the positive-ion vacancy to move away from the Fe⁺ ions.     

A symmetrization for finite two-person games

The symmetrization method of Gale, Kuhn and Tucker for matrix games is extended for bimatrix games. It is shown that the equilibria of a bimatrix game and its symmetrization correspond two by two. A similar result is found with respect to quasi-strong, regular and perfect equilibria.