Strongly essential coalitions and the nucleolus of peer group games

Most of the known efficient algorithms designed to compute the nucleolus for special classes of balanced games are based on two facts: (i) in any balanced game, the coalitions which actually determine the nucleolus are essential; and (ii) all essential coalitions in any of the games in the class belong to a prespecified collection of size polynomial in the number of players. We consider a subclass of essential coalitions, called strongly essential coalitions, and show that in any game, the collection of strongly essential coalitions contains all the coalitions which actually determine the core, and in case the core is not empty, the nucleolus and the kernelcore. As an application, we consider peer group games, and show that they admit at most 2n−1 strongly essential coalitions, whereas the number of essential coalitions could be as much as 2ⁿ⁻¹. We propose an algorithm that computes the nucleolus of an n-player peer group game in time directly from the data of the underlying peer group situation.Research supported in part by OTKA grant T030945. The authors thank a referee and the editor for their suggestions on how to improve the presentation     

Canonical Theorems for Convex Sets

Let F be a family of pairwise disjoint compact convex sets in the plane such that none of them is contained in the convex hull of two others, and let r be a positive integer. We show that F has r disjoint ⌊ c _r n⌋ -membered subfamilies F _i (1 ≤ i ≤ r) such that no matter how we pick one element F _i from each F _i , they are in convex position, i.e., every F _i appears on the boundary of the convex hull of ⋃ _i=1 ^r F _i . (Here c _r is a positive constant depending only on r .) This generalizes and sharpens some results of Erdős and Szekeres, Bisztriczky and Fejes Tóth, Bárány and Valtr, and others. <lsiheader> <onlinepub>26 June, 1998 <editor>Editors-in-Chief: &lsilt;a href=../edboard.html#chiefs&lsigt;Jacob E. Goodman, Richard Pollack&lsilt;/a&lsigt; <pdfname>19n3p427.pdf <pdfexist>yes <htmlexist>no <htmlfexist>no <texexist>yes <sectionname> </lsiheader> Received April 30, 1997, and in revised form August 5, 1997.     

Interaction of C2N2 with clean and oxygen dosed Cu(111) surface studied by AES,ELS and TDS measurements

The adsorption and surface reaction of cyanogen on clean and oxygen covered Cu(111) have been investigated. From electron energy loss measurements, thermal desorption spectroscopy and electron beam effects in Auger spectroscopy, it is proposed that cyanogen adsorbs dissociatively on Cu(111) at 300 K. The activation energy for the desorption was calculated to be 180 kJ/mol. Cyanogen adsorption onto oxygen predosed Cu(111) is inferred to produce the NCO surface species. This interpretation was aided by data of electron energy loss measurements and from HNCO adsorption onto Cu(111) at 300 K. A reaction began in the co-adsorbed layer above 400 K, yielding CO₂ and N₂.     

Effects of potassium on the adsorption of methanol on β-Mo2C(001) surface

We have studied the effect of K on the adsorption of methanol on the β-Mo₂C(001) surface and compared our experimental data with theoretical calculations. We have also performed high resolution electron energy loss spectroscopy (HREELS) (LK, ELS3000). For calculations we used the density functional theory under the VASP implementation. The most favorable sites for methanol adsorption are on top of a Mo atom in the clean surface and on top of a K atom in the pre-dosed surface. The changes in the work function fit our model as the surface withdraws charge from the adsorbate. The changes in the computed vibrational frequencies also agree with the HREELS results at very low coverage. The C–O bond distance increases while the O–H bond decreases making a C–O bond breakage a possibility on K covered surfaces.     

Adsorption and reactions of CH2I2 on Ru(001) surface

The adsorption and dissociation of CH₂I₂ were studied at 110 K with the aim of generating CH₂ species on the Ru(001) surface. The methods used included X-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), temperature programmed desorption (TPD), Auger electron spectroscopy (AES) and work function measurements. Adsorption of CH₂I₂ is characterized by a work function decrease (0.96 eV at monolayer), indicating that adsorbed CH₂I₂ has a positive outward dipole moment. Three adsorption states were distinguished: a multilayer (T_p=200 K), a weakly bonded state (T_p=220 K) and an irreversibly adsorbed state. A new feature is the formation of CH₃I, which desorbs with T_p=160 K. The adsorption of CH₂I₂ at 110 K is dissociative at submonolayer, but molecular at higher coverages. Dissociation of the monolayer to CH₂ and I proceeded at 198–230 K, as indicated by a shift in the I(3d_5/2) binding energy from 620.6 eV to 619.9 eV. A fraction of adsorbed CH₂ is self-hydrogenated into CH₄ (T_p=220 K), and another one is coupled to di-σ-bonded ethylene, which — instead of desorption — is converted to ethylidyne at 220–300 K. Illumination of the adsorbed CH₂I₂ initiated the dissociation of CH₂I₂ monolayer even at 110 K, and affected the reaction pathways of CH₂.     

Application of radioisotope-excited X-ray fluorescence to the determination of trace elements in blood

A radioisotope-excited energy-dispersive X-ray fluorescence system has been constructed and used for the analysis of blood samples for trace elements. The possibility of determination of trace elements in blood by X-ray fluorescence based on comparison with standard reference materials has been outlined and the applicability of the method demonstrated by the analysis of blood samples. The method enables fast, non-destructive direct analyses to be carried out without lengthy sample pretreatment on a routine basis.     

Dosimetric measurement of the disintegration rate of fission products

Investigations on the disintegration rate of fission products of²³⁸U and²³⁹Pu are presented. The intensity of the - and -radiation of fission products were measured continuously in an interval of 1–1300 hours following the fission, offering the possibility for determining the general and specific characteristics of the individual fission products. A universal measuring procedure was elaborated for the rapid in situ determination of the dosimetric features of fission products, which is suitable for the accurate evaluation and prediction of external absorbed dose even in case of fission products of various origin and unknown composition.     

Bargaining sets and the core in partitioning games

Partitioning games are useful on two counts: first, in modeling situations with restricted cooperative possibilities between the agents; second, as a general framework for many unrestricted cooperative games generated by combinatorial optimization problems.We show that the family of partitioning games defined on a fixed basic collection is closed under the strategic equivalence of games, and also for taking the monotonic cover of games. Based on these properties we establish the coincidence of the Mas-Colell, the classical, the semireactive, and the reactive bargaining setswith the core for interesting balanced subclasses of partitioning games, including assignment games, tree-restricted superadditive games, and simple network games. Prepared during the author’s Bolyai János Research Fellowship. Also supported by OTKA grant T46194.     

Development of an extractive-scintillating chromatographic resin for the detection of radioactive isotopes

In this paper, the development of a new-type of resin is presented, which contains selective complexing and scintillating molecules in a chemically bonded form. The resin material is produced via radiation polymerization of a solution of 2-(4-allyloxy-phenyl)-5-phenyl oxazole, 5-(allyloxy-phenyl)-2-[4-(5-phenyl-oxazole-2-il)-phenyl] oxazole, diethylene glycol dimethacrylate (DEGMA), styrene and the allyl derivative of a 18C6 crown ether-dicarbolic acid complexing agent. The product is a macroporous polymer matrix that shows fluorescent properties and ion binding capacity excellent for radioanalytical purposes.