Nash equilibria of discontinuous non-zero-sum two-person games

The paper investigates two classes of non-zero-sum two-person games on the unit square, where the payoff function of Player 1 is convex or concave in the first variable. It is shown that this assumption together with the boundedness of payoff functions imply the existence of -Nash equilibria consisting of two probability measures concentrated at most at two points each.This research project No. 211589101 was supported by KBN Grant under contract 664/2/91.     

X-ray structure of 3,3′-bis(4-methylthioquinolinyl) sulfide

The structure of the title compound has been solved by direct methods, and refined to anR value of 0.035 for 1613 reflections. Both methyl carbon atoms deviate from the plane of the pyridine ring by 1.505(3) Å in opposite directions. Both sulfur atoms S(1) and S(2) remain in short contact, at 3.247(1) Å. The two pyridine rings are inclined at 61.4(2)° to each other.Part XIV in the series of Azinyl Sulfides.     

X-ray structure of isomeric 3-chloro-4-(methylthio)- and 4-chloro-3-(methylthio)quinolines

The crystal and molecular structures of two isomeric 3,4- and 4,3-chloro-(methylthio)quinolines have been determined. For 3-chloro-4-(methylthio)-quinoline (3-Cl–4-MeS–Q); triclinic, space group ,a=7.199(3),b=7.919(3),c=8.921(3) Å, =89.74(3), =74.29(3), =78.55(3)°. For 4-chloro-3-(methylthio)quinoline (4-Cl–3-MeS–Q): monoclinic, space group P2₁/n,a=12.860(4),b=5.424(2),c=13.434(4) Å, =90.84(3)°. The values of the Cl...S distance as well as those for the Cl–C–C(S) and (Cl)C–C–S angles indicate the attractive interaction between ortho-situated heteroatoms in isomer 4-Cl–3-MeS–Q contrary to the effects observed in the case of 3-Cl–4-MeS–Q. The conclusions were confirmed by calculations of atomic charges withab initio method 4-31G basis set, which show positively charged sulfur atom in 4-Cl–3-MeS–Q and negatively charged sulfur in 3-Cl–4-MeS–Q.Part XXX in the series of Azinyl Sulfides.     

Ionic liquid functionalized polylactide by cationic polymerization: Synthesis and stabilization of carbon nanotube suspensions

Medium molecular weight poly(L ,L ‐lactide)s (PLA) containing at one chain end ionic group derived from imidazolium ionic liquid (IL) were synthesized by cationic polymerization using hydroxylated IL as initiator. matrix assisted laser desorption/ionization time‐of‐flight analysis confirmed the structure of products (PLA‐IL). Carbon nanotubes (CNT) were dispersed in solution of PLA‐IL in 1,4‐dioxane and significant improvement of stability of suspension was observed by measurements of suspension absorbance. Similar effect was, however, observed also for solutions of PLA which did not contain terminal IL group. CNT samples treated with PLA‐IL and PLA were isolated, thoroughly washed with 1,4‐dioxane and stability of suspensions was again measured. Sample treated with PLA after washing behave similarly to untreated CNT. Stability of suspension of CNT treated with PLA‐IL after washing was considerably higher than that of untreated CNT and the presence of polymer bound to CNT was clearly detectable in scanning electron microscopy images. Results indicate that there is indeed an interaction between end‐group derived from IL and CNT surface as postulated earlier but to observe solely this effect an excess of polymer should be removed, otherwise factors such as increase of viscosity of solution or weak interactions of PLA ester groups with CNT may obscure results. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Two-Dimensional Separation of Some Amino Acids by HPTLC and Pressurized Planar Electrochromatography

JPC – Journal of Planar Chromatography – Modern TLC - Two-dimensional (2D) separation of eight amino acids has been achieved by HPTLC in the first dimension and pressurized planar...     

Calcium chloride rhenate(VII) dihydrate

The crystal structure of calcium chloride rhenate(VII) dihydrate, CaCl(ReO₄)·2H₂O, investigated at 85 K, consists of calcium cations, chloride anions, rhenate(VII) anions and water molecules. In the nearly tetrahedral rhenate(VII) anion, all constituent atoms lie on special positions of m2m (Re) and m (O) site symmetries. The Cl⁻ anion and water O atom lie on special positions of m2m and 2 site symmetries, respectively. The Ca²⁺ ion, also on a special position (m2m), is eight‐coordinated in a distorted square‐antiprismatic coordination mode. The crystal has a layered structure stabilized by Ca—O coordination bonds and O—H...Cl hydrogen bonds.     

Kinetics of solid-state NMR cross-polarization from protons to carbon-13 in surgical sutures

Commercial Dexon surgical sutures, made of polyglycolide (PGA), were examined using ¹³C CP/MAS NMR. The study shows that detailed analysis of the cross-polarization (CP) process is useful in the peak assignments and in the assessment of molecular mobility in the polymer domains. Crystallinity of PGA in the sutures was estimated at ca. 55%.     

Enhanced cooperation in prisoner’s dilemma with aspiration

We develop an aspiration-based dynamic model which leads to enhanced cooperation in the Prisoner’s Dilemma game played by the continuous population of agents. The main idea is to limit the aggregate information available to the agents. The model–a system of three nonlinear differential equations–describes the evolution of the aspiration levels of players who use different strategies, and the evolution of the mean frequency of the cooperative strategy in the system of players. The stationary (partial) cooperation level is calculated explicitly. We demonstrate that, contrary to the similar model with only one global aspiration level, the stationary cooperation level can be greater than half.     

Discrete dynamic programming with outcomes in random variable structures

Multiobjective approach is the common way of generalization single-criterion dynamic programming models. Another way is to consider partially ordered criteria structures. That approach is rather rare. The aim of the paper is to present such a model. Generalization of Bellman’s principle of optimality is employed to create a forward procedure to find the set of all maximal elements. As this set is usual large, the second problem under consideration is to find its subsets. To reduce the number of solutions presented to decision maker we propose to apply a family of narrowing relations. That approach is similar to scalarization in multiobjective programming. Ordered structures of random variables based on mean–variance, stochastic dominance and inverse stochastic dominance are considered. Numerical illustration is given at the end of the paper.     

Dihydroxyacetone (DHA) monomer complexes with CaBr2 and CdCl2

Two hydrated complexes of monomeric dihydroxyacetone (DHA; the simplest ketose), viz. the calcium bromide complex bis(μ‐dihydroxyacetone)bis[tetraaquacalcium(II)] tetrabromide (isomorphous with the chloride compound reported previously), [Ca₂(C₃H₆O₃)₂(H₂O)₈]Br₄, (2e), and the cadmium chloride complex poly[[bis(μ‐dihydroxyacetone)bis[bis(dihydroxyacetone)cadmium(II)]] [diaquatetradeca‐μ‐chlorido‐dichloridohexacadmium(II)] tetrahydrate], {[Cd₂(C₃H₆O₃)₆][Cd₆Cl₁₆(H₂O)₂]·4H₂O}_n, (2f), are described. The Ca²⁺ or Cd²⁺ ions are bridged by the carbonyl O atoms from two DHA molecules to form centrosymmetric dimers, with Ca...Ca distances of 4.334 (2) and 4.300 (2) Å in (2e), and a Cd...Cd distance of 4.195 (1) Å in (2f). Almost identical in shape, the eight‐coordinate polyhedra of the Ca²⁺ and Cd²⁺ ions are composed of 2n O atoms from n DHA molecules [n = 2 in (2e) and n = 4 in (2f)] and are completed by four water molecules in (2e). DHA molecules chelate the cations via both the hydroxyl and carbonyl groups and exist in an extended conformation, with both hydroxyl groups being synperiplanar to the carbonyl O atom. The crystal structures are stabilized by similar extensive O—H...X (X = Cl or Br) and O—H...O hydrogen‐bond networks involving all hydroxyl groups and the water molecules.