Multicriteria Goal Games

In this paper, we deal with multicriteria matrix games. Different solution concepts have been proposed to cope with these games. Recently, the concept of Pareto-optimal security strategy which assures the property of security in the individual criteria against an opponent's deviation in strategy has been introduced. However, the idea of security behind this concept is based on expected values, so that this security might be violated by mixed strategies when replications are not allowed. To avoid this inconvenience, we propose in this paper a new concept of solution for these games: the G-goal security strategy, which includes as part of the solution the probability of obtaining prespecified values in the payoff functions. Thus, attitude toward risk together with payoff values are considered jointly in the solution analysis.     

Martingale property of empirical processes

It is shown that for a large collection of independent martingales, the martingale property is preserved on the empirical processes. Under the assumptions of independence and identical finite-dimensional distributions, it is proved that a large collection of stochastic processes are martingales essentially if and only if the empirical processes are also martingales. These two results have implications on the testability of the martingale property in scientific modeling. Extensions to submartingales and supermartingales are given.

     

Spectral Properties of Image Measures Under the Infinite Conflict Interaction

We introduce the conflict interaction with two positions between a couple of image probability measures and consider the associated dynamical system. We prove the existence of invariant limiting measures and find the criteria for these measures to be a pure point, absolutely continuous, or singular cotinuous as well as to have any topological type and arbitary Hausdorff dimension.     

A shell model for energy transfer in lanthanide elpasolite crystals

Published in Zhurnal Prikladnoi Spectroscopii, Vol. 62, No. 5, pp. 213–220, September–October, 1995.     

Diastereoselective [4+2] annulation of vinyl carbodiimides with N-alkyl imines. Asymmetric synthetic access to the batzelladine alkaloids

A diastereoselective [4+2] annulation of vinyl carbodiimides with chiral N-alkyl imines has been developed to access the stereochemically rich tricyclic core of the batzelladine alkaloids. Its application to the asymmetric synthesis of batzelladine D permitted the use of long-range, directed hydrogenation and stereoselective intramolecular iodoamination as additional key steps to establish the remaining stereocenters within the natural product with excellent stereocontrol.     

Influence of Temperature and Time on the Stability of Silver in Silica Sol-Gel Glasses

The darkening of silica sol-gel glasses doped with 0.05 mol% silver was studied. Six sols were prepared from TEOS and silver nitrate. Different additives were used, to influence the chemical and physical states of silver: oxidizing or reducing agents (H₂O₂, As₂O₅), colloid stabilizer (sodium citrate) and network modifiers (Li₂O, CaO). Sols were gelified at 60°C and densified at 600°C. The samples without additives and those prepared with H₂O₂ at room temperature even if they were protected from light. With increased temperature, the darkening became samples were heated above, 400°C, reversible bleaching took place. This darkening-bleaching is of thermal nature (“thermochromic effect”) and seems to be determined by a reversible aggregation-disaggregation of tiny silver particles. The presence of sodium citrate, as an additive delayed the darkening effect and the presence of CaO delayed it even further. Lithium oxide inhibited it totally.     

Diazoniapentaphenes. Synthesis from pyridine‐2‐carboxaldehyde and structural verifications

Reactions of pyridine‐2‐carboxaldehyde (9) with α,α′‐dibromo‐o‐ and p‐xylenes led to the corresponding bis‐pyridinium aldehydes 10 and 14. These aldehydes were quite reactive and the respective hydrates 11 and 15 were also formed. Cyclization of 10 or 11 with 48% HBr led to 12 while cyclization with PPA followed by conversion to the bis tribromide and loss of bromine led to 1. Cyclization of 14 or 15 with 48% HBr led to 3. Attempts to react α,α′‐dibromo‐m‐xylene with pyridine‐2‐carboxaldehyde (9) were not successful for the preparation of the bis‐pyridinium aldehyde 13. The bis‐pyridinium acetals 4, 5 and 6 were prepared and cyclized to afford 1, 2 and 3 , respectively, by the previously reported procedures. The structures of 1 and 2 were verified by ¹H‐NMR and ¹³C‐NMR spectroscopy while that of 3 was confirmed by X‐ray analysis.     

Thermodynamic properties of organic compounds in aqueous solution. II. Apparent molal heat capacities of piperidines,morpholines, and piperazines

Apparent molal heat capacities of some piperidine, morpholine, and piperazine derivatives in aqueous solution have been determined by adiabatic calorimetry in the temperature range 20–55°C and in the molality range 0.2–1m. Comparison of experimental values with those calculated through group contributions, found for monofunctional compounds, indicates strong interactions between the hydrophilic centers. An interpretation is given of the possible mechanism of this interaction. Also, values of ΔC _p for the addition reaction of proton to nitrogen centers of mono- and bifunctional organic compounds are examined.