Stationary,completely mixed and symmetric optimal and equilibrium strategies in stochastic games

In this paper, we address various types of two-person stochastic games—both zero-sum and nonzero-sum, discounted and undiscounted. In particular, we address different aspects of stochastic games, namely: (1) When is a two-person stochastic game completely mixed? (2) Can we identify classes of undiscounted zero-sum stochastic games that have stationary optimal strategies? (3) When does a two-person stochastic game possess symmetric optimal/equilibrium strategies? Firstly, we provide some necessary and some sufficient conditions under which certain classes of discounted and undiscounted stochastic games are completely mixed. In particular, we show that, if a discounted zero-sum switching control stochastic game with symmetric payoff matrices has a completely mixed stationary optimal strategy, then the stochastic game is completely mixed if and only if the matrix games restricted to states are all completely mixed. Secondly, we identify certain classes of undiscounted zero-sum stochastic games that have stationary optima under specific conditions for individual payoff matrices and transition probabilities. Thirdly, we provide sufficient conditions for discounted as well as certain classes of undiscounted stochastic games to have symmetric optimal/equilibrium strategies—namely, transitions are symmetric and the payoff matrices of one player are the transpose of those of the other. We also provide a sufficient condition for the stochastic game to have a symmetric pure strategy equilibrium. We also provide examples to show the sharpness of our results.     

Ultrasound-assisted rapid and efficient one-pot synthesis of furanyl spirooxindolo and spiroquinoxalinopyrrolizidines by 1,3-dipolar cycloaddition: a green protocol

Efficient synthesis of novel spirooxindolo and spiroquinoxalinopyrrolizidine derivatives was expediently accomplished with regioselectivity via one-pot, three-component 1,3-dipolar cycloaddition using ultrasonication. Chalcones derived from both heteroaryl methyl ketones and furfural were used as dipolarophiles in these reactions. The synthesized compounds were analyzed by ¹H and ¹³C nuclear magnetic resonance (NMR), mass spectrometry, and elemental (CHN) analysis. Single-crystal X-ray diffraction studies of one of the compounds (11d) proved the structure and regiochemistry of the cycloaddition. The ultrasound methodology is clearly advantageous, and the desired products were obtained in moderate to good yield in shorter reaction time compared with conventional heating and fusion methods.     

Amperometric hydrogen peroxide sensor based on the use of CoFe<Subscript>2</Subscript>O<Subscript>4</Subscript> hollow nanostructures

The authors report on the preparation of a hollow-structured cobalt ferrite (CoFe₂O₄) nanocomposite for use in a non-enzymatic sensor for hydrogen peroxide (H₂O₂). Silica (SiO₂) nanoparticles were exploited as template for the deposition of Fe₃O₄/CoFe₂O₄ nanosheets, which was followed by the removal of SiO₂ template under mild conditions. This leads to the formation of hollow-structured Fe₃O₄/CoFe₂O₄ interconnected nanosheets with cubic spinel structure of high crystallinity. The material was placed on a glassy carbon electrode where it acts as a viable sensor for non-enzymatic determination of H₂O₂. Operated at a potential of ?0.45 V vs. Ag/AgCl in 0.1 M NaOH solution, the modified GCE has a sensitivity of 17 nA μM^?1 cm^?2, a linear response in the range of 10 to 1200 μM H₂O₂ concentration range, and a 2.5 μM detection limit. The sensor is reproducible and stable and was applied to the analysis of spiked urine samples, where it provided excellent recoveries.

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Graphical abstract Schematic of a cobalt ferrite (CoFe₂O₄) hollow structure for use in electrochemical determination of H₂O₂. The sensor shows a low detection limit, a wide linear range, and excellent selectivity for H₂O₂.

     

Stereoselective Total Synthesis of Mangiferaelactone using D‐Mannose as a Chiral Pool

A convergent total synthesis of mangiferaelactone has been accomplished in a highly stereoselective manner from readily available D ‐mannose. The following methods like organocatalytic enantioselective epoxidation, ring‐closing metathesis, and Steglich esterification have been employed as key steps, which make this approach more attractive.     

Palladium‐Catalyzed Regio‐ and Stereoselective Cross‐Addition of Terminal Alkynes to Ynol Ethers and Synthesis of 1,4‐Enyn‐3‐ones

Conjugated enynes, enol ethers, and enynones are versatile building blocks that can be elaborated by a wide variety of synthetic transformations. The selective synthesis of such units is a prerequisite for their effective utilization. The synthesis of conjugated 2‐phenoxyenynes through a palladium‐catalyzed cross‐addition of terminal alkynes to phenylethynyl ethers (hydroalkynylation) is now presented. The reaction is highly regio‐, stereo‐, and chemoselective, and shows excellent tolerance toward functional groups. The addition further features very mild reaction conditions (room temperature) and an inexpensive catalytic system (without a ligand and with a cheaply available Pd catalyst). The thus synthesized enynyl ethers with allylic hydroxy tethers, which survived the reaction, were shown to be ready precursors for valuable 1‐en‐4‐yn‐3‐ones.     

Structural consequences of weak interactions in dispirooxindole derivatives

Spiro scaffolds are being increasingly utilized in drug discovery due to their inherent three‐dimensionality and structural variations, resulting in new synthetic routes to introduce spiro building blocks into more pharmaceutically active molecules. Multicomponent cascade reactions, involving the in situ generation of carbonyl ylides from α‐diazocarbonyl compounds and aldehydes, and 1,3‐dipolar cycloadditon with 3‐arylideneoxindoles gave a novel class of dispirooxindole derivatives, namely 1,1′′‐dibenzyl‐5′‐(4‐chlorophenyl)‐4′‐phenyl‐4′,5′‐dihydrodispiro[indoline‐3,2′‐furan‐3′,3′′‐indoline]‐2,2′′‐dione, C₄₄H₃₃ClN₂O₃, (I), 1′′‐acetyl‐1‐benzyl‐5′‐(4‐chlorophenyl)‐4′‐phenyl‐4′,5′‐dihydrodispiro[indoline‐3,2′‐furan‐3′,3′′‐indoline]‐2,2′′‐dione, C₃₉H₂₉ClN₂O₄, (II), 1′′‐acetyl‐1‐benzyl‐4′,5′‐diphenyl‐4′,5′‐dihydrodispiro[indoline‐3,2′‐furan‐3′,3′′‐indoline]‐2,2′′‐dione, C₃₉H₃₀N₂O₄, (III), and 1′′‐acetyl‐1‐benzyl‐4′,5′‐diphenyl‐4′,5′‐dihydrodispiro[indoline‐3,2′‐furan‐3′,3′′‐indoline]‐2,2′′‐dione acetonitrile hemisolvate, C₃₉H₃₀N₂O₄·0.5C₂H₃N, (IV). All four compounds exist as racemic mixtures of the SSSR and RRRS stereoisomers. In these structures, the two H atoms of the dihydrofuran ring and the two substituted oxindole rings are in a trans orientation, facilitating intramolecular C—H...O and π–π interactions. These weak interactions play a prominent role in the structural stability and aid the highly regio‐ and diastereoselective synthesis. In each of the four structures, the molecular assembly in the crystal is also governed by weak noncovalent interactions. Compound (IV) is the solvated analogue of (III) and the two compounds show similar structural features.     

Synthesis and antimicrobial activity of novel 3 substituted 1,5‐dihydro‐2,4,3‐benzodioxaphosphepine 3‐oxides

Novel 3 substituted 1,5‐dihydro‐2,4,3‐benzodioxaphosphepine 3‐oxides ( 5a–h ) were synthesized by reacting 1,2‐benzenedimethanol ( 1 ) with phosphorus tribromide in the presence of triethylamine at 0–30°C and subsequent reaction of the monobromide ( 2 ) with different Grignard reagents ( 3 ) at room temperature. The products ( 4 ) were converted to corresponding oxides 5a–i by oxidation with H₂O₂ at room temperature. The chemical structures of all the products were confirmed by analytical, IR and NMR (¹H, ¹³C, and ³¹P) spectral data. Their antifungal and antibacterial activity is also evaluated. Most of these compounds exhibited moderate antimicrobial activity in the assay. © 2005 Wiley Periodicals, Inc. Heteroatom Chem 16:572–575, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20154     

A distributed feedback dye laser based on higher order Bragg scattering

A distributed feedback dye laser based on second order Bragg scattering due to a sinusoidal susceptibility modulation is reported. Rhodamine 6G dye solution in three different solvents; methanol, ethanol and benzyl alcohol is pumped by interference fringes produced by two beams from the second harmonic of Nd:YAG laser. Output power is plotted as a function of the pump power. The spectrum of dye laser shows a new type of modulation.     

A host-guest optical sensor for aliphatic amines based on lipophilic cyclodextrin

A host-guest optical sensor for the determination of aliphatic amines as exemplified by octylamine is proposed. It is based on the reversible fluorescence enhancement of heptakis(2,6-di-O-isobutyl)-β-cyclodextrin(DOB-β-CD) hosting tetraphenylporphyrin (TPP) immobilized in poly(vinyl chloride) (PVC) membrane by aliphatic amine extracted from aqueous phase into membrane phase. The optimum membrane contained 1.15 wt % TPP, 6.15 wt % DOB-β-CD as sensing reagent and other membrane materials. The fluorescence enhancement of the membrane resulted from the formation of a stable three-component complex among DOB-β-CD, TPP, and aliphatic amines. With the optimum conditions described, the fluorescence response of the sensor to octylamine shows a good correlation with the theoretically derived equation in the range 1.0 × 10^–6 to 8.0 × 10^–4 mol/L. The response characteristics including reversibility, response time, reproducibility and lifetime and selectivity of this optical device are also discussed in detail. This sensor has also been applied for the determination of octylamine in water samples containing interferents with satisfactory recovery. Received: 21 November 1999 / Revised: 10 January 2000 / Accepted: 15 January 2000