Algorithmic aspects of mean–variance optimization in Markov decision processes

We consider finite horizon Markov decision processes under performance measures that involve both the mean and the variance of the cumulative reward. We show that either randomized or history-based policies can improve performance. We prove that the complexity of computing a policy that maximizes the mean reward under a variance constraint is NP-hard for some cases, and strongly NP-hard for others. We finally offer pseudopolynomial exact and approximation algorithms.     

Synthesis of polysubstituted benzothiophenes and sulfur-containing polycyclic aromatic compounds via samarium diiodide promoted three-component coupling reactions of thiophene-2-carboxylate

By the promotion of samarium diiodide, thiophene-2-carboxylate reacted with 2 equiv of ketones at the C-4 and C-5 positions to give diols such as 2 and 9. Because the intermediary organosamarium species were oxophilic but not too basic, the double hydroxyalkylations with various ketone substrates, including alkyl aryl ketones, acetylthiophenes, cyclohexanone, alpha-tetralone, and alpha-phenylacetophenones, were realized without complication of side reactions. The diol products underwent an acid-catalyzed dehydration to give dienes such as 3 and 10, which were treated with DDQ to give either polysubstituted thiophenes (e.g., 4 and 11) or benzothiophenes (e.g., 5, 13, and 14) depending on the reaction conditions. Oxidative annulations of 4,5-diarylthiophenes 11 and 4,5,6,7-tetraphenylbenzothiophenes 14 were carried out by photochemical or chemical methods to give the sulfur-containing polycyclic aromatic compounds, such as phenanthro[9,10-b]thiophene-2-carboxylate, piceno[13,14-b]thiophene-2-carboxylate, and tribenzo[fg,ij,rst]pentapheno[15,16-b]thiophene-2-carboxylates. This method is applicable to the preparation of polysubstituted thiophenes, benzothiophenes, and the related compounds possessing liquid crystalline, photochromic, and other functional properties.     

Interfacial reactions in As---Se/Zn

As-Se-based chalcogenide glasses are IR transparent, and are an ideal braze for the ZnSe and ZnS. Interfacial reactions between As-Se and Zn were investigated using reaction couples As-50 at.% Se/Zn at 350°C, As-50 at.% Se/Zn at 370°C and As-60 at.% Se/Zn at 350°C. Cross-sections of reaction couples were analyzed by using optical microscopy and electron probe micro-analysis. Two phases were formed at the interface, and diffusion paths were glass/ZnSe/As₂Zn₃/Zn. Growth rates of the intermetallic layers were determined and at 350°C follow a parabolic law which indicates a diffusion-controlled mechanism.     

Bis(μ‐di‐2‐pyridyl­aminato 1‐oxide)­bis­[(tri­fluoro­acetato)copper(II)] aceto­nitrile disolvate

The crystal structure of the title compound, [Cu₂(C₂F₃O₂)₂(C₁₀H₈N₃O)₂]·2CH₃CN, contains discrete [Cu₂(CF₃COO)₂(O‐dpa)₂] mol­ecules (O‐dpaH is di‐2‐pyridyl­amine 1‐oxide) which have imposed crystallographic twofold symmetry and an aceto­nitrile mol­ecule of solvation. The O‐dpa⁻ ligand is both bidentate and bridging, linking two Cu atoms with a separation of 3.4270 (11) Å. Each Cu atom is surrounded by four coordinated atoms that are almost coplanar, with dimensions Cu—N = 1.940 (2) and 1.984 (3) Å, and Cu—O = 1.912 (2) and 1.945 (2) Å.     

Synthesis and Structure Characterization of 2‐(Dimethylaminomethyl)pyrrolate and 2,5‐Bis(dimethylaminomethyl)pyrrolate Zirconium Complexes

Tetrakis(diethylamido)zirconium reacts with 2‐(dimethylamino)methyl pyrrole (DMAMP) and 2,5‐[bis(dimethylamino)methyl]pyrrole (BDMAMP) to give Zr(NEt)₂(DMAMP)₂ 1 and Zr(NEt)₃(BDMAMP) 2 , respectively. Both 1 and 2 have been characterized by ¹H and ¹³C NMR spectroscopies and 1 has also been characterized by X‐ray crystallography. Complex 1 shows an agostic interaction between Zr and H(21A) in solid state that is not sustained in solution. Reacting 1 with 2 equivalents of trimethylsilyl chloride in toluene yields ZrCl₂(DMAMP)₂ 3 in 75% yield which was characterized by ¹H and ¹³C NMR spectroscopies.