Interaction between Anions and Molybdenum Allyl Dicarbonyl Complexes of 1,4,7‐Trithiacyclononane

The labile complex [MoCl(η³‐methallyl)(CO)₂(NCMe)₂] reacts with the ligand 1,4,7‐trithiacyclononane ([9]aneS₃) and the salt NaBAr′₄ to afford [Mo(η³‐methallyl)(CO)₂([9]aneS₃)][BAr′₄] ( 1?BAr′₄ ). An analogous reaction of [MoBr(η³‐allyl)(CO)₂(NCMe)₂] yields [Mo(η³‐allyl)(CO)₂([9]aneS₃)][BAr′₄] ( 2?BAr′₄ ). The new compounds 1?BAr′₄ and 2?BAr′₄ were characterized by IR and NMR spectroscopic analysis and X‐ray diffraction studies. Both compounds feature the cyclic thioether [9]aneS₃ coordinated as a tridentate ligand to the molybdenum center. The allyl ligand in 2?BAr′₄ is aligned with the middle of the OC‐Mo‐CO angle, which is acute. Both of these features are typical of most pseudo‐octahedral allyl dicarbonyl molybdenum complexes. In contrast, the allyl group is rotated in 1?BAr′₄ , which is attributed to steric hindrance between the methyl substituent and the ligated thioether, and the OC‐Mo‐CO angle is obtuse. Compound 1?BAr′₄ undergoes rapid substitution of [9]aneS₃ by either chloride and fluoride ions in dichloromethane, and the products include the known species [{Mo(η³‐methallyl)(CO)₂}₂(μ‐Cl)₃]^? and a structurally similar new anionic complex with two fluoro and one hydroxo bridging ligands, respectively. Stable supramolecular adducts were formed in the reactions of 1?BAr′₄ and 2?BAr₄ with bromide, iodide, hydrogensulfate, and methanesulfonate compounds. The binding constants of these adducts in dichloromethane were calculated from ¹H NMR spectroscopic titration data, and the solid‐state structures of the 1?Br , 1?HSO₄ , 1?I , and 2?I adducts were determined by X‐ray diffraction studies. The surprising slightly higher stability of the iodide adduct relative to that of bromide was investigated theoretically, with the results pointing to an effect of the differential solvation of the halide ions.     

Avoiding unfairness of Owen allocations in linear production processes

This paper deals with cooperation situations in linear production problems in which a set of goods are to be produced from a set of resources so that a certain benefit function is maximized, assuming that resources not used in the production plan have no value by themselves. The Owen set is a well-known solution rule for the class of linear production processes. Despite their stability properties, Owen allocations might give null payoff to players that are necessary for optimal production plans. This paper shows that, in general, the aforementioned drawback cannot be avoided allowing only allocations within the core of the cooperative game associated to the original linear production process, and therefore a new solution set named EOwen is introduced. For any player whose resources are needed in at least one optimal production plan, the EOwen set contains at least one allocation that assigns a strictly positive payoff to such player.     

Lectures on the ekeland variational principle with applications and detours

Book Review

Lectures on the ekeland variational principle with applications and detoursD. G. de Figueiredo Tata Institute of Fundamental Research, Bombay, Lectures on Mathematics and Physics-Mathematics 81, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1989, 96 pp., Softcover DM20,-, ISBN 3-540-51179-2     

Dynamic programming analysis of the TV game “Who wants to be a millionaire?”

This paper uses dynamic programming to investigate when contestants should use lifelines or when they should just stop answering in the TV quiz show ‘Who wants to be a millionaire?’. It obtains the optimal strategies to maximize the expected reward and to maximize the probability of winning a given amount of money.     

Structural changes induced on strontium barium niobate glass by femtosecond laser irradiation

Localized modification of the optical properties of erbium doped strontium barium niobate (SBN) glass has been performed using femtosecond laser irradiation. The samples, with composition SrO–BaO–Nb₂O₅–B₂O₅ and doped with 5%mol of Er³⁺, were fabricated using a melt-quenching method. The samples were irradiated with different number of pulses per spot (1–50 pulses) at two different laser fluences (2.6 and 5.6 J/cm²) by using an fs laser amplifier operating at 800 nm and generating pulses with a duration of 120 fs. Micro-luminescent microscopy, using an Ar⁺ laser as excitation source, has been used to analyze the modifications of the luminescent properties of the sample upon fs laser exposure. The emissions of the Er³⁺: ⁴I_11/2→⁴I_15/2 and ⁴I_13/2→⁴I_15/2 transitions allow appreciating the structural modifications caused by femtosecond laser exposure. The lifetimes of the levels involved in these transitions were measured inside and outside the laser irradiated region. These measurements have been compared with those obtained in bulk glass ceramic sample, which is obtained from the glass precursor by a thermal treatment in order to estimate the optimal conditions to produce nanocrystals in a localized region by ultrafast laser irradiation.     

Extensive facility location problems on networks with equity measures

This paper deals with the problem of locating path-shaped facilities of unrestricted length on networks. We consider as objective functions measures conceptually related to the variability of the distribution of the distances from the demand points to a facility. We study the following problems: locating a path which minimizes the range, that is, the difference between the maximum and the minimum distance from the vertices of the network to a facility, and locating a path which minimizes a convex combination of the maximum and the minimum distance from the vertices of the network to a facility, also known in decision theory as the Hurwicz criterion. We show that these problems are NP-hard on general networks. For the discrete versions of these problems on trees, we provide a linear time algorithm for each objective function, and we show how our analysis can be extended also to the continuous case.     

Excitonic effects and optical properties of passivated CdSe clusters

We calculate the optical properties of a series of passivated nonstoichiometric CdSe clusters using two first-principles approaches: time-dependent density functional theory within the local-density approximation, and by solving the Bethe-Salpeter equation for optical excitations with the GW approximation for the self-energy. We analyze the character of optical excitations leading to the first low-energy peak in the absorption cross section of these clusters. Within time-dependent density functional theory, we find that the lowest-energy excitation is mostly a single-level to single-level transition. In contrast, many-body methods predict a strong mixture of several different transitions, which is a signature of excitonic effects. The majority of the clusters have a series of dark transitions before the first bright transition. This may explain the long radiative lifetimes observed experimentally.     

The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approaches

In this paper we introduce the Single Period Coverage Facility Location Problem. It is a multi-period discrete location problem in which each customer is serviced in exactly one period of the planning horizon. The locational decisions are made independently for each period, so that the facilities that are open need not be the same in different time periods. It is also assumed that at each period there is a minimum number of customers that can be assigned to the facilities that are open. The decisions to be made include not only the facilities to open at each time period and the time period in which each customer will be served, but also the allocation of customers to open facilities in their service period.