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.     

(2RS,4SR)‐7‐Bromo‐2‐exo‐(2‐chlorophenyl)‐2,3,4,5‐tetrahydro‐1,4‐epoxynaphtho[1,2‐b]azepine: sheets built by the π‐stacking of hydrogen‐bonded chains

The molecules of the title compound, C₂₀H₁₅BrClNO, are linked into chains by a C—H...π(arene) hydrogen bond, in which the acceptor is the brominated ring of the naphthalene unit, and these chains are linked by an aromatic π–π stacking interaction, again involving the naphthalene unit, into a sheet structure.     

Five 2‐aryl‐substituted tetrahydro‐1,4‐epoxy‐1‐benzazepines: isolated molecules and hydrogen‐bonded chains and sheets

(2SR,4RS)‐2‐exo‐Phenyl‐2,3,4,5‐tetrahydro‐1H‐1,4‐epoxy‐1‐benzazepine, C₁₆H₁₅NO, (I), (2SR,4RS)‐2‐exo‐(4‐chlorophenyl)‐2,3,4,5‐tetrahydro‐1H‐1,4‐epoxy‐1‐benzazepine, C₁₆H₁₄ClNO, (II), and (2SR,4RS)‐2‐exo‐(3‐methylphenyl)‐2,3,4,5‐tetrahydro‐1H‐1,4‐epoxy‐1‐benzazepine, C₁₇H₁₇NO, (III), all crystallize with Z′ = 2, in the space groups Cc, P2₁/n and P2₁/c, respectively. In each of (II) and (III), the conformations of the two independent molecules are significantly different. The molecules in (I) are linked by C—H...π(arene) hydrogen bonds to form two independent chains, each containing only one type of molecule. The molecules in (II) are linked into sheets by a combination of C—H...O, C—H...(N,O) and C—H...π(arene) hydrogen bonds, all of which link pairs of molecules related by inversion, while in (III), the molecules are linked into sheets by a combination of C—H...N, C—H...O and C—H...π(arene) hydrogen bonds. There are no direction‐specific intermolecular interactions of any kind in the structure of (2SR,4RS)‐7‐bromo‐2‐exo‐phenyl‐2,3,4,5‐tetrahydro‐1H‐1,4‐epoxy‐1‐benzazepine, C₁₆H₁₄BrNO, (IV), but in the structure of (2SR,4RS)‐2‐exo‐(4‐bromophenyl)‐7‐chloro‐2,3,4,5‐tetrahydro‐1H‐1,4‐epoxy‐1‐benzazepine, C₁₆H₁₃BrClNO, (V), a combination of one C—H...N hydrogen bond and one C—H...O hydrogen bond links the molecules into sheets of alternating centrosymmetric R²₂(14) and R⁶₆(22) rings. Comparisons are made with the structures of a number of related compounds.     

Self-lubricating Ti–C–N nanocomposite coatings prepared by double magnetron sputtering

This paper is devoted to the development of Ti(C,N)-based nanocomposite protective coatings consisting of nanocrystals of a hard phase (TiN or TiC_xN_y) embedded in an amorphous carbon-based matrix (a-C or a-CN_x). The objective here is the achievement of a good compromise between the mechanical and tribological properties by the appropriate control of the hard/soft phase ratio and the microstructural characteristics of the film. To achieve this purpose, dual magnetron sputtering technique was employed following two different strategies. In the first one, we use Ti and graphite targets and Ar/N₂ gas mixtures, while in the second case, TiN and graphite targets are sputtered in an Ar atmosphere. By changing the sputtering power applied to each magnetron, different sets of samples are prepared for each route. The effect of the bias voltage applied to the substrate is also studied in some selected cases. The mechanical and tribological properties of the films are characterized and correlated with the microstructure, crystallinity and phase composition. The establishment of correlations enables the development of advanced coatings with tailored mechanical and tribological properties for desired applications.     

(E)‐3‐(4‐Methylphenyl)‐2‐(2‐thienyl)acrylonitrile has Z′ = 0.75 in the space group C2/m: fourfold disordered molecules lie in channels enclosed by fully ordered molecules

The title compound, C₁₄H₁₁NS, crystallizes with Z′ = 0.75 in the space group C2/m. Two independent molecules are present, one of which lies with all the non‐H atoms on a mirror plane, while the other is fourfold disordered across a site of 2/m symmetry. The ordered molecules are stacked such that they enclose continuous channels running along twofold rotation axes, and the disordered molecules are positioned within these channels.     

Eight 7‐benzyl‐3‐tert‐butyl‐1‐phenylpyrazolo[3,4‐d]oxazines,encompassing structures containing no intermolecular hydrogen bonds,and hydrogen‐bonded structures in one,two or three dimensions

7‐Benzyl‐3‐tert‐butyl‐1‐phenyl‐6,7‐dihydro‐1H,4H‐pyrazolo[3,4‐d][1,3]oxazine, C₂₂H₂₅N₃O, (I), and 3‐tert‐butyl‐7‐(4‐methylbenzyl)‐1‐phenyl‐6,7‐dihydro‐1H,4H‐pyrazolo[3,4‐d][1,3]oxazine, C₂₃H₂₇N₃O, (II), are isomorphous in the space group P2₁, and molecules are linked into chains by C—H...O hydrogen bonds. In each of 3‐tert‐butyl‐7‐(4‐methoxybenzyl)‐1‐phenyl‐6,7‐dihydro‐1H,4H‐pyrazolo[3,4‐d][1,3]oxazine, C₂₃H₂₇N₃O₂, (III), which has cell dimensions rather similar to those of (I) and (II), also in P2₁, and 3‐tert‐butyl‐1‐phenyl‐7‐[4‐(trifluoromethyl)benzyl]‐6,7‐dihydro‐1H,4H‐pyrazolo[3,4‐d][1,3]oxazine, C₂₃H₂₄F₃N₃O, (IV), there are no direction‐specific interactions between the molecules. In 3‐tert‐butyl‐7‐(4‐nitrobenzyl)‐1‐phenyl‐6,7‐dihydro‐1H,4H‐pyrazolo[3,4‐d][1,3]oxazine, C₂₂H₂₄N₄O₃, (V), a combination of C—H...O and C—H...N hydrogen bonds links the molecules into complex sheets. There are no direction‐specific interactions between the molecules of 3‐tert‐butyl‐7‐(2,3‐dimethoxybenzyl)‐1‐phenyl‐6,7‐dihydro‐1H,4H‐pyrazolo[3,4‐d][1,3]oxazine, C₂₄H₂₉N₃O₃, (VI), but a three‐dimensional framework is formed in 3‐tert‐butyl‐7‐(3,4‐methylenedioxybenzyl)‐1‐phenyl‐6,7‐dihydro‐1H,4H‐pyrazolo[3,4‐d][1,3]oxazine, C₂₃H₂₅N₃O₃, (VII), by a combination of C—H...O, C—H...N and C—H...π(arene) hydrogen bonds, while a combination of C—H...O and C—H...π(arene) hydrogen bonds links the molecules of 3‐tert‐butyl‐1‐phenyl‐7‐(3,4,5‐trimethoxybenzyl)‐6,7‐dihydro‐1H,4H‐pyrazolo[3,4‐d][1,3]oxazine, C₂₅H₃₁N₃O₄, (VIII), into complex sheets. In each compound, the oxazine ring adopts a half‐chair conformation, while the orientations of the pendent phenyl and tert‐butyl substituents relative to the pyrazolo[3,4‐d]oxazine unit are all very similar.     

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.     

Translational and rotational pupil tracking by use of wavefront aberration data and image registration techniques

We present a methodology with which to evaluate translations and rotations of wavefront aberration measurements of systems in which the exit pupil suffers displacements and rotations with respect to the reference frame of the measuring device. We propose to use image registration techniques to account for rotations, translations, and scale changes of the pupil. We present a proof of principle, using an artificial eye in addition to computer simulations. The method is software based and requires no additional hardware.