Integration-segregation decisions under general value functions: "create your own bundle - choose 1, 2, or all 3!",

Whether to keep products segregated (e.g., unbundled) or integrate some or all of them (e.g., bundle) has been a problem of profound interest in areas such as portfolio theory in finance, risk capital allocations in insurance and marketing of consumer products. Such decisions are inherently complex and depend on factors such as the underlying product values and consumer preferences, the latter being frequently described using value functions, also known as utility functions in economics. In this paper, we develop decision rules for multiple products, which we generally call ‘exposure units’ to naturally cover manifold scenarios spanning well beyond ‘products’. Our findings show, e.g. that the celebrated Thaler's principles of mental accounting hold as originally postulated when the values of all exposure units are positive (i.e. all are gains) or all negative (i.e. all are losses). In the case of exposure units with mixed-sign values, decision rules are much more complex and rely on cataloging the Bell number of cases that grow very fast depending on the number of exposure units. Consequently, in the present paper, we provide detailed rules for the integration and segregation decisions in the case up to three exposure units, and partial rules for the arbitrary number of units.

Exploitation of the menshutkin reaction for the controlled assembly of halogen bonded architectures incorporating 1,2-diiodotetrafluorobenzene and 1,3,5-Triiodotrifluorobenzene

1,4-Diazabicyclo[2.2.2]octane (DABCO) forms well-defined co-crystals with 1,2-diiodotetrafluorobenzene (1,2-DITFB), [(1,2-DITFB)2DABCO], and 1,3,5-triiodotrifluorobenzene, [(1,3,5-TITFB)2DABCO]. Both systems exhibited lower-than-expected supramolecular connectivity, which inspired a search for polymorphs in alternative crystallization solvents. In dichloromethane solution, the Menshutkin reaction was found to occur, generating chloride anions and quaternary ammonium cations through the reaction between the solvent and DABCO. The controlled in situ production of chloride ions facilitated the crystallization of new halogen bonded networks, DABCO–CH2Cl[(1,2-DITFB)Cl] (zigzag X-bonded chains) and (DABCO–CH2Cl)3[(1,3,5-TITFB)2Cl3]·CHCl3 (2D pseudo-trigonal X-bonded nets displaying Borremean entanglement), propagating with charge-assisted C–I···Cl– halogen bonds. The method was found to be versatile, and substitution of DABCO with triethylamine (TEA) gave (TEA-CH2Cl)3[(1,2-DITFB)Cl3]·4(H2O) (mixed halogen bond hydrogen bond network with 2D supramolecular connectivity) and TEA-CH2Cl[(1,3,5-TITFB)Cl] (tightly packed planar trigonal nets). The co-crystals were typically produced in high yield and purity with relatively predictable supramolecular topology, particularly with respect to the connectivity of the iodobenzene molecules. The potential to use this synthetic methodology for crystal engineering of halogen bonded architectures is demonstrated and discussed.

1-(4-Chloro-3-fluorophenyl)-2-[(3-phenylisoquinolin-1-yl)sulfanyl]ethanone

In the title compound, C23H15ClFNOS, the isoquinoline system and the 4-chloro-3-fluorophenyl ring are aligned at 80.4 (1)degrees. The dihedral angle between the isoquinoline system and the pendant (unsubstituted) phenyl ring is 19.91 (1)degrees.

Synthesis, antimicrobial and cytotoxic activities of 1,3,4-oxadiazoles, 1,3,4-thiadiazoles and 1,2,4-triazoles

A new class of 1,3,4-oxadiazoles were prepared from acid hydrazides on treatment with different carboxylic acids in the presence of phosphorus oxychloride. Interconversion of oxadiazoles to thiadiazoles and triazoles was carried out with appropriate reagents. The antimicrobial and cytotoxic activities of compounds 7a-d to 12a-d were tested. Compounds 10d and 12d showed pronounced antimicrobial activity. Further, compound 10d exhibited maximum cytotoxicity. (C) 2008 Elsevier Masson SAS. All rights reserved.

Acid-catalysed cyclisations: structures of novel products isolated in the reaction of 2-[3-(2,6-dimethoxyphenyl)but-2-enyl]-2-methylcyclopentane-1,3-dione with MeOH-HCl

Reaction of the title compound (1a) with anhydrous MeOH-HCl gave 2-endo-(2,6-dimethoxyphenyl)-2-exo-methyl-5-methylbicyclo[3.2.1]octane-6,8-dione (3a), 1,5,14-timethoxy-5,8-seco-6,7-dinorestra-1,3,5(10),9(11)-tetraen-17-one (4), 1,5-dimethoxy-5,8-seco-6,7-dinorestra-1,3,5(10),8,14-pentaen-17-one (5), and 3,4,5,6-tetrahydro-2,7-dimethoxy-3,6-dimethyl-3,2,6-(13-oxopropan[1]yI[3]ylidene)-2H-1-benzoxocin (6). Structures assigned to compounds (3a), (4), and (6) are based on spectral data. The exo-tricyclic acetal structure (6) was further confirmed by the analysis of the 1H n.m.r. spectra of the isomeric alcohols (11) and (12), obtained by sodium borohydride reduction of (6).

Studies in terpenoids. Part 42. Synthesis of 3-(2-hydroxyisopropyl)5,8-dimethyl-1,2-naphthoquinone (emmotin-H)

Emmotin-H, a naturally occurring sesquiterpenoid 1,2-naphthoquinone pigment (1) has been synthesised in a four step sequence starting from the known 5,8-dimethyl-4-oxotetralin-2-carboxylic acid (3a). Selenium dioxide oxidation of its methyl ester (3b) gives 3-methoxycarbonyl-5,8-dimethyl-1,2-naphthoquinone (4) which on reductive acetylation affords the corresponding diacetoxynaphthalene ester (5). Its reaction with excess of methylmagnesium iodide is accompanied by aerial oxidation during work-up and furnishes emmotin-H (1).

Dialkyl (3-Aryl- 1,2,4-oxadiazol-5-yl)phosphonates: Synthesis and Thermal Behavior-Evidence for Monomeric Alkyl Metaphosphate

Dialkyl (3-aryl-l,2,4-oxadiazol-5-yl)phosphonate6sa -h have been obtained by 1,3-dipolar cycloaddition of arenenitrile oxides 5a-f to dialkyl phosphorocyanidates (4a and 4b) in yields ranging between 30% and 58%. A standardized method for obtaining cyanidates 4a and 4b has been established. The diethyl thiophosphorocyanidate (4c) is less reactive than 4a and 4b, only the 3-(4'-nitrophenyl) derivative 6i being obtainable. While the IR and NMFt spectra of 6a-i were unexceptional, their UV spectra showed evidence of conjugative interaction in high degrees between the phosphonate and heterocyclic moieties as well as a varying conjugative interaction between the heterocyclic and aryl moieties. The oxadiazoles 6a-h are thermally labile and yield trialkyl phosphates 7 as the only identifiable products. A mechanism based on the intermediacy of monomeric alkyl metaphosphate 11 in the formation of trialkyl phosphate was postulated, and supportive evidence in the form of trapping the metaphosphate with acetophenone has been obtained.

Structure of 7-methyl-1(2)a,1(6)a,3(4)a-trihomocubane-1(6)a,3(4)a-dione,star-c12h12o2- a case of enantiomeric and rotational disorder

M r = 188.22, monoclinic, P21/n, a = 6.219 (2), b= 10.508 (2), c=7.339 (1)A, t= 107.64 (2) °, V= 457 ,/k 3, Z = 2, D m - - 1.360 (3), D x = 1.366 (2)Mgm -3, ~,(MoKa) = 0.7107/~, #= 0.053 mm -I, F(000) = 200, T= 293 K. Final R = 5.8% for 614 significant reflections. The molecule, which does not possess a centre of symmetry, occupies a crystallographic centre of symmetry because of the statistical enantiomeric and rotational disorder. Latticeenergy calculations, based on van der Waals attractive and repulsive potentials, clearly show minima at the observed disordered positions.

1-(2,4-Dichlorophenyl)-3-[4-(dimethylamino)-phenyl]prop-2-enone

In the title compound, C17H15Cl2NO, the dimethylaminophenyl group is close to coplanar with the central propenone group [dihedral angle =13.1 (1)degrees between the mean planes], while the dichlorophenyl group is twisted from the plane [dihedral angle = 64.0 (1)degrees].In the crystal, C-H center dot center dot center dot O and weak C-H center dot center dot center dot pi interactions are formed between molecules.

High resolution genetic and physical mapping of the I-3 region of tomato chromosome 7 reveals almost continuous microsynteny with grape chromosome 12 but interspersed microsynteny with duplications on Arabidopsis chromosomes 1, 2 and 3

The tomato I-3 gene introgressed from the Lycopersicon pennellii accession LA716 confers resistance to race 3 of the fusarium wilt pathogen Fusarium oxysporum f. sp. lycopersici. We have improved the high-resolution map of the I-3 region of tomato chromosome 7 with the development and mapping of 31 new PCR-based markers. Recombinants recovered from L. esculentum cv. M82 × IL7-2 F2 and (IL7-2 × IL7-4) × M82 TC1F2 mapping populations, together with recombinants recovered from a previous M82 × IL7-3 F2 mapping population, were used to position these markers. A significantly higher recombination frequency was observed in the (IL7-2 × IL7-4) × M82 TC1F2 mapping population based on a reconstituted L. pennellii chromosome 7 compared to the other two mapping populations based on smaller segments of L. pennellii chromosome 7. A BAC contig consisting of L. esculentum cv. Heinz 1706 BACs covering the I-3 region has also been established. The new high-resolution map places the I-3 gene within a 0.38 cM interval between the molecular markers RGA332 and bP23/gPT with an estimated physical size of 50-60 kb. The I-3 region was found to display almost continuous microsynteny with grape chromosome 12 but interspersed microsynteny with Arabidopsis thaliana chromosomes 1, 2 and 3. An S-receptor-like kinase gene family present in the I-3 region of tomato chromosome 7 was found to be present in the microsyntenous region of grape chromosome 12 but was absent altogether from the A. thaliana genome.

Structure of (4S)-2,4-dimethyl-1,2-dihydropyrazino[2,1-b]quinazoline-3(4H),6-dione

C13HI3N302, orthorhombic, P2~2121, a = 17.443 (5), b = 11.650 (4), c = 5.784 (1)/~, Z = 4, d m = 1.456, d c = 1.429 Mg m -3, F(000) = 512, g(Cu Ka) = 0.843 mm-L The R index is 0.040 for 1358 significant reflections. The structure is stabilized by C-H...O interactions. The N-methylated eis peptide group which forms part of a six-membered ring is non-planar. The torsion angle about the peptide bond is -6.1 (4) ° and the peptide bond length is 1.337 (3) A.

1-Benzoyl-3-methyl-2,6-diphenyl-4-piperidone

In the title moleclue, C25H23NO2, the 4-piperidone ring adopts a boat conformation. The molecular conformation is stabilized by an intramolecular C-H center dot center dot center dot O hydrogen bond. In the crystal, molecules are connected through weak intermolecular C-H center dot center dot center dot O hydrogen bonds.

Structure of ethyl 1,2,2-tricyano 3-(4-nitrophenyl)-cyclopropane-1-carboxylate

C15HIoN404, monoclinic, P2~/c, a = 10.694(8), b = 11.743 (8), c - 12.658 (8) A, fl = 113.10 (7) °, V = 1462.1 A 3, Z = 4, O m = 1 "38, O c = 1.408 g cm -3, t,t(MoKa, ~, = 0.7107 ]~) = 0.99 cm -i, F(000) = 640. The structure was solved by direct methods and refined to an R value of 0.054 using 1398 intensity measurements. The relative magnitudes of interaction of the substituents and the extent to which a ring can accommodate interactions with substituents are discussed.

Reinvestigation of the structure of Feist's acid 3-methylene-trans-1,2-cyclopropanedicarboxylic acid

C6H604, Mr = 142, triclinic, P[, a = 4.842(1), b = 7.607(1), c = 9.168 (3) A, ~ = 98.41(2), fl = 99.89(2), y = 77.74(1) ° , V = 320.9/k 3, Z = 2, Dm= 1.45 (flotation), D x = 1.470 g cm -3, p(Mo Ktt, 2 = 0.7107 A) = 0.63 cm -~, F(000) = 148. The structure was solved by direct methods and refined to an R value of 0.038 for 723 intensity measurements. The geometrical changes in the cyclopropane ring are discussed in the light of substituent effects. In the crystal structure the carboxylic groups are disordered.