Asymmetric dynamic price competition with uncertainty

We consider a dynamic setting-price duopoly model in which a dominant (leader) firm moves first and a subordinate (follower) firm moves second. We suppose that each firm has two different technologies, and uses one of them according to a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We analyse the effect of the production costs uncertainty on the profits of the firms, for different values of the intercept demand parameters.

Waste collection routing-limited multiple landfills and heterogeneous fleet

This article deals with a real-life waste collection routing problem. To efficiently plan waste collection, large municipalities may be partitioned into convenient sectors and only then can routing problems be solved in each sector. Three diverse situations are described, resulting in three different new models. In the first situation, there is a single point of waste disposal from where the vehicles depart and to where they return. The vehicle fleet comprises three types of collection vehicles. In the second, the garage does not match any of the points of disposal. The vehicle is unique and the points of disposal (landfills or transfer stations) may have limitations in terms of the number of visits per day. In the third situation, disposal points are multiple (they do not coincide with the garage), they are limited in the number of visits, and the fleet is composed of two types of vehicles. Computational results based not only on instances adapted from the literature but also on real cases are presented and analyzed. In particular, the results also show the effectiveness of combining sectorization and routing to solve waste collection problems.

Effects of selection and drift on G matrix evolution in a heterogeneous environment: a multivariate Qst-Fst Test with the freshwater snail Galba truncatula.

Unraveling the effect of selection vs. drift on the evolution of quantitative traits is commonly achieved by one of two methods. Either one contrasts population differentiation estimates for genetic markers and quantitative traits (the Q(st)-F(st) contrast) or multivariate methods are used to study the covariance between sets of traits. In particular, many studies have focused on the genetic variance-covariance matrix (the G matrix). However, both drift and selection can cause changes in G. To understand their joint effects, we recently combined the two methods into a single test (accompanying article by Martin et al.), which we apply here to a network of 16 natural populations of the freshwater snail Galba truncatula. Using this new neutrality test, extended to hierarchical population structures, we studied the multivariate equivalent of the Q(st)-F(st) contrast for several life-history traits of G. truncatula. We found strong evidence of selection acting on multivariate phenotypes. Selection was homogeneous among populations within each habitat and heterogeneous between habitats. We found that the G matrices were relatively stable within each habitat, with proportionality between the among-populations (D) and the within-populations (G) covariance matrices. The effect of habitat heterogeneity is to break this proportionality because of selection for habitat-dependent optima. Individual-based simulations mimicking our empirical system confirmed that these patterns are expected under the selective regime inferred. We show that homogenizing selection can mimic some effect of drift on the G matrix (G and D almost proportional), but that incorporating information from molecular markers (multivariate Q(st)-F(st)) allows disentangling the two effects.

Hydrogeophysical data integration at larger scales: Application of Bayesian sequential simulation for the characterization of heterogeneous alluvial aquifers

Knowledge of the spatial distribution of hydraulic conductivity (K) within an aquifer is critical for reliable predictions of solute transport and the development of effective groundwater management and/or remediation strategies. While core analyses and hydraulic logging can provide highly detailed information, such information is inherently localized around boreholes that tend to be sparsely distributed throughout the aquifer volume. Conversely, larger-scale hydraulic experiments like pumping and tracer tests provide relatively low-resolution estimates of K in the investigated subsurface region. As a result, traditional hydrogeological measurement techniques contain a gap in terms of spatial resolution and coverage, and they are often alone inadequate for characterizing heterogeneous aquifers. Geophysical methods have the potential to bridge this gap. The recent increased interest in the application of geophysical methods to hydrogeological problems is clearly evidenced by the formation and rapid growth of the domain of hydrogeophysics over the past decade (e.g., Rubin and Hubbard, 2005).

Does the generalist parasitic plant Cuscuta campestris selectively forage in heterogeneous plant communities?

Cuscuta spp. are holoparasitic plants that can simultaneously parasitise several host plants. It has been suggested that Cuscuta has evolved a foraging strategy based on a positive relationship between preuptake investment and subsequent reward on different host species. Here we establish reliable parasite size measures and show that parasitism on individuals of different host species alters the biomass of C. campestris but that within host species size and age also contributes to the heterogeneous resource landscape. We then performed two additional experiments to test whether C. campestris achieves greater resource acquisition by parasitising two host species rather than one and whether C. campestris forages in communities of hosts offering different rewards (a choice experiment). There was no evidence in either experiment for direct benefits of a mixed host diet. Cuscuta campestris foraged by parasitising the most rewarding hosts the fastest and then investing the most on them. We conclude that our data present strong evidence for foraging in the parasitic plant C. campestris.

Design and synthesis of new monoterpenoid derived ligands for asymmetric catalysis /

The work to be presented herein illustrates several important facts. First, the synthesis of BIBOL (19), a 1,4-diol derived from the monoterpene camphor has allowed us to demonstrate that oxidative dimerizations of enolates can, and do proceed with nearly complete diastereoselectivity under kinetically controlled conditions. The yield of BIBOL is now 50% on average, with a 10% yield of a second diastereomer, which is likely the result of a non-kinetic hydride reduction, thereby affording the epimeric alcohol, 20, coupled on the exo face of camphor. This implies the production of 60% of a single coupling diastereomer. No other diastereomers from the reduction were observed. The utility of BEBOL has been illustrated in early asymmetric additions of diethylzinc to aryl aldehydes, with e.e.'s as high as 25-30%. '^' To further the oxidative coupling work, the same methodology which gave rise to BIBOL was applied to the chiral pool ketone, menthone. Interestingly, this gave an excellent yield of the a-halohydrin (31), which is the result of a chlorination of menthone. This result clearly indicates the high stereoselectivity of the process regardless of the outcome, and has illustrated an interesting dichotomy between camphor and menthone. The utility of the chlorination product as a precursor other chiral ligands is currently being investigated. > ' Finally, a new series of 1,3-diols as well as a new aminoalcohol have successfully been synthesized from highly diastereoselective aldol/mannich reactions. Early studies have indicated their potential in asymmetric catalysis, while employing pi-stack interactions as a means of controlling enantioselective aldol reactions.

Synthesis of chiral homoallylic alcohols and phthalans through the asymmetric allylation of carbonyl compounds /

The implementation of chiral centres within biologically active compounds has been a perplexing yet motivational force in chemistry. This work presents the attempted formation of a concurrent or sequential tandem catalyzed methodology of enantioselective nucleophilic addition and electrophilic cyclization. The 2'- arylalkynyl- aldehyde, ketone, and imine substrates used within were adeptly chosen with a dually activated structure; 1) for nucleophilic addition to the electrophilic substituents; and 2) for carbophilic activation of the alkyne substituent to undergo cyclization. To accomplish the nucleophilic addition, two distinct allylation methodologies were pursued: (/?)-BINOL catalyzed-allylboration and (5)- BINAP-AgF catalyzed-allylsilylation. BINAP catalyzed enantioselective allylation of 2'-arylalkynyl-aldehydes, to form chiral homoallylic alcohols, was successful. Homoallylic alcohols were isolated with high enantio-purity (>80%), which then underwent sequential cyclization to form chiral allylic phthalans, in moderate yields. An application of this methodology towards the construction of biologically active compounds was included with the partial synthesis of the natural product and H. pylori inhibitor, (+)-Spirolaxine methyl ether.

Attemped asymmetric dehydration with chiral carbodiimides /|nMin-jen Shiao. -- 260 0 St. Catharines [Ont. : s. n.],

This research work has been planned with the intention of synthesizing optically active bicyclo[3,l,0]-hexan-2-one using chiral carbodiimides. Several carbodiimides have been prepared for practice and for attempts at asymmetric induction. The total synthesis of dibenzo[e,g]- (l:3)diazonine and the partial synthesis of l:13-dimethyldibenzo[e,g]- (l:3)diazonine are reported. Attempts to resolve 6,6f-dimethyl-2,2t-diphenic acid were not successful. The NMR spectra of carbodiimides and the related thioureas are compared. The reaction transition state of the 4-hydroxycyclohexanone with optically pure R,R(+)-di(a-phenylethyl)-carbodiimide has been considered. The ORD application to chiral cyclohexanones is discussed.

Attempted asymmetric synthesis of Lactobacillic acid / |nFawzy F. Z. Georges. -- 260 St. Catharines, Ont. : [s. n.],

This research work has been planned with the intention of proving the absolute configuration of lactobacillc acid. During the course of this work, attempts have been made to synthesize cis-2-carboxycyclopropane- l-.acetic acid as,v,a suitable resolvable material. As the results were not satisfactory, the synthesis of ci,s-2-carboxycyclopropane-l-propionic acid has been alternatively attempted by ring opening of bicyclo- [4.1.~-heptan-2-onewithout much success. Attempts to resolve or prepare bicyclo[ 4.1.~-hePtan-2-one optically active are also reported. On the other hand, a complete scheme is described for the possible synthesis of optically active lactobacillic acid. If only bicyclo- ~.1.~ -heptan-2-one can be resolved or prepared optically active, this described scheme can be applied smoothly to the synthesis of enant~omeric lactobacillic acid.

Asymmetric cyclopropanation via catalysts incorporating the 1,4-diol ligands and the newly designed dioxaborolane /

The development of new methodology for the asymmetric synthesis of chiral organic compounds is a major focus in modem organic chemistry. The use of chiral catalysts is replacing chiral auxiliaries as a new tool for synthetic chemists. An efficient chiral catalyst allows for large quantities of optically active product to be obtained on use of relatively small amount of enantiopure material, without the need for the removal and recovery of a chiral auxiliary. Furthermore, the most practical catalytic methods utilize an inexpensive and readily available chiral ligand that can provide high and predictable enantioselectivity across a wide range of substrates. In our project, two type of versatile, upgraded chiral ligands have been designed and synthesized. Their application in Simmons-Smith type cyclopropanation is investigated, and the pleasing results suggest that they are the potential catalytic enantioselective candidates to build C-C bonds.

Stereoselective synthesis of substituted hexahydro-3a,4a-diazacyclopentaphenanthren-4-ones and aminoferrocenes

This thesis explored the development of several methodologies for the stereoselective construction of ligand frameworks and some of their applications. The first segment concerns the application of an enantioselective lithiation at an Sp3_ hybridized position adjacent to nitrogen by means of the widely used and typically highly effective enantioselective lithiation with ( -)-sparteine. This investigation was intended to develop a method to install chirality into a system that would be converted into a family of diaminoylidenes for use as phosphine mimics in transition metal catalysis or as nucleophilic reagents. Molecular modeling of the system revealed some key interactions between the substrate and (-)-sparteine that provided general insight into the diamine's mode of action and should lend some predictive value to its future applications. The second portion focuses on the development of methods to access 1,2- disubstituted aminoferrocenes, an underexplored class of metallocenes possessing planar chirality. Two routes were examined involving a diastereoselective and an enantioselective pathway, where the latter method made use of the first BF3-mediated lithiation-substitution to install planar chirality. Key derivatives such as 1,2- aminophosphines, made readily accessible by the new route, were evaluated as ligands for Pd(II), Pt(II) and Ir(I). These complexes show activity in a number of transformations with both achiral and prochiral substrates. Optimization experiments were conducted to prepare enantiomerically enriched 2-substituted-I-aminoferrocenes by direct asymmetric lithiation of BF3-coordinated tertiary aminoferrocenes. A predictive computational model describing the transition state of this reaction was developed in collaboration with Professor Travis Dudding's group (Department of Chemistry, Brock University). The predicted stereochemistry of the process was confirmed by single-crystal X-ray analysis of a 2-phosphino-l-dimethylaminoferrocene derivative. Enantiomerically pure samples of the aminophosphine ligands derived from this new process have given promising preliminary results in the enantioselective hydrogenation of prochiral alkenes and warrant further stUdy in metal-mediated catalysis.

Understanding the Origin of Selectivity in the Asymmetric Lithiation Reaction of N-Heterocycles: A Theoretical Study

The natural abundance of the N-heterocycle containing compounds has pushed the synthetic community toward the invention of new synthetic methods that result in the structural diversity of N-heterocycles. Among this, is the efficient and highly selective diamine mediated asymmetric lithiation process. Amongst the diamine chiral ligands, (-)-sparterine, which is a naturally occurring alkaloid proved to be an efficient one. Many successful, good yielding and highly selective lithiation reactions have been accomplished with the mediation by this chiral diamine base. Although, there are some examples of experimental and theoretical mechanistic studies in the literature, there is a lack of detailed understanding as to how it exactly induces the chirality. In this thesis is described a systematic investigation of how (-)-sparteine influences the stereoselectivity in the course of asymmetric lithiation reaction. This led us to the establishment of the function of A-ring’s β-CH2 effect and D-ring effect. Consequently, the importance of the A-ring and D-ring portions of (-)-sparteine in the stereoselectivity is unraveled. Another part of this thesis deals with the asymmetric lithiation of BF3-activated N,N- dimethylaminoferrocene in the presence of (1R, 2R)-N1,N2-bis(3,3-dimethylbutyl)-N1,N2-dimethylcyclohexane-1,2-diamine ( a (R,R)-TMCDA surrogate) with i-PrLi. Computational findings were in full accord with the experimental observations. Subsequently, the theoretically provided insights into the mechanism of the reaction were exploited in computational design of a new ligand. Unfortunately, the outcome of this design was not experimentally robust and an updated approach towards a successful design was explained.

Experimental and Computational Studies on Copper and Hydrobenzoin Derivatives in Catalytic Asymmetric Reactions

The use of theory to understand and facilitate catalytic enantioselective organic transformations involving copper and hydrobenzoin derivatives is reported. Section A details the use of theory to predict, facilitate, and understand a copper promoted amino oxygenation reaction reported by Chemler et al. Using Density Functional Theory (DFT), employing the hybrid B3LYP functional and a LanL2DZ/6-31G(d) basis set, the mechanistic details were studied on a N-tosyl-o-allylaniline and a [alpha]-methyl-[gamma]-alkenyl sulfonamide substrate. The results suggest the N-C bond formation proceeds via a cisaminocupration, and not through a radical-type mechanism. Additionally, the origin of diastereoselection observed with [alpha]-methyl-[gamma]-alkenyl sulfonamide arises from avoidance of unfavourable steric interactions between the methyl substituent and the N -protecting group. Section B details the computationally guided, experimental investigation of two hydrobenzoin derivatives as ligands/ catalysts, as well as the attempted synthesis of a third hydrobenzoin derivative. The bis-boronic acid derived from hydrobenzoin was successful as a Lewis acid catalyst in the Bignielli reaction and the Conia ene reaction, but provided only racemic products. The chiral diol derived from hydrobenzoin successfully increased the rate of the addition of diethyl zinc to benzaldehyde in the presence of titanium tetraisopropoxide, however poor enantioinduction was obseverved. Notably, the observed reactivity was successfully predicted by theoretical calculations.

Racemic and Enantioselective Total Syntheses of Mosquito Oviposition Pheromone from a Naturally Available Unsaturated Fatty Acid

The unnatural threo-6-acetoxy-5-hexadecanolide and the natural mosquito oviposition pheromone erythro-6-acetoxy-5-hexadecanolide were synthesized in a diastereodivergent fashion in 44% and 33% overall yield respectively from 5-bromovaleric acid and undecanal. The key step utilized a chemoenzymatic epoxidation-lactonization of a naturally available fatty acid to form the 6-hydroxy-5-hexadecanolide core.17 The epoxidation strategy was later adapted to allow for an asymmetric synthesis. Shi epoxidation afforded highly enantioenriched (5R, 6R)-6-hydroxyhexadecanolide (er = 10) in 70 % overall yield. Other derivatives of the chiral ketone catalyst were also screened. Finally, attempts were made to obtain the correct stereochemistry at C(6) of the target with a dynamic kinetic transformation using lipase and a transfer hydrogenation catalyst. Epimerization of the lactol with the transfer hydrogenation catalyst was successful, but lipase mediated reactions halted at <10 % conversion.