Discrete velocity models with small data

Summary It is shown that all discrete velocity models conserving mass, momentum and energy and without self-interactions have global, uniformly bounded solutions for small enough initial data with compact support. This is interesting because of a recent example with small data inL ¹ L whose solution is not bounded, and shows the unboundedness is due to mass being fed in from infinity.

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Sommario Si dimostra che tutti i modelli con velocità discretizzate che conservano la massa, la quantità di moto e l'energia e senza autointerazioni hanno soluzioni globali, uniformemente limitate per dati iniziali a supporto compatto e abbastanza piccoli. Questo è interessante a causa di un esempio recente con dati piccoli inL ¹ L la cui soluzione non è limitata e mostra che l'illimitatezza è dovuta ad un flusso di massa dall'infinito.

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Research supported by the Natural Science and Engineering Research Council Canada under Grant No. A8560.     

Interactive classification using data envelopment analysis

In this paper, we illustrate how data envelopment analysis (DEA) can be used to aid interactive classification. We assume that the scoring function for the classification problem is known. We use DEA to identify difficult to classify cases from a database and present them to the decision-maker one at a time. The decision-maker assigns a class to the presented case and based on the decision-maker class assignment, a tradeoff cutting plane is drawn using the scoring function and decision-maker’s input. The procedure continues for finite number of iterations and terminates with the final discriminant function. We also show how a hybrid DEA and mathematical programming approach can be used when user interaction is not desired. For non-interactive case, we compare a hybrid DEA and mathematical programming based approach with several statistical and machine learning approaches, and show that the hybrid approach provides competitive performance when compared to the other machine learning approaches.     

Spying on the cost structure of naive bidding competitors via linear programming models

A linear programming model is constructed which enables a firm to estimate its competitor's cost structure when the competitor adheres to a non-randomized strategy. The existence of the model makes randomized bidding prudent apart from game theory considerations. The need for increased curriculum attention to optimal bidding is highlighted.     

Design and synthesis of a novel protected mixed ligand siderophore

A novel siderophore analog (4) has been designed to facilitate iron transport-mediated drug delivery and drug release. This mixed ligand siderophore analog includes three bidentate ligands intended to octahedrally coordinate iron (III). The ligands include a 2,3-dihydroxy benzoic acid moiety, N⁵-acetyl-N⁵-hydroxy-l-ornithine, and a β-N-hydroxy-α,β-diaminopropionic acid derivative. The total synthesis of 15, a form of 4 that is suitably protected, yet contains a free carboxylic acid for subsequent drug conjugation, is described.     

Multiblock Copolymers Based on Highly Crystalline Polyethylene and Soft Poly(ethylene-co-butadiene) Segments: Towards Polyolefin Thermoplastic Elastomers

Block copolymers based on polyethylene (PE) and ethylene butadiene rubber (EBR) were obtained by successive controlled coordinative chain transfer polymerization (CCTP) of a mixture of ethylene and butadiene (80/20) and pure ethylene. EBR-b-PE diblock copolymers were synthesized using the {Me₂Si(C₁₃H₈)₂Nd(BH₄)₂Li(THF)}₂ complex in combination with n-butyl,n-octyl magnesium (BOMAG) used as both the alkylating and chain transfer agent (CTA). Triblock and multiblock copolymers featuring highly semi-crystalline PE hard segments and soft EBR segments were further obtained by the development of a bimetallic CTA, the pentanediyl-1,5-di(magnesium bromide) (PDMB). These new block copolymers undergo crystallization-driven organization into lamellar structures and exhibit a variety of mechanical properties, including excellent extensibility and elastic recovery in the case of triblock and multiblock copolymers.     

Polymerizations of olefins and diolefins catalyzed by monocyclopentadienyltitanium complexes containing a (dimethylamino)ethyl substituent and comparison with ansa-zirconocene systems

{[2-(dimethylamino)ethyl]cyclopentadienyl}titanium trichloride (Cp^NTiCl₃, 1 ) was activated with methylaluminoxane (MAO) to catalyze polymerizations of ethylene (E), propylene (P), ethylidene norbornene (ENB), vinylcyclohexene (VCH), and 1,4-hexadiene (HD). The dependence of homopolymerization activity ( A ) of 1 /MAO on olefin concentration ([M]ⁿ) is n = 2.0 ± 0.5 for E and n = 1.8 ± 0.2 for P. The value of n is 2.4 ± 0.2 for CpTiCl₃/MAO catalysis of ethylene polymerization; this system does not polymerize propylene. 1 /MAO catalyzes HD polymerization at one-tenth of A _H for 1-hexene, probably because of chelation effects in the HD case. The copolymerization of E and P has reactivity ratios of r_E = 6.4 and r_P = 0.29 at 20°C, and r_Er_P = 1.9, which suggests 1 /MAO may be a multisite catalyst. The copolymerization activity of CpTiCl₃/MAO is 50 times smaller than that of Cp^NTiCl₃/MAO. Terpolymerization of E/P/ENB has A of 10⁵ g of polymer/(mol of Ti h), incorporates up to 14 mol % (∼ 40 wt %) of ENB, and high MW's of 1 to 3 × 10⁵. All of these parameters are surprisingly insensitive to the ENB concentration. The E/P/VCH terpolymerization has comparable A value of (1.3 ± 0.3) × 10⁵ g/(mol of Ti h). The incorporation of VCH in terpolymer increases with increasing [VCH]. Terpolymerization with HD occurs at about one-third of the A of either ENB or VCH; the product HD–EPDM is low in molecular weight and contains less than 4% of HD. These terpolymerization results are compared with those obtained previously for three zirconocene precursors: rac-ethylenebis(1-η⁵-indenyl)dichlorozirconium ( 6 ), rac-(dimethylsilylene)bis(1-η⁵-indenyl)dichlorozirconium ( 7 ), and ethylenebis(9-η⁵-fluorenyl)dichlorozirconium ( 8 ). The last compound is a particularly poor terpolymerization catalyst; it incorporates very little VCH or HD and no ENB at all. 7 /MAO is a better catalyst for E/P/VCH terpolymerization, while 6 /MAO is superior in E/P/HD terpolymerization. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 319–328, 1998     

Uragogin and blepharodin, unprecedented hetero-Diels-Alder adducts from Celastraceae species

Uragogin and blepharodin were isolated from Crossopetalum uragoga and Maytenus magellanica, respectively. They represent the first examples of a triterpene-neolignan ester and a heptacyclic arylpropanoid-nor-triterpenephenol, hetero-Diels-Alder adducts built with dioxane bridges. Their proposed biosynthetic route is discussed.     

A Convenient Synthesis of N-Methoxy-N-Methylamides from Carboxylic Acids

Carboxylic acids can be converted to their corresponding N-methoxy-N-methylamides in high yields using 2-chloro-1-methylpyridinium iodide as the coupling agent. The reaction proceeds without racemization when chiral carboxylic acids are used as the starting material.