Non-totally transcendental unidimensional theories

Supported by NSF Grant DMS 8601289 and a Humboldt Foundation Fellowship     

Efficient assembly of 3-substituted oxindole-based isoxazolines leading to the synthesis of (±)-flustraminol-B and related natural product building blocks

An efficient synthesis of oxindole-based isoxazolines has been developed and the resulting spirocyclic intermediates have been elaborated to synthetically versatile 3-hydroxy-3-alkyl oxindole building blocks such as the 3-hydroxy-3-methylenecyano-2-oxindoles (6) and γ-amino alcohols (12). Utility of this methodology is demonstrated through the synthesis of pyrrolo[2,3-b]indolines including the marine natural product (±)-flustraminol-B.     

Studies on dynamic mechanical and mechanical properties of vinyloxyaminosilane grafted ethylene propylene diene terpolymer/linear low density polyethylene (EPDM-g-VOS/LLDPE) blends

The dynamic mechanical properties of vinyloxyaminosilane grafted ethylene propylene diene terpolymer/linear low density polyethylene (EPDM-g-VOS/LLDPE) blends have been evaluated with special reference to the effect of blend ratio. It has been found that increasing the proportion of LLDPE in the blends decreases the T_g values and increases the storage modulus (E^′) and loss modulus (E^′′) due to increase in crystallinity. A gradual increase in the values of tanδ_max is observed for the blends with increase in EPDM-g-VOS concentration, which indicates that no phase inversion occurs. But however the higher increase in tanδ_max after 50 wt.% of EPDM-g-VOS composition is due to small change in crystallinity and is ascertained by SEM micrographs. Mechanical properties such as tensile strength, Young’s modulus and hardness increase with increases in LLDPE concentration in the blends and with dicumyl peroxide (DCP) concentration whereas the values of elongation at break are decreased with increase in LLDPE and DCP concentration.     

Groups definable in local fields and pseudo-finite fields

Using model-theoretic methods we prove: Theorem A If G is a Nash group over the real or p-adic field, then there is a Nash isomorphism between neighbourhoods of the identity of G and of the set of F-rational points of an algebraic group defined over F. Theorem B Let G be a connected affine Nash group over ℝ. Then G is Nash isogeneous with the (real) connected component of the set of real points of an algebraic group defined over ℝ. Theorem C Let G be a group definable in a pseudo-finite field F. Then G is definably virtually isogeneous with the set of F-rational points of an algebraic group defined over F. Both authors supported by NSF grants.     

Prompt neutron emission spectra and multiplicities in the thermal neutron induced fission of235U

The emission spectra of prompt fission neutrons from mass and kinetic energy selected fission fragments have been measured in²³⁵U(n _th,f). Neutron energies were determined from the measurement of the neutron time of flight using a NE213 scintillation detector. The fragment energies were measured by a pair of surface barrier detectors in one set of measurements and by a back-to-back gridded ionization chamber in the second set of measurements. The data were analysed event by event to deduce neutron energy in the rest frame of the emitting fragment for the determination of neutron emission spectra and multiplicities as a function of the fragment mass and total kinetic energy. The results are compared with statistical model calculations using shell and excitation energy dependent level density formulations to deduce the level density parameters of the neutron rich fragment nuclei over a large range of fragment masses.     

On Groups and Rings Definable In O-Minimal Expansions of Real Closed Fields

Let R, >,+,• be a real closed field, and let M be ano-minimal expansion of R. We prove here several results regardingrings and groups which are definable in M. We show that everyM–definable ring without zero divisors is definably isomorphicto R, R((–l)) or the ring of quaternions over R. One corollaryis that no model of T_exp is interpretable in a model of T_an.     

A possible basis for structure–function relationship of estrogens

It is well known that a wide variety of molecules compete for binding to the estrogen receptor and act as estrogens and/or antiestrogens. These molecules such as estradiol, diethylstilbestrol, doisynolic acid, the triarylethylenes, and cyclofenyl apparently share little resemblance which could account for their interaction with a common estrogen binding site. Knowledge of the receptor binding of triarylethylene and cyclofenyl prototypes, in particular, relative to that of the other estrogens is critical for understanding their structure-function relationship. We have carried out a study on the receptor binding specificity of triarylethylene and cyclofenyl prototypes. This study has revealed that these molecular types share considerable resemblance in their receptor binding specificity and differ from estradiol and other similar molecules in some important respects. However, comparison of their substructural binding specificities reveals the possibility that the triarylethylene and estradiol prototypes may interact with at least some common regions of the estrogen binding site. Based on this reasoning the comparative receptor binding of estrogens has been rationalized on the basis of a subsite hypothesis for the estrogen binding site. According to this hypothesis, the composite estrogen binding site is composed of essentially five subsites, and that the structurally different estrogenic prototypes can interact with different set of subsites, and thus differ in their binding orientation. The essential difference in the activity profile of estradiol prototypes and the triarylethylene antiestrogens reveals the possibility of a causal relationship between the binding orientation of a ligand and its activity profile. This model for receptor site can thus serve as a working hypothesis to rationalize the structure-function relationship of estrogens.     

Optimal pricing and advertising in a durable-good duopoly

This paper analyzes dynamic advertising and pricing policies in a durable-good duopoly. The proposed infinite-horizon model, while general enough to capture dynamic price and advertising interactions in a competitive setting, also permits closed-form solutions. We use differential game theory to analyze two different demand specifications – linear demand and isoelastic demand – for symmetric and asymmetric competitors. We find that the optimal price is constant and does not vary with cumulative sales, while the optimal advertising is decreasing with cumulative sales. Comparative statics for the results are presented.     

Integrated fleet mix and routing decision for hazmat transportation: A developing country perspective

In developing countries, truck purchase cost is the dominant criteria for fleet acquisition-related decisions. However, we contend that other cost factors such as loss due to the number of en route truck stoppages based on a truck type and recovery cost associated with a route choice decision, should also be considered for deciding the fleet mix and minimizing the overall costs for long-haul shipments. The resulting non-linear model, with integer variables for the number and type of trucks, and the route choices, is solved via genetic algorithm. Using real data from a bulk liquid hazmat transporter, the trade-offs between the cost of travel, loss due to number of truck stoppages, and the long-term recovery cost associated with the risk of exposure due to a hazmat carrier accident are discussed. The numerical experiments show that when factors related to public safety and truck stoppages are taken into account for transportation, the lowest total cost and optimal route choice do not align with the cheapest truck type option; rather, the optimal solution corresponds to another truck type and route with total costs significantly less than the total costs associated with the cheapest truck type. Our model challenges the current truck purchasing strategy adopted in developing countries using the cheapest truck criteria.     

Catalytic reduction of 4-nitrophenol using synthesized and characterized CoS@MorphcdtH/CoS@4-MPipzcdtH nanoparticles

CoS@MorphcdtH NPs and CoS@4-MPipzcdtH NPs were synthesized by precipitation method involving three mechanisms: inclusion, occlusion, and adsorption. The synthesized NPs were characterized with the help of UV-Vis spectroscopy, FESEM-EDAX, powder x-ray diffraction, TEM, ESIMS, TG/DSC analysis. The morphology of the CoS@MorphcdtH NPs and CoS@4-MPipzcdtH NPs were hexagonal and rectangular, and the particles were in the range 7–12 nm. UV–visible spectral measurements showed surface plasmon resonance at 320 nm–340 nm with band gap of 3.65 eV–3.86 eV. The catalytically active CoSNPs called were investigated for the reduction of 4-nitrophenol (4-NP) via hydrogenation using sodium borohydride (NaBH₄) as a reducing agent. Both the CoS NPs successfully reduced 4-NP to 4- aminophenol (4-AP) in a short time, catalytic performances are almost unchanged for the first five cycles. Herein, we report the preparation and characterizations of efficient active CoS NPs consisting carbodithioic acid framework as a support/capping material, along with catalytic property.