On the formality of equivariant classifying spaces

Partially supported by NSF MCS 7701623     

An IR study of poly-1,4-phenylenevinylene (PPV), the 2,5-dimethoxy derivative [(MeO)2-PPV], and their corresponding xanthate precursor polymers and monomers

A detailed comparison of the infrared (IR) spectra of poly-1,4-phenylenevinylene (PPV), its xanthate precursor polymer, and its bis-xanthate precursor monomer along with the corresponding 2,5-dimethoxy derivatives has provided a clearer basis for characterizing these species with regard to both structure and purity. All the xanthate precursor monomers and polymers exhibit characteristic intense absorptions typical of the xanthate group near 1220, 1110, and 1050 cm(-1). Upon complete conversion of the precursor polymer to the vinylene linked final product, the intense IR peaks of the xanthate group have disappeared and new bands resulting from the vinylene linkages are found. The latter include a moderately strong band near 965 cm(-1) due to the out-of-plane -CHCH- deformation of the trans-vinylene conjugated with and linking the phenyl rings into an optoelectronic polymer. Unfortunately, the corresponding C-H stretching vibration of this same group of atoms expected to appear near 3020 cm(-1) falls in the same region of the spectrum as the aromatic C-H stretches of the phenyl rings. Similarly, for the 2,5-dimethoxy polymer derivative, [(MeO)(2)-PPV], the C-H stretching vibration near 3055 cm(-1) contains contributions from both aromatic and vinylene C-H. Density functional theory (DFT) calculations on the monomers were instrumental in assigning the infrared spectra of these materials. This study provides a systemic means for verifying that the precursor monomer has been polymerized into the precursor polymer and that thermal conversion to the conjugated polymer is complete.     

Polypyridyl-Based Copper Phenanthrene Complexes: Combining Stability with Enhanced DNA Recognition

We report a series of copper(II) artificial metallo-nucleases (AMNs) and demonstrate their DNA damaging properties and in-vitro cytotoxicity against human-derived pancreatic cancer cells. The compounds combine a tris-chelating polypyridyl ligand, di-(2-pycolyl)amine (DPA), and a DNA intercalating phenanthrene unit. Their general formula is Cu-DPA-N,N' (where N,N'=1,10-phenanthroline (Phen), dipyridoquinoxaline (DPQ) or dipyridophenazine (DPPZ)). Characterisation was achieved by X-ray crystallography and continuous-wave EPR (cw-EPR), hyperfine sublevel correlation (HYSCORE) and Davies electron-nuclear double resonance (ENDOR) spectroscopies. The presence of the DPA ligand enhances solution stability and facilitates enhanced DNA recognition with apparent binding constants (K_app) rising from 10⁵ to 10⁷ m ⁻¹ with increasing extent of planar phenanthrene. Cu-DPA-DPPZ, the complex with greatest DNA binding and intercalation effects, recognises the minor groove of guanine–cytosine (G-C) rich sequences. Oxidative DNA damage also occurs in the minor groove and can be inhibited by superoxide and hydroxyl radical trapping agents. The complexes, particularly Cu-DPA-DPPZ, display promising anticancer activity against human pancreatic tumour cells with in-vitro results surpassing the clinical platinum(II) drug oxaliplatin.     

Potential Benefits and Barriers to Integration

The rhetoric surrounding integration of mathematics and science abounds. Professional organizations’ standards and recommendations for reform in mathematics and science education each point out the need to make connections among various disciplines. However, some remain unconvinced, citing a lack of research supporting the assertion that integration improves student achievement. This article examines the current situation, discusses the growing body of related research, and examines the implementation issues related to integrated curriculum projects. The conclusion calls for mathematics and science educators to work collaboratively to address implementation issues surrounding reform of any kind and to explore further the possibilities of integration.     

Vapor liquid equilibrium modeling of alkane systems with Equations of State: “Simplicity versus complexity”

Two types of Equations of State (EoS), which are characterized here as “simple” and “complex” EoS, are evaluated in this study. The “simple” type involves two versions of the Peng–Robinson (PR) EoS: the traditional one that utilizes the experimental critical properties and the acentric factor and the other, referred to as PR-fitted (PR-f), where these parameters are determined by fitting pure compound vapor pressure and saturated liquid volume data. As “complex” EoS in this study are characterized the EoS derived from statistical mechanics considerations and involve the Sanchez–Lacombe (SL) EoS and two versions of the Statistical Associating Fluid Theory (SAFT) EoS, the original and the Perturbed-Chain SAFT (PC-SAFT).

The evaluation of these two types of EoS is carried out with respect to their performance in the prediction and correlation of vapor liquid equilibria in binary and multicomponent mixtures of methane or ethane with alkanes of various degree of asymmetry. It is concluded that for this kind of systems complexity offers no significant advantages over simplicity. Furthermore, the results obtained with the PR-f EoS, especially those for multicomponent systems that are encountered in practice, even with the use of zero binary interaction parameters, indicate that this EoS may become a powerful tool for reservoir fluid phase equilibria modeling.     

Competitive Multi-period Pricing for Perishable Products: A Robust Optimization Approach

We study a multi-period oligopolistic market for a single perishable product with fixed inventory. Our goal is to address the competitive aspect of the problem together with demand uncertainty using ideas from robust optimization and variational inequalities. The demand function for each seller has some associated uncertainty and we assume that the sellers would like to adopt a policy that is robust to adverse uncertain circumstances. We believe this is the first paper that uses robust optimization for dynamic pricing under competition. In particular, starting with a given fixed inventory, each seller competes over a multi-period time horizon in the market by setting prices and protection levels for each period at the beginning of the time horizon. Any unsold inventory at the end of the horizon is worthless. The sellers do not have the option of periodically reviewing and replenishing their inventory. We study non-cooperative Nash equilibrium policies for sellers under such a model. This kind of a setup can be used to model pricing of air fares, hotel reservations, bandwidth in communication networks, etc. In this paper we demonstrate our results through some numerical examples.     

The centroid of extended affine and root graded Lie algebras

We develop general results on centroids of Lie algebras and apply them to determine the centroid of extended affine Lie algebras, loop-like and Kac-Moody Lie algebras, and Lie algebras graded by finite root systems.