Generalizing the notion of Koszul algebra

We introduce a generalization of the notion of a Koszul algebra, which includes graded algebras with relations in different degrees, and we establish some of the basic properties of these algebras. This class is closed under twists, twisted tensor products, regular central extensions and Ore extensions. We explore the monomial algebras in this class and we include some well-known examples of algebras that fall into this class.     

Synthesis of dendrimers through divergent iterative thio‐bromo “Click” chemistry

The development of a novel nucleophilic thio‐bromo “Click” reaction, specifically base‐mediated thioetherification of thioglycerol with α‐bromoesters, is reported. Combination of this thio‐bromo click reaction with subsequent acylation with 2‐bromopropionyl bromide provides an iterative two‐step divergent growth approach to the synthesis of a new class of poly(thioglycerol‐2‐propionate) (PTP) dendrimers. This approach is demonstrated in the rapid preparation of four generation (G1–G4) of PTP dendrimers with high‐structural fidelity. The isolated G1–G4 bromide‐terminated dendrimers can be used directly as dendritic macroinitiators for the synthesis of star‐polymers via SET‐LRP. Additionally, the intermediate hydroxy‐terminated dendrimers are analogs of other water‐soluble polyester and polyether dendrimers. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3931–3939, 2009     

Implications of monomer and initiator structure on the dissociative electron‐transfer step of SET‐LRP

The heterolytic dissociation process associated with the activation of Single Electron‐Transfer Living Radical Polymerization is examined through the use of energy profile modeling. Monomer and initiator structure is correlated with the approximate activation barriers, energies of electrostatic ion‐radical pair formation, and stability of ion‐radical pair generated from the counteranion halide leaving group and the radical atom with partial positive charge density induced by its electron‐withdrawing substituent. Energy profiles permit access not just to one, but to all local minima, in the dissociation pathway and the identification of a global minimum. The location and energy of this global minimum allows for the placement of various initiators and dormant propagating macroradicals on the spectrum between stepwise and concerted dissociative electron‐transfer. The barrier for the activation step for alkyl‐halides derived from acrylates, vinyl halides, and styrenes, as well as from initiators bearing electron‐withdrawing groups is decreased in comparison to relatively more electron‐rich alkyl halides. This rate enhancement is explained through the sticky dissociative model wherein electron‐transfer is accelerated by the formation of strong ion‐radical pairs between radicals with partial positive charge density and their counteranion leaving group. Greater electron‐withdrawing capacity of the alkyl halide substituent increases the stability of the ion‐radical pair, reduces its equilibrium bond length, and accelerates electron‐transfer. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5663–5697, 2008     

Wave-based defect detection and interwire friction modeling for overhead transmission lines

In this study, the feasibility of continuous, online monitoring of power lines using ultrasonic waves is considered. Local and global wave-based approaches for wire break detection in overhead transmission lines are presented. Both methods use a sending/receiving transducer to generate an ultrasonic, longitudinal, elastic wave in the cable. Defects in the cable cause a portion of the incident ultrasonic wave to be reflected back to the transducer, which when received, can be used to identify the presence of the defect. Although the transducers can only be attached to the surface of the cable, subsurface wires can also be interrogated since elastic energy spreads to these wires through friction contact. This study also explores how the elastic energy of a propagating wave becomes distributed among contacting rods via friction contact. This work focuses specifically on a two-rod system in which the wave energy from an excited “active” rod is transmitted to a neighboring “passive” rod through friction contact. An energy-based model is used to approximate the time average elastic wave power in the two rods as a function of propagation distance. Power predictions from the energy-based model compare well with experimental measurements and finite element simulations.     

A parametric model of the vocal tract area function for vowel and consonant simulation

A model of the vocal-tract area function is described that consists of four tiers. The first tier is a vowel substrate defined by a system of spatial eigenmodes and a neutral area function determined from MRI-based vocal-tract data. The input parameters to the first tier are coefficient values that, when multiplied by the appropriate eigenmode and added to the neutral area function, construct a desired vowel. The second tier consists of a consonant shaping function defined along the length of the vocal tract that can be used to modify the vowel substrate such that a constriction is formed. Input parameters consist of the location, area, and range of the constriction. Location and area roughly correspond to the standard phonetic specifications of place and degree of constriction, whereas the range defines the amount of vocal-tract length over which the constriction will influence the tract shape. The third tier allows length modifications for articulatory maneuvers such as lip rounding/spreading and larynx lowering/raising. Finally, the fourth tier provides control of the level of acoustic coupling of the vocal tract to the nasal tract. All parameters can be specified either as static or time varying, which allows for multiple levels of coarticulation or coproduction.     

Maps of m-pires on the projective plane

In this paper the authors study maps of m-pires (empires). It is shown that Heawood's m-pire formula holds, for all values of m, for maps on the projective plane using the theory of current graphs.     

Triangular embeddings of K((i-2) n,n,…,n)

For complete i-partite graphs of the form K(n₁, n, n, …, n) the largest value of n₁ that allows the graph to be triangularly-embedded into a surface is (i-2)n. In this paper the author constructs triangular embeddings into surfaces of some complete partite graphs of the form K((i-2)n, n, …, n). The embeddings are exhibited using embedding schemes but the surfaces into which K((i-2)n, n, …, n) are triangularly embedded can be seen to be particularly nice branched covers of a surface into which K(i-2, 1, 1,…,1) is triangularly embedded.     

Electron-hydrogen scattering in a modified Glauber theory with exchange

We analyze the elastic scattering of e-H with the modified Glauber amplitude recently proposed by us and with the Glauber exchange effect included through the formula by Foster and Williamson [1]. The results are found in very good agreement with experimental data.     

Automated parallel solid-phase synthesis of non-peptide CCR1 receptor antagonists

An automated, parallel, solid-phase synthesis and screening strategy using commercially available aryl acetic acids as starting materials has discovered novel, non-peptide CCR1 antagonists (K(i) < 100 nM).     

A combined experimental and theoretical study of resonance emission spectra of SO2( B2)

Experimental and theoretical resonance emission spectra are obtained for a number of vibrational states of SO₂( ¹B₂). The experimental emission spectra are dominated by (n₁ν₁, n₂ν₂, 0) bands, but some weak activity in the anti-symmetric stretch (ν₃) is observed. The calculated emission spectra based on an empirical near-equilibrium potential energy surface agree reasonably well with experiment for two lowest states investigated here, but fail to reproduce higher ones. Resonance Raman spectra are also calculated and agree well with an earlier experiment.