P-amenable locally compact groups

LetG denote a locally compact group andP(G) [P _c (G)] the topological semigroup of absolutely continuous [absolutely continuous and compactly supported] probability measures onG. We say thatG isP-amenable [P _c -amenable] if the topological semigroupP(G)[P _c (G)] is amenable. Some combinatorial properties of this class of groups are studied. The relationship between amenability andP-amenability ofG is investigated. It is shown that for a connected solvableP _c -amenable groupG, G has polynomial growth if, and only if,P _c (S)={fP _c (G)suppfS} is amenable for any open subsemigroupS ofG.This paper contains a part of the author's doctoral thesis at the State University of New York at Albany. The author wishes to thank ProfessorJoe Jenkins for his valuable suggestions and encouragement during the course of this work.     

Synthesis of functionalized 1,5-cyclooctadienes by LICKOR metalation

1,5-Cyclooctadiene was lithiated under LICKOR superbase conditions followed by reaction with alkyl halides or ethylene oxide to yield 3-substituted 1,5-cyclooctadienes in high yield and purity. This procedure is suitable for preparation of 1,5-cyclooctadienes carrying pendant functional groups for immobilization on solid-phase resins.     

In vivo pharmacokinetics of 8-aminolevulinic acid-induced protoporphyrin IX during pre- and post-photodynamic therapy in 7,12-dimethylbenz(a)nthracene-treated skin carcinogenesis in Swiss mice: a comparison by three-compartment model

Delta-aminolevulinic acid-photodynamic therapy (ALA-PDT) has emerged as a useful technique in the treatment of superficial basal cell carcinoma, actinic keratosis, squamous cell carcinoma and tumors of other organs. Earlier reports mention that there is reappearance of protoporphyrin IX (PpIX) after photoirradiation of tumors. This property of reappearance of PpIX is being utilized to treat nodular tumors by fractionated light dose delivery. However, there is still no unanimously accepted reason for this reappearance phenomenon and the rate of resynthesis after PDT. On account of this, studies are carried out on the estimation of the pharmacokinetics of the ALA-induced PpIX in mice tumor models and the surrounding normal tissues before and after PDT. Further, a mathematical model based on a multiple compartment system is proposed to estimate the rate parameter for the diffusion of PpIX from the surrounding normal tissues into the tumor tissue (km) caused by photobleaching during PDT with irradiating fluences of 36.0 and 57.6 J/cm2. The km value at two different fluences, 36.0 and 57.6 J/cm2, are estimated as 3.0636+/-0.7083 h(-1) and 6.9231+/-2.17651 h(-1), respectively. Further, the rate parameter for the cleavage and efflux of ALA (k1) and the rate parameter for the evasion of PpIX from the tumor tissues after PDT (kt) were also estimated by fitting the experimental data to the developed mathematical model. The statistical significance of the estimated parameters was determined using Student's t-test. The experimental results and the rate parameters obtained using the proposed compartment model suggest that in addition to the earlier reported reasons, the invasion or diffusion of PpIX from the surrounding tissues to the tumor tissues after photoirradiation might also contribute to the reappearance of PpIX after PDT.     

Mechanisms of ion transport in lithium salt-doped polymeric ionic liquid electrolytes at higher salt concentrations

We used atomistic simulations to study the mechanisms of ion transport in salt-doped polymeric ionic liquid systems at higher salt concentrations. Consistent with the experimental observations, our simulations indicate that at higher salt concentrations, the anion mobilities become lower than that of the lithium cations. Further, the anion mobilities become relatively insensitive to the salt concentration, while the mobilities of lithium increase with increasing salt concentration. We rationalize the results for the anion mobilities by considering the fractions of anions which are exclusively coordinated with the polycations (Type1); co-coordinated with cations and lithium (Type2); and those exclusively coordinated with lithium (Type3). By considering the coordination characteristics of the different types of anions and their hopping motions, we demonstrate that the net anion mobilities results from a compensation effect of the salt concentration dependence of the mobilities of the different anions. With respect to the mobilities of the lithium ions, we demonstrate that the latter moves primarily by a structural diffusion mechanism involving refreshing of the solvation shell during hopping. Further, for the majority of the lithium ions, the solvation shell is shown to be comprised of co-coordinated Type2 anions, and that the number of polycations and the unique polymer chains involved in such coordination decreases with increasing salt concentration. Such changes are shown to weaken the solvation shell around the lithium, thereby facilitating faster ion motion. Together, our results suggest that systems in which the anion which exhibits a stronger coordination to the polycation in comparison to that of the lithium can facilitate higher transference numbers without a concomitant reduction in the mechanical strength.     

Complexities and algorithms for synchronized scheduling of parallel machine assembly and air transportation in consumer electronics supply chain

In this paper, we study the problem of synchronized scheduling of assembly and air transportation to achieve accurate delivery with minimized cost in consumer electronics supply chain. This problem was motivated by a major PC manufacturer in consumer electronics industry. The overall problem is decomposed into two sub-problems, which consist of an air transportation allocation problem and an assembly scheduling problem. The air transportation allocation problem is formulated as an integer linear programming problem with the objective of minimizing transportation cost and delivery earliness tardiness penalties. The assembly scheduling problem seeks to determine a schedule ensuring that the orders are completed on time and catch the flights such that the waiting penalties between assembly and transportation is minimized. The problem is formulated as a parallel machine scheduling problem with earliness penalties. The computational complexities of the two sub-problems are investigated. The air transportation allocation problem with split delivery is shown to be solvable. The parallel machine assembly scheduling problem is shown to be NP-complete. Simulated annealing based heuristic algorithms are presented to solve the parallel machine problem.     

Local projection stabilization of equal order interpolation applied to the Stokes problem

The local projection stabilization allows us to circumvent the Babuška-Brezzi condition and to use equal order interpolation for discretizing the Stokes problem. The projection is usually done in a two-level approach by projecting the pressure gradient onto a discontinuous finite element space living on a patch of elements. We propose a new local projection stabilization method based on (possibly) enriched finite element spaces and discontinuous projection spaces defined on the same mesh. Optimal order of convergence is shown for pairs of approximation and projection spaces satisfying a certain inf-sup condition. Examples are enriched simplicial finite elements and standard quadrilateral/hexahedral elements. The new approach overcomes the problem of an increasing discretization stencil and, thus, is simple to implement in existing computer codes. Numerical tests confirm the theoretical convergence results which are robust with respect to the user-chosen stabilization parameter.

     

Modeling viscoelastic properties of triblock copolymers: A DPD simulation study

Gel systems based on self‐assembled, amphiphilic ABA triblock copolymers in midblock‐selective solvent form stable, spatially extended networks with controllable morphology and tunable viscoelastic behavior. In this work, we systematically evaluate the mechanical properties of these gels using morphology calculations, and a nonequilibrium oscillatory shear technique based on the dissipative particle dynamics (DPD) method. Our simulations demonstrate that low molecular weight triblock copolymers with incompatible blocks self‐assemble into micelles connected with bridges and loop‐like chains comprised of the solvent‐selective polymer midblocks. The fraction of bridges, ?_b, generally increases with increasing relative volume of the midblock, x, defined as the ratio of midblock and endblock volumes ( ). For our model, ?_b reaches a plateau at approximately x > 9 for a strongly selective solvent. At this limit, the value of ?_b increases from 0.40 to about 0.66 as the copolymer concentration, c, increases from 0.2 to 0.5; however, this increase is less significant at higher concentrations. The elastic response of the gel studied here is comparable with the Rouse modulus. The elastic modulus increases with polymer concentration, and it exhibits a broad peak within 6 < x < 12. Finally, we present an approximate method to predict the elastic modulus of unentangled ABA triblock copolymers based solely on the morphology of the micellar gel, which can be gleaned from equilibrium DPD simulations. We demonstrate that our simulation results are in good qualitative agreement with other theoretical predictions and experimental data. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 15–25, 2010     

Nanowires Formed by the Co‐Assembly of a Negatively Charged Low‐Molecular Weight Gelator and a Zwitterionic Polythiophene

Conjugated organic nanowires have been prepared by co‐assembling a carboxylate containing low‐molecular weight gelator (LMWG) and an amino acid substituted polythiophene derivative (PTT). Upon introducing the zwitterionic polyelectrolyte PTT to a basic molecular solution of the organogelator, the negative charges on the LMWG are compensated by the positive charges of the PTT. As a result, nanowires form through co‐assembly. These nanowires are visualized by both transmission electron microscopy (TEM) and atomic force microscopy (AFM). Depending on the concentration and ratio of the components these nanowires can be micrometers long. These measurements further suggest that the aggregates adopt a helical conformation. The morphology of these nanowires are studied with fluorescent confocal laser scanning microscopy (CLSM). The interactions between LMWG and PTT are characterized by steady‐state and time‐resolved fluorescence spectroscopy studies. The steady‐state spectra indicate that the backbone of the PTT adopts a more planar and more aggregated conformation when interacting with LMWG. The time‐ resolved fluorescence decay studies confirm this interpretation.