On the Mean Square Formula of the Error Termfor a Class of Arithmetical Functions

 Based on the method in Meurman [5], we study the mean square formula of the error term for a class of Arithmetical functions whose Dirichlet series satisfies a functional equation with multiple gamma factors. We obtain improvements on some results of Chandrasekharan and Narasimhan [1].     

Ethynyl and Propynylpyrene Inhibitors of Cytochrome P450

Abstract  

The single-crystal X-ray structures and in vivo activities of three aryl acetylenic inhibitors of cytochromes P450 1A1, 1A2, 2A6, and 2B1 have been determined and are reported herein. These are 1-ethynylpyrene, 1-propynylpyrene, and 4-propynylpyrene. To investigate electronic influences on the mechanism of enzyme inhibition, the experimental electron density distribution of 1-ethynylpyrene has been determined using low-temperature X-ray diffraction measurements, and the resulting net atomic charges compared with various theoretical calculations. A total of 82,390 reflections were measured with Mo Kα radiation to a (sinθ/λ)_max = 0.985 Å⁻¹. Averaging symmetry equivalent reflections yielded 8,889 unique reflections. A least squares refinement procedure was used in which multipole parameters were added to describe the distortions of the atomic electron distributions from spherical symmetry. A map of the model electron density distribution of 1-ethynylpyrene was obtained. Net atomic charges calculated from refined monopole population parameters yielded charges that showed that the terminal acetylenic carbon atom (C18) is more negative than the internal carbon (C17). Net atomic charges calculated by ab initio, density functional theory, and semi-empirical methods are consistent with this trend suggesting that the terminal acetylenic carbon atom is more likely to be the site of oxidation. This is consistent with the inhibition mechanism pathway that results in the formation of a reactive ketene intermediate. This is also consistent with assay results that determined that 1-ethynylpyrene acts as a mechanism-based inhibitor of P450s 1A1 and 1A2 and as a reversible inhibitor of P450 2B1. Crystallographic data: 1-ethynylpyrene, C₁₈H₁₀, P2₁/c, a = 14.571(2) Å, b = 3.9094(5) Å, c = 20.242(3) Å, β = 105.042(2)°, V = 1,113.5(2) Å³; 1-propynylpyrene, C₁₉H₁₂, P2₁/n, a = 8.970(2) Å, b = 10.136(1) Å, c = 14.080(3) Å, β = 99.77(2)°, V = 1,261.5(4) Å³; 4-propynylpyrene, C₁₉H₁₂, Pbca, a = 9.904(1) Å, b = 13.174(2) Å, c = 19.401(1) Å, V = 2,531.4(5) Å³.     

A note on the dynamical zeta function of general toral endomorphisms

It is well-known that the Artin-Mazur dynamical zeta function of a hyperbolic or quasi-hyperbolic toral automorphism is a rational function, which can be calculated in terms of the eigenvalues of the corresponding integer matrix. We give an elementary proof of this fact that extends to the case of general toral endomorphisms without change. The result is a closed formula that can be calculated by integer arithmetic only. We also address the functional equation and the relation between the Artin-Mazur and Lefschetz zeta functions.     

Flow behavior and deposition study of pollen-shape carrier particles in an idealized inhalation path model

Pollen-shape (spiked sphere) hydroxyapatite (HA) particles for drug carrier application are studied. The particle shape and size effect on flow characteristics and deposition are assessed. The pollen-shape HA particles are synthesized to have comparable size as typical carrier particles with mean diameter of 30-50 m and effective density less than 0.3 g/cm 3 . The flow behaviors of HA and commonly used lactose (LA) carrier particles are characterized by the Carr's compressibility index (CI). The HA particle...     

Universal Alignment Probabilities and Subset Selection for Ordinal Optimization

We examine in this paper the subset selection procedure in the context of ordinal optimization introduced in Ref. 1. Major concepts including goal softening, selection subset, alignment probability, and ordered performance curve are formally introduced. A two-parameter model is devised to calculate alignment probabilities for a wide range of cases using two different selection rules: blind pick and horse race. Our major result includes the suggestion of quantifiable subset selection sizes which are universally applicable to many simulation and modeling problems, as demonstrated by the examples in this paper.     

Preparation of poly(ethylene oxide)‐block‐poly(isoprene) by nitroxide‐mediated free radical polymerization from PEO macroinitiators

Amphiphilic poly(ethylene oxide)‐block‐poly(isoprene) (PEO‐b‐PI) diblock copolymers were prepared by nitroxide‐mediated polymerization of isoprene from alkoxyamine‐terminal poly(ethylene oxide) (PEO). PEO monomethyl ether (M_n ≈ 5200 g/mol) was functionalized by esterification with 2‐bromopropionyl bromide with subsequent copper‐mediated replacement of the terminal bromine with 2,2,5‐trimethyl‐4‐phenyl‐3‐azahexane‐3‐nitroxide. The resulting PEO‐alkoxyamine macroinitiator was used to initiate polymerization of isoprene in bulk and in solution at 125 °C to yield PEO‐b‐PI block copolymers with narrow molecular weight distributions (M_w/M_n ≤ 1.1). Polymerizations were first order in isoprene through 35% conversion. Micellar aggregates of PEO‐b‐PI in aqueous solution were crosslinked by treatment with a water‐soluble redox initiating system, and persistent micellar structures were observed in the dry state by AFM. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2977–2984, 2005     

Pricing and volume discounting for a dominant retailer with uncertain manufacturing cost information

A product costs the manufacturer c/unit to produce; the retailer sells it at p/unit to the consumers. The retail-market demand volume V varies with p according to a given demand curve D_p. How would or should the “players” (i.e., the manufacturer and the retailer) set their prices? In contrast to many studies that assume a dominant manufacturer implementing the “manufacturer-Stackelberg” (“[mS]”) game, this paper examines how a dominant retailer should operate when his knowledge of c is imperfect. We first derive optimal decisions (some of them counter-intuitive) for the dominant retailer when he is restricted to choosing between [rS] (retailer-Stackelberg) and [mS]. Second, we propose a “reverse quantity discount” scheme that the dominant retailer (i.e., the downstream player) can offer to the manufacturer (note that the standard discount scheme is offered by the upstream player). We show that this discounting scheme is quite effective compared to the considerably more complicated though nevertheless theoretically optimal “menu of contracts.” We also reveal a largely overlooked function of discounting; i.e., discounting enables an “ignorant” but dominant player to usurp the earnings attributable to the knowledge of the dominated player. Finally, we also show that discounting works well when the demand curve is linear, but becomes ineffective when the demand curve is iso-elastic – a result echoing the conclusions of some earlier related works.     

Piezoelectric PMN-PT fibre hydrophone for ultrasonic transducer calibration

A newly developed ceramic fibre hydrophone with an active element as small as 0.25 mm in diameter is described in this work. Lead magnesium niobate-lead titanate (PMN-PT) ceramic fibre with a nominal composition of 0.65Pb(Mg_1/3Nb_2/3)O₃-0.35PbTiO₃ was fabricated by an extrusion method. PMN-PT single crystals were ground to a powder form and then mixed with poly(acrylic) acid to form a homogenous slurry. The fibre was extruded by pressing the slurry through a spinneret and then sintering at 1250 °C for crystallization. The electrical characteristics of the PMN-PT fibre were evaluated by measuring the relative permittivity and the impedance spectrum. A piezoelectric PMN-PT fibre hydrophone was fabricated and its sensitivity, angular response, and spatial resolution were evaluated. The fibre hydrophone provides good spatial resolution, angular response and receiving sensitivity. PACS 43.58.+z; 77.84.Dy     

Two extensions of asymptotic methods in controlled Markov chains

The application of the Skorokhod representation of martingales and of the local asymptotic normality to derive limit inequalities for the cost in controlled finite state Markov chains is reviewed. The inequalities are usable in self-optimizing control. The methods are taken from the references listed but, with the exception of proposition 4, the results are formulated for Markov chains for the first time.