Analysis of G/D/1 Queueing Systems with Inputs Satisfying Large Deviation Principle under Weak* Topology

The large deviation principle (LDP) which has been effectively used in queueing analysis is the sample path LDP, the LDP in a function space endowed with the uniform topology. Chang [5] has shown that in the discrete-time G/D/1 queueing system under the FIFO discipline, the departure process satisfies the sample path LDP if so does the arrival process. In this paper, we consider arrival processes satisfying the LDP in a space of measures endowed with the weak^* topology (Lynch and Sethuraman [12]) which holds under a weaker condition. It is shown that in the queueing system mentioned above, the departure processes still satisfies the sample path LDP. Our result thus covers arrival processes which can be ruled out in the work of Chang [5]. The result is then applied to obtain the exponential decay rate of the queue length probability in an intree network as was obtained by Chang [5], who considered the arrival process satisfying the sample path LDP.     

Corrected mirror systems with double reflection

We propose objectives consisting of two mirrors with central holes for passage of a light beam. The optical layout ensures multiple reflection of rays from both mirrors. We consider several approaches to calculating the design parameters for which three and four aberrations do not occur. The objectives can be used in optical devices operating in the UV and IR regions of the spectrum. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 2, pp. 267–270, March–April, 2007.     

<Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript> linear interpolator for missing values in time series

We propose a minimum mean absolute error linear interpolator (MMAELI), based on theL ₁ approach. A linear functional of the observed time series due to non-normal innovations is derived. The solution equation for the coefficients of this linear functional is established in terms of the innovation series. It is found that information implied in the innovation series is useful for the interpolation of missing values. The MMAELIs of the AR(1) model with innovations following mixed normal andt distributions are studied in detail. The MMAELI also approximates the minimum mean squared error linear interpolator (MMSELI) well in mean squared error but outperforms the MMSELI in mean absolute error. An application to a real series is presented. Extensions to the general ARMA model and other time series models are discussed. This research was supported by a CityU Research Grant and Natural Science Foundation of China.     

Contributions of restructuring and oxidation to the aging of the surface of plasma polymers containing heteroatoms

The properties and composition of plasma polymer surfaces stored in air can change considerably over time, especially as a result of oxidative reactions. When plasma polymers contain an element other than O, it is possible to probe for mechanisms in addition to oxidation that contribute to the aging of the surface. Plasma polymers containing N were fabricated from either 1,3-diaminopropane (DAP),n-heptylamine (nHA), or allylamine (AA), and studied by X-ray photo-electron spectroscopy (XPS) and air/water contact angles (CA). For each of the plasma polymers, a multiexponential increase in the O/C ratio was observed over time using XPS. The N/C ratios remained constant (AA) or decreased somewhat (nHA and DAP). In contrast, the trends in CA values differed, declining for the nHA surfaces, rising for the AA, and changing little for the DAP. Surface roughness, assessed by scanning tunnelling or atomic force microscopy, did not change over time. The diverse adjustments in the polarity of each surface and the similar compositional changes between them are reconcilable if the aging of the plasma polymer surface is a manifestation of the superposition of concurrent oxidative reactions and partial surface reorientation; the former introduce polar groups and the latter transports then from the surface to deeper regions beyond the CA probe depth but within the XPS analysis depth. These processes vary between different plasma polymers. Data for the alkylamine plasma polymers is also compared with that for two plasma polymers fabricated from methanol. The change in composition, but not polarity, of the DAP surface after 4 days of storage demonstrates the importance of using multiple techniques to characterize the aging of plasma polymer surfaces.     

Preparation and characterization of functional group gradient surfaces

Functional group gradient surfaces where the density of functional groups changes gradually along the sample length were prepared. The functional group (? COOH, ? CONH₂, and ? OH group) gradient surfaces were produced by the treatment of low-density PE sheets using a corona with gradually increasing power, followed by the graft copolymerization of acrylic acid and subsequent substitution reaction of carboxylic acid groups to amide or hydroxyl groups. The prepared gradient surfaces were characterized by the measurement of water contact angle, FTIR-ATR, and ESCA. The gradient surfaces prepared can be used to systematically investigate the interactions of biological or other species in terms of the surface functional groups and their density of polymeric materials. © 1994 John Wiley & Sons, Inc.     

Surface free energy of a solid from contact angle hysteresis

Nature of contact angle hysteresis is discussed basing on the literature data (Colloids Surf. A 189 (2001) 265) of dynamic advancing and receding contact angles of n-alkanes and n-alcohols on a very smooth surface of 1,1,2,-trichloro-1,2,2,-trifluoroethane (FC-732) film deposited on a silicon plate. The authors considered the liquid absorption and/or retention (swelling) processes responsible for the observed hysteresis. In this paper hysteresis is considered to be due to the liquid film left behind the drop during retreating of its contact line. Using the contact angle hysteresis an approach is suggested for evaluation of the solid surface free energy. Molecular spacing and the film structure are discussed to explain the difference in n-alkanes and n-alcohols behaviour as well as to explain the difference between dispersion free energy gamma(s)(d) and total surface free energy gamma(s)(tot) of FC-732, as determined from the advancing contact angles and the hysteresis, respectively.     

A sequence and structural study of transmembrane helices

A comparison is made between the distribution of residue preferences, three dimensional nearest neighbour contacts, preferred rotamers, helix-helix crossover angles and peptide bond angles in three sets of proteins: a non-redundant set of accurately determined globular protein structures, a set of four-helix bundle structures and a set of membrane protein structures. Residue preferences for the latter two sets may reflect overall helix stabilising propensities but may also highlight differences arising out of the contrasting nature of the solvent environments in these two cases. The results bear out the expectation that there may be differences between residue type preferences in membrane proteins and in water soluble globular proteins. For example, the -branched residue types valine and isoleucine are considerably more frequently encountered in membrane helices. Likewise, glycine and proline, residue types normally associated with `helix-breaking' propensity are found to be relatively more common in membrane helices. Three dimensional nearest neighbour contacts along the helix, preferred rotamers, and peptide bond angles are very similar in the three sets of proteins as far as can be ascertained within the limits of the relatively low resolution of the membrane proteins dataset. Crossing angles for helices in the membrane protein set resemble the four helix bundle set more than the general non-redundant set, but in contrast to both sets they have smaller crossing angles consistent with the dual requirements for the helices to form a compact structure while having to span the membrane. In addition to the pairwise packing of helices we investigate their global packing and consider the question of helix supercoiling in helix bundle proteins.     

A tandem of discrete-time queues with arrivals and departures at each stage

A discrete-time system of a tandem of queues with exogenous arrivals and departures at each stage is considered. A customer leaving queuek–1 departs the system with probability 1– ^[k] and continues to queuek with probability ^[k] . Exogenous arrivals to each stage are i.i.d. at each time slot. An approximate analysis of the occupancy and busy-period distributions of each stage based on a General Busy-period with batches and Memoryless (geometric) Idle period renewal Process (GBMIP) provides improved performance over two-state Markov approximations and gives exact results when there are no interstage departures.This research was supported in part by NSF grant NCR-8708282.     

Surface properties of ω-perfluorooctyl-alkyl polyacrylates: odd–even effect

A series of ω-perfluorooctyl-alkyl polyacrylates has been prepared and analysed. The odd–even effect, already observed in the case of liquid crystalline polymers has been exhibited for perfluorinated ones. Values of the contact angles to advanced (θ_a), with withdrawal (θ_r), as well as the contact angle hysteresis (Δθ) of various ω-perfluorooctyl-alkyl polyacrylates in water at 20 °C are described. Contrary to the advancing contact angle which is almost independent of spacer length, the receding one varies strongly with it.     

Effect of surface treatment on the Hamaker constant of intermediate modulus carbon fibers

The Hamaker constant of unsized intermediate modulus carbon fibers was evaluated by contact angle measurement following the Fowkes theory of interfacial energetics. The effects of a surface treatment (performed by the manufacturer) and an oxygen plasma treatment (performed by us), both of oxidizing nature, proved to slightly increase the value of the Hamaker constant to a level that enhanced by about 9% the Lifshitz-van der Waals contribution to the theoretical adhesion force between the fiber and an epoxy matrix. A possible explanation of the observed increase of the Hamaker constant is the higher contribution to the overall Lifshitz-van der Waals interaction of Keesom (orientation) and Debye (induction) forces.