Allocation of jobs and identical resources with two pooling centers

We examine the resource allocation problem of partitioning identical servers into two parallel pooling centers, and simultaneously assigning job types to pooling centers. Each job type has a distinct Poisson arrival rate and a distinct holding cost per unit time. Each pooling center becomes a queueing system with an exponential service time distribution. The goal is to minimize the total holding cost. The problem is shown to be polynomial if a job type can be divided between the pooling centers, and NP-hard if dividing job types is not possible. When there are two servers and jobs cannot be divided, we demonstrate that the two pooling center configuration is rarely optimal. A heuristic which checks the single pooling center has an upper bound on the relative error of 4/3. The heuristic is extended for the multiple server problem, where relative error is bounded above by the number of servers.      

Sub-Riemannian geometry of the coefficients of univalent functions

We consider coefficient bodies Mn for univalent functions. Based on the Löwner-Kufarev parametric representation we get a partially integrable Hamiltonian system in which the first integrals are Kirillov's operators for a representation of the Virasoro algebra. Then Mn are defined as sub-Riemannian manifolds. Given a Lie-Poisson bracket they form a grading of subspaces with the first subspace as a bracket-generating distribution of complex dimension two. With this sub-Riemannian structure we construct a new Hamiltonian system to calculate regular geodesics which turn to be horizontal. Lagrangian formulation is also given in the particular case M₃.     

多级轴流压气机全工况特性计算

本文使用三维粘性流动计算软件Fine／Numeca,对某十五级轴流压气机进行了内流流场和全工况特性的数值计算尝试。分析了该压气机在设计工况和非设计工况的性能,同时把整机计算结果和前七级叶片的计算结果进行了比较。计算结果表明,当计算的级数较少时,目前的软件和硬件平台可以比较合理地预测压气机的全工况特性;而当计算的级数较多时,准确的数值模拟仍需要更为准确的多级模型和数值方法。     

Synthesis of poly(p‐phenylene sulfide) from bis(4‐bromophenyl) disulfide

Improved reaction conditions for the preparation of poly(p‐phenylene sulfide) (PPS) directly from bis(4‐bromophenyl) disulfide (BBD) have been established. Heating BBD with magnesium metal afforded only a low molecular weight polymer. PPS with a melting temperature around 280 °C was obtained from BBD in the presence of sodium carbonate or zinc metal. The best results were obtained with the addition of a catalytic amount of KI to the zinc–BBD mixture. Polymers prepared by the above methods are semicrystalline and dissolve in 1‐chloronaphthalene and have properties comparable to commercial PPS. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 900–904, 2006     

Effect of stoichiometry on liquid crystalline supramolecular polymers formed with complementary nucleobase pair interactions

We report herein studies on the liquid crystalline behavior of a series of supramolecular materials that contain different ratios of two complementary symmetrically-substituted alkoxy-bis(phenylethynyl)benzene AA- and BB-type monomers. One monomer has thymine units placed at either end of the rigid mesogenic core, while the other has N⁶-(4-methoxybenzoyl)-adenine units placed on the ends. Differential scanning calorimetric and polarized optical microscopy studies have been carried out on these systems. These studies show that the material's behavior is strongly dependent on its thermal history. As a result, the materials can exhibit, on heating, either a liquid crystalline phase, a crystalline phase, or the coexistence of crystalline and liquid crystalline regions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5049–5059, 2006     

Synthesis and liquid crystalline properties of new amide‐modified poly(1,4‐cyclohexanedimethylene terephthalate)

New series of cycloaliphatic poly(ester‐amide)s, poly(1,4‐cyclohexanedimethyleneterephthalate‐co‐1,3‐cyclohexanedimethylene terephthalamide), were synthesized through solution polymerization route. The compositions of ester/amide units in the copolymers were varied from 0 to 100% by varying the amount of 1,4‐cyclohexanedimethanol and 1,3‐cyclohexanebis(methylamine) in the feed. The structures of the polymers were confirmed by NMR and FTIR, and the molecular weights were determined by inherent viscosity. The composition analysis by NMR reveals that the reactivity of the diamine toward the acid chlorides is lowered than that of diol, which results in the formation of more ester content in the poly (ester‐amides). The thermal analysis indicate that the new poly(ester‐amide)s having less than 10 mol % of amide linkages are thermotropic liquid crystalline from 200 to 250 °C and a thread like nematic phases are observed under the polarizing microscope. WXRD studies suggest that the liquid crystalline domains promote the nucleation process in the polyester chains and increases the percent crystallinity of the poly(ester‐amide)s. The glass transition temperature of the copolymers initially increases with increase in amide units because of the presence of nematic phases and subsequently follows the Flory–Fox behavior. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 42–52, 2006     

Lightly crosslinked,mesomorphic networks obtained through the reaction of dimeric,liquid‐crystalline epoxy–imine monomers and heptanedioic acid

We reacted various dimeric, liquid‐crystalline epoxy–imine monomers, differing in the length of the central aliphatic spacer or the dipolar moments, with heptanedioic acid. The resulting systems showed a liquid‐crystalline phase in some cases, depending on the dimer and on the reaction conditions. The systems were characterized with respect to their mesomorphic properties and then were submitted to dynamic mechanical thermal analysis in both fixed‐frequency and frequency‐sweep modes in the shear sandwich configuration. The arrangement in the liquid‐crystalline phase seemed to be mainly affected both by the polarization of the mesogen and by the reaction temperature, which favored the liquid‐crystalline arrangement when it was lying in the range of stability of the dimer mesophase. In agreement with other recent literature data, dynamic mechanical thermal analysis results suggested that the presence of the mesogen directly incorporated into the main chain increased the lifetimes of the elastic modes both in the isotropic phase and in the liquid‐crystalline phase with respect to side‐chain liquid‐crystalline elastomers and that the time–temperature superposition principle did not hold through the liquid‐crystalline‐to‐isotropic transition. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44:6270–6286, 2006     

Chemically modified proton‐conducting membranes based on sulfonated polyimides: Improved water stability and fuel‐cell performance

A series of branched/crosslinked sulfonated polyimide (B/C‐SPI) membranes were prepared and evaluated as proton‐conducting ionomers based on the new concept of in situ crosslinking from sulfonated polyimide (SPI) oligomers and triamine monomers. Chemical branching and crosslinking in SPI oligomers with 1,3,5‐tris(4‐aminophenoxy)benzene as a crosslinker gave the polymer membranes very good water stability and mechanical properties under an accelerated aging treatment in water at 130 °C, despite their high ion‐exchange capacity (2.2–2.6 mequiv g^?1). The resulting polymer electrolytes displayed high proton conductivities of 0.2–0.3 S cm^?1 at 120 °C in water and reasonably high conductivities of 0.02–0.03 S cm^?1 at 50% relative humidity. In a single H₂/O₂ fuel‐cell system at 90 °C, they exhibited high fuel‐cell performances comparable to those of Nafion 112. The B/C‐SPI membranes also displayed good performances in a direct methanol fuel cell with methanol concentrations as high as 50 wt % that were superior to those of Nafion 112. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3751–3762, 2006     

Vinyl‐terminated side‐chain liquid‐crystalline polyethers containing mesogenic benzylideneaniline moieties

The synthesis of two vinyl‐terminated side‐chain liquid‐crystalline polyethers containing benzylideneaniline moieties as mesogenic cores was approached in two different ways: by chemically modifying poly(epichlorohydrin) with suitable mesogenic acids or by polymerizing analogous glycidyl ester or glycidyl ether derivatives. In all the conditions tested, the first approach led to materials in which the imine group was hydrolyzed. The second approach led to the desired polymers PG2a and PG2b , but only from the glycidyl ether derivatives and when the initiator was the system that combined polyiminophosphazene base t‐Bu‐P₄ and 3,5‐di‐t‐butylphenol. These polymers were chemically characterized by IR and ¹H and ¹³C NMR spectroscopies. The estimated degrees of polymerization ranged from 30 to 36. The liquid crystalline behavior of the synthesized polymers was studied by differential scanning calorimetry, polarized optical microscopy (POM) and X‐ray diffraction. Both polymers behave like liquid crystals and exhibited a single mesophase, which was recognized as a smectic C mesophase, probably with a bilayer arrangement, i.e., a smectic C₂ mesophase. The crosslinking of both polymers was performed with dicumyl peroxide as initiator, which led to liquid crystalline thermosets. POM and X‐ray diffraction confirmed that the mesophase organization mantained on the crosslinked materials. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1877–1889, 2006