Order statistics applications to queueing and scheduling problems

We prove several basic combinatorial identities and use them in two applications: the queue inference engine (QIE) and earliest due date rule (EDD) scheduling. Larson (1990) introduced the QIE. His objective was to deduce the behavior of a multiserver queueing system without observing the queue. With only a Poisson arrival assumption, he analyzed the performance during a busy period. Such a period starts once all servers are busy with the queue empty, and it ends as soon as a server becomes idle. We generalize the standard order statistics result for Poisson processes, and show how to sample a busy period in the M/M/c system. We derive simple expressions for the variance of the total waiting time in the M/M/c and M/D/1 queues given that n Poisson arrivals and departures occur during a busy period. We also perform a probabilistic analysis of the EDD for a one-machine scheduling problem with earliness and tardiness penalties. The schedule is without preemption and with no inserted idle time. The jobs are independent and each may have a different due date. For large n, we show that the variance of the total penalty costs of the EDD is linear in n. The mean of the total penalty costs of the EDD is known to be proportional to the square root of n (see Harel (1993)). This revised version was published online in June 2006 with corrections to the Cover Date.     

Liquid crystalline properties of salicylaldimine-based dimers: influence of terminal alkyl chain length and central part

The synthesis and thermotropic properties of four homologous series of salicylaldimine-based dimer liquid crystals are reported. Two 4-(4-alkoxy-2-hydroxybenzylideneamino)benzoyloxy groups are connected to a central part consisting of a 1,3-phenylene, 1,5-pentylene, 2,2-dimethyl-1,5-pentylene or 3,3-dimethyl-1,5-pentylene unit. The terminal alkoxy chains have been varied from 4 to 16 carbon atoms in length. All the compounds exhibit liquid crystalline phases whose behaviour depends on the nature of the central part and the length of the alkoxy terminal chains. All compounds of the series with the central phenyl part exhibit enantiotropic B-phases, and the sequence B₆-B₁-B₂ on increasing terminal chain length was observed. Replacement of the phenyl group with a pentyl central group partly suppresses the formation of B-phases. The longer homologues of this series show the B₁ phase, while the shorter exhibit an intercalated SmC_c mesophase. The introduction of methyl substituents to the pentyl spacer causes the melting points to fall dramatically and the formation of B-phases is totally suppressed. The compounds with the long tails show intercalated SmA_c phases and those with short tails show intercalated SmC_c phases.     

Locating two obnoxious facilities using the weighted maximin criterion

Given are a finite set of points P and a compact polygonal set S in R². The problem is to locate two new facilities in S, maximizing the minimum of all weighted distances between the points in P and the two new facilities, and the distance between the pair of new facilities. We present subquadratic algorithms.     

Propellanes. Part LXXXII. Preparation and Labelling of [20.3.3]Propellane-24,27-dione

The title diketone has been prepared by a synthetic sequence beginning with decane-1,10-dicarboxylic acid.     

Construction and characterization of a frequency-domain fluorescence lifetime imaging microscopy system

The construction of a homodyne frequency domain fluorescence lifetime imaging microscope is described. The system consists of (i) an intensity-modulated laser excitation source, (ii) an epifluorescence microscope, (iii) a gain-modulated microchannel plate (MCP) image intensifier, and (iv) a slow-scan CCD camera. The phase and modulation homogeneity of the MCP image intensifier were determined at frequencies of 40, 100, 160, and 240 MHz. The detected modulation depths were 65, 52, 32, and 23%, respectively, and were highly homogeneously distributed. The phasedistribution image revealed iris effects at frequencies of 160 and 240 MHz but was homogeneous at lower frequencies. Lifetime imaging of a solution of the fluorescent flavoprotein lipoamide dehydrogenase demonstrated (i) the accuracy of the determined lifetimes (< 60 ps), (ii) the time resolution of the instrument (< 50 ps), and (iii) the average precision for single pixel fluorescence lifetimes (50 ps is feasible). The imaging of tiny fluorescent microspheres revealed that even in a volume of 0.3 x 10^-15 L, the standard error in the lifetimes can be as low as 79 ps. The spatial resolution of the instrument is estimated to be < 400 nm in the object plane at a 100 x magnification.     

Asymmetric banana-shaped liquid crystals with two different terminal alkoxy chains

Two series of asymmetric banana-shaped compounds have been synthesized and studied. In the 1,3-phenylene bis[4-(4'-alkoxybenzoyloxy)]benzoate series the lack of symmetry was derived solely from the difference in length of the two terminal alkoxy chains. In the 3,4'-biphenylene bis[4-(4'-alkoxybenzoyloxy)]benzoate series the asymmetric nature originates from the 3,4'-substitution of the central biphenyl group and from the difference in length of the two terminal chains. All the melting points of the asymmetrical compounds in the series with the central phenyl unit are lower than those of the symmetrical compounds. The liquid crystalline B₁ or B₂ phase was retained in all cases. In the series with the central biphenyl unit the compounds with the shortest chain attached to the para-position of the central biphenyl unit have the lowest melting points. A significant lowering of the melting points in comparison with the symmetrically substituted compounds, however, could not be achieved. All the compounds of both series show a layer spacing which is comparable to those of the symmetrically substituted parent compounds. The observed switching behaviour of both the symmetric and asymmetric compounds with a B₂ phase was antiferroelectric.     

A new six-coordinate organotin(IV) complex of OP[NC5H10]3: A comparison with an analogous five-coordinate complex by means of X-ray crystallography,Hirshfeld surface analysis and DFT calculations

A new six-coordinate organotin(IV)-phosphoric triamide complex of OP[NC₅H₁₀]₃ = OP was synthesized ([Cl₂Sn(CH₃)₂(OP)₂], 1) and characterized by X-ray crystallography and spectroscopic methods (FT-IR, UV–Vis, and ¹H/¹³C/³¹P-NMR). The crystal structures of 1 and the analogous previously reported five-coordinate complex [Cl₂Sn(CH₃)₂(OP)] (IZOVIE) were compared on a structural level and by computational means using Hirshfeld surface analysis, density functional theory calculations and the atom in molecule method. The investigation of intermolecular interactions in the crystal structures of the two complexes by the Hirshfeld surface method indicates that in the absence of normal hydrogen bonds, the chlorine-based interactions H?Cl/Cl?H (for 1 and IZOVIE) and Cl?Sn/Sn?Cl (for IZOVIE) play a determinant role in the molecular assemblies. However, the prominent contacts are of H?H type. From calculated electronic parameters such as bond order, Mulliken charge and electron delocalization energy, it was found that the Sn-OP contact has a lower strength in IZOVIE than in 1, suggesting more ionic character of the metal-oxygen contact in five-coordinate complex IZOVIE. Furthermore, we discuss the similarities and differences of the two complexes 1 and IZOVIE derived from the same ligand OP by density functional theory calculations to present an insight into the organotin(IV)-phosphoric triamide coordination chemistry affected by different geometries and coordination numbers.     

Probing the interaction of HTI-286 with tubulin using a stilbene analogue

HTI-286 is a synthetic analogue of the natural product hemiasterlin. HTI-286 is a potent antitumor agent that induces tubulin oligomerization. To investigate the binding stoichiometry and the binding site during this ligand-induced tubulin association, we synthesized an analogue of HTI-286 containing the chromophore stilbene. Using the distinct absorbance of the stilbene analogue, we determined the amounts of inhibitors bound to different tubulin oligomers by analytical ultracentrifugation. Herein we describe our findings based on these experiments. At the ratio of inhibitor to protein equal to or greater than 1, the stilbene analogue induces oligomerization of tubulin to a ring structure. The binding stoichiometry in the ring is one inhibitor per tubulin monomer (defined as an alpha/beta-heterodimer). At the ratio of inhibitor to protein less than 1, tubulin forms multiple intermediates, with the binding stoichiometry less than one inhibitor per tubulin monomer for all intermediates. The stable complex between the inhibitor and tubulin monomer was not detected under our experimental conditions. The binding site of the stilbene analogue does not overlap with the classic tubulin-binding agent, colchicine.     

Ion-driven ATP pump by self-organized hybrid membrane materials

We report new hybrid organic-inorganic materials, based on macrocyclic receptors 1-3 self-organized in tubular superstructures prepared by sol-gel process. Fourier transform infrared (FTIR) and NMR spectroscopic analyses demonstrate that the self-organization by hydrogen bonding of organogel superstructures of 2 and 3 were preserved in the hybrid materials throughout the sol-gel process. The molecular arrangement of heteroditopic receptors defines a particularly attractive functional transport device for both cation (tubular macrocycles) and anion (sandwich-urea) directional-diffusion transport mechanism in the hybrid membrane material. This system has been employed successfully to design a solid dense membrane, functioning as an ion-powered adenosine triphosphate (ATP(2)(-)) pump, and illustrates how a self-organized hybrid material performs interesting and potentially useful functions.     

A silyl-α-cyclodextrin intermediate. Preparation and characterization of dodeca-t-butyldimethylsilyl-hexahydroxy-α-cyclodextrin

The title compound (II) was prepared by treating dry, purified α-cyclodextrin with 20 equivalents oft-butyldimethylsilyl chloride 20 hr at 110° in DMF/pyridine. Work-up of the product mixture gave 60%II, which was identified by¹H and¹³C NMR. Treatment ofII with Bu₄NF 6 hr in refluxing dry THF efficiently removed the protecting groups.