Stationary remaining service time conditional on queue length

In Mandelbaum and Yechiali [The conditional residual service time in the M/G/1 queue, http://www.math.tau.ac.il/∼uriy/publications (No. 30a), 1979] and in Fakinos [The expected remaining service time in a single-server queue, Oper. Res. 30 (1982) 1014-1018] a simple formula is derived for the (stationary) expected remaining service time in a M/G/1 queue, conditional on the number of customers in the system. We give a short new proof of the formula using Rate Conservation Law, and generalize to handle higher moments.     

Jordan homomorphisms,chain geometries and the fundamental theorem

This research was supported by M.P.I. (R.S. 40%).     

Optimal Algorithms for Probabilistic Solitude Detection on Anonymous Rings

Probabilistic algorithms are developed for a basic problem in distributed computation, assuming anonymous, asynchronous, unidirectional rings of processors. The problem, known as Solitude Detection, requires that a nonempty subset of the processors, calledcontenders, determine whether or not there is exactly one contender. Monte Carlo algorithms are developed that err with probability bounded by a specified parameter and exhibit either message or processor termination. The algorithms transmit an optimal expected number of bits, to within a constant factor. Their bit complexities display a surprisingly rich dependence on the kind of termination exhibited and on the processors' knowledge of the size of the ring. Two probabilistic tools are isolated and then combined in various ways to achieve all our algorithms.     

Microbial Baeyer-Villiger Oxidation of Ketones by Cyclohexanone and Cyclopentanone Monooxygenase – A Computational Rational for Biocatalyst Performance

Summary. Recombinant Escherichia coli overexpressing Pseudomonas sp. NCIMB 9872 cyclopentanone monooxygenase (CPMO, EC 1.14.13.16) and Acinetobacter sp. NCIMB 9871 cyclohexanone monooxygenase (CHMO, EC 1.14.13.22) have been utilized in whole-cell Baeyer-Villiger biotransformations of prochiral bicycloketones. A significant difference in substrate acceptance and stereoselectivity was observed for bicyclo[3.3.0] and bicyclo[4.3.0] substrates. A plausible mechanism of these transformations was established by means of high level DFT/B3LYP calculations suggesting an essential difference in electronic requirements for a successful enzymatic conversion, which was similarly encountered in recombinant whole-cell mediated biooxidations. Some of the lactones produced in the biocatalytic Baeyer-Villiger oxidation represent key intermediates for the synthesis of indole alkaloids.     

Low energy positron scattering from atoms in and on solids observed with low energy positron diffraction and reemission microscopy

The present status of low energy positron diffraction (LEPD) and positron reemission microscopy (PRM) is reviewed in the context of unanswered questions regarding the elastic scattering of positrons in the 1–300 eV energy range from atoms in solids and at solid surfaces. Recent LEPD studies yield an agreement between theoretical and experimental diffraction intensities for semiconductors that has never been equalled in electron diffraction studies. This situation is discussed in terms of the repulsive interaction between the positron and the embedded atomic potential and the lack of exchange with the nonspherically distributed valence electrons. The scattering of re-emitted positrons in PRM from atoms chemisorbed or physisorbed on the re-emitting surface has not yet received the same theoretical attention as scattering from embedded atoms in LEPD. Possible ways in which positron scattering from overlying atomic structures manifests itself in PRM as well as positron re-emission holography are discussed, both from the practical viewpoint of observing these structures and in the context of fundamental questions regarding the positron re-emission process itself.     

Preparation of well-aligned carbon nanotubes by pyrolysis of phenolic resin in anodic alumina pores

Well-aligned carbon nanotubes (CNTs) of high quality were synthesized by pyrolysis of phenolic resin at 800 °C in anodic alumina oxide (AAO) pores under argon protection. The innocuous source materials and safe operational conditions permit this method to synthesize well-aligned CNTs in large-scale and low cost. The formation mechanism of the synthesized CNTs is also proposed in this work by a series of visual sketches and is proved with obvious evidence. Firstly, phenolic resin nanotubes form in the template pores through the evaporation of solvent. Heat treatment then transfers these tubes into CNTs.