Waiting Time Variability in some Single-Server Queueing Systems

This paper considers the range of values of the coefficient of variation of waiting time in some general single-server queueing systems. It is shown that in M/G/1 systems with given ρ, the square of this coefficient increases linearly with m₁m₃/m²₂, where m_i is the ith moment of the service distribution. This implies always a lower bound, and for some widely used distributions an upper bound as well. A few ranges are illustrated and compared to those implied in two GI/M/1 systems. The usefulness of knowing such ranges for modelling purposes is explained.     

On the singular graph and the Weyr characteristic of anM-matrix

LetA be anM-matrix in standard lower block triangular form, with diagonal blocksA _ii irreducible. LetS be the set of indices such that the diagonal blockA is singular. We define the singular graph ofA to be the setS with partial order defined by > if there exists a chain of non-zero blocksA _i, A_ij, , A_l.Let ₁ be the set of maximal elements ofS, and define thep-th level _p ,p = 2, 3, , inductively as the set of maximal elements ofS \( _{1 p-1}). Denote by _p the number of elements in _p . The Weyr characteristic (associated with 0) ofA is defined to be (A) = ( ₁, ₂,, _h ), where ₁ + + _p = dim KerA ^p ,p = 1, 2, , and _h > 0, _h+1 = 0.Using a special type of basis, called anS-basis, for the generalized eigenspaceE(A) of 0 ofA, we associate a matrixD withA. We show that(A) = ( ₁, , _h) if and only if certain submatricesD _p,p+1 ,p = 1, , h – 1, ofD have full column rank. This condition is also necessary and sufficient forE(A) to have a basis consisting of non-negative vectors, which is a Jordan basis for –A. We also consider a given finite partially ordered setS, and we find a necessary and sufficient condition that allM-matricesA with singular graphS have(A) = ( ₁, , _h). This condition is satisfied ifS is a rooted forest.The work of the second-named author was partly supported by the National Science Foundation, under grant MPS-08618 A02.     

Molecules organiques coordinees a un metal. : Nouveaux complexes olefiniques d'α-enones par le fer(0)

Heterodienetricarbonyliron complexes react with ligands ( L = PMe₂Ph, P(OMe)₃ or P(OPh)₃) to give the adducts (enone)Fe(CO)₃L with the ethylenic double bond coordinated only to the iron(0). Electron-releasing and low-steric effects of L make the reaction which is specific for enones easier compared to that for dienes. PMe₂Ph allows enone exchange and P(OPh)₃ promotes carbonyl elimination. Ligand influence is shown by infrared spectroscopy and by the shielding of ethylenic protons in NMR spectroscopy.     

Ferrocenyltrithiocarbonates : I. Direct access from α-ferrocenylcarbinols by a SNi mechanism. Absolute x-ray structure determination of (R)-ferrocenylmethylmethane S-methyl-trithiocarbonate

¹⁰³Rh Chemical shifts of a variety of mono- and di-nuclear rhodium carbonyl complexes are reported together with the modifications to the probe and decoupler unit of a JEOL PS-100 PFT spectrometer which enable these ¹⁰³Rh-decoupled ¹³C NMR measurements to be made. These data are discussed in conjunction with ¹³C NMR data on other rhodium carbonyls.     

Preparation of Neutral Ionophores for Alkali and Alkaline Earth Metal Cations and their application in ion selective membrane electrodes

The preparation of a series of non-cyclic, uncharged ligands able to selectively complex alkali and alkaline earth metal cations is described. These molecules are designed to be used as carriers for cations through membranes. Some of the compounds show high Ca²⁺ and Na⁺ selectivity, respectively, in liquid membrane electrodes.     

Incorporation of pseudoproline derivatives allows the facile synthesis of human IAPP, a highly amyloidogenic and aggregation-prone polypeptide

The efficient Fmoc solid-phase peptide synthesis of the 37-residue human Amylin and its amyloidogenic 8-37 fragment was achieved using pseudoproline (oxazolidine) dipeptide derivatives. Syntheses of hAmylin(8-37) using Fmoc amino acids produced only traces of the desired peptide. Incorporation of pseudoproline dipeptides produced the desired product with high yield and allowed for the synthesis of the full length peptide. The crude material was pure enough to allow formation of the Cys-2 to Cys-7 disulfide by air oxidation. [Structure: see text]     

Non-aqueous capillary electrophoresis of the positional isomers of a sulfated monosaccharide

A non-aqueous capillary electrophoresis (NACE) method coupled to indirect absorbance detection has been developed for the separation of the three positional isomers of monosulfated fucose. The optimized electrolyte was composed of 12 mM ethanolamine, 2 mM trimesic acid buffer in a methanol-ethanol (1:1, v/v) mixture. As the retained electrolyte entails no separating agent other than the pH buffer, the NACE separation of the positional isomers has been ascribed mainly to selective ion-pairing with the electrolyte counter-ion and the possibility of a selective solvation effect in the alcohol mixture. In the absence of pure isomeric standards, peak identification was completed by MS and NMR spectroscopy and selective enzymatic desulfation. This method should be of interest for the structure elucidation of monosulfated fucose-based polysaccharides and for the screening of sulfoesterase of unknown activity.     

A facile retro-ene reaction of 5-(methoxyamino)-3-aryl-1,3,4-oxadiazol-2(3H)-ones

5-(N-Methoxy-N-methyl)amino-3-aryl-1,3,4-oxadiazol-2(3H)-ones 3 undergo a heteroretro-ene reaction in refluxing methanol in which the leaving enophile is formaldehyde. The resulting 5-(methylimino)-3-aryl-1,3,4-oxadiazolidin-2-one 4 may be viewed as a kinetic product which tautomerizes to the more stable 5-(methylamino)-3-aryl-1,3,4-oxadiazol-2(3H)-one 5 as the thermodynamic product. Comparison of calculated reaction energies reveals that the presence of the heterocyclic ring facilitates the retro-ene reaction, but the expulsion of formaldehyde is predicted to be highly exothermic even in its absence.     

Avalanches and self-organized criticality in simulations of particle piles

Simulations are carried out for an athermal pile of particles in the presence of a gravity-like force. As the force increases, the pile structure rearranges through discrete avalanche events. The sizes of the avalanche events are characterized by the change in energy, and it is found that the avalanche size follows a power-law probability distribution with a power-law exponent of −0.96. These results suggest that the particle pile is in a self-organized critical state.     

Capture-ROMP-release: application to the synthesis of amines and alkyl hydrazines

Application of a capture-ROMP-release strategy for the chromatography-free purification of Mitsunobu reaction products is described. Norbornenyl-tagged reagents are utilized for standard solution phase Mitsunobu chemistry. Post-reaction phase-switching is accomplished via in situ ring-opening metathesis polymerization (ROMP) followed by precipitation of the polymer with methanol. Release of the product from the polymer affords amines and alkyl hydrazine derivatives with good yields and purities.