On the departure process of a leaky bucket system with long-range dependent input traffic

Due to the strong experimental evidence that the traffic to be offered to future broadband networks will display long-range dependence, it is important to study the possible implications that such traffic may have for the design and performance of these networks. In particular, an important question is whether the offered traffic preserves its long-range dependent nature after passing through a policing mechanism at the interface of the network. One of the proposed solutions for flow control in the context of the emerging ATM standard is the so-called leaky bucket scheme. In this paper we consider a leaky bucket system with long-range dependent input traffic. We adopt the following popular model for long-range dependent traffic: Time is discrete. At each unit time a random number of sessions is initiated, having the distribution of a Poisson random variable with mean λ. Each of these sessions has a random duration τ, where the integer random variable τ has finite mean, infinite variance, and a regularly varying tail, i.e., P(τ >К) ~ К^-Lα L(К), where 1 < α < 2 L(·) is a slowly varying function. Once a session is initiated, it generates one cell at each unit of time until its termination. We examine the departure process of the leaky bucket policing mechanism driven by such an arrival process, and show that it too is long-range dependent for any token buffer size and any - finite or infinite - cell buffer size. Moreover, upper and lower bounds for the covariance sequence of the output process are established. The above results demonstrate that long-range dependence cannot be removed by the kinds of flow control schemes that are currently being envisioned for broadband networks. This revised version was published online in June 2006 with corrections to the Cover Date.     

Asymmetric synthesis of 6-(2′,3′,4′,5′,6′-pentafluorophenyl)-δ-lactones via “allyl”boranes: application for the synthesis of fluorinated analog of key pharmacophore of statin drugs

Asymmetric “allyl”boration of pentafluorobenzaldehyde with various α-pinene based “allyl”boranes provides homoallylic alcohols in high de and ee; the alcohols have been converted into δ-lactones via acryloylation, ring-closing metathesis and hydrogenation. Pentafluorophenyl analog of key pharmacophore of statin drugs has been synthesized using diastereoselective epoxidation and regioselective reduction as key steps.     

Tuning size and catalytic activity of nano-clusters of cobalt oxide

Cobalt oxides were prepared by three different methods: (1) by reacting cobalt nitrate with oxalic acid, (2) co-precipitating cobalt nitrate with sodium carbonate, and (3) using sodium dodecyl sulphate as organic surfactant. All three samples were characterized before and after calcination by solvent extraction and the resulting products examined by IR spectroscopy. In the case of method 3, the removal of surfactant was followed by TGA studies. Products from all three methods were identified by XRD. Peaks in low angle XRD indicate the porous nature of the oxides. The morphology of the pores was studied by transmission electron microscopy. Some irregular pore structures were obtained for samples from methods 1 and 2, with an average size of 4–6 nm. Only the product from method 3 using SDS as template showed ordered structure and optimum size, and Brunauer-Emmet-Teller surface areas of the as-prepared, as well as the treated samples, exhibited H3 type hysteresis. The samples from the three methods were used as catalysts in the oxidation reaction of cyclohexane under mild conditions and the catalytic efficiency of the cobalt oxide was comparable with mesoporous cobalt oxides.     

Propargyloxycarbonyl (Poc) as a protective group for the hydroxyl function in carbohydrate synthesis

[reaction: see text] The propargyloxycarbonyl (Poc) group can be used for the selective protection of the hydroxyl function in carbohydrates and can be removed under neutral conditions using tetrathiomolybdate MoS(4)(2-) (1) in CH(3)CN at room temperature. Under the conditions of deprotection benzylidine acetals, benzyl ethers, acetyl and levulinoyl esters, and allyl and benzyl carbonates are left untouched. It has also been shown that the new protective group (Poc) is compatible with acidic, basic, and also glycosylation conditions.     

Determination of trace metallic impurities in high-purity quartz by ion chromatography

A method has been developed for the determination of relevant trace impurities (alkali, alkaline and transition metals) in high purity quartz by ion-chromatography. In situ reagent (HF) purification and simultaneous sample dissolution was achieved in a multichannel vapour phase digestion assembly. Twenty-one samples can be digested at a time in this vapour phase system. Significant decrease in the process blank levels for all the analytes was observed. Drastic reduction (250 times) of NH4+ blank was achieved in the described vapour phase digestion, which enables the determination of trace concentration of sodium in high purity quartz. After volatilisation of the matrix and unreacted HF, the clear water leached solutions were injected into an ion-chromatograph equipped with conductivity detector for the determination of alkali and alkaline earth metals. In the case of transition metals, the trace residues were leached with 10 mM HCl and after separation on a mixed bed analytical column (IonPac CS5) were detected by spectrophotometry after post column derivatisation using 4-(2-pyridylazo)resorcinol (PAR). The accuracy of the result was checked by their comparison with those obtained by independent methods like inductively coupled plasma (ICP) MS and ICP atomic emission spectrometry. The achievable detection limits are between 0.4 ng/g (Li) and 22 ng/g (Mn). The application of the method to the determination of the above trace metals in two high-purity-grade quartz samples is demonstrated.     

Synthesis and Molecular Structures of Pyridine-Containing Large-Membered Cyclic Bis(alkoxy)silanes(1)

The new cyclic silanes [(C(5)H(3)N)(CH(2)O)(2)SiMe(2)](2) (1) and (C(5)H(3)N)(CH(2)CPh(2)O)(2)SiMe(2) (2) containing 16-membered and 10-membered rings, respectively, were prepared by the condensation reaction of Me(2)SiCl(2) with an appropriate pyridine diol in the presence of Et(3)N. X-ray studies show that the dimeric formulation for 1 represents a tetracoordinate cyclic silane, whereas 2 has a geometry halfway from a tetrahedron toward a trigonal bipyramid (TBP) as a result of Si-N(ax) donor action. (29)Si and (1)H NMR indicate retention of the coordination geometry for 2 in solution that undergoes rapid Si-N cleavage and ring rearrangement. In comparison with other silanes containing five- and six-membered rings that exhibit nitrogen or oxygen coordination, the presence of larger rings, as in 2 and related silanes having sulfur coordination, indicates that retention of donor action persists, thus largely ruling out ring size as a dominant factor controlling the possibility of donor action at silicon. The dimeric silane 1 crystallizes in the triclinic space group P&onemacr; with a = 6.347(3) ?, b = 12.455(4) ?, c = 14.289(5) ?, alpha = 101.63(3) degrees, beta = 102.99(3) degrees, gamma = 104.71(3) degrees, and Z = 2. The cyclic silane 2 crystallizes in the triclinic space group P&onemacr; with a = 9.733(4) ?, b = 10.938(2) ?, c = 14.312(3) ?, alpha = 89.03(2) degrees, beta = 74.59(3) degrees, gamma = 79.24(3) degrees, and Z = 2. The final conventional unweighted residuals are 0.040 (1) and 0.039 (2).     

Synthesis of homoallylic chiral tertiary alcohols via chelation-controlled diastereoselective nucleophilic addition on alpha-alkoxyketones: application for the synthesis of the C(1)-C(11) subunit of 8-epi-fostriecin

[reaction: see text] Chiral beta-syn-alkoxyhomoallylic alcohols derived from alkoxyallylboration of aldehydes upon oxidation provided the corresponding chiral ketones. Chelation-controlled nucleophilic addition to these ketones occurred in a highly stereoselective manner to afford anti-homoallylic tertiary alcohols. This methodology has been applied for the synthesis of the C(1)-C(11) subunit of C(8)-epi-fostriecin.     

Asymmetric allylboration of alpha,beta-enals as a surrogate for the enantioselective synthesis of allylic amines and alpha-amino acids

[reaction: see text] Optically pure allylic amines have been synthesized from alpha,beta-unsaturated aldehydes via allylboration with (-)-B-allyldiisopinocampheylborane, followed by Overman rearrangement. By incorporating crotyl and alkoxyallylboration, functionalization at delta-position was readily accomplished. By applying this methodology, the synthesis of several chiral alpha-amino acids has been achieved.     

Selective reduction of anomeric azides to amines with tetrathiomolybdate: synthesis of beta-D-glycosylamines

A number of beta-d-glycosyl azide derivatives undergo reduction on treatment with tetrathiomolybdate to produce the corresponding beta-d-glycosylamines exclusively without anomerization under very mild and neutral reaction conditions. Acetyl, allyl, benzoyl, and benzyl protective groups are left untouched under the reaction conditions. An exclusive selectivity in the reduction of anomeric azides is observed, while the C-2 and C-6 azides are left untouched.     

Highly selective deblocking of propargyl carbonates in the presence of propargyl carbamates with tetrathiomolybdate

Propargyloxycarbonyl chloride, 1, has been used to protect the hydroxyl and amino functionalities of amino alcohols and aminophenols in one pot using triethylamine or pyridine as a base. The increased reactivity of benzyltriethylammonium tetrathiomolybdate, 2, toward propargyl carbonates over propargyl carbamates is studied in detail and has been exploited further to develop an orthogonal protection strategy for the hydroxyl and amino functionalities. For example, 2-amino-1-butanol, 6a, was treated with 1 to get the N,O-diPoc compound 7a in 90% yield, which when treated with 1.1 equiv of 2 at room temperature removes the Poc group attached to oxygen while leaving the one attached to nitrogen intact to yield compound 8a in 85% yield. This particular observation offers a new protecting strategy where an amine and an alcohol group can be protected simultaneously in one pot, and in a later synthetic step, if the alcohol group has to be deprotected selectively, it can be achieved with 1 equiv of 2.