Duality in Truncated Steady-State Erlang Distribution-Based Queueing Processes

In this paper, the notion of duality and a generalized methodology to identify the dual for an Erlang distribution-based truncated steady-state queueing process is suggested. This procedure provides insight into truncated queueing processes. At first glance, the relationship between the primal problem and the dual problem may not be intuitive. Several such relationships are identified. For example, the dual of the M/E_s/C/C queueing process is shown to be the M/M/1 machine interference problem with C machines and the solution to one of these provides the solution to the other. An example is presented.     

Sodium alizarin-3-sulphonate as a chromophoric reagent

Summary A method has been recommended for the determination of thorium and molybdenum when present in micro-quantities, based on the formation of a red coloured water soluble chelate ( _max=520 nm for thorium and _max=470 nm for molybdenum) of the composition MRe=12, with sodium-alizarin-3-sulphonate. A large number of ions, however, interfere and should be removed before measurements are made. The solution of thorium chloride or ammonium molybdate may then be treated with a freshly prepared solution of Alizarin Red S. The p_H should be kept within the range 3.2 to 8.0 for thorium, 3.5 to 5.6 (preferably at 5.0) for molybdenum and the colour intensity may be measured with a photoelectric colorimeter or with a spectrophotometer. Temperature has no influence on the colour intensity. Determinations are possible between 0.23 and 16.70 ppm of thorium and 0.19 to 6.9 ppm of molybdenum.

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Zusammenfassung Zur Bestimmung von Mikromengen Thorium und Molybdän wird ein Verfahren vorgeschlagen, das auf der Bildung einer rotgefärbten, wasserlöslichen Komplexverbindung mit Natriumalizarin-3-sulfonat beruht. Die Zusammensetzung des Komplexes beträgt in beiden Fällen MeReagens=12. Die Absorptionsmaxima liegen bei 520 nm (Th) bzw. bei 470 nm (Mo). Viele Fremdionen verursachen Störungen und müssen vor der Messung entfernt werden. Die Lösung von Thoriumchlorid bzw. Ammoniummolybdat werden mit frisch bereiteter Alizarinrot S-Lösung behandelt; der p_H-Wert soll im Bereich 3,2–8,0 für Thorium bzw. 3,5–5,6 (am besten 5,0) für Molybdän liegen. Die Farbintensität wird mit einem photoelektrischen Colorimeter oder einem Spektrophotometer gemessen; sie wird von der Temperatur nicht beeinflußt. Die Bestimmung läßt sich im Bereich 0,23–16,70 ppm Thorium bzw. 0,19–6,9 ppm Molybdän durchführen.

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Part. II: Sinha, S. N., and A. K. Dey: Z. analyt. Chem. 183, 182 (1963).     

Grob-type fragmentation of 5-oxabicyclo[2.1.1]hexane system: a strategy for synthesis of annulated and 2,2,5-trisubstituted tetrahydrofurans

Acid mediated, efficient Grob-type fragmentation reaction facilitated by vicinal ketal and ester moieties in variety of 5-oxabicyclo[2.1.1]hexanes leading to the corresponding annulated and 2,2,5-trisubstituted tetrahydrofurans is reported. Among the Brønsted and Lewis acids tested, BF₃·OEt₂ appears to give the best results, furnishing near quantitative yield (>99%) of tetrahydrofuran tricarboxylate derivatives under mild reaction condition. In case of unsymmetrical monosubstituted 5-oxabicyclo[2.1.1]hexanes two regioisomeric products are obtained. A strategy to transform one of the ester groups of the title compounds to protected hydroxymethyl moiety was evolved, which allows access to differentially protected 2-hydroxymethyl THF derivatives upon fragmentation. Employing TiCl₄/R or S-BINOL as chiral Lewis acid, an enantioselective fragmentation (up to 66% ee) was described for the meso bis-furan derivative.     

Relationships of labile pool of Mn with some general soil properties and extractable soil Mn contents

Labile pool (E-value) of Mn and extractable soil Mn content using six multinutrient extractants were estimated in fifty surface (0–15 cm) soil samples. Labile pool of Mn was poorly correlated to the general soil properties and modified Olsen’s-; 0.01 M CaCl₂- and 1 M MgCl₂-extractable Mn contents but it was positively and significantly correlated to diethylene triamine pentaacetic acid (DTPA), pH 7.3; ammonium bicarbonate + DTPA (pH 7.6); and Mehlich-3-extractable soil Mn contents. The multinutrient extractants involving only simple salt solutions were not useful to assess the availability of Mn in soils.     

Resonances of nanocylinders with gap defects

We have investigated the plasmonic resonance characteristics of canonical circular and square cylinders, with gap defects, that are illuminated by a plane wave. The circular and square cylinders have vee shaped gaps and constant width gaps, respectively. The electric and magnetic fields are obtained by solving the Lippmann–Schwinger equation from which we compute the far-field scattering cross-section and near-field local electromagnetic energy density.Numerical results are given for numerous wavelength and gap dimensions to qualitatively present the effects of gap defects on the scattering cross-section and local electromagnetic energy density.     

Unambiguous evidence for wurtzite phase in capped CdS quantum dots

The problem of identification of the correct crystalline structure of CdS nanoclusters below 2.5 nm in size is outlined. Structure of thiophenol capped CdS nanoclusters in the size range 1.2–4.3 nm, synthesized using cadmium acetate solution in methanol, is discussed using powder XRD and electron diffraction data. Unambiguous confirmation of the wurtzite phase in CdS nanoclusters below 2.5 nm size is reported. The observation of 102 wurtzite peak in the XRD patterns of such nanoclusters indicates low stacking fault concentration.     

Stereoselective Cross-Coupling of Baylis–Hillman Acetates with Diphenyl Disulfides and Diselenides Using Palladium Acetate

An efficient method is described for the stereoselective synthesis of diorganyl chalcogenides from a variety of Baylis–Hillman acetates and diaryl chalcogens using palladium catalyst. This reaction is a convenient new method to produce unsymmetrical sulfides and selenides in good yields.     

Manganese(II) complexes of 5-(4-pyridyl), 5-phenyl and 5-(4-methoxy-phenyl)-1,3,4-oxadiazole-2-thione containing 2, 2′-bipyridyl/ethylenediamine: synthesis,spectral, and X-ray characterization

Three new mixed ligand complexes [Mn(4-pytone)₂(bipy)₂]bipy (1), [Mn(pot)₂(en)₂] (2) and [Mn(4-mot)₂(en)₂] (3) (4-pytone = 5-(4-pyridyl)-1,3,4-oxadiazole-2-thione, pot = 5-phenyl-1,3,4-oxadiazole-2-thione, 4-mot = 5-(4-methoxy-phenyl)-1,3,4-oxadiazole-2-thione) have been prepared containing bipy/en as coligands. The starting material potassium N-(aryl-carbonyl)-hydrazinecarbodithioates (RCONHNHCSSK) underwent cyclization during complexation in the presence of bipy or en to give the corresponding 5-aryl-1,3,4-oxadiazole-2-thiones. The complexes have been characterized by physicochemical techniques and single crystal X-ray structure determination. In all cases, the manganese has a six coordinate octahedral arrangement coordinated by 4N atoms of two bipy/en and two covalently bonded N atoms of the oxadiazole-2-thione anions.     

Silver nanocluster redox-couple-promoted nonclassical electron transfer: an efficient electrochemical Wolff rearrangement of alpha-diazoketones

In this work we report the unique electrocatalytic role of benzoic acid protected silver nanoclusters (Ag(n), mean core diameter 2.5 nm) in the Wolff rearrangement (Scheme 1) of alpha-diazoketones. More specifically, the presence of a Ag(n) (0)/Ag(n) (+) redox couple facilitates a nonclassical electron-transfer process, involving chemical reaction(s) interposed between two electron-transfer steps occurring in opposite directions. Consequently, the net electron transfer between the electron mediator (Ag(n)) and alpha-diazoketone is zero. In-situ UV-visible studies using pyridine as a nucleophilic probe indicate the participation of alpha-ketocarbene/ketene as important reaction intermediates. Controlled potential coulometry of alpha-diazoketones using Ag(n) as the anode results in the formation of Wolff rearranged carboxylic acids in excellent yield, without sacrificing the electrocatalyst.     

Functionalized chiral vinyl aminosulfoxonium salts: asymmetric synthesis and application to the synthesis of enantiopure unsaturated prolines, beta,gamma-dehydro amino acids, and cyclopentanoid keto aminosulfoxonium ylides

Methylation of the enantiopure functionalized vinyl sulfoximines 5a-e and 14a-d followed by a F- ion or DBU-mediated isomerization of the vinyl aminosulfoxonium salts 7a-e and 15a-d, respectively, gave the allyl aminosulfoxonium salts 10a-e and 17a-d, respectively. A concomitant intramolecular substitution of the aminosulfoxonium group of 10a-e and 17a-d by the amino group afforded the unsaturated prolines 8a-e and 18a-d, respectively. The starting vinyl sulfoximines are accessible through a highly selective and stereo-complementary aminoalkylation of the corresponding sulfonimidoyl-substituted mono- and bis(allyl)titanium complexes with the imino ester 4. The vinyl aminosulfoxonium salts 34, 7a-d, and E-15c experienced upon treatment with the Cl- ion a migratory substitution with formation of the delta-chloro-beta,gamma-dehydro amino acids 36, E/Z-37a-d, and 38, respectively. A migratory substitution of the hydroxy-substituted vinyl aminosulfoxonium salts 46a and 46b furnished the delta-chloro allyl alcohols E/Z-48a and E-48b, respectively. A facile one-pot conversion of the vinyl sulfoximines 31b, 5c and 45a to the allyl chlorides 36, E/Z-37c and E/Z-48a, respectively, was achieved upon treatment with a chloroformiate. A tandem cyclization of the vinyl aminosulfoxonium salts 7b, Al-7b and 57 with LiN(H)tBu yielded the cyclopentanoid keto aminosulfoxonium ylides 54, Al-54, 59, 60 and 61, respectively. The structure of the tricyclic keto aminosulfoxonium ylide Al-54 has been determined by X-ray crystal structure analysis. Ab initio calculations and a NBO analysis of the tricyclic keto aminosulfoxonium ylide XXIII show a polar structure stabilized by electrostatic interactions between the ylidic C atom and both the carbonyl C atom and the S atom.