Maximal flow through a domain

It is proved that, if the DFP or BFGS algorithm with step-lengths of one is applied to a functionF(x) that has a Lipschitz continuous second derivative, and if the calculated vectors of variables converge to a point at which ?F is zero and ?² F is positive definite, then the sequence of variable metric matrices also converges. The limit of this sequence is identified in the case whenF(x) is a strictly convex quadratic function.     

The mass spectrometric fragmentation of n-benzylacetamide

The low energy mass spectra of N-benzylacetamide have been recorded. The major fragmentations of the molecular ion are similar to those observed in the acetanilide spectrum. In addition, the secondary dissociation of the [C₆H₅CH₂NH]⁺ ion by loss of HCN is shown to occur with transfer of the -N–H hydrogen to the ring.     

Coupling insertion reactions of diphenylbuta-1, 4-diyne into iron-carbene bonds of [Fe2(CO)7{μ-C(Ph)C(NEt2}]. Syntheses and reactivities of the ferracyclopentadiene [Fe2(CO)6{C(Ph)C(NEt2)C(Ph)C(C2Ph)}] with [Fe2(CO)9]

The diiron ynamine complex [Fe₂(CO)₇{-C(Ph)C(NEt₂)}] (1) reacts with the diphenylbuta-1, 4-diyne, PhCC-CCPh, in refluxing hexane to yield three isomer complexes [Fe₂(CO)₆{C(Ph)C(NEt₂)C(Ph)C(C₂Ph}] (2a), [Fe₂(CO)₆{C(Ph)C(NEt₂)C(C₂Ph)C(Ph)}] (2b), and [Fe₂(CO)₆{NEt₂)C(Ph)C(C₂)C(Ph)}] (2c) All three compounds were identified by their¹H NMR spectra. Compounds2a and2c were characterized by single crystal X-ray diffraction analyses. Crystal data: for2a: space group = P2₁/n,a = 17.873(1) Å, = 18.388(6) Å,c = 9.429(3) Å = 91.99(3)°,Z = 4.3751 reflections,R = 0.044; for2c: space group = P2₁/n,a = 40.58(2) å,b = 12.101(9) Å,c = 12.551(5) Å, = 94.29(7)°,Z = 8.4723 reflection,R = 0.076. Complexes2a and2b result from a [2 + 2] cycloaddition between one of the CC triple bonds of the diyne ligand and the FeC carbene bond, whereas2c results from insertion of one of the CC group into the bridging carbene. Addition of [Fe₂(CO)₉] on2a gave two major products, the tripledecker [Fe₃(CO)₈{C(Ph)C(NEt₂)C(C₂Ph)}], (3 and a tetrairon cluster [Fe₄(CO)₁₁{C(Ph)C(NEt₂)C(Ph)C(C₂Ph)}] (4). Both compounds were characterized by single crystal diffraction analyses. Crystal data: for3: space group = P2₁/n,a = 12.039(3) Å,b = 18.046(3) å,c = 15.270(2) Å, = 90.11(2)°,Z = 4, 1430 reflections,R = 0.067; for4 space group = C2/c,a = 18.633(3) Å,b = 21.467(1)_Å,c = 20.742(2) Å, = 115.03(8)°,Z = 8.992 reflections, R = 0.076. Complex4 is based on a spiked triangular cluster with the alkynyl triple bond attached in ₃-parallel mode on the triangular grouping.     

Neutron activation determination of noble metals for the analysis of technological and natural materials

Two previously developed methods of noble metal neutron activation (NA) determination have been applied for the analysis of technological materials. While comparing the data obtained by both methods with those obtained in Central Chemical Laboratory the systematical discreapences have been shown to be absent. A new method of Pd, Au, Pt and Ir NA determination in natural and technological specimens based on the selective extraction of Pd and Au preliminary to irradiation has been developed. Results of the analysis of “Glomar Cellenger”'s deep-water drilling samples are discussed obtained by this method.     

Gas‐phase functionalized carbon‐carbon coupling reactions catalyzed by Ni (II) complexes

Gas‐phase C―C coupling reactions mediated by Ni (II) complexes were studied using a linear quadrupole ion trap mass spectrometer. Ternary nickel cationic carboxylate complexes, [(phen)Ni (OOCR¹)]⁺ (where phen = 1,10‐phenanthroline), were formed by electrospray ionization. Upon collision‐induced dissociation (CID), they extrude CO₂ forming the organometallic cation [(phen)Ni(R¹)]⁺, which undergoes gas‐phase ion‐molecule reactions (IMR) with acetate esters CH₃COOR² to yield the acetate complex [(phen)Ni (OOCCH₃)]⁺ and a C―C coupling product R¹‐R². These Ni(II)/phenanthroline‐mediated coupling reactions can be performed with a variety of carbon substituents R¹ and R² (sp³, sp², or aromatic), some of them functionalized. Reaction rates do not seem to be strongly dependent on the nature of the substituents, as sp³‐sp³ or sp²‐sp² coupling reactions proceed rapidly. Experimental results are supported by density functional theory calculations, which provide insights into the energetics associated with the C―C bond coupling step.     

Diffusion coefficients of the monomer and oligomers in hydroxyethyl methacrylate

The diffusion coefficients are reported of rubbery ternary systems consisting of the polymer, its monomer analogue (i.e., the saturated equivalent of the monomer), and trace quantities of oligomers (dimer, trimer, tetramer and hexamer) for 2‐hydroxyethyl methacrylate (HEMA). These have been obtained with pulsed‐field‐gradient NMR spectroscopy with a polymer weight fraction (f_p) of 0 ≤ f_p ≤ 0.4. The oligomers are macromonomers synthesized with a cobalt catalytic chain‐transfer agent. The diffusion coefficients are about an order of magnitude smaller than those for monomers such as methyl methacrylate; this effect is ascribed to hydrogen bonding in HEMA. The diffusion coefficient D_i of an i‐meric oligomer has been fitted with moderate accuracy by an empirical universal scaling relation, D_i(f_p)/D₁(f_p) ≈ i, previously found to provide an adequate fit to corresponding data for styrene and for methyl and butyl methacrylates. The approximate empirical scaling relation seems to hold for a remarkably wide range of types of monomer/polymer systems. These results are of use in modeling rates and molecular weight distributions in free‐radical polymerization, particularly for termination (which is chain‐length‐dependent and is controlled by the diffusion coefficient of chains of the low degrees of polymerization studied here). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2491–2501, 2003     

Spectrophotometric study of the ruthenium(III,II)–2,2′,2″- terpyridine system

Ruthenium(III) reacts with 2,2′,2″-terpyridine in aqueous solution at pH 3.0–4.5, when heated at 85 °C for 2 min, giving a green cationic complex with an absorbance maximum at 690 nm. The color is stable for at least 25 h. The system conforms to Beer's law. The optimal range for measurement (1.00-cm optical path) is 2–10 p.p.m. Ru; the molar absorptivity is 8.3 ·10³. Ruthenium(II) reacts with terpyridine at pH 5.5 to develop an amber cationic complex (absorption maximum at 475 nm) on heating at 95° C for 45 min. The color is apparently stable indefinitely. The system conforms to Beer's law; the optimal range is 1–5 p.p.m. Ru; the molar absorptivity is 1.45·10⁴ l mol^?1 cm^?1. Common anions do not interfere; separation as RuO₄ is necessary when iron and a few other transition cations are present. The green complex, a strong oxidant, is converted to the ruthenium(II) complex by oxidation of water, slowly at room temperature, or more quickly by longer heating and/or higher temperature, and by increase of pH. The Ru(II) complex can be converted to the Ru(III) complex by strong oxidants such as Ce(IV). In the amber complex, the reaction ratio is 1 Ru: 2 terpyridine, in which the ligand is tridentate, whereas in the green complex the reaction ratio is 1 Ru : 3 terpyridine, the latter acting only as a bidentate ligand. Short gentle warming of a mixture of ruthenium(III) and terpyridine first produces a transient unidentified blue-colored species (absorbance at 790 nm).     

Photoaddition reactions of trans dichloroethylene with benzenoid compounds: facile formation of tetracyclo[3.3.0.02,804,6]octanes and semibullvalenes

$\text{trans}$ 1,2-Dichloroethylene undergoes a stereospecific photoreaction with benzonitrile, the three tolunitriles, α,α,α-trifluorotoluene, fluorobenzene, and chlorobenzene to give substituted 6-$\text{exo}$ 7-$\text{endo}$ dichlorotricyclo[3,3,0,0_2,8]oct-3-enes which on treatment with base yield cyclised products or semibullvalenes: phenol yields dichlorobicyclo[3.2.1]oct-2-en-8-one with this ethylene photochemically.     

Photochemistry of cation radicals in solution : photoinduced oxidation by the phenothiazine cation radical

Irradiation of phenothiazine cation radical, Ph^.+, with 1,1-diphenylethylene, DPE, causes its reduction to Ph and oxidation of DPE. Cyclodimeric products are formed from DPE^.+.