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  • 1990-1994  (8,054)
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  • 101
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994) 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 102
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. ii 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 103
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 325-351 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Aromatic nitration is effectively carried out by the deliberate irradiation of the charge-transfer absorption band (hvCT) of the transient electron donor-acceptor complex [ArH, NO2Y+], where NO2Y+ represents common nitrating agents. Time-resolved spectroscopy demonstrates that the charge-transfer nitration effected in this way proceeds via an electron-transfer mechanism, in which the collapse of the reactive triad, [ArH+ ·, NO2·, Y] is critical to the formation of the Wheland intermediate. Comparative product analyses of toluene and anisole nitrations together with the ‘non-conventional’ products arising from NO+ catalysis, ipso attack and addition/elimination show that the activation process leading to charge-transfer (photochemical) nitration is indistinguishable from that leading to electrophilic (thermal) aromatic nitration.
    Additional Material: 2 Ill.
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  • 104
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The stereochemistry and kinetics of the methoxide ion substitution reactions (Z)- and (E)-methylbenzohydroximoyl cyanidc [PhC(CN)=NOCH3] were investigated. The reaction of the (Z)-hydroximoyl cyanide with sodium methoxide in DMSO-methanol (9:1) solution at 44·8°C gives a mixture of methyl (Z)-O-methylbenzohydroximate [PhC(OCH3)=NOCH3] and the O-methyloxime of α-ketophenylacetamide PhC(CONH2)=NOCH3. The (E)-hydroximoyl cyanide undergoes methoxide ion-catalyzed isomerization to the E-isomer faster than it undergoes nucleophilic substitution. These observations were interpreted in terms of an addition-elimination mechanism in which the rate-limiting step is elimination of the nucleofuge (AN + DN#).
    Additional Material: 2 Tab.
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  • 105
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 359-363 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Nucleophilic substitution reactions of 1-(trimethylsilyl)ethyl arenesulphonates with anilines and benzylamines in acetonitrile and methanol at 65·0°C were studied. The cross-interaction constants, ρXZ, between substituents in the nucleophile (X) and leaving group (Z) are relatively small (0·10 for XC6H4NH2 in MeCN) but similar to those for other SN2 processes at a secondary carbon atom. This provides further evidence for an approximately constant, loose SN2 transition state at a secondary carbon regardless of the size of the Cα substituent. The transition-state variations with substituents X and Z are in accord with that expected from the positive ρXZ value observed: a stronger nucleophile and/or nucleofuge leads to an earlier transition state, i.e. a lower degree of bond making and breaking.
    Additional Material: 3 Tab.
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  • 106
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 364-370 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The role of orbital control in product selectivity during electrophilic aromatic alkylation catalysed by zeolites was studied both theoretically and experimentally. In order to discuss this, the alkylation of toluene and m-xylene by methanol was carried out on a series of large-pore zeolites (HY). The changes in the para to ortho ratio observed on changing the framework Si/Al ratio of the zeolites were related to ab initio molecular orbital calculations of the LUMO energy of structurally alike model clusters but containing different tetrahedral cations around the active site. The observed correlation is discussed in terms of the HSAB principle by taking into account the influence of the catalyst composition on the reactivity of the electrophilic reagent.
    Additional Material: 4 Ill.
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  • 107
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 394-394 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
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  • 108
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 385-393 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Substrate and positional selectivity in the nitration reactions of benzene and its derivatives (halobenzenes, toluene and o-xylene) by nitric acid and acyl nitrates supported on zeolites H-Y and H-ZSM-11 were studied. The reaction mechanism and effects governing selectivity of the process are discussed.
    Additional Material: 3 Ill.
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  • 109
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 371-376 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Aniline (or aniline hydrochloride) was intercalated into zeolite, zirconium phosphate and zirconium arsenate (proton form and sodium form) and subsequently oxidized to polyaniline (PAN) by ammonium peroxodisulphate. The structure of PAN in the host was studied by electron paramagnetic resonance spectroscopy. PAN in the host gave a free-radical EPR signal at 2·0035-2·0037 for the hydrogen or 2·0047-2·0049 for the sodium form of the host, similarly to the ermeraldine salt (PAN-2S) or emeraldine base (PAN-2A) form of PAN. Saturation occurs in PAN-HZ and PAN-HS. In contrast, the intrachannel PAN in HY was unsaturated under the same conditions. Conduction in PAN-HZ and PAN-HS was predominately carried out by variable-range hopping and tunnelling respectively, and PAN-HY showed insulating properties.
    Additional Material: 4 Ill.
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  • 110
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 377-384 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: N-Substituted carbonimidodithioic acid dimethyl esters, when reacted with an active methylene compound such as nitromethane, undergo carbon-carbon bond formation followed by carbon-sulphur bond cleavage in the presence of zeolite catalysts to give 1-substituted amino-1-methylthio-2-nitroethenes. This carbon-sulphur bond cleavage is facilitated by the presence of rare earth cations in the zeolite-Y framework. The shape selectivity of the zeolite also plays an important role in this cleavage reaction. Force field calculations adopted for the molecules involved in the reaction indicate the geometry and conformational flexibility of these molecules. The computer-simulated model for the zeolite-Y is correlated with the conformation and shape of the reactant and product molecules to explain the variation in yields obtained in the conversion of substituted dimethyl esters.
    Additional Material: 2 Ill.
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  • 111
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994) 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 112
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 395-398 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The reaction which forms hydroxymethylbenzodioxane from epibromohydrin and catecholate anion was examined by ultraviolet spectroscopy for the kinetics and by proton nuclear magnetic resonance spectroscopy to follow the fate of CD2 from reactant to product. Over the practical temperature range it was found that both CH2 positions in the epihalohydrin are attacked by catecholate anion to give product. Therefore, the difference in energy for the two pathways was small. The individual rate constants were obtained from the total rate constants. Further, the individual ΔH
    Additional Material: 4 Tab.
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  • 113
    Electronic Resource
    Electronic Resource
    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 399-402 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The reaction of nitrosobenzene with aniline, to give azobenzene, in basic conditions was studied. It was shown that the reaction exhibits general base catalysis by different buffers giving a Brønsted coefficient β = 0·318. As in previous studies, a two-step process with a first step of attack of aniline on nitrosobenzene to give an addition intermediate and a second step of dehydration of this intermediate is proposed to interpret the mechanism of the reaction. The analysis of the Brønsted relationship and of the intermediate of the reaction led to the suggestion that hydoxide ion catalyses the reaction by a mechanism of general base catalysis in the dehydration step.
    Additional Material: 3 Ill.
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  • 114
    Electronic Resource
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 403-411 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A means for determining the stabilization energies, Ec(X), resulting from σ-π and n-π interactions in vinyl and phenyl compounds is described. It is based on extensions of the additivity principle for thermochemical data for organic compounds. The results also provide a method for predicting heats of formation of unsaturated compounds from those of (known) saturated analogues. It is shown that there is a linear relationship between the stabilization energies Ec(X) and the Hammett substituent constants σp+(X). The new results have been used to predict the heats of formation of a number of saturated and unsaturated Si-, Ge-, Sn-, P-, As-, Se-, Zn-, Cd- and Hg-containing species.
    Additional Material: 2 Ill.
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  • 115
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 412-419 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The effects of the concentrations of LiCl, NaCl, KCl, CsCl, Na2CO3 and BaCl2 on the rates of reactions of hydroxide ion with ionized N-hydroxyphthalimide (NHP-) at 30°C and in H2O-MeCN solvents containing 10, 50, 60, 66, 70, 76 and 80% (v/v) MeCN reveal the formation of ion-pair complexes between cations of the salts, which probably exist in solvent-separated loose ion-pair forms (Mn+⃛Xk-) and NHP-. An increase in MeCN content from 2 to 76% (v/v) causes an increase in the association constants (K) by factors of 40, 21 and 9 for LiCl, NaCl and KCl, respectively, while the respective increase in the rate constants (k′s1) for the collapse of the ion-pair complexes to product is ca two-fold. The values of k′s1 remain almost unchanged whereas the values of K increase 7·5-fold with an increase in MeCN content from 2 to 70% (v/v) for CsCl. Ion-pair complex formation was not detected in the presence of Me4NCl at 70% (v/v) MeCN. The observed pseudo-first-order rate constants are highly sensitive to the valence state of cations and almost insensitive to the valence state of the anions of the salts.
    Additional Material: 5 Ill.
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  • 116
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 420-430 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The MM3 force field has been extended to cover alkyl iodides. Structures, vibrational spectra and heats of formation have been well fitted to available experimental data. The experimental and ab initio conformational relationships are also satisfactorily reproduced.
    Additional Material: 2 Ill.
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  • 117
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 431-436 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Imidazole (Imz)-catalysed hydrolysis of benzoate esters proceeds via the intermediate formation of N-benzoylimidazoles. This paper considers the second step of this reaction, viz., Imz-catalysed hydrolysis of N-(4-X-benzoyl)imidazoles, X = CH3, H, Cl, CN and NO2, and N-(disubstituted benzoyl)imidazoles, 2-chloro-4-nitro, 2, 4-dinitro and 3,5-dinitro, in water-acetonitrile mixtures (10% or 14%, v/v, in organic solvent). On the basis of catalytic rate constants and the kinetic solvent isotope effect, it is shown that catalysis by Imz is of the general-base type. Unexpectedly, the hydrolysis of N-(2,4-dinitrobenzoyl)imidazole was found to be slower than that of N-(4-nitrobenzoyl)imidazole. It is shown that this reactivity order is due to a combination of a steric effect and stabilization of the reactant state due to a donor-acceptor interaction between the Imz moiety and the 2,4-dinitrophenyl ring.
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  • 118
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The critical micelle concentration of solutions of cetyltrimethylammonium bromide and of tetradecyltrimethylammonium bromides were determined by a kinetic method. This involved the determination of the rates of the hydroxydehalogenation of some activated aromatic substrates over a wide range of detergent concentrations. Measurements were made in solutions containing significant quantities of added hydroxyl ion and substrates which were themselves amphiphilic. Conventional methods cannot be applied with confidence to such systems. The effects of changing hydroxyl ion concentrations, added sodium bromide, changing the nature of the aromatic substrate (whether neutral or charged), the identity of the micellar counterion and the temperature were investigated. It was wound that added bromide or hydroxyl ions resulted in a lower CMC whereas increased temperature led to an increase in the CMC. The nature of the micellar counterion (Br, F, OH, SO4) had little effect on the CMC. The presence of a charged aromatic substrate led to a considerable lowering of the CMC, whereas the neutral aromatic substrate used showed very little effect.
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  • 119
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 442-447 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The reaction of several nitro activated aromatic halides with hydroxide ions was studied in the presence of hydroxy functionalized micelles containing bulky head groups, e.g. C16H33N+R2CH2CH2OH Br-, where R = Me, Et, Bu. In a biphasic reaction, the aryl halide is first converted into an aryl mincellar ether which subsequently reacts with hydroxide ions to form the phenolic product. Despite the increased nucleophilicity of hydroxide ions as water is squeezed away from the micelle surface by the bulky head groups, no direct reaction of the aromatic substrate with hydroxide ion is detectable. In the second phase of reaction, the breakdown of the aryl micellar ether to form the phenolic product, the order of reactivity in the different micelles is dependent on the steric interactions between substituents ortho to the reaction centre and the head group of the micelle. For compounds having one substituent ortho to the reaction centre, the order of reactivity is Bu 〉 Me 〉 Et, whereas for 2-chloro-1,3-dinitrobenzene, which has two substituents ortho to the reaction centre, the order is Me 〉 Et 〉 Bu.
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  • 120
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994), S. 448-454 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A characteristic feature in the bimolecular nucleophilic substitution reactions at a resonance-stabilized carbenium ion has been shown to be an imbalanced transition state resulting in an elevated value of the cross-interaction constant, which in turn leads to a non-interactive phenomenon. Examples of the reactions of ring-substituted phenylethyl and benzhydryl cations are given.
    Additional Material: 2 Ill.
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  • 121
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    Chichester : Wiley-Blackwell
    Journal of Physical Organic Chemistry 7 (1994) 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 122
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The rates and products of solvolyses of 4-methylene-2ax- and -2eq-adamantyl p-toluenesulphonates (tosylates) (4a-OTs and 4e-OTs, respectively) were studied. Compound 4a-OTs solvolysed more slowly than 2-adamantyl tosylate (1) in methanol and 2,2,2-trifluoroethanol (TFE) by factors of 2·3 and 2·5, respectively, at 25°C. However, by taking the inductive decelerating effect of a β-methylene substituent into account, the rates were revealed to be enhanced by α-participation by a factor of 50. The products of solvolyses of 4a-OTs in methanol, 80% acetone and TFE at 100°C were 2ax- and 2eq-alkoxy(or hydroxy)-4-methyleneadamantanes (4a-OR and 4e-OR, respectively), exo-4-alkoxy(or hydroxy)-5-methyleneprotoadamantane (exo-5-OR) and 5-[alkoxy(or hydroxy)methyl]-4-protoadamantene (6-OR) with adamantyl to protoadamantyl product ratio of 39:61 (in methanol), 56:44 (in 80% acetone) and 71:29 (in TFE). Despite the nearly symmetric nature of the intermediate cation, the 4a-OR: 4e-OR product ratio was essentially constant with 83:17 (in methanol), 85:15 (in 80% acetone) and 82:18 (in TFE). The formation of considerable amounts of 4e-OR was interpreted as showing the intermediacy of a pair of rapidly equilibrating classical ions. The rates of 4e-OTs were 2300-4300 times faster than those expected from inductive electron-withdrawing effect of a β-methylene substituent. The major product (84·5% in methanolysis and 98·7% in trifluoroethanolysis) was 4e-OR accompanied by small amounts of 2-alkoxy-2,4-methanoadamantane (9-OR) and 2-(alkoxymethyl)-2,4-didehydroadamantane (10-OR), no formation of 4a-OR having been observed. These results suggested that 4e-OTs solvolyses via a π-bridged intermediate cation.
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  • 123
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    Journal of Physical Organic Chemistry 7 (1994), S. 479-484 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The determination of stability constants by measuring the increase in solubility of a nearly insoluble host molecule due to complex formation with a soluble guest is discussed. If the host molecule absorbs in the UV-visible region, spectrophotometric measurements are easily performed to obtain the stability constants. The solubilities of the crown ether dibenzo-18-crown-6 and of the cryptand (222BB) in aqueous solutions and the molar absorptivities of these ligands and their complexes with alkali and alkaline earth metal cations were determined. The increase in solubility of these ligands due to complex formation with cations was used to calculate the stabilities of the complexes formed. Even under the assumption that neither the molar absorptivities nor the solubilities are known, the calculated stability constants agree very well with those obtained using the measured values of the molar absorptivities and solubilities. The accuracy of the stability constants even increases with decreasing solubility of the ligands.
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  • 124
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The utility of desorption/ionization mass spectrometric (DI/MS) techniques in dealing with physical organic problems involving fragile onium salts and carbocation salts has been explored. The efficacy of these methods, especially when coupled to tandem mass spectrometry, goes much beyond the analytical aspects dealing with identity/purity determinations. For example, insight can be gained regarding the role of the counterion in subsequent cation decomposition pathways. Guest-host chemistry of onium ions and various hosts (crowns, calixarenes) can be probed. The decomposition chemistry of the resulting ion-molecule clusters can be studied. Examples of onium salts and carbocation salts that have been studied are few, probably because research in this area has been mainly a domain for analytical chemists. This paper calls attention to the possibilities for dealing with topical physical organic problems.
    Additional Material: 23 Ill.
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  • 125
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The rates of the solvolysis of 3-R-4-homoadamantyl methanesulphonates (mesylates) (3) were determined in 80% aqueous ethanol. The relative first-order rate constants at 25 °C were 1·0 (R = H), 2·29 (R = Ph), 3·26 (R = p-anisyl), 73·6 (R = Me) and 209 (R = Et). The methanolysis of 3 gave rearranged methyl ethers and rearranged olefins as major products together with small amounts (0·9-3·4%) of unrearranged products. The order of the accelerating effect suggests that the transition states involve significant σ-participation, despite the fact that 3 (R = H) solvolyses via a classical ion intermediate. The logarithms of the solvolysis rate constants of 3 showed linear correlations with those of 1-R-2-adamantyl tosylates (1) and 1-R-exo-2-norbornyl tosylates (2), indicating that the linear free-energy relationship between the β-substituent effects on the solvolysis rate is not a definite measure to distinguish between classical and non-classical intermediates.
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  • 126
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    Journal of Physical Organic Chemistry 7 (1994), S. 495-502 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A series of m,n′-diazidodiphenyl ethers (m ≤ n, m = 3,4; n = 3,4) was photolyzed at 77 K in frozen, glassy 2-methyltetrahydrofuran matrices to generate the corresponding diphenyl ether m,n′-dinitrenes for study by electron spin resonance (ESR) spectroscopy. 3,4′-Diazidodiphenyl ether gave an ESR spectrum dominated by a mononitrene peak with ∣D/hc∣ = 0·972 cm-1, and also showed a weak dinitrene quintet spectrum with ∣D/hc∣ = 0·162 cm-1 having ESR spectral intensity vs temperature dependence (Curie law) consistent with either a high-spin ground state or a very small singlet-quintet gap. Di(3-azidophenyl) ether gave a strong mononitrene peak with ∣D/hc∣ = 0·996 cm-1 and a quintet dinitrene ESR spectrum (∣D/hc∣ = 0·162 cm-1) which exhibited non-linear Curie law intensity behavior consistent with the quintet being a thermally populated excited state 40 cal mol-1 above a singlet ground state. Di(4-azidophenyl) ether gave a strong mononitrene peak with ∣D/hc∣ = 0·961 cm-1, but no observable spectrum related to a high-spin open-shell dinitrene. The results are consistent with oxygen being a weak exchange coupling linker in pi-conjugated open-shell molecules. The observed ground-state spin multiplicities are in accord with qualitative superexchange and connectivity models, despite any perturbations due to resonance effects between the oxygen linker and p-nitrene sites.
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  • 127
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    Journal of Physical Organic Chemistry 7 (1994), S. 518-524 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The kinetics of the nucleophilic cleavage of phthalimide (PTH) in buffer solutions of ammonia and pyrrolidine were determined. The reaction rates for ammonolysis of PTH revealed a buffer-catalysed second-order term in the rate law, but the reaction rates for pyrrolidinolysis of PTH showed buffer-catalysed second- and third-order terms in the rate law. Both ammonia and pyrrolidine revealed nucleophilic reactivity towards ionized PTH (S-) only within the pH range of the present study. This is attributed to the occurrence of intramolecular general base-acid catalysis. General base catalysis is detected in the reactions of pyrrolidine with both non-ionized PTH (SH) and S-. The general base-catalysed third-order rate constant for pyrrolidinolysis of SH is nearly 28 times larger than that of S-.
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  • 128
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    Journal of Physical Organic Chemistry 7 (1994), S. 503-510 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The mechanism of the photochemical decomposition of 1,4-oxazin-2-one to azacyclobutadiene and carbon dioxide was investigated by the semi-empirical MO method SINDO1. The relevant singlet and low-lying triplet potential energy hypersurfaces were studied and intermediates and transition structures were optimized with limited configuration interaction. The first step transforms 1,4-oxazin-2-one into a bicyclic lactone via internal cyclization. Then a stepwise bond breaking mechanism on the first excited triplet state yields azacyclobutadiene and CO2, whereas a reaction on the first excited singlet state is not common. It is shown that a simultaneous bond-breaking mechanism on the first excited singlet or on the first excited triplet is possible.
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  • 129
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    Journal of Physical Organic Chemistry 7 (1994), S. 511-517 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The gas-phase acidity and basicity of thioacetamide and the basicity of N,N-dimethylthioformamide were measured by Fourier transform ion cyclotron resonance (FT-ICR) mass sectrometry under conditions which minimized the extent of their decomposition. Thiocarboxamides are both much stronger acids and stronger bases than carboxamides. The relative stabilities of individual neutral and ionic species were assessed in terms of isodesmic reactions, using the published or estimated enthalpies of formation. The neutral molecules of carboxamides and thiocarboxamides are stabilized by interaction between the C = X and NH2 functional groups. This interaction is of a similar magnitude in the corresponding protonated forms but it is of greater strength in the deprotonated forms. With regard to the difference between thiocarboxamides and carboxamides, the most significant factor is probably the Ione pair-Ione pair repulsion operating in the anions.
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  • 130
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    Journal of Physical Organic Chemistry 7 (1994) 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 131
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    Journal of Physical Organic Chemistry 7 (1994), S. 525-533 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The influence of a number of factors, i.e. amine basicity, substrate structure, temperature and deuterium isotope effect, on the rate of phenyl β-bromoethyl sulphone and aryl β-chloroethyl sulphone 1,2-elimination by reaction with amines in acetonitrile was investigated. On the basis of a comparative analysis of the ρ0, β, kH/kD, ΔH
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  • 132
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    Journal of Physical Organic Chemistry 7 (1994), S. 534-544 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The bisporphyria N,N′-bis[4″-(meso-triphenylporphyrinyl)benzyl]-4,13-diaza-18-crown-6 and its mono- and dizinc derivatives were synthesized in 66%, 46% and 53% yields, respectively, from 5-(4′-bromomethylphenyl)-10,15,20-triphenylporphyrin or its zinc derivative and 4,13-diaza-18-crown-6. The zinc-containing bisporphyrins form dimers in solution at low temperature or at high concentration. The unsymmetrical bisporphyrin; monozinc N,N′-bis[4″-(meso-triphenylporphyrinyl)benzyl]-4,13-diaza-18-crown-6 shows singlet-singlet energy transfer from the zinc porphyrin moiety to the free base moiety in both the monomeric and the dimeric form. The energy transfer rates were determined using time-resolved fluorescence spectroscopy and were found to be 1·26 × 109 and 2·29 × 109 s-1 for the monomeric and dimeric form, respectively. The difference in energy transfer rates between the two forms can be rationalized by the difference in overlap between the donor fluorescence spectrum and acceptor absorption spectrum, donor-acceptor distance and donor-acceptor orientation.
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  • 133
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    Journal of Physical Organic Chemistry 7 (1994), S. 551-554 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Molecular mechanics (MM3) calculations were carried out on the title compounds. Comparison between the MM3 results and those of semi-empirical and ab initio calculations and experiment indicates that the MM3 results are at least as good as results of much more expensive calculations. The MM3 calculations predict that unlike corannulene and cyclopentacorannulene, the transition state of the bowl-to-bowl inversion of the related C30H10 is non-planar, and the activation barrier is too high for this motion to occur.
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  • 134
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    Journal of Physical Organic Chemistry 7 (1994), S. 545-550 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The rate of the reaction of 2-chloroquinoxaline with piperidine in dimethyl sulphoxide was measured over a wide range of amine concentrations and at several temperatures. It was found that the order with respect to the nucleophile is close to 1 between 300 and 320 K, but is definitely less at lower and higher temperature. It is suggested that below 300 K an unreactive charge-transfer complex is formed between the reactants which dissociates at higher temperatures, whereas at temperatures higher than 320 K an unproductive σ complex is formed, the concentration of which increases with increase in temperature.
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  • 135
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    Journal of Physical Organic Chemistry 7 (1994), S. 555-560 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Kinetic studies on the reversible reactions of benzyl bromides with N, N-dimethylanilines were carried out for both the forward (kf) and reverse (kr) directions. The equilibrium constants, K were calculated using the ratio kf/kr and the equilibrium cross-interaction constant, ρeXY was determined. The ρeXY value was shown to represent a maximum intensity of interactions between substituents X and Y through covalent bonds within a molecule. The normalized values of ρX (ρnuc) and ρXY indicate that in the transition state the fractional development or loss of polar and resonance interactions in the benzyl system are imbalanced or non-perfectly synchronized. In the forward reaction the fractional loss of resonance interaction becomes enhanced, whereas in the reverse reaction the fractional development of resonance interaction lags behind the corresponding changes of polar interactions by ca 45%.
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  • 136
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    Journal of Physical Organic Chemistry 7 (1994), S. 561-566 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The enthalpic contribution to the anomeric effect in r-2-carboethoxy-trans-4,trans-6- and r-2-carboethoxy-cis-4,cis-6-dimethyl-1,3-dithianes was determined by reaction-solution calorimetry. The enthalpy of solution of both isomers in pure p-dioxane and the enthalpy of solution and isomerization in the same solvent and in the presence of trifluoroacetic acid were experimentally measured. From these results the corresponding enthalpies of isomerization in solution were calculated, and were found to be ΔHax→eq = -0·16 ± 0·04 kcal mol-1 (-0·67 ± 0·18 kJ mol-1) and ΔSax→eq = -2·68 ± 0·1 cal K-1 mol-1 (-11·2 ± 0·4 J K-1 mol-1). The slightly negative ΔH term nevertheless reflects a substantial anomeric effect owing to the countervailing steric effects in the axial isomer. The significant entropy loss in the equatorial isomer was explained in terms of intramolecular electrostatic effects. The results are in agreement with those obtained from NMR studies of the conformational behaviour of 2-carboethoxy-5-methyl-5-aza-1,3-dithiacyclohexane.
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  • 137
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    Journal of Physical Organic Chemistry 7 (1994) 
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 138
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    Keywords: Organic Chemistry ; Physical Chemistry
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    Notes: Reactions of benzo-, naphtho- and anthraquinone derivatives (unsubstituted and substituted) with aryliminodimagnesium [ArN(MgBr)2] and aryloxymagnesium of a weak electron-donating ability were studied. In addition to the reduction products (quinhydrones and hydroquinones), nuclear substitution and condensation products were formed. The efficiency of single electron transfer (SET) from ArN(MgBr)2, evaluated by the relative values of the difference between the oxidation and reduction potentials of the reactants (ΔE = Eox - Ered), varies with the electron-accepting power of quinones. ΔE governs the modes of semiquinone appearance (ESR signals) and the relative amounts of the heat of reactions, reflecting the types and yields of the products. It is concluded that condensation products of both components are produced in the reactions of quinones with the lower SET efficiency by the presence of a fused benzene ring or MeO substituent. The structure-reactivity relationship proposed previously for reactions of various magnesium reagents is extended in the reactions with a variety of quinones even in cases of higher SET efficiency.
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  • 139
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    Journal of Physical Organic Chemistry 7 (1994), S. 578-584 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The acid-catalysed solvolysis of 9-(2-phenoxy-2-propyl)fluorene in mixtures of water with acetonitrile or methanol at 25°C provides 9-(2-hydroxy-2-propyl)fluorene, 9-(2-propenyl)fluorene, and 9-(2-acetamido-2-propyl)fluorene or 9-(2-methoxy-2-propyl)fluorene, respectively. The overall kinetic deuterium isotope effects for the reactions of the hexadeuterated analogue 9-(1,1,1,3,3,3-2H6)-9-(2-phenoxy-2-propyl)fluorene in 90 vol.% acetonitrile in water were measured as (kEH + kSH)/(kED6 + kSD6) = 1·54 ± 0·05, which is composed of the isotope effect kSH/kSD6 = 1·4 ± 0·1 for formation of the substitution products and kEH/kED6 = 4·0 ± 0·2 for production of 9-(2-methoxy-2-propyl)fluorene. Similar isotope effects were measured in other solvent mixtures. The results strongly indicate a branched mechanism involving rate-limiting formation of a common carbocation-molecule pair (with a secondary isotope effect of 1·54), which either undergoes nucleophilic attack by a solvent molecule (with a secondary isotope effect of ca 1), or is dehydronated (isotope effect ca 2·8) by the leaving group or by the solvent. The ion-molecule pair shows very low selectivities. Thus, in 50 vol.% acetonitrile in water, an acetonitrile molecule is as efficient as a water molecule as a nucleophile towards the ion-molecule pair, kMeCN/kHOH ≥ 1 (ratio of second-order rate constants). The discrimination between methanol and water is anomalously small, kMeOH/kHOH = 0·7.
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  • 140
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    Journal of Physical Organic Chemistry 7 (1994), S. 591-609 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The MM3 molecular mechanics program calculates a fair representation of hydrogen bonding interactions, but to improve the MM3 hydrogen bond potential, a directional term has been added to the hydrogen bonding function. The resulting total function was reoptimized. Comparisons of the hydrogen bonding potential functions from ab initio, the original MM3, the current MM3(92) force field and the reoptimized MM3 force field MM3(94) for a variety of C,N,O systems are described.
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  • 141
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    Journal of Physical Organic Chemistry 7 (1994), S. 585-590 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The title sulphenamides were pyrolysed in a stirred-flow reactor at temperatures of 310-410°C, pressures of 8-15 Torr and residence times of 0·4-2 s using toluene as the carrier gas. N-(tert-Butylthio)allylamine formed 73 ± 4% isobutene, 23 ± 3% propene and N-allylthiohydroxylamine. The first-order rate coefficients for the formation of isobutene and propene, respectively, followed the Arrhenius equations kC4(s-1) = 1012·52 ± 0·36 exp(-163 ± 5 kJ mol-1 RT) and kC3(s-1) = 1010·99 ± 0·29 exp(-151 ± 4 kJ mol-1 RT) N-(tert-Butylthio)diethylamine gave 97 ± 1% isobutene, 1·9 ± 0·4% isobutane and N,N-diethylthiohydroxylamine. The first-order rate coefficients for isobutene elimination followed the Arrhenius equation k(s-1) = 1013·45 ± 0·24 exp(-164 ± 3 kJ mol-1 RT). The formation of the products is interpreted in terms of an elimination reaction with a unimolecular, four-centered, cyclic transition state. The reactivity of these sulphenamides was found to be much higher than that of previously studied alkyl or aryl tert-butyl sulphides and disulphides.
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  • 142
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    Keywords: Organic Chemistry ; Physical Chemistry
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    Topics: Chemistry and Pharmacology , Physics
    Notes: The reactivity of 1,3-dihaloadamantanes with diphenylphosphide ions (Ph2P-) in liquid ammonia was studied. 1,3-Dichloroadamantane (1a), 1-bromo-3-chloroadamantane (1b) and 1,3-dibromoadamantane (1c) reacted with Ph2P- ions under photostimulation by the SRN1 mechanism. Irradiation of 1c without Ph2P- ions gave no reaction (〈5%). Three products were found: 1,3-bis(diphenyphosphinyl)adamantane (2), (3-X-1-adamantyl)diphenylphosphine (X = Cl, 3a; X = Br, 3b) and 1-adamantyldiphenylphosphine (4). Compounds 2 and 4 were formed by intramolecular electron transfer (ET) of the radical anion 3a-· (3b-·); whereas 3a (3b) were formed by intermolecular ET of this radical anion to the substrates. It was observed that the product distribution depends on the substrate and reaction conditions.
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  • 143
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    Journal of Physical Organic Chemistry 7 (1994), S. 625-628 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Over the H0 acidity range from + 2 to -8, four different mechanistic variations occur in the Fischer indole reaction, leading to an unusual parabolic dependence of the rate constants on the acidity of the medium. In strongly acidic media kinetic isotope effects indicate that the rate-determining step is deprotonation to form the ene-hydrazine tautomer, whereas in weakly acidic media the tautomerization is so rapid that [3,3]-rearrangement becomes rate limiting. At an intermediate acidity, the deprotonation is rate determining, with the rate being strongly dependent on the concentration of the anionic counter ion.
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  • 144
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    Journal of Physical Organic Chemistry 7 (1994), S. 629-633 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Kinetic studies were carried out on the aminolysis of propargly and 1-methylpropargyl arenesulphonates in acetonitrile at 45·0°C. The cross-interaction constants, ρxz and βxz, are similar to, but smaller than, those for the SN2 processes at other primary and secondary carbon centers. Compared with the allyl series, the smaller magnitude of ρxz and βxz reflects a looser transition state, which in turn leads to a lower rate despite the greater Taft's σ* value and the lower intrinsic (ΔE0≠) and thermodynamic barriers (ΔE0).
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  • 145
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    Journal of Physical Organic Chemistry 7 (1994), S. 615-624 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Substitutent effects of acceptor groups were measured for the gas-phase basicities of some substituted benzonitriles, methyl benzoates and acetophenones, and for gas-phase acidities of some substituted benzoic acids. Substitutents considered were NO2, CN, SO2CH3, SO2F, CF3, CH2Cl, COCH3 and COOCH3, always in the meta and para positions. By combination with the literature data, a general conclusion is drawn that the substituent effects are proportional in the two positions and almost equal (the para:meta ratio is 1·06). No sign of any resonance effect was detected within the accuracy of the approach. The substituent effects in solution were recalculated statistically and the result was similar with a higher ratio, 1·09-1·19. It follows that the conjugation of acceptor groups, particularly of NO2 as a typical example, has been overestimated by current theories when compared with the much stronger conjugation of typical donors. Moreover, the inductive effect is propagated more effectively from the para than from the meta position. Many correlations in the literature, neglecting this situation, have been in fact controlled by the more complex, and more striking, behaviour of donors, which has obscured the simpler and more monotonous effect of acceptors, usually less represented in the sample.
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  • 146
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    Topics: Chemistry and Pharmacology , Physics
    Notes: The label incorporation and Z → E isomerization in the reaction of 3-azidomethylenedihydro-(3H)-furan-2-one with Na15NN2 in 1:1 water-acetone were measured as a probe for internal clockwise vs anticlockwise rotation in the intermediate carbanion.
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  • 147
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Transition structures for the Diels-Alder reactions of 1,3,4-oxadiazole with ethylene, acrylonitrile, maleonitrile, fumaronitrile, and 1,1-dicyanoethylene were located with ab initio molecular orbital calculations with the RHF/3-21G theoretical model. The activation energies were calculated by single-point calculations with the RHF/6-31G* and MP2/6-31G* theory levels on the RHF/3-21G geometries. Geometries of two transition structures and the corresponding reactants were generated at the MP2/6-31G* and the energies evaluated at the MP3/6-31G* level. The values obtained are comparable to those generated by MP2/6-31G*//3-21G. The asynchronicity of the transition structures follow the same trend as the corresponding all-carbon Diels-Alder reactions with buta-1,3-diene and cyclopentadiene, but the activation energies are almost in opposite correlation. This behavior is explained by the oxadiazole nitrogen lone pair repulsion with the π-orbitals of the nitrile groups.
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  • 148
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    Journal of Physical Organic Chemistry 7 (1994) 
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    Keywords: Organic Chemistry ; Physical Chemistry
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  • 149
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    Journal of Physical Organic Chemistry 7 (1994), S. 646-651 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The reaction of 2-(p-nitrophenyl)ethyl bromide with hydroxide ion was studied at 50 and 25°C in the presence of cationic chemodegradable surfactants, i.e. [2-alkyl(1,3-dioxolan-4-yl)methyl] trimethylammonium bromides Ia-c (alkyl: a = n-C9H19, b = n-C11H23, c = n-C13H27). The kinetic data were interpreted with the pseudo-phase ion-exchange (PIE) formalizm at both temperatures. The results indicate that the major source of rate enhancement is the increased reactant concentration in the small micellar reaction volume. The surfactant stability in micellar conditions was probed by means of a hydrolysis reaction of the surfactant 1,3-dioxolane ring. The kinetics of acid hydrolysis of Ia-c micelles, as a result of specific hydronium ion concentration, is one order of magnitude smaller than that of unaggregated systems.
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  • 150
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    Journal of Physical Organic Chemistry 7 (1994), S. 641-645 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Transition states for the hetero-Diels-Alder addition of formaldehyde, formaldimine, diazene and nitrosyl hydride to cyclopentadiene were located with ab initio molecular orbital calculations. Asynchronous transition structures were located for the asymmetric hetero-dienophiles, whereas the symmetrical hetero-dienophile, cis-diazene, produced a synchronous transition structure. The relative reactivities are in good agreement with the LUMO energies of the hetero-dienophiles, and the transition states with the exo oxygen or nitrogen lone pairs have lower energies than the corresponding endo lone electron pair transition states. Endo/exo energy differences are much higher than in the addition of ethylene derivatives to cyclopentadiene.
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  • 151
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    Journal of Physical Organic Chemistry 7 (1994), S. 655-656 
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
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  • 152
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The gas-phase basicities of eight pyrazoles substituted only at position 4 (R4 = H, NO2, F, Cl, CO2C2H5, CH3, NH2, 1-adamantyl) were measured by Fourier transform ion cyclotron resonance. The experimental values were treated in two ways, first by comparing these values with the AM1-calculated proton affinities. Since the correlation was reasonably good [PA(calc.) = -11·3 + 1·063PA(exp.), n = 8, r = 0·984], a set of 17 further 4-substituted pyrazoles and their cations were calculated using the AM1 approximation and their gas-phase basicities were estimated. Second, both the experimental and the AM1-calculated values were considered within the framework of the Taft-Topsom analysis of substituent effects. Comparison of the analyses for pyrazoles and pyridines led to the unexpected result that, in spite of differences in ring size and number of heteroatoms, both systems behave remarkably alike.
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  • 153
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    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: A calorimetric method is described for the determination of the hydride affinities, ΔHH-(R+) of seven dioxolenium ions from the title compounds and also tropylium, trityl and 9-phenyl xanthylium cations by hydride transfer to the carbocations from BH3CN-. Cyclic voltammetric methods yield free energies for reduction of the cations to the conjugate radicals and to the carbanions. The ΔHH-(R+) values correlate well with the first reduction potentials of the cations.
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  • 154
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    Journal of Physical Organic Chemistry 7 (1994), S. 696-704 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The dissociation pK values of picric acid, tetrabutylammonium picrate, bromide and hydroxide and tetramethylammonium hydroxide in some 2-methylpropan-2-ol-cosolvent mixtures were determined and correlated with the Taft and Kamlet solvatochromic parameters π*, δ, α and β. The results show the most important solvent properties that affect electrolyte dissociation are polarity, polarizability and hydrogen bond acidity. These results were confirmed by analysis of published literature data.
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  • 155
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    Journal of Physical Organic Chemistry 7 (1994), S. 672-684 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Reversed-phase HPLC capacity factors, as log k′, have been correlated through the LFER equation: \documentclass{article}\pagestyle{empty}\begin{document}$${\rm log k}^\prime = {\rm c} + {\rm rR}_2 + {\rm s\pi }_2^{\rm H} + {\rm a}\sum {\rm \beta }_2^0 + {\rm vV}_{\rm X}$$\end{document} where k′ is the capacity factor for a series of solutes in a given stationary phase-mobile phase system, and the explanatory variables are the solute descriptors: R2 an excess molar refraction, π2H the dipolarity/polarizability, Σα2H the overall hydrogen-bond acidity, Σβ20 the overall hydrogen-bond basicity and Vx the McGowan volume. This equation was applied to various C18 stationary phases with methanol-water, acetonitrile-water and tetrahydrofuran-water buffered mobile phases. The solute and mobile phase factors that influence log k′ values are set out, and a comparison is made between log k′ values and water-octanol partition coefficients.
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  • 156
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    Journal of Physical Organic Chemistry 7 (1994), S. 685-695 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The substituent effects on the intrinsic basicity of a wide variety of thiocarbonyl compounds were investigated by means of a topological analysis of the electronic charge densities and their Laplacians for the neutral and the protonated species, and also by means of their harmonic vibrational frequencies. For the sake of comparison, a similar analysis was carried out for a reduced set of carbonyl compounds with similar substituents. The results show that the behaviour of the thiocarbonyl group with regard to the protonation process is similar to that predicted for the carbonyl group, in the sense that both groups are not much affected by protonation. The charge transferred to the proton results basically in a polarization and, in some cases, in a depopulation of the bonds in which the thiocarbonyl carbon atom participates. Accordingly, the intrinsic basicities of these kinds of compounds depend strongly on the ability of the substituents to be polarized. This conclusion seems to be ratified also by the shiftings undergone by the C=S stretching frequencies on protonation.
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  • 157
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    Journal of Physical Organic Chemistry 7 (1994), S. 705-711 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: An infrared spectroscopic study of the 1 : 1 hydrogen-bond association of amidates with both methanol and 4-fluorophenol showed that the site of complexation is the oxygen of the amidate function. However the formamidate HCON2Me3 forms a second 1 : 1 complex on the nitrogen of the amidate. The formation constants of the hydrogen-bond complexes of the amidates with the reference hydrogen-bond donor 4-FC6H4OH indicate that the amidates are stronger hydrogen-bond bases than are amides and amide vinylogues. As such, the amidates constitute the strongest carbonyl bases hitherto investigated on the hydrogen-bond basicity scale.
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  • 158
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    Journal of Physical Organic Chemistry 7 (1994), S. 712-716 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The general solvation equation \documentclass{article}\pagestyle{empty}\begin{document}$${\rm logSP} = {\rm c} + {\rm rR}_2 + {\rm s\pi }_2^{\rm H} + {\rm a}\sum {\rm \beta }_2^{\rm H} + {\rm vV}_{\rm X}$$\end{document} was applied to the partition of solutes between water and isobutanol, pentanol, hexanol, octanol, decanol and oleyl alcohol. It is shown that the two main factors that influence partitioning are solute hydrogen-bond basicity Σβ2H and solute volume Vx. The b coefficient becomes steadily more negative along the above series of alcohols, showing that the alcoholic phases, which are all less acidic than water, become less and less acidic as the chain length increases, and the water content of the alcoholic phase decreases. The v coefficient, on the other hand, becomes gradually more positive, indicating that as the chain length increases and the water content decreases, the alcoholic phase becomes more and more hydrophobic. Of great significance is that for all six alcohols, the a coefficient is effectively zero, so that all alcoholic phases have the same basicity as bulk water, no matter what their water content is. It is suggested that, contrary to results of solvatochromic measurements, the alcohols have similar hydrogen-bond basicity to water.
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  • 159
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    Journal of Physical Organic Chemistry 7 (1994), S. 725-733 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The superbase gas-phase scale has been further extended up to proton affinities of ca 1080 kJ mol-1 by use of cyclic and acyclic guanidines and vinamidines. Structural features such as Y-conjugation, vinylogy and intramolecular ionic hydrogen bonding leading to their superbasic behaviour are analysed. Solvation effects by water and acetonitrile on basicity are discussed. From a correlation pKa(acetonitrile) vs gas-phase basicity, proton affinity values in the range 1070-1410 kJ mol-1 are predicted for Schwesinger phosphazene compounds.
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  • 160
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    Journal of Physical Organic Chemistry 7 (1994), S. 717-724 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Fourier transform ion cyclotron resonance (FT-ICR) spectrometry was used to study and recheck the proton transfer equilibria for a large number of low-basicity compounds, particularly those which are less basic than H2O. The data obtained were used for the construction of a continuous scale of the relative gas-phase basicities between H2S and SO2F2. The present results are compared with the results obtained by McMahon and co-workers using ICR spectrometry and high-pressure mass spectrometric (HPMS) techniques. Satisfactory agreement is found with the existing ICR spectrometric data. The results, however, show unexplained variances with earlier and recent HPMS results that also not internally self-consistent. The substituent effects for some families of low-basicity compounds (nitriles, carbonyl compounds, ethers and some others) are discussed.
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  • 161
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    Journal of Physical Organic Chemistry 7 (1994), S. 743-750 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: An LSER analysis based on the partitioning of 15 proton acceptor heterocycles has succeeded in extracting Σβ values, but only at the cost of demonstrating solvent dependence for some of them. As noted by Abraham, the division lies between protic and aprotic organic phases. His observation that pyridine and quinoline are less effective acceptors when surrounded by solvent than in 1 : 1 association was confirmed, and possible reasons for this are discussed. Two other such cases are N-methylimidazole and pyridazine, both of which give lower Σβ values in octanol than in PGDP. For both, Σβ in PGDP is what would be expected on the basis of log Kβ. The value for pyridazine in octanol suggests that, here, the ‘α-effect’ is no longer operative; it is possible that this result can be generalized to other such heterocycles. Elsewhere, the most remarkable finding is that, where there are two proton acceptor sites in one heterocyclic ring, Σβ is the simple unattenuated sum of the separate βf values. If this result is general, it leads to a very simple way of estimating Σβ for heterocycles by calculation where data are unavailable. Evidence was also found, in certain cases, for hydrogen bonding to the π-donor heteroatom or the aromatic ring. The QSAR implications of these results are discussed.
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  • 162
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    Journal of Physical Organic Chemistry 7 (1994), S. 734-742 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: This paper extends previous work on the dynamic averaging of distinct liquid environments by cage exchange to include potential energy fluctuations at the cage centers due to Brownian motions of molecules in the cage walls. After a brief review of the effect of cage exchange on the Schrödinger wave train associated with the electronic ground state of the caged molecule, typical magnitudes and time-scales for the Brownian potential energy fluctuations are estimated. Then a zig-zag model for the resulting noise in the wave trains is developed, and applied to analyze distinguishability in the presence of noisy cage exchange. When distinguishability survives the noise, the distinct caged species are fully fledged environmental isomers. Applications of these concepts are discussed.
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  • 163
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    Journal of Physical Organic Chemistry 7 (1994), S. 751-756 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The equilibrium acidities, pKHA, of 18 dialkyl malonates, five alkyl 2-cyanoacetates and nine malononitriles and the oxidation potentials of their conjugate anions, EOX(A-), were measured in dimethyl sulfoxide solution. The homolytic bond dissociation enthalpies (BDEs) of their acidic C-H were estimated by combining their pKHA and EOX(A-) values. The pKHA values of the dialkyl malonates were found to increase from 15·9 to 16·4 to 18·4 as the dialkyl groups were changed from dimethyl to diethyl to di-tert-butyl, but the BDEs of the acidic C-H bonds remained constant [95·3±0·3 kcal mol-1] (1 kcal = 4·184 kJ). Introduction of methyl, ethyl, isopropyl and tert-butyl groups into the 2-position of diethyl malonate caused the equilibrium acidities to increase by 2·0, 2·4, 3·8 and 8·0 pKHA units, respectively, and the BDE values to decrease by 4·4, 3·7, 2·5 and 0·8 kcal mol-1, respectively. Introduction of a phenyl group into the 2-position of diethyl malonate had no effect on the acidity, but weakened the acidic C-H bond by 10 kcal mol-1. The effects on acidity and BDE of introducing 3,4,5- (MeO)3C6H2CO, CF3, Me3N+, c-C5H10N, p-MeC6H4, p-NO2C6H4, PhO, F and c-C5H5N+ groups into the 2-position of diethyl malonate were also examined.
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  • 164
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    Journal of Physical Organic Chemistry 7 (1994), S. 757-769 
    ISSN: 0894-3230
    Keywords: Organic Chemistry ; Physical Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: The solvatochromic hydrogen bond donor (HBD) acidity parameter (αmix) of aqueous mixtures of methanol, acetonitrile, propan-2-ol and tetrahydrofuran were determined spectrophotometrically. The study was carried out at 25deg;C as a function of composition. The indicators used were 2,6-diphenyl-4-(2,4,6-triphenyl-N-pyridino)phenolate, 2,6-dichloro-4-(2,4,6-triphenyl-N-pyridino)phenolate and Fe(LL)2(CN)2 (LL = N-(2-pyridylbenzylidene)-3,4-dimethylaniline). The HBD acidity of the aqueous organic mixtures was related to retention in reversed-phase liquid chromatography.
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  • 165
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    Numerical Linear Algebra with Applications 1 (1994), S. 105-105 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 166
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    Numerical Linear Algebra with Applications 1 (1994), S. 151-154 
    ISSN: 1070-5325
    Keywords: Linear systems ; Singular systems ; Iterative methods ; Convergent methods ; Index of the iteration operator ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Equivalence is shown between different conditions for convergence of iterative methods for consistent singular systems of linear equations on Banach spaces. These systems appear in many applications, such as Markov chains and Markov processes. The conditions considered relate the range and null spaces of different operators.
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    Numerical Linear Algebra with Applications 1 (1994), S. 211-212 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 168
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    Numerical Linear Algebra with Applications 1 (1994), S. 179-210 
    ISSN: 1070-5325
    Keywords: Linear system solvers ; Conjugate gradients ; Iteration number estimates ; Explicit preconditionings ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Instead of the standard estimate in terms of the spectral condition number we develop a new CG iteration number estimate depending on the quantity B = 1/ntr M/(det M)1/n, where M is an n × n preconditioned matrix. A new family of iterative methods for solving symmetric positive definite systems based on B-reducing strategies is described. Numerical results are presented for the new algorithms and compared with several well-known preconditioned CG methods.
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  • 169
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    Numerical Linear Algebra with Applications 1 (1994), S. 155-177 
    ISSN: 1070-5325
    Keywords: Preconditioning ; Diagonal compensation ; Eigenvalue bounds ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: When solving linear algebraic equations with large and sparse coefficient matrices, arising, for instance, from the discretization of partial differential equations, it is quite common to use preconditioning to accelerate the convergence of a basic iterative scheme. Incomplete factorizations and sparse approximate inverses can provide efficient preconditioning methods but their existence and convergence theory is based mostly on M-matrices (H-matrices). In some application areas, however, the arising coefficient matrices are not H-matrices. This is the case, for instance, when higher-order finite element approximations are used, which is typical for structural mechanics problems. We show that modification of a symmetric, positive definite matrix by reduction of positive offdiagonal entries and diagonal compensation of them leads to an M-matrix. This diagonally compensated reduction can take place in the whole matrix or only at the current pivot block in a recursive incomplete factorization method. Applications for constructing preconditioning matrices for finite element matrices are described.
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    Numerical Linear Algebra with Applications 1 (1994) 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 171
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    Numerical Linear Algebra with Applications 1 (1994), S. 237-245 
    ISSN: 1070-5325
    Keywords: Korovkin theorem ; Heat conduction equation ; Lax theorem ; Difference scheme ; Convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Sufficient conditions are obtained for the convergence of difference schemes for the numerical solution of the Cauchy problem for a heat conduction equation in two space variables. The sufficient conditions are derived in a form similar to those for the convergence of a sequence of linear positive operators in the Korovkin theorem. As an application it is shown that difference schemes that are widely used in practice can easily be checked for convergence by these conditions.
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  • 172
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    Numerical Linear Algebra with Applications 1 (1994), S. 213-236 
    ISSN: 1070-5325
    Keywords: Optimal order preconditioners ; Algebraic multilevel ; Chebyshev polynomial approximation ; Diagonal compensation ; Approximate inverses ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The numerical solution of elliptic selfadjoint second-order boundary value problems leads to a class of linear systems of equations with symmetric, positive definite, large and sparse matrices which can be solved iteratively using a preconditioned version of some algorithm. Such differential equations originate from various applications such as heat conducting and electromagnetics. Systems of equations of similar type can also arise in the finite element analysis of structures.We discuss a recursive method constructing preconditioners to a symmetric, positive definite matrix. An algebraic multilevel technique based on partitioning of the matrix in two by two matrix block form, approximating some of these by other matrices with more simple sparsity structure and using the corresponding Schur complement as a matrix on the lower level, is considered.The quality of the preconditioners is improved by special matrix polynomials which recursively connect the preconditioners on every two adjoining levels. Upper and lower bounds for the degree of the polynomials are derived as conditions for a computational complexity of optimal order for each level and for an optimal rate of convergence, respectively.The method is an extended and more accurate algebraic formulation of a method for nine-point and mixed five- and nine-point difference matrices, presented in some previous papers.
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    Numerical Linear Algebra with Applications 1 (1994) 
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    Keywords: Engineering ; Engineering General
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    Topics: Mathematics
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  • 174
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    Numerical Linear Algebra with Applications 1 (1994), S. 1-1 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 175
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    Numerical Linear Algebra with Applications 1 (1994), S. 33-44 
    ISSN: 1070-5325
    Keywords: Rank revealing QR factorization ; Column pivoting ; Numerical rank ; Subset selection ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Rank revealing factorizations are used extensively in signal processing in connection with, for example, linear prediction and signal subspace algorithms. We present an algorithm for computing rank revealing QR factorizations of low-rank matrices. The algorithm produces tight upper and lower bounds for all the largest singular values, thus making it particularly useful for treating rank deficient problems by means of subset selection, truncated QR, etc. The algorithm is similar in spirit to an algorithm suggested earlier by Chan for matrices with a small nullity, and it can also be considered as an extension of ordinary column pivoting.
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    Numerical Linear Algebra with Applications 1 (1994), S. 571-581 
    ISSN: 1070-5325
    Keywords: GMRES ; GMRES(m) ; Large-scale nonsymmetric linear systems ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The generalized minimal residual (GMRES) method is widely used for solving very large, nonsymmetric linear systems, particularly those that arise through discretization of continuous mathematical models in science and engineering. By shifting the Arnoldi process to begin with Ar0 instead of r0, we obtain simpler Gram-Schmidt and Householder implementations of the GMRES method that do not require upper Hessenberg factorization. The Gram-Schmidt implementation also maintains the residual vector at each iteration, which allows cheaper restarts of GMRES(m) and may otherwise be useful.
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  • 177
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    Numerical Linear Algebra with Applications 1 (1994), S. 555-570 
    ISSN: 1070-5325
    Keywords: Linear system of equations ; Iterative method ; Fast algorithm ; Arnoldi process ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: A new iterative scheme is described for the solution of large linear systems of equations with a matrix of the form A = ρU + ζI, where ρ and ζ are constants, U is a unitary matrix and I is the identity matrix. We show that for such matrices a Krylov subspace basis can be generated by recursion formulas with few terms. This leads to a minimal residual algorithm that requires little storage and makes it possible to determine each iterate with fairly little arithmetic work. This algorithm provides a model for iterative methods for non-Hermitian linear systems of equations, in a similar way to the conjugate gradient and conjugate residual algorithms. Our iterative scheme illustrates that results by Faber and Manteuffel [3,4] on the existence of conjugate gradient algorithms with short recurrence relations, and related results by Joubert and Young [13], can be extended.
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    Numerical Linear Algebra with Applications 1 (1994), S. 583-587 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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  • 179
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    Numerical Linear Algebra with Applications 1 (1994), S. 45-63 
    ISSN: 1070-5325
    Keywords: Conjugate gradients ; Convergence ; Linear systems ; Acceleration of conjugate gradients ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The solution of linear systems has considerable importance for the computation of problems resulting from engineering, physics, chemistry, computer science, mathematics, medicine and economics. The calculation of costly and time-consuming problems, e.g. crash tests, simulation of the human lung and skin, calculation of electrical and magnetical fields, thermal analysis and fluid dynamics, to name only a few, has become possible with the recent developments of advanced computer architectures and iterative solvers. Generalized conjugate gradient (CG) methods are the most important iterative solvers because they converge very quickly under certain conditions. Therefore they are widely used and in a rapid further development.The purpose of this paper is to present new results for the convergence of generalized CG methods. A convergence result for non-symmetric and non-positive definite matrices is given that includes the classical theory for symmetric, positive definite matrices as a special case.The norm of the residuals resulting from CG methods may oscillate heavily. Different remedies for smoothing this sequence have been proposed, for example by van der Vorst. Schönauer introduced in the 1980s a smoothing algorithm to get a norm nonincreasing function of the iteration index. For this algorithm a complete theoretical analysis is given. A surprising result is obtained showing that the smoothing algorithm is in a sense optimal. Convergence estimates are derived therefrom. A geometric interpretation of the smoothing algorithm is given showing the propagation of the errors.It should be stressed that a smooth convergence of the residuals is not equivalent to a smooth convergence of the errors which is the proper aim. A class of error minimizing methods can be easily derived from the theory.
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    Numerical Linear Algebra with Applications 1 (1994), S. 107-128 
    ISSN: 1070-5325
    Keywords: Incomplete factorization ; Preconditioning ; Linear elasticity problems ; Displacement decomposition ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Two preconditioning techniques for the numerical solution of linear elasticity problems are described and studied. Both techniques are based on spectral equivalence approach. The first technique consists in an incomplete factorization of the separate displacement component part of the stiffness matrix. The second technique uses an incomplete factorization of the isotropic approximation to the stiffness matrix. Results concerning existence, stability and efficiency of these preconditioning techniques are presented. The efficiency and robustness of the described techniques are illustrated by numerical experiments.
    Additional Material: 2 Ill.
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    Numerical Linear Algebra with Applications 1 (1994), S. 129-139 
    ISSN: 1070-5325
    Keywords: Conjugate gradient method ; Nonsymmetric linear system ; Krylov subspace method ; Conjugate residual method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Yserentant's and Bramble/Pasciak/Xu's hierarchical preconditioners only require the hierarchical node connection of a finite element grid. So they could be applied to nonsymmetric FE-systems too, having a symmetric preconditioner. We investigate the question whether this fact could be useful in the CG-like iterative methods. The main key is the consideration of an appropriate choice of the inner product defined in the N-vector space. It is shown, how the inner product influences the formulas of the methods, the rate of convergence and some other properties.
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    Numerical Linear Algebra with Applications 1 (1994), S. 141-150 
    ISSN: 1070-5325
    Keywords: Invariant manifolds ; Error estimates ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Many processes in the sciences and in engineering are modelled by dynamical systems and - in discretized version - by nonlinear maps. To understand the often complicated dynamical behaviour it is a well established tool to use the concept of invariant manifolds of the system. In this way it is often possible to reduce the dimension of the system considerably. In this paper we propose a new method to calculate numerically invariant manifolds near fixed points of maps. We prove convergence of our procedure and provide an error estimation. Finally, the application of the method is illustrated by examples.
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    Numerical Linear Algebra with Applications 1 (1994), S. 335-335 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
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    Numerical Linear Algebra with Applications 1 (1994), S. 369-386 
    ISSN: 1070-5325
    Keywords: GMRES ; Unsymmetric linear systems ; Iterative solver ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Recently Eirola and Nevanlinna have proposed an iterative solution method for unsymmetric linear systems, in which the preconditioner is updated from step to step. Following their ideas we suggest variants of GMRES, in which a preconditioner is constructed per iteration step by a suitable approximation process, e.g., by GMRES itself. Our numerical experiments indicate that this may lead to considerable savings in CPU-time and memory requirements in typical CFD applications.
    Additional Material: 10 Tab.
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  • 185
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    Numerical Linear Algebra with Applications 1 (1994), S. 337-368 
    ISSN: 1070-5325
    Keywords: Local refinement ; Preconditioning ; Two-grid method ; Cell-centered grids ; Finite differences ; Elliptic problem ; Optimal rate of convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Two preconditioning techniques for solving difference equations arising in finite difference approximation of elliptic problems on cell-centered grids are studied. It is proven that the BEPS and the FAC preconditioners are spectrally equivalent to the corresponding finite difference schemes, including a nonsymmetric one, which is of higher-order accuracy. Numerical experiments that demonstrate the fast convergence of the preconditioned iterative methods (CG and GCG-LS in the nonsymmetric case) are presented.
    Additional Material: 3 Ill.
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  • 186
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    Numerical Linear Algebra with Applications 1 (1994), S. 421-425 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 187
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    Numerical Linear Algebra with Applications 1 (1994), S. 403-420 
    ISSN: 1070-5325
    Keywords: Quasi-minimal residual iteration ; Non-Hermitian matrix ; Singular linear system ; Markov chain modeling ; Krylov-subspace method ; Convergence ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Recently, Freund and Nachtigal proposed the quasi-minimal residual algorithm (QMR) for solving general nonsingular non-Hermitian linear systems. The method is based on the Lanczos process, and thus it involves matrix - vector products with both the coefficient matrix of the linear system and its transpose. Freund developed a variant of QMR, the transpose-free QMR algorithm (TFQMR), that only requires products with the coefficient matrix. In this paper, the use of QMR and TFQMR for solving singular systems is explored. First, a convergence result for the general class of Krylov-subspace methods applied to singular systems is presented. Then, it is shown that QMR and TFQMR both converge for consistent singular linear systems with coefficient matrices of index 1. Singular systems of this type arise in Markov chain modeling. For this particular application, numerical experiments are reported.
    Additional Material: 2 Ill.
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  • 188
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    Numerical Linear Algebra with Applications 1 (1994) 
    ISSN: 1070-5325
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
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  • 189
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    Numerical Linear Algebra with Applications 1 (1994), S. 387-402 
    ISSN: 1070-5325
    Keywords: Preconditioning ; Incomplete LU ; Threshold strategies ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: In this paper we describe an Incomplete LU factorization technique based on a strategy which combines two heuristics. This ILUT factorization extends the usual ILU(O) factorization without using the concept of level of fill-in. There are two traditional ways of developing incomplete factorization preconditioners. The first uses a symbolic factorization approach in which a level of fill is attributed to each fill-in element using only the graph of the matrix. Then each fill-in that is introduced is dropped whenever its level of fill exceeds a certain threshold. The second class of methods consists of techniques derived from modifications of a given direct solver by including a dropoff rule, based on the numerical size of the fill-ins introduced, traditionally referred to as threshold preconditioners. The first type of approach may not be reliable for indefinite problems, since it does not consider numerical values. The second is often far more expensive than the standard ILU(O). The strategy we propose is a compromise between these two extremes.
    Additional Material: 5 Ill.
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  • 190
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    Numerical Linear Algebra with Applications 1 (1994), S. 427-447 
    ISSN: 1070-5325
    Keywords: Nonsymmetric linear systems ; Conjugate gradient type iterative methods ; GMRES ; Restarting ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: The solution of nonsymmetric systems of linear equations continues to be a difficult problem. A main algorithm for solving nonsymmetric problems is restarted GMRES. The algorithm is based on restarting full GMRES every s iterations, for some integer s〉0. This paper considers the impact of the restart frequency s on the convergence and work requirements of the method. It is shown that a good choice of this parameter can lead to reduced solution time, while an improper choice may hinder or preclude convergence. An adaptive procedure is also presented for determining automatically when to restart. The results of numerical experiments are presented.
    Additional Material: 4 Tab.
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  • 191
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    Communications in Numerical Methods in Engineering 10 (1994) 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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  • 192
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    Communications in Numerical Methods in Engineering 10 (1994), S. 1-9 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An iterative method is introduced for computing second-order partial derivatives (sensitivities) of eigenvalues and eigenvectors of matrices which depend on a number of real design parameters. Numerical tests confirm the viability of the method and support our theoretical analysis. Alternative methods are reviewed briefly and compared with the one proposed here.
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  • 193
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    Communications in Numerical Methods in Engineering 10 (1994), S. 11-19 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In the formulation of the semi-Loof element the rotation of the tangent plane is derived from the interpolation of the transverse displacement, while the rotation of the normal is interpolated separately by another set of shape functions. The geometric stiffness matrix can be formulated by use of either of the two rotation representations. It is demonstrated that the use of the tangent plane representation in the geometric stiffness matrix is far superior to the common form at present.
    Additional Material: 4 Ill.
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  • 194
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    Communications in Numerical Methods in Engineering 10 (1994), S. 21-32 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An efficient solution to boundary-value problems may be based on the application of a suitably truncated T-complete set of Trefftz functions over individual subdomains and on linking the fields by a least-squares procedure. Although it yields a symmetric system of linear equations, this approach as originally presented by Zielinski and Zienkiewicz is not suited for implementation into FE codes. The present paper presents two equivalent formulations, which take respectively the form of the finite (FE) and non-conventional boundary-element (BE) approach. Both allow the resulting simultaneous equations to be assembled following the standard direct stiffness methods and can readily be implemented into existing FE codes.As in the conventional p-method, the accuracy may be controlled within large limits without increasing the number of elements. The present approach allows substantial saving in computer time in comparison with the so-called hybrid-Trefftz (HT) elements, though the assumed displacement fields are identical. The practical efficiency of the new T-element approach is assessed on the problem of stress concentration in a symmetrically compressed perforated panel.
    Additional Material: 6 Ill.
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  • 195
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    Communications in Numerical Methods in Engineering 10 (1994), S. 43-58 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A method is presented for the solution of elliptical problems defined on general-shape multiconnected three-dimensional domains approximated by means of polyhedra. The boundary conditions may be of the Neumann type. The differential operator and the normal derivative are discretized by generalized finite-difference (GFD) methods using an orthogonal non-uniform Cartesian grid. The convergence properties are analysed and the solutions of some Poisson and biharmonic problem are presented.
    Additional Material: 7 Ill.
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  • 196
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    Communications in Numerical Methods in Engineering 10 (1994), S. 59-65 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A heuristic optimization design methodology based on redesign rules for composite laminated plates is presented. It is modelled on the cyclic approach to the design process observed in designers of structural components using composites. In comparison with a simple weight minimization algorithm it gives quasioptimal ply thicknesses, but takes under ten iterations. It is thereby shown to be most suitable for initial design studies. Multiaxial combinations of in-plane loads and bending moments are considered in the design procedure.
    Additional Material: 5 Tab.
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  • 197
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    Communications in Numerical Methods in Engineering 10 (1994), S. 33-42 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Reduction of reheating time saves on energy input and increases the production rate in the steel-making process. Reductions can be achieved by allowing the centre temperature of a steel bar to be lower than the surface temperature by a small margin, before starting with the hot rolling process. This can only be done if the temperature difference does not adversely affect the quality of the final product or the rolling equipment. The paper presents numerical simulations to investigate the savings that can be obtained for various temperature differences between surface and centre temperatures to evaluate the feasibility of the concept. The results presented include the cross-sectional temperature distribution in a typical steel bar during reheating at hourly intervals as well as the effect of various differences between centre and surface temperatures on reheating time. The reheating time predicted for various steel bar sizes as well as for various differences between surface and centre temperatures are then compared against measured reheating times. To indicate the practical applicability of the concept to the hot rolling process the detailed temperature distribution in a typical steel bar, with an initial temperature difference between the surface and centre of the bar, was simulated numerically. This was compared to a similar simulation for a well soaked steel bar for which experimental measurements are also available. The numerical method used to obtain the simulations is also presented. Boundary conditions account for radiation, convection and conduction inside the steel bar. It is concluded that the concept of allowing differences between surface and centre temperatures of a steel bar during reheating holds great potential for energy savings in the steel-making process.
    Additional Material: 5 Ill.
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  • 198
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    Communications in Numerical Methods in Engineering 10 (1994), S. 73-80 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Standard isoparametric finite elements can be used as singular crack-tip elements in fracture mechanical computations by placing the middle nodes in the neighbourhood of the crack tip. Such elements have already been applied to several plane and three-dimensional problems, so this method can be considered as commonly well accepted. The paper shows that singularity of order r(1 - m)/m is obtained with an nth-order isoparametric element.
    Additional Material: 3 Ill.
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  • 199
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    Communications in Numerical Methods in Engineering 10 (1994), S. 67-71 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: In this paper, an iterative method of statistic linearization (IMSL) is presented to solve non-linear stochastic vibration equations. This method represents an improvement over the classical linearization method. The method uses the solution of the corresponding linear vibration equation as an initial value in an iterative procedure. To obtain information about essential statistical average values, the method uses a ‘boot-strapping’ procedure, which defines a pseudorandom process based on the statistical characteristics of the linear solution and then uses samples from the process to estimate them. For Gaussian input excitation, the statistical average values are obtained by theoretical analysis.
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  • 200
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    Communications in Numerical Methods in Engineering 10 (1994), S. 89-91 
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
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