A hybrid Arnoldi-Faber iterative method for nonsymmetric systems of linear equations

Summary We present here a new hybrid method for the iterative solution of large sparse nonsymmetric systems of linear equations, say of the formAx=b, whereA ^{N, N} , withA nonsingular, andb ^N are given. This hybrid method begins with a limited number of steps of the Arnoldi method to obtain some information on the location of the spectrum ofA, and then switches to a Richardson iterative method based on Faber polynomials. For a polygonal domain, the Faber polynomials can be constructed recursively from the parameters in the Schwarz-Christoffel mapping function. In four specific numerical examples of non-normal matrices, we show that this hybrid algorithm converges quite well and is approximately as fast or faster than the hybrid GMRES or restarted versions of the GMRES algorithm. It is, however, sensitive (as other hybrid methods also are) to the amount of information on the spectrum ofA acquired during the first (Arnoldi) phase of this procedure.     

High-Resolution,Higher-Order UV/VIS Derivative Spectrophotometry

Derivative spectrophotometry has gained increasing importance in the past two years and is currently experiencing vigorous development. Following and introduction the present article provides a review of this extremely effective method. In particular, the advantages of higher-order derivative spectrophotometry (HODS method, n > 2) are discussed on the basis of practical examples from a wide range of analytical fields. The results are achieved with the aid of a newly developed analog computer unit, whereby for the first time readily reproducible, low-noise, on-line spectra can be obtained up to the 7th order and even, in favorable cases, up to the 9th order. In practice it has proved valuable to work with spectra of the 3rd to 5th order; but even higher derivations could be profitable for the separation of strongly superposed signals or for “fingerprinting”.     

Estimating the pore size distribution of activated carbons from adsorption data of different adsorbates by various methods

Experimental adsorption isotherms of four adsorbates (N2, Ar, C6H6, and CCl4) as well as adsorption enthalpy (C6H6 and CCl4) measured on two strictly microporous carbons are used to evaluate the porosity of adsorbents (i.e., pore size distributions (PSDs) and average pore diameter ( Lav )). The influence of the diameter of adsorbates ( dA) as well as of the temperature ( T ) is analyzed in order to explain the differences or similarities between the above-mentioned quantities for all systems. Proposed previously, the general relationships between the parameters of the Dubinin-Astakhov (DA) isotherm equation (the characteristic energy of adsorption ( E0 ) and the exponent of this equation ( n )) and the average slit-width of carbon micropores are investigated. Moreover, the thermodynamic verification of the Horvath-Kawazoe (HK) theory and the ND model is presented based on data of the adsorption and enthalpy of adsorption of benzene and carbon tetrachloride on two carbons. Finally, the pore diameters calculated from calorimetry data using the Everett and Powl method and those calculated applying the recently developed equations are compared. In our opinion the change of apparent PSD should be monitored by performing a series of isotherm measurements from high (equal and higher than room temperature) to low temperatures (ca. 77.5 K) as was presented in the current study. Moreover, the analysis of the experimental data leads to the conclusion that the entropy of C6H6 and CCl4 can approach to the values characteristic of quasi-solid (a partially ordered structure). Therefore, this behavior of the adsorbate should be taken into consideration in the theoretical assumptions of model and its thermodynamic verification.     

Asymmetric synthesis of unsaturated, fused bicyclic proline analogues through amino alkylation of cyclic bis(allylsulfoximine)titanium complexes and migratory cyclization of delta-amino alkenyl aminosulfoxonium salts

Described is an asymmetric synthesis of new Delta(3a,4)-unsaturated, fused bicyclic proline analogues from cyclic bis(allylsulfoximine)titanium complexes and N-tert-butylsulfonyl imino ethyl ester. Treatment of the enantiomerically pure five-, six-, seven-, and eight-membered cyclic bis(allylsulfoximine)titanium complexes with the imino ester gave mixtures of the corresponding (E,syn)- and (Z,syn)-configured, delta-sulfoximine substituted, cyclic gamma,delta-unsaturated alpha-amino acid esters with high regio- and diastereoselectivities in good yields. Activation of the N-methyl sulfoximine group of these amino acid derivatives through methylation with Me(3)OBF(4) afforded in nearly quantitative yields the corresponding (dimethylamino)sulfoxonium salts. A novel migratory cyclization of these salts with DBU gave via an isomerization to the corresponding allylic (dimethylamino)sulfoxonium salts and an intramolecular substitution of the (dimethylamino)sulfoxonium group the enantio- and diastereomerically pure, bicyclic, N-tert-butylsulfonyl protected proline analogues having a six- and eight-membered unsaturated carbocyclic ring. Cyclization of the alkenyl (dimethylamino)sulfoxonium salts was independent of the configuration of the double bond. N,N-Dimethylphenylsulfinamide of > or =99% ee was obtained in good yield as a further reaction product. Conversion of the sulfinamide to N,S-dimethyl-S-phenylsulfoximine of > or =99% ee, the starting material for the synthesis of the allylic sulfoximines, had been accomplished previously. Finally, cleavage of the tert-butylsulfonyl protecting group with anhydrous acid furnished the fused bicyclic proline analogue containing an unsaturated six-membered ring in high yield.     

Synthesis of pyrroles from 1-dialkylamino-3-phosphoryl(or phosphanyl)allenes through 1,5-cyclization of conjugated azomethine ylide intermediates

1-Dialkylamino-1,3-diaryl-3-diphenylphosphanylallenes 3a-e are thermally converted into a-annulated 3,5-diarylpyrroles 6a-f and [a]-annulated benzo[c]azepines 7a,b,d. These transformations are likely to include conjugated azomethine ylide intermediates that can undergo either a 1,5- or a 1,7-electrocyclization. The periselectivity is markedly shifted toward 1,5-cyclization when the diphenylphosphanyl substituent is replaced by the diphenylphosphoryl group. Thus, 1-dialkylamino-3-(diphenylphosphoryl)allenes 4a-f yield pyrroles 6 exclusively and with improved yields, unless the 3-aryl substituent in the allene is too electron-rich (e.g., benzodioxol-5-yl, 4f --> 7f). The preparation and thermal transformation of aminoallenes 4 over three or four steps can be conducted as a one-pot procedure, thus providing a convenient synthesis of [a]-annulated 3,5-diarylpyrroles from enaminoketones.     

Structure and reactivity of xanthocorrinoids. Part V. Formation of trans-diol derivatives of 5,6-dihydrocobyrinic acid from xanthocorrinoids under acidic conditions

On treatment with H₂SO₄/MeOH, epimerization of hexamethyl cis-5,6-dihydroxycobyrinate c,8-lactam ( 3 ) takes place quantitatively at C(6), yielding the corresponding trans-diol 4 . The corresponding lactone 7 , whose structure has been established by X-ray analysis, is obtained from xanthocorrinoids 5 and 6 under similar conditions.     

Fluid phase equilibria of binary and ternary mixtures of supercritical carbon dioxide with tetradecanoic acid and docosane up to 43 MPa and 393 K: cosolvency effect and miscibility windows

Isothermal pressure (p)-mass fraction (w) phase diagrams were measured for CO₂ + tetradecanoic acid at six temperatures from 328.2 K to 373.2 K and for CO₂ + docosane at four temperatures from 343.2 K to 393.2 K as well as isobaric temperature (T)-mass fraction (w) phase diagrams for both systems at 34.5 MPa. In addition the isothermal and isobaric Gibbs phase prisms at 373.2 K and 34.5 MPa respectively were determined for the ternary system CO₂ + tetradecanoic acid + docosane, and and isobaric miscibility window was found between 333 K and 385 K at 34.5 MPa.     

Electronic states and radiative transitions in LiAr

Ab initio MRD-CI calculations have been carried out on the ground and the eight lowest excited electronic states of LiAr, correlating with excited Li atom states up to 3d ²D. The ground (X²∑⁺ (2s)) and 2 ²Σ⁺ (2p) electronic states are repulsive while the higher excited states show shallow Rydberg minima. Rates of radiative bound-bound and bound-free transitions have been also calculated.