On the interpretation of random forces derived by projection operators

We study the derivation of a Langevin equation from a microscopic basis in order to elucidate the nature of the random force. We arrive at the conclusion that the consistent interpretation of the microscopic Langevin equation in terms of a stochastic differential equation (SDE) is according to I o rules. In addition, the random force is in general not Gaussian, and it is hence not completely characterized by its second moments.     

Geometric modules and Quinn homology theory

LetR be a ring with unit and invariant basis property. In [1], the authors define a functorK(_;R):TOP/LIP _c-LPEP by combining the open cone construction of [7] with a geometric module construction and show this functor is a homology theory. This paper shows that if attention is restricted to objects TOP/LIP _c with a homotopy colimit structure, then the functorK(_;R) is a Quinn homology theory, In particular, for each having a homotopy colimit structure,K(;R) is a homotopy colimit in the category of -spectra. Furthermore, the constituent spectra of this homotopy colimit are obtained naturally from the fibres of .Partially supported by the National Science Foundation under grant number DMS88-03148.Partially supported by the SNF (Denmark) under grant number 11-7792.     

Two-photon spectroscopy of the low-lying singlet states of naphthalene and acenaphthene

Two-photon excitation spectra of naphthalene and acenaphthene have been measured up to 50000 cm^?1. In naphthalene. three two-photon allowed states are observed for which the symmetry assignment is confirmed by polarization. The corre- sponding transitions are also seen in acenaphthene. The experimental data are in excellent agreement with theoretical predictions.     

Structures and magnetic properties of tetranuclear nickel(II) complexes with unusual mu3-1,1,3 azido bridges

Pyrazolate-based dinucleating ligands with thioether-containing chelate arms have been used for the synthesis of a family of novel tetranuclear nickel(II) complexes [L2Ni4(N3)3(O2CR)](ClO4)2 that incorporate three azido bridges and one carboxylate (R = Me, Ph). Molecular structures have been elucidated by X-ray crystallography in four cases, revealing Ni4 cores with a unique topology in which two of the azido ligands adopt an unusual mu3-1,1,3 bridging mode. The compounds were further characterized by mass spectrometry, IR spectroscopy, and variable-temperature magnetic susceptibility measurements. Magnetic data analyses indicate a combination of significant intramolecular ferromagnetic and antiferromagnetic exchange interactions that give rise to an overall S(T) = 0 ground state. The sign and the magnitude of the individual couplings have been rationalized in the framework of the common magnetostructural correlations for end-to-end and end-on azido linkages, suggesting that these correlations also remain valid for the respective fragments of multiply bridging mu3-1,1,3 azido ligands.     

Catalytic transesterification of dialkyl phosphates by a bioinspired dicopper(II) macrocyclic complex

For a number of phosphoryltransfer enzymes, including the exonuclease subunit of DNA polymerase I, a mechanism involving two-metal ions and double Lewis-acid activation of the substrate, combined with leaving group stabilization, has been proposed. Inspired by the active site structure of this enzyme, we have designed as a synthetic phosphoryl transfer catalyst the dicopper(II) macrocyclic complex LCu(2). Crystal structures of complexes [(L)Cu(2)(mu-NO(3))(NO(3))](NO(3))(2) (1), [(L)Cu(2)(mu-CO(3))(CH(3)OH)](BF(4))(2) (2), and [(L)Cu(2)(mu-O(2)P(OCH(3))(2))(NO(3))](NO(3))(2) (3) illustrate various possibilities for the interaction of oxoanions with the dicopper(II) site. 1 efficiently promotes the transesterification of dimethyl phosphate (DMP) in CD(3)OD, k(cat) = 2 x 10(-)(4) s(-)(1) at 55 degrees C. 1 is the only available catalyst for the smooth transesterification of highly inert simple dialkyl phosphates. From photometric titrations and the pH dependence of reactivity, we conclude that a complex [(L)Cu(2)(DMP)(OCH(3))](2+) is the reactive species. Steric bulk at the -OR substituents of phosphodiester substrates O(2)P(OR)(2)(-) drastically reduces the reactivity of 1. This is explained with -OR leaving group stabilization by Cu coordination, an interaction which is sensitive to steric crowding at the alpha-C-atom of substituent R. A proposed reaction mechanism related to that of the exonuclease unit of DNA polymerase I is supported by DFT calculations on reaction intermediates. The complex [(L)Cu(3)(mu(3)-OH)(mu-CH(3)O)(2)(CH(3)CN)(2)](ClO(4))(3) (4) incorporates a [Cu(OH)(OCH(3))(2)(CH(3)CN)(2)](-) complex anion, which might be considered as an analogue of the [PO(2)(OCH(3))(2)(OCD(3))](2)(-) transition state (or intermediate) of DMP transesterification catalyzed by LCu(2).     

Selective mixed coupling of carboxylic acids (II). — photolysis of unsymmetrical diacylperoxides with alkenyl-, halo-, keto-, carboxyl-groups and a chiral α-carbon. Comparison with the mixed kolbe electrolysis

Alkenoyl and functionalized alkanoyl dodecanoyl peroxides are prepared in 70 to 97 % yield and photolyzed at ?78° C. Thereby 4- to 10-alkenoyl and 4-alkanoyl peroxides afford good yields (56 – 68 %) of unsymmetrical coupling products. Similarly α- to σ-haloalkanoyl, cholanoyl or 3- and 4-carboxyalkanoyl peroxides can be coupled (40 – 70 %). The α-chiral diacyl peroxide ls undergoes the photochemical coupling reaction with 80 % retention of its configuration. The photolysis of diacyl peroxides at ?78° C proves to be a favorable supplement of the Kolbe-electrolysis in cases, where the electrolysis fails or produces low yields.     

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”.