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Item type: Item , High accuracy quasi-interpolation using a new class of generalized multiquadrics(2024) Ortmann, Mathis; Buhmann, MartinA new generalization of multiquadric functions phi ( x ) = root c(2d) + || x ||(2d) , where x is an element of R-n , c is an element of R, d is an element of N, is presented to increase the accuracy of quasi -interpolation further. With the restriction to Euclidean spaces of odd dimensionality, the generalization can be used to generate a quasi -Lagrange operator that reproduces all polynomials of degree 2 d - 1. In contrast to the classical multiquadric, the convergence rate of the quasi -interpolation operator can be significantly improved by a factor h(2d -n - 1) , where h > 0 represents the grid spacing. Among other things, we compute the generalized Fourier transform of this new multiquadric function. Finally, an infinite regular grid is employed to analyse the properties of the aforementioned generalization in detail. We also present numerical results to demonstrate the advantages of our new multiquadric functions.Item type: Item , New methods for quasi-interpolation approximations: Resolution of odd-degree singularities(2024) Buhmann, Martin; Jäger, Janin; Jódar, Joaquín; Rodríguez, Miguel L.In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange functions when the orders of the singularities of the radial function’s Fourier transforms at zero do not match the parity of the dimension of the space, and therefore new expansions and coefficients are needed to overcome this problem. We develop explicit constructions of infinite Fourier expansions that provide these coefficients and make an extensive comparison of the approximation qualities and – with a particular focus – polynomial reproduction and uniform approximation order of the various formulae. One of the interesting observations concerns the link between algebraic conditions of expansion coefficients and analytic properties of localness and convergence.Item type: Item , Reduction of anthranilic acid to 2-aminobenzaldehyde by the white-rot fungus Bjerkandera adusta DSMZ 4708(2024) Babkina, Valeriia; Haiduk, Yana; Kurtash, Yuliia; Zorn, Holger; Zhuk, TatyanaThe biocatalytic aerobic “in-water” reduction of anthranilic acid to 2-aminobenzaldehyde by growing cultures of the basidiomycetous white-rot fungus Bjerkandera adusta has been studied. The high specific activity of Bjerkandera adusta towards the carboxylic group of anthranilic acid that allows avoiding the formation of the corresponding alcohol has been demonstrated using different substrate concentrations. The presence of ethanol as co-solvent allows increasing the yield of target product. In contrast to chemical reducing agents that usually yield 2-aminobenzyl alcohol, an overreduction of anthranilic acid is completely suppressed by the fungus and gives the target flavor compound in satisfactory preparative yields. It was shown that the activity of Bjerkandera adusta towards anthranilic acid does not apply to its m- and p-isomers.Item type: Item , Unexpected reaction of antimony pentafluoride with a fluorinated propellane(2024) Bremer, MatthiasWhile 1,3-dehydro-5,7-difluoroadamantane 11 reacts with SbF5 in super acid media (SO2ClF) to generate the 1,3-dehydroadamant-5,7-diyl dication 1, 1,3-dehydro-5-fluoroadamantane 12 fails to react analogously to produce the 1,3-dehydroadamant-5-yl cation 9; instead, the 3,5-difluoro-1-adamantylcation 13 is formed. We present a computational study that explains this surprising behavior by the initial addition of Sb2F10 to the propellane bond present in 12. This is computed to be highly exothermic and leads to a zwitterionic (or ion-pair) species, which in turn reacts autocatalytically with HF to produce the observed fluorinated cation 13, SbF3, and SbF6–.Item type: Item , MutL Activates UvrD by Interaction Between the MutL C-terminal Domain and the UvrD 2B Domain(2024) Storozhuk, Olha; Bruekner, Susanne R.; Paul, Ankon; Lebbink, Joyce H.G.; Sixma, Titia K.; Friedhoff, PeterUvrD is a helicase vital for DNA replication and quality control processes. In its monomeric state, UvrD exhibits limited helicase activity, necessitating either dimerization or assistance from an accessory protein to efficiently unwind DNA. Within the DNA mismatch repair pathway, MutL plays a pivotal role in relaying the repair signal, enabling UvrD to unwind DNA from the strand incision site up to and beyond the mismatch. Although this interdependence is well-established, the precise mechanism of activation and the specific MutL-UvrD interactions that trigger helicase activity remain elusive. To address these questions, we employed site-specific crosslinking techniques using single-cysteine variants of MutL and UvrD followed by functional assays. Our investigation unveils that the C-terminal domain of MutL not only engages with UvrD but also acts as a self-sufficient activator of UvrD helicase activity on DNA substrates with 3′-single-stranded tails. Especially when MutL is covalently attached to the 2B or 1B domain the tail length can be reduced to a minimal substrate of 5 nucleotides without affecting unwinding efficiency.