Tools for Malliavin Calculus in UMD Banach Spaces

In this paper we study the Malliavin derivatives and Skorohod integrals for processes taking values in an infinite dimensional space. Such results are motivated by their applications to SPDEs and in particular financial mathematics. Vector-valued Malliavin theory in Banach space E is naturally restricted to spaces E which have the so-called umd property, which arises in harmonic analysis and stochastic integration theory. We provide several new results and tools for the Malliavin derivatives and Skorohod integrals in an infinite dimensional setting. In particular, we prove weak characterizations, a chain rule for Lipschitz functions, a sufficient condition for pathwise continuity and an Itô formula for non-adapted processes.     

The Class of Clifford-Fourier Transforms

Recently, there has been an increasing interest in the study of hypercomplex signals and their Fourier transforms. This paper aims to study such integral transforms from general principles, using 4 different yet equivalent definitions of the classical Fourier transform. This is applied to the so-called Clifford-Fourier transform (see Brackx et al., J. Fourier Anal. Appl. 11:669–681, 2005). The integral kernel of this transform is a particular solution of a system of PDEs in a Clifford algebra, but is, contrary to the classical Fourier transform, not the unique solution. Here we determine an entire class of solutions of this system of PDEs, under certain constraints. For each solution, series expressions in terms of Gegenbauer polynomials and Bessel functions are obtained. This allows to compute explicitly the eigenvalues of the associated integral transforms. In the even-dimensional case, this also yields the inverse transform for each of the solutions. Finally, several properties of the entire class of solutions are proven.     

Dilithiation of Bis(benzene)molybdenum and subsequent isolation of a molybdenum-containing paracyclophane

The homoleptic sandwich complex bis(benzene)molybdenum, [Mo(eta6-C6H6)2], was successfully dilithiated by employing an excess of BuLi in the presence of N,N,N',N'-tetramethylethylenediamine (up to 6 equiv each) at slightly elevated temperatures furnishing the highly reactive, ring metalated species [Mo(eta6-C6H5Li)2].tmeda in high yields. Alternatively, this compound was synthesized upon prolonged sonication with 5 equiv of tBuLi/tmeda without heating. An X-ray crystal structure determination revealed a symmetrical, dimeric composition in the solid state, i.e., a formula of [Mo(eta6-C6H5Li)2]2.(thf)6, where the six-membered rings are connected by two pairs of bridging lithium atoms. The synthesis of an elusive ansa-bridged complex failed in the case of a [1]bora and a [1]sila bridge due to the thermal lability of the resulting compounds. Instead, reverse addition of the dilithio precursor to an excess of the appropriate element dihalide facilitated the isolation of several unstrained, 1,1'-disubstituted derivatives, namely, [Mo{eta6-C6H5(BN(SiMe3)2X)}2] (X = Cl, Br) and [Mo{eta6-C6H5(SiiPr2Cl)}2], respectively. However, the incorporation of a less congesting [2]sila bridge was accomplished. In addition to the formation of [Mo{(eta6-C6H5)2Si2Me4}], a molybdenum-containing paracylophane complex was isolated and characterized by means of crystal structure analysis. The ancillary formation of 1 equiv of bis(benzene)molybdenum strongly suggests that this species is generated by deprotonation of the ansa-bridged complex by the dilithiated precursor and subsequent reaction with a second equivalent of the disilane.     

Ruthenium complexes bearing bidentate Schiff base ligands as efficient catalysts for organic and polymer syntheses

A concise overview is given on mononuclear and dinuclear, bidentate Schiff base ruthenium complexes with different additional ligands and on their applications in various chemical transformations such as Kharasch addition, enol-ester synthesis, alkyne dimerization, olefin metathesis and atom transfer radical polymerization. These new ruthenium complexes, conveniently prepared from commonly available ruthenium compounds, are very stable, exhibit a good tolerance towards organic functionalities, air and moisture and display high activity and chemoselectivity in chemical transformations. Relevant features of coordination chemistry connected with the reaction mechanism and chemoselectivity are also fully described. Since the nature of Schiff bases can be changed in a variety of ways, appealing routes for designing and preparing novel ruthenium complexes can be foreseen in the future.     

The relationship between nanoscale architecture and function in photovoltaic multichromophoric arrays as visualized by Kelvin probe force microscopy

The physicochemical properties of organic (multi)component films for optoelectronic applications depend on both the mesoscopic and nanoscale architectures within the semiconducting material. Two main classes of semiconducting materials are commonly used: polymers and (liquid) crystals of small aromatic molecules. Whereas polymers (e.g., polyphenylenevinylenes and polythiophenes) are easy to process in solution in thin and uniform layers, small molecules can form highly defined (liquid) crystals featuring high charge mobilities. Herein, we combine the two material types by employing structurally well-defined polyisocyanopeptide polymers as scaffolds to precisely arrange thousands of electron-accepting molecules, namely, perylenebis(dicarboximides) (PDIs), in defined chromophoric wires with lengths of hundreds of nanometers. The polymer backbone enforces high control over the spatial location of PDI dyes, favoring both enhanced exciton and charge transfer. When blended with an electron-donor system such as regioregular poly(3-hexylthiophene), this polymeric PDI shows a relative improvement in charge generation and diffusion with respect to monomeric, aggregated PDI. In order to correlate this enhanced behavior with respect to the architecture, atomic force microscopy investigations on the mixtures were carried out. These studies revealed that the two polymers form interpenetrated bundles having a nanophase-segregated character and featuring a high density of contact points between the two different phases. In order to visualize the relationship between the architecture and the photovoltaic efficiency, Kelvin probe force microscopy measurements were carried out on submonolayer-thick films. This technique allowed for the first time the direct visualization of the photovoltaic activity occurring in such a nanoscale phase-segregated ultrathin film with true nanoscale spatial resolution, thus making possible a study of the correlation between function and architecture with nanoscale resolution.     

Resin-bound sulfonyl azides: efficient loading and activation strategy for the preparation of the N-acyl sulfonamide linker

This paper describes an optimized protocol for the efficient loading of resin-bound aminoethane sulfonyl azides by either Boc- or Fmoc-protected amino thioacids. The resulting N-acyl sulfonamide is a convenient linker for use in Boc- or Fmoc-based solid-phase peptide synthesis. Activation of the N-acyl sulfonamide via a microwave-assisted alkylation procedure and subsequent treatment with functionalized nucleophiles yields C-terminally modified peptides that can be applied in chemoselective (bio)conjugation or ligation reactions.     

Numerical investigation of the effective Skempton coefficient in fluid-saturated fractured rock

Characterization of hydro-mechanical processes in reservoir rocks is an essential issue for many geo investigations such as characterization of subsurface fluid flow or geothermal exploitation. For geothermal applications, the role of fractures as storage and transport components of a hydraulic system are highly important. In the present contribution we focus on investigating the effective Skempton coefficient of a damaged porous rock analyzing a modified Cryer problem, which provides a simple model of a porous rock containing a storage and transport pat. The effective Skempton coefficient is defined as the ratio of the increase in mean pore pressure induced by change in confining pressure for undrained boundary conditions. Using approaches from computational homogenization, we evaluate the confining pressure as the negative volume average of the total mean stress. Similarly, we compute the effective fluid pressure in terms of the volume-averaged fluid pressure in the rocks. We compare the numerical results to those from typical experiments and highlight the problems with the latter. The proposed concept for determination of an effective Skempton coefficient based on numerically evaluated volume averages helps to generate a better understanding of the process-inherent constituents. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)