Shintani lifts and fractional derivatives for harmonic weak Maass forms

In this paper, we construct Shintani lifts from integral weight weakly holomorphic modular forms to half-integral weight weakly holomorphic modular forms. Although defined by different methods, these coincide with the classical Shintani lifts when restricted to the space of cusp forms. As a side effect, this gives the coefficients of the classical Shintani lifts as new cycle integrals. This yields new formulas for the L-values of Hecke eigenforms. When restricted to the space of weakly holomorphic modular forms orthogonal to cusp forms, the Shintani lifts introduce a definition of weakly holomorphic Hecke eigenforms. Along the way, auxiliary lifts are constructed from the space of harmonic weak Maass forms which yield a “fractional derivative” from the space of half-integral weight harmonic weak Maass forms to half-integral weight weakly holomorphic modular forms. This fractional derivative complements the usual ξ-operator introduced by Bruinier and Funke.     

Simulation of oscillatory flow in an aortic bifurcation using FVM and FEM: A comparative study of implementation strategies

Cardiovascular diseases are one of the major causes of long‐term morbidity and mortality in human beings. The nearly epidemic increase in prevalence of such diseases poses a serious threat to public health and calls for efficient methods of diagnosis and treatment. Non‐invasive diagnostic procedures such as MRI are often used in this context; however, these are limited in terms of spatial and temporal resolution and do not provide information on time‐dependent pressures and wall shear stresses—key quantities considered to be partially responsible for the formation and development of related pathologies. The present study is concerned with the numerical simulation of oscillatory flow through the abdominal aortic bifurcation. Computational fluid dynamics simulation of oscillatory flow in a branched geometry at high Reynolds numbers poses considerable challenges. The present study reports a detailed comparison of simulations performed with a finite volume and a finite element method, two approaches with significant differences in their discretization strategy, treatment of boundary conditions and other numerical aspects. Both solvers were parallelized, using loop parallelization of the BiCGStab linear solver for the finite volume and domain decomposition based on the Schur complement method for the finite element technique. The experience gained with these two approaches for the solution of flow in a bifurcation forms the focus of this study. Although similar results were obtained for both methods, the computation time required for convergence was found to be significantly smaller for the finite element approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Introducing oblique norms into multiple criteria programming

We propose to use block norms to generate nondominated solutions of multiple criteria programs and introduce the new concept of the oblique norm that is specially tailored to handle general problems. We prove the equivalence of finding the properly nondominated solutions of a multiple criteria program and solving its scalarization by means of oblique norms.     

Learning with classroom videos: conception and first results of an online teacher-training program

Within the framework of a yearlong teacher education program we examined the conditions and effectiveness of learning with classroom videos. In online phases and face-to-face sessions (blended learning), 20 teachers from two different countries. (Germany and Switzerland) analyzed videos of their own mathlessons and math-lessons of other teachers. Using different instruments, the training program was evaluated from a scientific perspective. The evaluation aimed to obtain information about processes within the training, about the acceptance of the training by the teachers and the patterns of perception of teaching processes of the teachers.     

Lewis Acid Promoted Ruthenium(II)‐Catalyzed Etherifications by Selective Hydrogenation of Carboxylic Acids/Esters

Ethers are of fundamental importance in organic chemistry and they are an integral part of valuable flavors, fragrances, and numerous bioactive compounds. In general, the reduction of esters constitutes the most straightforward preparation of ethers. Unfortunately, this transformation requires large amounts of metal hydrides. Presented herein is a bifunctional catalyst system, consisting of Ru/phosphine complex and aluminum triflate, which allows selective synthesis of ethers by hydrogenation of esters or carboxylic acids. Different lactones were reduced in good yields to the desired products. Even challenging aromatic and aliphatic esters were reduced to the desired products. Notably, the in situ formed catalyst can be reused several times without any significant loss of activity.     

Pinensins: The First Antifungal Lantibiotics

Lantibiotics (lanthionine‐containing antibiotics) from Gram‐positive bacteria typically exhibit activity against Gram‐positive bacteria. The activity and structure of pinensin A ( 1 ) and B ( 2 ), lantibiotics isolated from a native Gram‐negative producer Chitinophaga pinensis are described. Surprisingly, the pinensins were found to be highly active against many filamentous fungi and yeasts but show only weak antibacterial activity. To the best of our knowledge, lantibiotic fungicides have not been described before. An in‐depth bioinformatic analysis of the biosynthetic gene cluster established the ribosomal origin of these compounds and identified candidate genes encoding all of the enzymes required for post‐translational modification. Additional encoded functions enabled us to build up a hypothesis for the biosynthesis, export, sensing, and import of this intriguing lantibiotic.     

Nannocystin A: an Elongation Factor 1 Inhibitor from Myxobacteria with Differential Anti‐Cancer Properties

Cultivation of myxobacteria of the Nannocystis genus led to the isolation and structure elucidation of a class of novel cyclic lactone inhibitors of elongation factor 1. Whole genome sequence analysis and annotation enabled identification of the putative biosynthetic cluster and synthesis process. In biological assays the compounds displayed anti‐fungal and cytotoxic activity. Combined genetic and proteomic approaches identified the eukaryotic translation elongation factor 1α (EF‐1α) as the primary target for this compound class. Nannocystin A ( 1 ) displayed differential activity across various cancer cell lines and EEF1A1 expression levels appear to be the main differentiating factor. Biochemical and genetic evidence support an overlapping binding site of 1 with the anti‐cancer compound didemnin B on EF‐1α. This myxobacterial chemotype thus offers an interesting starting point for further investigations of the potential of therapeutics targeting elongation factor 1.