Constructing nonresidues in finite fields and the extended Riemann hypothesis

We present a new deterministic algorithm for the problem of constructing th power nonresidues in finite fields , where is prime and is a prime divisor of . We prove under the assumption of the Extended Riemann Hypothesis (ERH), that for fixed and , our algorithm runs in polynomial time. Unlike other deterministic algorithms for this problem, this polynomial-time bound holds even if is exponentially large. More generally, assuming the ERH, in time we can construct a set of elements that generates the multiplicative group . An extended abstract of this paper appeared in Proc. 23rd Ann. ACM Symp. on Theory of Computing, 1991.

     

An efficient and robust integration scheme for the equations of motion of the multiconfiguration time-dependent Hartree (MCTDH) method

An efficient and robust integration scheme tailored to the equations of motion of the multiconfiguration time-dependent Hartree (MCTDH) method is presented. An error estimation allows the automatical adjustment of the step size and hence controls the integration error. The integration scheme decouples the MCTDH equations of motion into several disjoined subsystems, of which one determines the time evolution of the MCTDH-coefficients. While the conventional MCTDH equations are non-linear, the working equation for the MCTDH-coefficients becomes linear in the present integration scheme. To investigate the integrator’s performance it is applied to the photodissociation process of methyl iodide. The results of the novel integration scheme are in perfect agreement to those obtained by solving the MCTDH working equations conventionally. The computation time, however, is reduced by a factor of about ten when the new integration scheme is used to propagate large systems.     

Prediction of aqueous solubility of drugs and pesticides with COSMO-RS

The COSMO-RS method, originally developed for the prediction of liquid-liquid and liquid-vapor equilibrium constants based on quantum chemical calculations, has been extended to solid compounds by addition of a heuristic expression for the Gibbs free energy of fusion. By this addition, COSMO-RS is now capable of a priori prediction of aqueous solubilities of a wide range of typical neutral drug and pesticide compounds. Only three parameters in the heuristic expression have been fitted on a data set of 150 drug-like compounds. On these data an rms deviation of 0.66 log-units was achieved. Later, the model was tested on a set of 107 pesticides, which have been critically selected based on two experimental data sources and by a crosscheck with an independent HQSAR model. On this data set an rms of 0.61 log-units was achieved, without any adjustments to the structurally extremely diverse pesticides. This result verifies the ability of this extended COSMO-RS to predict aqueous solubilities of drugs and pesticides of almost arbitrary structural classes. The new method is COSMO-RSol.     

Chiral hydroperoxides as oxygen source in the catalytic stereoselective epoxidation of allylic alcohols by sandwich-type polyoxometalates: control of enantioselectivity through a metal-coordinated template

The epoxidation of allylic alcohols is shown to be efficiently and selectively catalyzed by the oxidatively resistant sandwich-type polyoxometalates, POMs, namely [WZnM(2)(ZnW(9)O(34))(2)](q)(-) [M = OV(IV), Mn(II), Ru(III), Fe(III), Pd(II), Pt(II), Zn(II); q = 10-12], with organic hydroperoxides as oxygen source. Conspicuous is the fact that the nature of the transition metal M in the central ring of polyoxometalate affects significantly the reactivity, chemoselectivity, regioselectivity, and stereoselectivity of the allylic alcohol epoxidation. For the first time, it is demonstrated that the oxovanadium(IV)-substituted POM, namely [ZnW(VO)(2)(ZnW(9)O(34))(2)](12-), is a highly chemoselective, regioselective, and also stereoselective catalyst for the clean epoxidation of allylic alcohols. A high enantioselectivity (er values up to 95:5) has been achieved with [ZnW(VO)(2)(ZnW(9)O(34))(2)](12)(-) and the sterically demanding TADOOL-derived hydroperoxide TADOOH as regenerative chiral oxygen source. Thus, a POM-catalyzed asymmetric epoxidation of excellent catalytic efficiency (up to 42 000 TON) has been made available for the development of sustainable oxidation processes. The high reactivity and selectivity of this unprecedented oxygen-transfer process are mechanistically rationalized in terms of a peroxy-type vanadium(V) template.     

Die Kristallstrukturen der Diquecksilber(I)-Salze von Aminobenzolsulfonsäuren

Crystal Structures of Dimercuri (I) Salts of p- and m-Sulfanilic Acids The crystal structures of the compounds Hg₂(p-H₂N–C₆H₄–SO₃)₂ ( 1 ), Hg₂(m-H₂N–C₆H₄–SO₃)₂ ( 2 ), and Hg₂(m-H₂N–C₆H₄–SO₃)₂ · 2H₂O ( 3 ) contain leaf-structures ( 1 and 3 ) or chain-structures ( 2 ), with nearly linear groups N–Hg–Hg–N, Hg–O-contacts and hydrogen-bridging bonds. The smaller density of 3 compared with 1 –caused by the steric hindrance through the ligand – declared the incorporation of water for raising the stabilising interaction in the crystals. The compound 3 is the kinetic controlled, the compound 2 the thermodynamic controlled product.     

Molecular chaperones--cellular machines for protein folding

Proteins are linear polymers synthesized by ribosomes from activated amino acids. The product of this biosynthetic process is a polypeptide chain, which has to adopt the unique three-dimensional structure required for its function in the cell. In 1972, Christian Anfinsen was awarded the Nobel Prize for Chemistry for showing that this folding process is autonomous in that it does not require any additional factors or input of energy. Based on in vitro experiments with purified proteins, it was suggested that the correct three-dimensional structure can form spontaneously in vivo once the newly synthesized protein leaves the ribosome. Furthermore, proteins were assumed to maintain their native conformation until they were degraded by specific enzymes. In the last decade this view of cellular protein folding has changed considerably. It has become clear that a complicated and sophisticated machinery of proteins exists which assists protein folding and allows the functional state of proteins to be maintained under conditions in which they would normally unfold and aggregate. These proteins are collectively called molecular chaperones, because, like their human counterparts, they prevent unwanted interactions between their immature clients. In this review, we discuss the principal features of this peculiar class of proteins, their structure-function relationships, and the underlying molecular mechanisms.     

Flow-through microdispenser for interfacing micro-HPLC to Raman and mid-IR spectroscopic detection

A flow-through microdispenser has been coupled to a micro HPLC separation system and used as a solvent elimination interface for Fourier transform infrared (FTIR) and Raman spectroscopic detection of the separated compounds. Using the microdispenser picoliter sized droplets can be generated and deposited on an appropriate target placed on a computerized x, y-stage. Evaporation of volatile solvent and buffer is rapid and allows analysis of the obtained dry deposits by various techniques. Due to the destruction free character of Raman and FTIR spectroscopy they can be applied sequentially to interrogate the same deposit. In the reported application five phenolic acids typically present in wine have been separated on a C-18 column technique using a mixture of water, methanol and acetic acid as mobile phase. For spectrum acquisition infrared and Raman microscopes have been used. The spectra recorded from the dried deposits of the separated compounds agreed well with the reference spectra of corresponding components.