A Refined Version of the Lang-Trotter Conjecture

Let E be an elliptic curve defined over the rational numbersand r a fixed integer. Using a probabilistic model consistentwith the Chebotarev density theorem for the division fieldsof E and the Sato–Tate distribution, Lang and Trotterconjectured an asymptotic formula for the number of primes upto x which have Frobenius trace equal to r, where r is a fixedinteger. However, as shown in this note, this asymptotic estimatecannot hold for all r in the interval with a uniform bound for the error term, becausean estimate of this kind would contradict the Chebotarev densitytheorem as well as the Sato–Tate conjecture. The purposeof this note is to refine the Lang–Trotter conjecture,by taking into account the "semicircular law," to an asymptoticformula that conjecturally holds for arbitrary integers r inthe interval , with auniform error term. We demonstrate consistency of our refinementwith the Chebotarev density theorem for a fixed division field,and with the Sato–Tate conjecture. We also present numericalevidence for the refined conjecture.     

A family of ferro- and antiferromagnetically coupled decametallic chromium(III) wheels

The synthesis and crystal structures of a family of decametallic Cr(III) "molecular wheels" are reported, namely [Cr10(OR)20(O2CR')10] [R' = Me, R = Me (1), Et (2); R' = Et, R = Me (3), Et (4); R' = CMe3, R = Me (5), Et (6)]. Magnetic studies on 1-6 reveal a remarkable dependence of the magnetic behaviour on the nature of R. In each pair of complexes with a common carboxylate (R') the nearest neighbour CrCr magnetic exchange coupling is more antiferromagnetic for the ethoxide-bridged (R = Et) cluster than for the methoxide analogue. In complexes 2, 4 and 6 the overall coupling is weakly antiferromagnetic resulting in diamagnetic (S = 0) ground states for the cluster, whilst in 1 and 5 it is weakly ferromagnetic thus resulting in very high-spin ground states. This ground state has been probed directly in the perdeuterated version of 1 ([D]1) by inelastic neutron scattering experiments, and these support the S = 15 ground state expected for ferromagnetic coupling of ten Cr(III) ions, and they also indicate that a single J-value model is inadequate. The ground state of 5 is large but not well defined. The trends in J on changing R are further supported by density functional calculations on 1-6, which are in excellent agreement with experiment. The very large changes in the nature of the ground state between 1 and 2, and 5 and 6 are the result of relatively small changes in J that happen to cross J = 0, hence changing the sign of J.     

Isolation and structure elucidation of two new cytotoxic metabolites from red yeast rice

In this study, 10 already described secondary metabolites and 2 unknown metabolites were identified in an extract of Monascus purpureus by high-performance liquid chromatography-diode array detection. The unknown metabolites were isolated and their chemical structures were elucidated. The new metabolites possess the molecular formulas C(21)H(27)NO(4) and C(23)H(31)NO(4). They were named monascopyridines E and F due to their pyridine backbone. The cytotoxicity of the new compounds was studied using immortalised human kidney epithelial cells displaying IC(50) values in the micromolar range.     

Using the Transfer Function of an Isoperibolic Reaction Calorimeter for Thermo-kinetic Analysis

It is an aim of the present work to determine the chemical heat flow rate of a reaction without explicitly solving the heat balance equations. Therefore, it is necessary to calculate the heat flow rate directly from the temperature course of an experimentally determined reaction. For this transformation the transfer function of the calorimeter is needed 1 . An isoperibol reaction calorimeter was used for the experiments. With different calibrations and gained transfer functions, it is shown that the chemical heat flow rate can be determined from the temperature course of a reaction. The evaluation is fast and easy to use, which improves automation and prevents possible input errors.     

Online-Analysis on Acoustically Levitated Droplets

Summary: Aqueous solutions of acrylic acid were levitated in a 40 kHz acoustic levitator. The monomer amount in the levitated droplets was monitored by Raman spectroscopy relating to an internal standard. Thus evaporation of the monomer as well as polymerization reactions initiated by a redox system were investigated by Raman spectroscopy and resultant data were compared to HPLC data. Decreases in monomer amount due to evaporation can be clearly distinguished from polymerization reactions. Additionally, temperature measurement within the droplet throughout a polymerization reaction shows the typical temperature course originating from the heat of polymerization.     

Temperature and pH Dependency of Copolymerization Parameters of Acrylic Acid and 2-Hydroxypropyl Acrylate

Summary: Since copolymerization parameters of acrylic acid (AA) and 2-hydroxypropyl acrylate (HPA) in aqueous solutions are scarcely investigated a new method and different experimental setups were developed to run copolymerization experiments at different temperatures and pH values. The experiments were done with UV- or azo- initiation and analyzed by residual monomer analytics with HPLC and GPC methods. Based on the data obtained the conversion and copolymerization parameters were calculated with different mathematical models.     

Process Intensification of Emulsion Polymerization in the Continuous Taylor Reactor

Summary: Process intensification is investigated by the emulsion polymerization of styrene in the continuous Taylor reactor. The result is an increase in space time yield up to a factor 200 in comparison to a semi-batch polymerization process. This is obtained by a fast emulsion polymerization with a mean residence time, which is reduced to 60 seconds. The article presented the results of the process and the economical aspects of the Taylor reactor plant.     

Isobar configurations in the two nucleon system with separable potentials

A set of separable potentials forNN, NΔ andΔΔ configuration transition potentials was fitted toNN phase shifts, the deuteron binding energy and the quadrupole moment. Our results agree quite well with more realistic calculations and will be especially useful for numerical investigations of Faddeev like relativistic few body problems.