Pair correlation of torsion points on elliptic curves

We prove the existence of the pair correlation measure associated to torsion points on the real locus E(R) of an elliptic curve E and provide an explicit formula for the limiting pair correlation function.     

Nonvanishing of Fourier coefficients of modular forms

Let be a cusp form with integer weight that is not a linear combination of forms with complex multiplication. For , let

Improving on work of Balog, Ono, and Serre we show that for almost all , where is any good function (e.g. such as ) monotonically tending to infinity with . Using a result of Fouvry and Iwaniec, if is a weight 2 cusp form for an elliptic curve without complex multiplication, then we show for all that . We also obtain conditional results depending on the Generalized Riemann Hypothesis and the Lang-Trotter Conjecture.

     

Simultaneous Preparation of Multiple Polymer Brushes under Ambient Conditions using Microliter Volumes

The fabrication of well‐defined, multifunctional polymer brushes under ambient conditions is described. This facile method uses light‐mediated, metal‐free atom‐transfer radical polymerization (ATRP) to grow polymer brushes with only microliter volumes required. Key to the success of this strategy is the dual action of N‐phenylphenothiazine (PTH) as both an oxygen scavenger and polymerization catalyst. Use of simple glass cover slips results in a high degree of spatial and temporal control and allows for multiple polymer brushes to be grown simultaneously. The preparation of arbitrary 3D patterns and functional/emissive polymer brushes demonstrates the practicality and versatility of this novel strategy.     

Highly selective oxidation of glucose to formic acid over synthesized hydrotalcite-like catalysts under base free mild conditions

Sustainable and renewable production of platform chemicals and fuels has been gradually rising. Formic acid is one of the important chemicals for leather, cosmetic and pharmaceutical industries as well as hydrogen source. In this study, selective oxidation of biomass-derived glucose to formic acid was investigated under base free medium at 70 °C over synthesized hydrotalcite-like catalysts using hydrogen peroxide as oxidant. Effect of Mg/Al ratio (6/1, 3/1, 1/1, 1/3 and 1/6) and heat treatment (drying and calcination) on catalyst structure and product distributions; effect of calcination temperature (450, 650 and 900 °C), solvent composition (ethanol/water) and reaction temperature (30, 50 and 70 °C) on catalytic activity and product selectivity were investigated. Reducing the Mg/Al ratio enhanced the density of metal-OH bonds, surface area and uniformity of pores up to some extent. The highest glucose conversion and formic acid selectivity were achieved over Mg–Al (1:3) catalyst as 38.7 and 99.0%, respectively. The calcined catalysts (at 450 °C) exhibited 7 times higher selectivities and 4 times higher activities than the dried ones. However, higher calcination temperatures did not show remarkable increments in activities and yields. Easily prepared, cheap Mg–Al (1:3) catalyst provided promising results even at low temperature with hydrogen peroxide at atmospheric medium in a low boiling point solvent (ethanol).

Graphical abstract

     

Boron-incorporated Sulfonated polysulfone/polyphosphoric acid electrolytes for supercapacitor application

In the present work, boron-doped multicomponent gel polymer electrolytes composed of host polymer, sulfonated polysulfone (SPSU) and the additives; ionic liquid, 1-ethyl-3-methyl-imidazolium tetrafluoroborate (IL), H₃BO₃, polyphosphoric acid (PPA) were prepared. Fourier transform infrared spectroscopy (FT-IR), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA) techniques were used to characterize the sulfonated polysulfone-based electrolytes. Ion conductivity of these gel electrolytes were studied by dielectric impedance analyzer within the temperature from ?20 to 100°C. The ionic conductivity of the SPSU-5IL-1PPA and SPSU-5IL-1H₃BO₃-1PPA were measured as 4.8 × 10^?3 and 9 × 10^?4 S cm^?1, respectively. Supercapacitor having activated carbon-based composite electrode and electrolyte was constructed with the configuration: Al/C/electrolyte/C/Al. The electrochemical properties and ion transfer characteristics of the supercapacitor were investigated by the cyclic voltammetry (CV). Galvanostatic charge—discharge experiments exhibited good electrochemical reversibility and produced a specific capacitance value of 120 F g^?1 at 1 A g^?1. The symmetric supercapacitor system was retained almost 85% of its initial activity after 1000 cycle.     

An unstructured grid Reynolds stress model for separated turbulent flow simulations

Most of the turbulence models in the literature contain simplified assumptions which make them computationally inexpensive but of limited accuracy for the solution of separated turbulent flows. Dramatic improvements in computer processing speed and parallel processing make it possible to use more complete models, such as Reynolds Stress Models, for separated turbulent flow simulations, which is the focus of this work. The Reynolds Stress Model consists of coupling the Reynolds transport equations with the Favre–Reynolds averaged Navier–Stokes equations, which results in a system of 12 coupled non-linear partial differential equations. The solutions are obtained by running the PUMA_RSM computational fluid dynamics code on unstructured meshes. The equations are solved all the way to the wall without using any wall functions. Results for high Reynolds number flow around a 6:1 prolate spheroid and a Bell 214ST fuselage are presented. For the prolate spheroid basic flow features such as cross-flow separation are simulated. Predictions of circumferential locations of cross flow separation points are in good agreement with the experiment. A grid refinement study is performed to improve the computations. The fine mesh solution predicted locations of primary and secondary separation points with errors of roughly 2° and 0°, respectively. Flow simulations around an isolated Bell 214ST helicopter fuselage were also performed. Predicted pressure and drag force correlate well with the wind tunnel data, with a less than 10% deviation from the experiment. Drag predictions also show relative speed of Reynolds Stress Model compared to Large Eddy Simulation to compute time averaged quantities. For numerical solutions parallel processing is applied with the MPI communication standard. The code used in this study is run on Beowulf clusters. The parallel performance of the code PUMA_RSM is analysed and presented.     

High-pressure X-ray diffraction study of tungsten diselenide

Synchrotron X-ray diffraction was used in conjunction with a diamond anvil cell to investigate the properties of a tungsten diselenide (WSe₂) sample to 35.8 GPa at room temperature. By fitting the pressure-volume data to the third-order Birch-Murnaghan equation of state, the bulk modulus, K_0T, of WSe₂ was determined to be 72±1 GPa with its pressure derivative, , being 4.1±0.1. It was also found that the c-direction of the hexagonal structure is significantly more compressible than the a-direction. No phase transformation was clearly observed in the pressure range of our measurements.     

Delooping level of Nakayama algebras

Archiv der Mathematik - We give another proof of the recent result of Ringel, which asserts equality between the finitistic dimension and delooping level of Nakayama algebras. The main tool is the...     

Green synthesis of silver nanoparticles by using eugenol and evaluation of antimicrobial potential

The importance of green synthesis was revealed with advantages such as: eliminating the use of expensive chemicals; consume less energy; and generate environmentally benign products. With this aim, silver nanoparticles (AgNPs) were synthesized by using isolated eugenol from clove extract. Its antimicrobial potential was determined on three different microorganisms. Clove was extracted and eugenol was isolated from this extract. Green synthesis was performed and an anti‐microbial study was performed. All extraction and isolation analyses were performed by high‐performance liquid chromatography (HPLC); identification and confirmation were achieved using liquid chromatography–mass spectrometry (LC–MS); and scanning electron microscopy was used for characterization. Both HPLC and LC–MS analyses showed that eugenol obtained purely synthesized AgNPs and 20‐25‐nm‐sized and homogeneous shaped particles seen in images. The antimicrobial effects of AgNPs at eight concentrations were determinated against Staphylococcus aureus, Escherichia coli and Candida albicans, and maximum inhibition zone diameters were found as 2.6 cm, 2.4 cm and 1.5 cm, respectively. The results of the antimicrobial study showed that eugenol as a biological material brought higher antimicrobial effect to AgNPs in comparison to the other materials found in the literature.