Asymptotics for the sum of powers of distances between power residues modulo a prime

For fixed q ∈ (0, 4), prime p → ∞, and \(d \leqslant \exp \left( {c\sqrt {\ln p} } \right)\), where c > 0 is a constant, we obtain the asymptotics for the sum of qth powers of distances between neighboring residues of degree d modulo p.     

New estimates of double trigonometric sums with exponential functions

We establish a new bound for the exponential sum

Synthesis of azidourethane block copolymers

Methods of structuring thermoreversible urethane block copolymers on the basis 3,3-bis-(azidomethyl)oxetane (BAMO) and 3-(azidomethyl)-3-methyloxetane (AMMO) were developed for the first time. Type (AB)_n copolymers of BAMO and AMMO have an amorphous crystalline structure but differ from the type B(AB)_n copolymers in that they contain less crystal phase and have a higher glass transition temperature and better physicomechanical properties.     

Synthesis and Reactions of Trifluoromethyl-Substituted 1,3,5-Triazines

A variety of di- and trifluoromethyl-s-triazines are prepared following straightforward synthetic protocols from simple, commercially available starting materials. Trichloromethyl-substituted triazine electrophiles are obtained in good yield and react with amine nucleophiles to afford aminotriazine products in good to excellent yield. The nucleophilic aromatic substitution reaction is broad in scope and proceeds smoothly with both aromatic and aliphatic (primary, secondary, and branched) amines in the presence of non-participating functional groups including alcohols, carboxylic acids, indoles, and common amine protecting groups. Furthermore, most reactions require only a catalytic amount of 4-DMAP with no stoichiometric base and are complete within two hours at ambient temperature.     

On a Series with Simple Zeros of ζ(s)

Mathematical Notes -     

Liquid chromatography time-of-flight mass spectrometry following sorptive microextraction for the determination of fungicide residues in wine

This work evaluates the suitability of sorptive microextraction, using disposable silicone sorbents, and liquid chromatography time-of-flight mass spectrometry (LC-TOF-MS) for the determination of 15 fungicides in wine. Under optimized conditions, wine samples (10 mL) were diluted with the same volume of ultrapure water and poured in a glass vessel containing a magnetic stirrer and 4 g of sodium chloride. Extractions were performed at room temperature for 4 h, using an inexpensive silicone disk (12 μL volume) exposed directly to the sample. Thereafter, analytes were recovered with 0.2 mL of acetonitrile. The electrospray ionization (ESI) source was operated in the fast polarity switching mode obtaining, in the same injection, selective LC-MS records (extracted with a mass window of 10 ppm) of compounds rendering [M + H]⁺ and [M-H]⁻ ions. The method provided limits of quantification (LOQs) between 0.1 and 2.2 ng mL⁻¹, linear response ranges up to 500 ng mL⁻¹, relative recoveries from 75% to 117% and an inter-day variability below 15% for all analytes in red and white wine samples. The feasibility of in situ sample enrichment followed by delayed desorption and analysis is also assessed.     

Luminscent graphene quantum dots for organic photovoltaic devices

Recent research in organic photovoltaic (OPV) is largely focused on developing low cost OPV materials such as graphene. However, graphene sheets (GSs) blended conjugated polymers are known to show inferior OPV characteristics as compared to fullerene adduct blended with conjugated polymer. Here, we demonstrate that graphene quantum dots blended with regioregular poly(3-hexylthiophene-2,5-diyl) or poly(2-methoxy-5-(2-ethylhexyloxy)-1,4phenylenevinylene) polymer results in a significant improvement in the OPV characteristics as compared to GSs blended conjugated polymers. This work has implications for inexpensive and efficient solar cells as well as organic light emitting diodes.     

Solid-phase extraction followed by liquid chromatography quadrupole time-of-flight tandem mass spectrometry for the selective determination of fungicides in wine samples

In this work, a reliable and selective procedure for the determination of thirteen fungicides in red and white wine samples is proposed. Solid-phase extraction (SPE) and liquid chromatography (LC) tandem mass spectrometry (MS/MS), based on a hybrid quadrupole time-of-flight (QTOF) system, were used as sample preparation and determination techniques, respectively. Extraction and purification of target analytes was carried out simultaneously by using a reversed-phase Oasis HLB (200mg) SPE cartridge combined with acetonitrile as elution solvent. Fungicides were determined operating the electrospray source in the positive ionization mode, with MS/MS conditions adjusted to obtain at least two intense product ions per compound, or registering two transitions per species when a single product was noticed. High selective MS/MS chromatograms were extracted using a mass window of 20 ppms for each product ion. Considering external calibration as quantification technique, the overall recoveries (accuracy) of the procedure ranged between 81% and 114% for red and white wine samples (10-20 mL), spiked at different concentrations between 5 and 100 ng mL(-1). Relative standard deviations of the above data stayed below 12% and the limits of quantification (LOQs) of the method, calculated for 10 mL of wine, varied between 0.1 ng mL(-1) for cyprodinil (CYP) and 0.7 ng mL(-1) for myclobutanil (MYC). The optimized method was applied to seventeen commercial wines produced in Spain and obtained from local supermarkets. Nine fungicides were determined, at levels above the LOQs of the method, in the above samples. The maximum concentrations and the highest occurrence frequencies corresponded to metalaxyl (MET) and iprovalicarb (IPR).     

Concentration of Points on Two and Three Dimensional Modular Hyperbolas and Applications

Let p be a large prime number, K, L, M, λ be integers with 1 ≤ M ≤ p and gcd(λ, p) = 1. The aim of our paper is to obtain sharp upper bound estimates for the number I ₂(M; K, L) of solutions of the congruence