Exceptional set of a representation with fractional powers

We prove that for any given c, 1 < c < 17/11, almost all natural numbers are representable in the form [x ^c] + [p ^c], where x is a natural number and p is a prime.     

Optimization of a microwave-assisted extraction method for the analysis of polychlorinated biphenyls in ash samples

An alternative method for the extraction of polychlorinated biphenyls (PCBs) in ash samples, which is less time and solvent consuming than Soxhlet extraction, is presented. A study was carried out to evaluate the possibilities of microwave-assisted extraction (MAE) to determine exactly which parameters affect the efficiency of the process, since direct extrapolation of extraction conditions for PCBs in other solid matrices, failed when applied to coplanar congeners in ash samples. Influence of the organic solvent on the yield of the extraction was first evaluated using two ash samples with different percentages of carbon. Once the extraction solvent was fixed, the effects of solvent volume, extraction temperature and extraction time were investigated using an experimental design. It was found that the volume of organic solvent played a more important role in the extraction efficiency than the other factors. In the optimal conditions microwave extractions were performed at 110 degrees C. for 10 min and using 30 ml of toluene. Recoveries higher than 80% were obtained for all the highly chlorinated congeners. including coplanar species, in a spiked ash sample containing a relatively high concentration of carbon. The proposed method was also applied to the determination of PCBs in a reference material of urban dust. Recoveries were similar to those obtained for spiked ash samples.     

Intramolecular [4 + 2] cycloaddition of nitroalkenes for construction of vicinal quaternary stereocenters

[chemical reaction: see text]. Nitroalkene (E)-1 has been synthesized to test the feasibility of an intramolecular [4 + 2] cycloaddition in a planned synthesis of daphnilactone B. This nitro olefin contains two unique structural features, a nitromethylene lactone and a pendant diene, that combine under the action of SnCl4 in a highly selective fashion to afford nitronates 2a and 2b. These products represent the correct relationship for the vicinal quaternary stereogenic centers in the core of daphnilactone B.     

Synthesis and Therapeutic Use of Dimephosphone

Abstract

The synthesis of dimephosphone (1) was carried out on Pudovik's reaction.     

On congruences with products of variables from short intervals and applications

We obtain upper bounds on the number of solutions to congruences of the type (x ₁ + s)... (x _ν + s) ≡ (y ₁ + s)... (x _ν + s) ? 0 (mod p) modulo a prime p with variables from some short intervals. We give some applications of our results and in particular improve several recent estimates of J. Cilleruelo and M.Z. Garaev on exponential congruences and on cardinalities of products of short intervals, some double character sum estimates of J. Friedlander and H. Iwaniec and some results of M.-C. Chang and A.A. Karatsuba on character sums twisted with the divisor function.     

Determination of fungicides in wine by mixed-mode solid phase extraction and liquid chromatography coupled to tandem mass spectrometry

A novel procedure for the determination of nine selected fungicides (metalaxyl-M, azoxystrobin, myclobutanil, flusilazole, penconazole, tebuconazole, propiconazole, diniconazole and difenoconazole) in wine samples is presented. Sample enrichment and purification is simultaneously performed using mixed-mode, anion exchange and reversed-phase, OASIS MAX solid-phase extraction (SPE) cartridges. Analytes were determined by liquid chromatography coupled to tandem mass spectrometry using atmospheric pressure electrospray ionization (LC-ESI-MS/MS). Parameters affecting the chromatographic determination and the extraction-purification processes were thoroughly investigated. Under optimized conditions, 10 mL of wine were firstly diluted 1:1 with ultrapure water and then passed through the mixed-mode SPE cartridge at a flow of ca. 5 mLmin(-1). After a washing step with 5 mL of an aqueous NH(4)OH solution (5%, w:v), analytes were recovered with just 1 mL of methanol and injected in the LC-MS/MS system without any additional purification. The selective extraction process avoided significant changes in the ionization efficiency for red and white wine extracts in comparison with pure standards in methanol. Performance of the method was good in terms of precision (RSDs<11%) and accuracy (absolute recoveries>72%, determined against pure standards in methanol) reporting method LOQs in the range of 0.01-0.79 ngmL(-1) for target compounds, which are far below the EU maxima residue levels (MRLs) for fungicides in vinification grapes and wine. Several commercial wines from different geographic areas in Spain were analyzed. In most samples, metalaxyl-M and azoxystrobin were found at concentrations up to several ngmL(-1).     

Multiplicative congruences with variables from short intervals

Recently, several bounds have been obtained on the number of solutions of congruences of the type $$({x_1} + s) \cdots ({x_v} + s) \equiv ({y_1} + s) \cdots ({y_v} + s)\not \equiv 0{\text{ (mod }}p{\text{),}}$$ where p is prime and variables take values in some short interval. Here, for almost all p and all s and also for a fixed p and almost all s, we derive stronger bounds. We also use similar ideas to show that for almost all p, one can always find an element of a large order in any rather short interval.     

Character Sums in Short Intervals and the Multiplication Table Modulo a Large Prime

We obtain nontrivial estimates of character sums over short intervals for almost all moduli. These bounds and the method of Karatsuba for solving multiplicative ternary problems are used to prove that for π(X)(1 + o(1)) primes p,p ≤ X, there are p(1 + o(1)) residue classes modulo p of the form xy (mod p), where 1 ≤ x, y ≤ p^?(log p)^1,087. We also prove that for any prime p there are p(1 + o(1)) residue classes modulo p of the form xy^* (mod p), where 1 ≤ x, y ≤ p^?(log p)^1+o(1) and y^* is defined by yy^* ≡ 1 (mod p).     

Single component and binary diffusion of n-heptane and toluene in SBA-15 materials

In this work, the diffusion properties of single component n-heptane and toluene as well as their binary mixtures in two SBA-15 samples with different structural characteristics were studied by the standard Zero Length Column (ZLC) technique under three different concentration levels. A theoretical ZLC desorption model considering the Generalized Maxwell-Stefan (GMS) formulation was developed. Using the independently measured single component equilibrium and kinetic parameters, the model was able to reasonably predict experimental binary ZLC desorption curve for countercurrent diffusion of toluene in the presence of n-heptane. However, there was a significant deviation between model prediction results and experimental data for countercurrent desorption of n-heptane in the presence of toluene. The diffusion of n-heptane is reduced by the presence of toluene, regardless of the relative content of micropores in the intrawall pores, while that of toluene is virtually unaffected by the counter-diffusion of n-heptane. The observed phenomena cannot be addressed by the simple model considering the cross term diffusion effect. The structural property of material and the molecular characteristics of probe molecules were used to account for the difference in the behavior between n-heptane and toluene.