Formal proofs of operator identities by a single formal computation

A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be modelled by noncommutative polynomials and such a formal computation proves that the polynomial corresponding to the new identity lies in the ideal generated by the polynomials corresponding to the known identities. In order to prove an operator identity, however, just proving membership of the polynomial in the ideal is not enough, since the ring of noncommutative polynomials ignores domains and codomains. We show that it suffices to additionally verify compatibility of this polynomial and of the generators of the ideal with the labelled quiver that encodes which polynomials can be realized as linear operators. Then, for every consistent representation of such a quiver in a linear category, there exists a computation in the category that proves the corresponding instance of the identity. Moreover, by assigning the same label to several edges of the quiver, the algebraic framework developed allows to model different versions of an operator by the same indeterminate in the noncommutative polynomials.     

Application of microcrystalline cellulose as an efficient and cheap sorbent for the extraction of metoprolol from plasma and wastewater before HPLC–MS/MS determination

A dispersive solid-phase extraction method based on a new sorbent has been performed on plasma and wastewater samples to determine metoprolol by high-performance liquid chromatography–tandem mass spectrometry. In this study, the analyte was adsorbed from the samples onto microcrystalline cellulose as a green and efficient sorbent and then eluted for use in the determination step. In the mass spectrometer, the analyte was detected in the positive mode and selectivity of the analysis was increased by sequential mass analysis through multiple reaction monitoring. All of the effective parameters in the extraction of metoprolol from plasma and wastewater were optimized. Under optimal conditions the method was linear in the ranges of 1–1,000 and 0.1–1,000 ng/ml in plasma and wastewater samples, respectively. The detection limits of the method were 0.30 and 0.03 ng/ml in plasma and wastewater samples, respectively. The data showed that the method provides low detection limit, wide linear range, good precision and high extraction recovery. Finally several plasma and wastewater samples were successfully analyzed using the method. The use of a small amount of a green and inexpensive sorbent and a low volume of plasma without the need for further pretreatment steps are the main advantages of the method.     

Packing properties of cubic square-free monomial ideals

Journal of Algebraic Combinatorics - The symbolic powers, in general, are not equal to the ordinary powers. Therefore, one interesting question here is for what classes of ideals ordinary and...     

A sensitive and efficient method for trace analysis of some phenolic compounds using simultaneous derivatization and air‐assisted liquid–liquid microextraction from human urine and plasma samples followed by gas chromatography–nitrogen phosphorous detection

In present study, a simultaneous derivatization and air‐assisted liquid–liquid microextraction method combined with gas chromatography–nitrogen phosphorous detection has been developed for the determination of some phenolic compounds in biological samples. The analytes are derivatized and extracted simultaneously by a fast reaction with 1‐flouro‐2,4‐dinitrobenzene under mild conditions. Under optimal conditions low limits of detection in the range of 0.05–0.34 ng mL^?1 are achievable. The obtained extraction recoveries are between 84 and 97% and the relative standard deviations are less than 7.2% for intraday (n = 6) and interday (n = 4) precisions. The proposed method was demonstrated to be a simple and efficient method for the analysis of phenols in biological samples. Copyright © 2015 John Wiley & Sons, Ltd.     

Characteristics investigation on heat transfer growth of sonochemically synthesized ZnO-DW based nanofluids inside square heat exchanger

Journal of Thermal Analysis and Calorimetry - In recent decades, the growth of heat transfer using nanomaterials in the conventional base fluid has caught the attention of researchers...     

Hybrid (ND-Co3O4/EG) nanoliquid through a permeable cylinder under homogeneous-heterogeneous reactions and slip effects

Journal of Thermal Analysis and Calorimetry - Modeling and computations are performed to study the ND-Co3O4/EG hybrid nanoliquid mixed convective flow past a vertical porous cylinder. The flow...