Sturm's Method in Counting Roots of Random Polynomial Equations

The problem of finding the probability distribution of the number of zeros in some real interval of a random polynomial whose coefficients have a given continuous joint density function is considered. An algorithm which enables one to express this probability as a multiple integral is presented. Formulas for the number of zeros of random quadratic polynomials and random polynomials of higher order, some coefficients of which are non-random and equal to zero, are derived via use of the algorithm. Finally, the applicability of these formulas in numerical calculations is illustrated.     

The double centralizer theorem for division algebras

AssumeV is a finite-dimensional vector space over a division ringD having centerF. It is shown that ifT∈ End _D (V) is algebraic overF then the double centralizerC(C(T)) ofT is the setF[T] of all polynomials inT with coefficients fromF. Consequently, eachn×n matrix ring overD is an algebraicF-algebra if and only ifC(C(T))=F[T] for allT and all finite-dimensionalV.     

Role of pseudoephedrine as chiral auxiliary in the "acetate-type" aldol reaction with chiral aldehydes; asymmetric synthesis of highly functionalized chiral building blocks

We have studied in depth the aldol reaction between acetamide enolates and chiral α-heterosubstituted aldehydes using pseudoephedrine as chiral auxiliary under double stereodifferentiation conditions, showing that high diastereoselectivities can only be achieved under the matched combination of reagents and provided that the α-heteroatom-containing substituent of the chiral aldehyde is conveniently protected. Moreover, the obtained highly functionalized aldols have been employed as very useful starting materials for the stereocontrolled preparation of other interesting compounds and chiral building blocks such as pyrrolidines, indolizidines, and densely functionalized β-hydroxy and β-amino ketones using simple and high-yielding methodologies.     

Accurate mass screening of pharmaceuticals and fungicides in water by U-HPLC–Exactive Orbitrap MS

The use of pharmaceuticals in livestock production is a potential source of surface water, groundwater and soil contamination. Possible impacts of antibiotics on the environment include toxicity and the emergence of antibiotic resistance. Monitoring programs are required to record the presence of these substances in the environment. A rapid, versatile and selective multi-method was developed and validated for screening 43 pharmaceutical and fungicides compounds, in surface and groundwater, in one single full-scan MS method, using benchtop U-HPLC-Exactive Orbitrap MS at 50,000 (FWHM) resolution. Detection was based on calculated exact masses and on retention time. Sample volume, pH conditions and solid-phase extraction (SPE) sample clean-up conditions were optimized. In the final method, 74 % of the compounds had recoveries higher than 80 %, 15 % of the compounds had recoveries between 60 % and 80 %, and 7 % of the compounds had recoveries between 40 % and 50 %. One of the compounds (itraconazole) had a recovery lower than 10 % and nystatin was not detected. The level of detection was 10 ng L(-1) for 61 % of the compounds, 50 ng L(-1) for 32 % and 100 ng L(-1) for 5%. In-house validation, based on EU guidelines, proves that the detection capability CCβ is lower than 10 ng L(-1) (for β error 5 %) for 37 % of the compounds, lower than 50 ng L(-1) for 35 % of the compounds and lower than 100 ng L(-1) for 14 % of compounds. This study demonstrates that the ultra-high resolution and reliable mass accuracy of Exactive Orbitrap MS permits the detection of pharmaceutical residues in a concentration range of 10-100 ng L(-1), applying a post target screening approach, in the multi-method conditions.     

Acyclic amino acid-catalyzed direct asymmetric aldol reactions: alanine, the simplest stereoselective organocatalyst

The linear amino acid-catalyzed direct asymmetric intermolecular aldol reaction is presented; simple amino acids such as alanine, valine, isoleucine, aspartate, alanine tetrazole and serine catalyzed the direct catalytic asymmetric intermolecular aldol reactions between unmodified ketones and aldehydes with excellent stereocontrol and furnished the corresponding aldol products in up to 98% yield and with up to > 99% ee.     

Electronic Filtering of Interferometric Homodyne Crosstalk in WDM Systems with Absolute Frequency Reference

Electronic high pass filtering of interferometric crosstalk noise is investigated theoretically and experimentally in systems with absolute frequency reference employing external modulation and DC balanced coding. 4 dB improvement in the tolerance to crosstalk is demonstrated.