Sequences of consecutive smooth polynomials over a finite field

Given , we show that there are infinitely many sequences of consecutive -smooth polynomials over a finite field. The number of polynomials in each sequence is approximately .

     

Control consolidation with a threshold: an algorithm

Email: ariane.chapelle{at}ulb.ac.be Corresponding author. Email: aszafarz{at}ulb.ac.be Received on 14 October 2005. Accepted on 21 November 2006. Besides multiple voting rights, board representation and shareholders’monitoring, control tunnelling over firms can be reached throughpyramids, cross-ownership and other complex features. This phenomenonis frequent in Europe and Asia. However, the theoretical literaturehas not yet converged towards a well-defined and robust measurementof integrated control that takes into account the thresholdfor control as applied in practice. Based on graph theory, thispaper aims at filling this gap and proposes a new algorithmfor evaluating the control tunnelling exerted by the firms’ultimate shareholders. Then, the paper discusses the variousforms of control existing next to voting shares, like multiplevoting rights, board representation and active monitoring, beforesuggesting ways to include them into the modelling of control.     

Compared behavior of 5-deoxy-5-iodo-D-xylo- and L-arabinofuranosides in the reductive elimination reaction: a strong dependence on structural parameters and on the presence of Zn2+. A combined experimental and theoretical investigation

In the framework of a project devoted to the chemical transformation of monosaccharides from hemicelluloses into higher added value materials, the zinc-induced reductive elimination from 5-deoxy-5-iodo derivatives of D-xylose and L-arabinose was carried out. This study gave us the opportunity to observe surprising behaviors. In particular, the reaction strongly depends on structural parameters (protecting group pattern, configuration at C-4) and on the presence of Zn2+ ions. Collaterally with the experimental work, water solvent PCM HF-DFT (MPW1K/LANL2DZ) computations were performed to obtain insight into the mechanism for the reductive part of the reaction sequence. Without Zn2+, the zinc insertion reaction was found to proceed through a concerted but non-synchronous process involving a relatively large energy barrier (32 kcal mol-1) that directly leads to the presumed organozinc intermediate. In the presence of Zn2+, a three-step mechanism was identified in which the cation coordinates the anomeric and ring oxygen atoms and also the sugar iodine atom, causing an activating effect on the zinc insertion process by facilitating the homolytic rupture of the C-I bond. Complexes between zinc and Zn2+ bound carbohydrates were characterized with large stabilization energies, suggesting that Zn2+ might enhance the affinity of the organic compound with the zinc metal surface.     

Ex vivo fluorescence imaging of normal and malignant urothelial cells to enhance early diagnosis

Urinary cytology is a noninvasive and unconstraining technique for urothelial cancer diagnosis but lacks sensitivity for detecting low-grade lesions. In this study, the fluorescence properties of classical Papanicolaou-stained urothelial cytological slides from patients or from cell lines were monitored to investigate metabolic changes in normal and tumoral cells. Time- and spectrally-resolved fluorescence imaging was performed at the single cell level to assess the spectral and temporal properties as well as the spatial distribution of the fluorescence emitted by urothelial cells. The results reveal quite different fluorescence distributions between tumoral urothelial cells, characterized by a perimembrane fluorescence localization, and the normal cells which exhibit an intracellular fluorescence. This is not caused by differences in the fluorescence emission of the endogenous fluorophores NAD(P)H, flavoproteins or porphyrins but by various localization of the EA 50 Papanicolaou stain as revealed by both the spectral and time-resolved parameters. The present results demonstrate that the use of single-cell endofluorescence emission of Papanicolaou-stained urothelial cytological slides can allow an early ex vivo diagnosis of low-grade bladder cancers.     

New palladium-catalyzed cross-coupling routes to carbon functionalized metallatricarbadecaboranes

A general method for the synthesis of cage-carbon-functionalized cyclopentadienyl iron and cyclopentadienyl ruthenium tricarbadecaboranyl complexes has been developed that employs palladium-catalyzed Sonogashira, Heck, and Stille cross-coupling reactions directed at a cage-carbon haloaryl substituent. The key Li(+)[6-(p-XC(6)H(4))-nido-5,6,9-C(3)B(7)H(9)(-)] (X = I (1), Br (2), Cl (3)) haloaryl-tricarbadecaboranyl anionic ligands were synthesized in high yields via the reaction of the arachno-4,6-C(2)B(7)H(12)(-) anion with the corresponding p-halobenzonitriles (p-XC(6)H(4)-CN). The reactions of the salts 1-3 with (η(5)-C(5)H(5))Fe(CO)(2)I and (η(5)-C(5)H(5))Ru(CH(3)CN)(3)PF(6) were then used to produce the haloaryl complexes 1-(η(5)-C(5)H(5))-2-(p-XC(6)H(4))-closo-1,2,3,4-MC(3)B(7)H(9) (M = Fe, X = I (4), Br (5), Cl (6) and M = Ru, X = I (7), Br (8), Cl (9)). The sonication-promoted Sonogashira coupling reactions of 4 with terminal alkynes catalyzed by Pd(dppf)(2)Cl(2)/CuI yielded the alkynyl-linked derivatives 1-(η(5)-C(5)H(5))-2-p-RC(6)H(4)-closo-1,2,3,4-FeC(3)B(7)H(9) (R = (PhC≡C)- (10), (CH(3)CH(2)C(O)OCH(2)C≡C)- (11), ((η(5)-C(5)H(5))Fe(η(5)-C(5)H(4)C≡C))- (12)). Heck reactions of 4 with terminal alkenes catalyzed by Pd(OAc)(2) yielded the alkene-functionalized products 1-(η(5)-C(5)H(5))-2-p-RC(6)H(4)-closo-1,2,3,4-FeC(3)B(7)H(9) (R = (PhCH(2)CH═CH)- (13), (CH(3)(CH(2))(2)CH═CH)- (14)), while the Stille cross-coupling reactions of 4 with organotin compounds catalyzed by Pd(PPh(3))(2)Cl(2) afforded the complexes 1-(η(5)-C(5)H(5))-2-p-RC(6)H(4)-closo-1,2,3,4-FeC(3)B(7)H(9) (R = Ph- (15), (CH(2)═CH)- (16), (CH(2)═CHCH(2))- (17)). These reactions thus provide facile and systematic access to a wide variety of new types of functionalized metallatricarbadecaboranyl complexes with substituents needed for potential metallocene-like biomedical and/or optoelectronic applications.     

Sensitive quantification of clozapine and its main metabolites norclozapine and clozapine-<Emphasis Type="Italic">N</Emphasis>-oxide in serum and urine using LC-MS/MS after simple liquid–liquid extraction work-up

An LC-MS/MS method for the determination of the atypic neuroleptic clozapine and its two main metabolites norclozapine and clozapine-N-oxide has been developed and validated for serum and urine. After addition of d4-clozapine as deuterated internal standard a fast single-step liquid–liquid extraction under alkaline conditions and with ethyl acetate as organic solvent followed. The analytes were chromatographically separated on a Synergi Polar RP column using gradient elution with 1 mM ammonium formate and methanol. Data acquisition was performed on a QTrap 2000 tandem mass spectrometer in multiple reaction monitoring mode with positive electrospray ionization. Two transitions were monitored for each analyte in order to fulfill the established identification criteria. The validation included the determination of the limits of quantification (1.0 ng/mL for all analytes in serum and 2.0 ng/mL for all analytes in urine), assessment of matrix effects (77% to 92% in serum, 21 to 78% in urine) and the determination of extraction efficiencies (52% to 85% for serum, 59% to 88% for urine) and accuracy data. Imprecision was <10%, only the quantification of norclozapine in urine yielded higher relative standard deviations (11.2% and 15.7%). Bias values were below ±10%. Dilution of samples had no impact on the correctness for clozapine and norclozapine in both matrices and for clozapine-N-oxide in serum. For quantification of clozapine-N-oxide in urine a calibration with diluted calibrators has to be used. Calibration curves were measured from the LOQ up to 2,000 ng/mL and proved to be linear over the whole range with regression coefficients higher than 0.98. The method was finally applied to several clinical serum and urine samples and a cerebro-spinal fluid sample of an intoxicated 13-month-old girl.     

Determination of calcium, magnesium and zinc in lubricating oils by flame atomic absorption spectrometry using a three-component solution

Lubricating oils are used to decrease wear and friction of movable parts of engines and turbines, being in that way essential for the performance and the increase of that equipment lifespan. The presence of some metals shows the addition of specific additives such as detergents, dispersals and antioxidants that improve the performance of these lubricants. In this work, a method for determination of calcium, magnesium and zinc in lubricating oil by flame atomic absorption spectrometry (F AAS) was developed. The samples were diluted with a small quantity of aviation kerosene (AVK), n-propanol and water to form a three-component solution before its introduction in the F AAS. Aqueous inorganic standards diluted in the same way have been used for calibration. To assess the accuracy of the new method, it was compared with ABNT NBR 14066 standard method, which consists in diluting the sample with AVK and in quantification by F AAS. Two other validating methods have also been used: the acid digestion and the certified reference material NIST (SRM 1084a). The proposed method provides the following advantages in relation to the standard method: significant reduction of the use of AVK, higher stability of the analytes in the medium and application of aqueous inorganic standards for calibration. The limits of detection for calcium, magnesium and zinc were 1.3 μg g⁻¹, 0.052 μg g⁻¹ and 0.41 μg g⁻¹, respectively. Concentrations of calcium, magnesium and zinc in six different samples obtained by the developed method did not differ significantly from the results obtained by the reference methods at the 95% confidence level (Student's t-test and ANOVA). Therefore, the proposed method becomes an efficient alternative for determination of metals in lubricating oil.     

Thermodynamic, electrochemical, high-pressure kinetic, and mechanistic studies of the formation of oxo Fe(IV)-TAML species in water

Stopped-flow kinetic studies of the oxidation of Fe(III)-TAML catalysts, [ F e{1,2-X(2)C(6)H(2)-4,5-( NCOCMe(2) NCO)(2)CMe(2)}(OH(2))](-) (1), by t-BuOOH and H(2)O(2) in water affording Fe(IV) species has helped to clarify the mechanism of the interaction of 1 with primary oxidants. The data collected for substituted Fe(III)-TAMLs at pH 6.0-13.8 and 17-45 °C has confirmed that the reaction is first order both in 1 and in peroxides. Bell-shaped pH profiles of the effective second-order rate constants k(I) have maximum values in the pH range of 10.5-12.5 depending on the nature of 1 and the selected peroxide. The "acidic" part is governed by the deprotonation of the diaqua form of 1 and therefore electron-withdrawing groups move the lower pH limit of the reactivity toward neutral pH, although the rate constants k(I) do not change much. The dissection of k(I) into individual intrinsic rate constants k(1) ([FeL(OH(2))(2)](-) + ROOH), k(2) ([FeL(OH(2))OH)](2-) + ROOH), k(3) ([FeL(OH(2))(2)](-) + ROO(-)), and k(4) ([FeL(OH(2))OH)](2-) + ROO(-)) provides a model for understanding the bell-shaped pH-profiles. Analysis of the pressure and substituent effects on the reaction kinetics suggest that the k(2) pathway is (i) more probable than the kinetically indistinguishable k(3) pathway, and (ii) presumably mechanistically similar to the induced cleavage of the peroxide O-O bond postulated for cytochrome P450 enzymes. The redox titration of 1 by Ir(IV) and electrochemical data suggest that under basic conditions the reduction potential for the half-reaction [Fe(IV)L(=O)(OH(2))](2-) + e(-) + H(2)O → [Fe(III)L(OH)(OH(2))](2-) + OH(-) is close to 0.87 V (vs NHE).     

A fast and inexpensive procedure for the isolation of synthetic cannabinoids from ‘Spice’ products using a flash chromatography system

In the age of the Internet, the variety of drugs offered online is constantly increasing, and new drugs emerge every month. One group of drugs showing such an enormous increase is that of synthetic cannabinoids. Since their first identification in ‘herbal mixtures’, new structural modifications continue to appear on the market. In order to keep up with this process, toxicological screening methods need to be up to date. This can become extremely difficult if no reference material is available. In this article, a fast and effective way to extract and purify synthetic cannabinoids from ‘herbal mixtures’ is presented. This method opens a new opportunity for a timely reaction by obtaining reference material straight out of the ‘herbal mixtures’ ordered via the Internet. Isolation was carried out on a flash chromatography system with gradient elution on a C18 column using methanol and 0.55 % formic acid as mobile phases. The obtained purity of all compounds exceeded 99 %. In addition to the isolation of single compounds, the method proved to be suitable for the separation of various synthetic cannabinoids in one mixture, including the diastereomers cis- and trans-CP-47,497-C8. This approach for obtaining pure standards of new drugs proved to be effective, inexpensive and much quicker than waiting for the substances to be commercially available as reference material.