Carlsson's rank conjecture and a conjecture on square-zero upper triangular matrices

Let k be an algebraically closed field and A the polynomial algebra in r variables with coefficients in k. In case the characteristic of k is 2, Carlsson [9] conjectured that for any DG-A-module M of dimension N as a free A-module, if the homology of M is nontrivial and finite dimensional as a k-vector space, then $2^r\le N$. Here we state a stronger conjecture about varieties of square-zero upper triangular $N\times N$ matrices with entries in A. Using stratifications of these varieties via Borel orbits, we show that the stronger conjecture holds when $N<8$ or $r<3$ without any restriction on the characteristic of k. As a consequence, we obtain a new proof for many of the known cases of Carlsson's conjecture and give new results when $N>4$ and $r=2$.     

Theoretical analysis of frontier orbitals,electronic transitions,and global reactivity descriptors of M(CO)4L2 type metal carbonyl complexes: a DFT/TDDFT study

Structural Chemistry - Metal carbonyl complexes, which have been known as effective catalysts since early days, find use in many fields both directly and indirectly. Although the use of metal...     

Statistical Extensions of Some Classical Tauberian Theorems for Cesàro Summability of Triple Sequences

Some growth conditions of the resolvent function of a Banach space operator are investigated using higher order Cesàro means. More precisely, Abel and Nevanlinna estimates are obtained under the condition of boundedness of some weighted Cesàro averages. Also, certains results related to the (strong or uniform) convergence of Cesàro means are mentioned.     

The measurement of the magnetic susceptibility of some elements (Fe,Co, Ni,Ge, Sn,Te) in the liquid state

A magnetic balance was used for measuring the susceptibility of metals and alloys, in an atmosphere of purified argon, up to 1800°c.

Comparison of the susceptibilities of liquid Fe, Co and Ni gives information on the liquid state. The changes in the susceptibilities of Ge, Sn and Te on melting are typical of semi-metallic elements and semiconductors, but their behaviour differs according to the degree of symmetry in the solid state.     

Hypercoordination in Organotin Chemistry – A Novel O,C,O-Coordinating Ligand

Recent results are reported on the application of the novel O,C,O-coordinating pincer ligand {2,6-[P(O)(OEt)₂]₂-4-tert-Bu-C₆H₂} (A) for the synthesis of hypercoordinate organotin(IV) compounds ASnR₃ (R = Ph, Cl), heteroleptic stannylenes ASnR (R = Cl, CH₂SiMe3) and intramolecularly coordinated 1,2,5-oxaphosphastannolanes.     

Metal ion complexation in acetonitrile by cone,di-ionised calix[4]arene-1,2-crown ethers with two pendant dansyl fluorophores

Four cone calix[4]arene-1,2-crown ethers each with two ionisable side arms containing dansyl groups are synthesised. The crown ether ring on the lower rim is varied from crown-4 to crown-5 with hydrogen or tert-butyl groups on the para position of the upper rim. Di(tetramethylammonium) salts of the di-ionised ligands are utilised for spectrofluorimetric titration experiments in MeCN. The influence of alkali metal, alkaline earth metal and selected transition and heavy metal (Co²⁺, Fe²⁺, Hg²⁺, Mn²⁺, Pb²⁺, Zn²⁺ and Fe³⁺) cations on the spectroscopic properties of the two dansyl groups linked to the lower rim of the conformationally locked, di-ionised calix[4]arene-1,2-crown ether frameworks is investigated by emission spectrophotometry. All of the metal cations induce red shifts in the emission spectra of the di-ionised ligands. The metal cations produce enhancement or quenching of the fluorescence emissions. Changes in the fluorescence emission as a function of the metal cation identity, the lower rim crown ether ring size and the absence or presence of upper rim tert-butyl groups are investigated.     

The synthesis and fluorescence properties of novel chromenone-crown ethers

o-Dihyroxy-3-phenylchromenone derivatives, namely, 6,7-dihydroxy-3-(3′,4′-dimethoxyphenyl)chromenone and 6,7-dimethoxy-3-(3′,4′-dihydroxyphenyl)chromenone, were obtained from 2,4,5-trihydroxybenzaldehyde/3,4-dimethoxyphenylacetic acid and 2-hydroxy-4,5-dimethoxybenzaldehyde/3,4-dihydroxyphenylacetic acid, respectively, in the presence of acetic anhydride and sodium acetate under an inert atmosphere, after treatment with MeOH/HCl(aq). The chromenone-crown ethers were prepared from cyclic condensation of o-dihydroxy-3-phenylchromenones with poly(ethylene glycol) ditosylates in the presence of CH₃CN/alkali metal carbonates. The chromatographically purified novel chromenone-crown ethers were identified by ¹H NMR, MALDI-TOF mass spectrometry and elemental analysis. The fluorescence and UV–vis spectroscopic properties of the obtained chromenone-crown ethers and their complexes with Li⁺, Na⁺ and K⁺ perchlorate salts were estimated in acetonitrile. The quantum yields of novel chromenone-crown ethers were determined by the comparative method.

     

Sonochemical synthesis and electrochemical characterization of α-nickel hydroxide: precursor effects

Sonochemical degradation of urea was employed to synthesize alpha-nickel hydroxide from different nickel salts. Utilization of ultrasound yielded products with properties significantly different than the products obtained by thermal degradation of urea. The effect of intercalating chloride, nitrate, acetate, and sulfate anions on morphology and electrochemical performance was studied. The sulfate-intercalated sample had the smallest interlayer spacing when obtained by the sonochemical method, contradicting all the previous thermal synthesis results. The specific capacitance trend also differed from the literature values, and the value for the sulfate-intercalated sample was larger than that of acetate- and nitrate-intercalated samples. Ultrasonic synthesis increased the specific capacitance of the sulfate-intercalated sample significantly. This sample was also the most reversible and had the highest charge efficiency.     

Synthesis,characterization, and application of silver nanoparticle‐thiophenol nanocomposite film on the glassy carbon surface

In this study, 4‐thiophenol modified glassy carbon electrode was prepared by the reduction of 4‐diazothiophenol tetrafluoroborate salt. Silver nanoparticles were attached to the thiophenol modified surface to prepare a thiophenol‐silver nanoparticle composite film. 4‐Aminothiopenol molecules were deposited by self‐assembling technique to form multi‐layered nanofilms of TP/SNP/PhNH₂ on glassy carbon substrate. These surfaces were characterized by cyclic voltammetry, electrochemical impedance spectroscopy, X‐ray photoelectron spectroscopy, reflectance‐absorption infrared spectroscopy, and ellipsometry at each multilayer film growth process. Atomic force microscopic images of GC/TP/SNP/PhNH₂ surfaces were also acquired. The characterization methods show that the amine group containing surface permits the subsequent modification by a variety of coupling reactions for the immobilization of more complex systems. An application of the electrode modification for the determination of uric acid with a significantly lower detection limit is described. Copyright © 2013 John Wiley & Sons, Ltd.     

Inorganic arsenic speciation in various water samples with GFAAS using coprecipitation

A simple, economic and sensitive method for selective determination of As(III) and As(V) in water samples is described. The method is based on selective coprecipitation of As(III) with Ce(IV) hydroxide in presence of an ammonia/ammonium buffer at pH 9. The coprecipitant was collected on a 0.45 µm membrane filter, dissolved with 0.5 mL of conc. nitric acid and the solution was completed to 2 or 5 mL with distilled water. As(III) in the final solutions was determined by graphite furnace atomic absorption spectrometry (GFAAS). Under the working condition, As(V) was not coprecipitated. Total inorganic arsenic was determined after the reduction of As(V) to As(III) with NaI. The concentration of As(V) was calculated by the difference of the concentrations obtained by the above determinations. Both the determination of arsenic with GF-AAS in presence of cerium and the coprecipitation of arsenic with Ce(IV) hydroxide were optimised. The suitability of the method for determining inorganic arsenic species was checked by analysis of water samples spiked with 4–20 µg L^?1 each of As(III) and As(V). The preconcentration factor was found to be 75 with quantitative recovery (≥95%). The accuracy of the present method was controlled with a reference method based on TXRF. The relative error was under 5%. The relative standard deviations for the replicate analysis ( n?=?5) ranged from 4.3 to 8.0% for both As(III) and As(V) in the water samples. The limit of detection (3σ) for both As (III) and As(V) were 0.05 µg L^?1. The proposed method produced satisfactory results for the analysis of inorganic arsenic species in drinking water, wastewater and hot spring water samples.