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 $r=2$.     

Potassium Sensing by Using a Newly Synthesized Squaraine Dye in Sol-Gel Matrix

Squaraines are a group of fluorescent dyes and pigments derived from squaric acid and dialkylanilines well known in applications such as photoreceptors, organic solar cells, optical recording media, and non-linear optics. Their very promising spectral properties, long wavelength absorption and emission, and high absorptivity and quantum yields have not been exploited so far in relation to optical sensor design. They exhibit excellent solubility in sol-gel matrices, and the ligand is an integral part of the fluorophore system, which makes the molecule a fluoroionophore. In this work, potassium-sensing agent, bis[4-N-(1-aza-4,7,10,13,16-pentaox acyclooctadecyl)-3,5-dihydroxyphenyl] squaraine has been used for potassium sensing in a sol-gel matrix. The spectrofluorimetric response of dye-doped tetraethyl ortosilicate (TEOS) film after exposure to certain concentrations of K⁺ has been investigated, and 62% of relative signal change was achieved. The dynamic working range of the sensor membrane has been found between 10^–9 and 10^–6 M K⁺, in other terms from nanomolar to micromolar levels, which is an advantage over flame emission spectroscopy, in view of detection limit. The sensor is fully reversible within the dynamic range and the response time (₉₀) is found to be 2 min under batch conditions. The cross-sensitivity of the molecule to Na⁺, Ba²⁺, Ca²⁺, and NH⁺ ₄ was also tested in separate solutions.     

Selective solid phase extraction and preconcentration of ultra-trace inorganic mercury in water samples using 2,6-dimethyl-morpholine dithiocarbamate

A sensitive and selective solid-phase spectrophotometric method for the determination of trace amounts of Hg(II) cation in water is described. A complex was created with Hg(II) using 2,6-dimethyl-morpholine dithiocarbamate (DMMDTC) to form Hg(II)–(DMMDTC) and this complex was adsorbed onto microcrystalline naphthalene (MN) and then eluted with 5% acetic acid (in ethanol) solution. A preconcentration factor of 187 and a recovery of 95% were observed at pH of 5.0 and for 10 min. of extraction. The separated Hg(II) ions were quantified by using ultraviolet-visible spectrophotometer at 490.0 nm by creating a colored complex with dithizone in Triton X-100 surfactant media. Molar absorptivity and sandell’s sensitivity for the Hg(II)-dithizone were determined as 4.96 × 10⁵ Lmol^?1cm^?1 and 0.4032 µg cm^?2, respectively. The detection limit (LOD) was 1.7 μg L^?1 under the optimized conditions of the analytical method.     

Effect of temperature and pH on droplet aggregation and phase separation characteristics of flocs formed in oil–water emulsions after coagulation

Coagulation process is used for destabilization of emulsions to promote aggregation of oil droplets on flocs which can be subsequently removed by sedimentation or flotation. The objectives of this study were to investigate the effect of temperature and pH on the effectiveness of destabilization of olive oil–water emulsions in relation to floc morphology and aggregation characteristics of oil droplets, and to quantify the ability of flocs to capture and separate oil. A cationic polyelectrolyte was used for the coagulation of oil droplets in edible olive oil–water emulsions using a jar test apparatus. The flocs formed in olive oil–water emulsions after coagulant addition were analyzed using microscopic image analysis techniques. Fractal dimension, radius of captured oil droplets on flocs, number of oil droplets aggregated on flocs, and floc size were used to quantitatively characterize and compared the effectiveness of the coagulation process at different conditions (pH and temperature) and the ability of flocs to remove oil from water. Analysis of microscopic images showed that floc size was not always the best measure of effectiveness of coagulation process in oil–water emulsions. The flocs forming at different pH levels and temperatures had significant morphological differences in their ability to aggregate different sizes and numbers of oil droplets, resulting in significant differences in their ability for separating oil. Fractal dimension did not correlate with the ability of flocs to aggregate oil droplets nor the total amount of oil captured on flocs. Temperature had a significant effect on droplet size and number of droplets captured on flocs. The differences in floc sizes at different temperatures were not significant. However, the flocs forming at 20 °C had fewer but larger droplets aggregating larger amounts of oil than flocs formed at 30 °C and 40 °C. The size of droplets at different pH levels was similar, however, there were significant differences in number of droplets aggregating on flocs and floc sizes. The amount of oil captured on flocs at pH 7 and pH 9 was significantly higher than those at pH 5 and pH 11. The calculated fractal dimensions of the flocs (all less than 1.8) indicated that the coagulation process was diffusion limited implying that there was no repulsion between the colliding particles (i.e., droplets and flocs); hence, each collision between flocs and droplets resulted in attachment.     

Synthesis and spectral characterization of macrocyclic Schiff base by reaction of 2,6-diaminopyridine and 1,4- bis (2-carboxyaldehydephenoxy)butane and its CuII, NiII, PbII, CoIII and LaIII complexes

A new macrocyclic ligand, 1,3,5-triaza-2,4:7,8:15,16-tribenzo-9,15-dioxacycloheptadeca-1,5-diene (L) was synthesized by reaction of 2,6-diaminopyridine with 1,4-bis(2-carboxyaldehydephenoxy)butane. Then, its Cu^II, Ni^II, Pb^II, Co^III and La^III complexes were synthesized by the template effect by reaction of 2,6-diaminopyridine and 1,4-bis (2-carboxyaldehydephenoxy)butane and Cu(NO₃)₂ · 3H₂O, Ni(NO₃)₂ · 6H₂O, Pb(NO₃)₂, Co(NO₃)₂ · 6H₂O, La (NO₃)₃ · 6H₂O, respectively. The ligand and its metal complexes were characterized by elemental analysis, IR, ¹H- and ¹³C-n.m.r., UV-vis spectra, magnetic susceptibility, thermal gravimetric analysis, conductivity measurements and mass spectra. All complexes are diamagnetic and the Cu^II complex is binuclear. The Co^II complex was oxidised to Co^III.     

Spectroscopic and Electrochemical Studies of Transition Metal Complexes with N,N′-Bis(2-aminothiophenol)-1,7-bis(2-formylphenyl)-1,4,7-trioxaheptane and Structure Effects on Extractability of Ligand towards some Divalent Cations

Summary. La(III), Cu(II), Ni(II), and Zn(II) metal complexes with a novel quadridentate Schiff base derived from 1,7-bis(2-formylphenyl)-1,4,7-trioxaheptane and 2-aminothiophenol were synthesized and characterized by microanalytical data, elemental analysis, magnetic measurements, ¹H NMR, ¹³C NMR, UV-Vis, IR, mass spectra, cyclic voltammetric and conductance measurements. The extractability of divalent cations was evaluated as a function of relationship between distribution ratio of the metal and pH or ligand concentration. The highest extraction percentage of Cu²⁺ and Ni²⁺ showed pH 7.0 and 6.4. It was concluded that the ligand can effectively be used in solvent extraction of copper(II) and nickel(II) from the aqueous phase to the organic phase.     

Separation,optimization, and quantification of cytokinins by a recently developed amide-embedded stationary phase

In this study, some plant growth regulators known as cytokinins [kinetin (K), zeatin (Z), thidiazuron (TDZ), benzylaminopurine (BAP), and dimethylallylaminopurine (AAP)] were separated by HPLC using an amide-embedded mixed-mode stationary phase which was synthesized by Aral et al. in recent years. The effect of mobile phase content, mobile phase pH, buffer concentration, and temperature on separation process was studied. In addition, a quantitative determination of cytokinins from Salvia limbata extract was studied, and some validation parameters such as limit of detection (LOD), limit of quantification (LOQ), and relative standard deviation (RSD) were calculated as a range of 0.03–0.1, 0.1–0.26?mg/L, and 0.03–0.08, respectively.     

Synthesis, characterization and structure effects on extractability and selectivity of N,N'-bis(salicylaldehydene)-1,4-bis-(m-aminophenoxy)butane towards some divalent cations

The extraction of copper(II), nickel(II) and cobalt(II) from the aqueous phase with N,N'-bis(salicylaldehydene)-1,4-bis-(m-aminophenoxy)butane (MAS), which was synthesized from 1,4-bis(m-aminophenoxy)butane and salicylaldehyde, was studied. Microanalytical data, elemental analysis, UV-visible 1H and 13C n.m.r. spectra and IR-spectra were used to confirm the structures. The extractability and selectivity of divalent cations were evaluated as a function of relationship between distribution ratio of the metal and pH or ligand concentration. Cu+2 showed the highest extractability and selectivity at pH 6.0, whereas Ni+2 and Co+2 showed at pH 9.2. The stoichiometries of the compounds formed were estimated to be CuL, CoL, NiL, where L is N,N'-bis(salicylaldehydene)-1,4-bis-(m-aminophenoxy)butane. It was concluded that MAS can effectively be used in solvent extraction of copper(II), nickel(II) and cobalt(II) from the aqeous phase to the organic phase.     

Highly sensitive sensing of zinc(II) by development and characterization of a PVC-based fluorescent chemical sensor

A sensor membrane with excellent performance based on 1-methyl-1-phenyl-3-[1-hydroxyimino-2-(succinimido)ethyl]cyclobutane has been developed for the determination of zinc(II) ions. The sensing membrane is capable of determining zinc(II) with an outstanding high selectivity over a dynamic range between 8.0×10(-8) and 1.6×10(-4) mol L(-1) with a limit of detection of 2.5×10(-8) mol L(-1) (1.6 μg L(-1)). It can be easily and completely regenerated by using 0.1 mol L(-1) EDTA solution. The optical sensor developed here was found to be stable, cost effective, easy to prepare, and has unique selectivity towards Zn(2+) ion with respect to common metal ions. The proposed sensor was then applied for the determination of zinc in tap water and hair samples with satisfactory results.     

HPLC Separation of Different Groups of Small Polar Compounds on a Novel Amide-Embedded Stationary Phase

Retention behaviors of an amide-embedded silica base stationary phase, which was recently developed by our group, were studied by using six different groups of small polar compounds including phenolic compounds, substituted anilines, chlorinated herbicides, Sudan dyes and some nucleotides and nucleosides in HPLC. The chromatographic behaviors of the prepared stationary phase for these analytes were compared with those of a commercially available reversed-phase column ACE C18 under same conditions. Among the six groups of analytes studied, the amide-silica stationary phase showed enhanced selectivity towards phenolic compounds, substituted anilines, Sudan dyes and herbicides under reversed-phase conditions and satisfactory selectivity towards nucleosides and nucleotides which could not be separated with ACE C18 column under HILIC conditions. Experimental data provided some evidence that functional groups on the stationary phases might have certain degrees of influence on selectivity possibly through secondary interactions with the model compounds. The retentions of the moderately polar compounds such as phenolic acids, anilines and herbicides on the stationary phase are higher than highly polar compounds such as nucleotides and nucleosides due to both the hydrophobic and hydrophilic interactions between the stationary phase and analytes. The quantitative determination of Sudan dyes (I, II, III, and IV) in red chilli peppers was performed. Many red chilli peppers were screened and three of them contained Sudans dyes.