Lower bounds for dimensions of representation varieties

The set of -dimensional complex representations of a finitely generated group form a complex affine variety . Suppose that is such a representation and consider the associated representation on complex matrices obtained by following with conjugation of matrices. Then it is shown that the dimension of at is at least the difference of the complex dimensions of and . It is further shown that in the latter cohomology may be replaced by various proalgebraic groups associated to and .

     

A study of the polarographic reduction of methaqualone

Methaqualone [2-methyl-3-o-tolyl-4(3H)-quinazolinone] is reduced at pH 1.5–5 in a single two-electron step. At pH 1.5–3, wave i₁ appears and is gradually replaced by wave i₂ which predomiantes in the solution between pH 4.5 and 6.5. At pH > 5, the height of wave i₂ decreases in the shape of a dissociaton curve with increasing pH. For both waves, the diprotonated form of methaqualone (I_a) is reduced to 1,2,-dihydromethaqualone as the final product. In wave i₁, the monoprotonated form I_b is further protonated at the electrode surface before it accepts the first electron; in wave i₂, the free base form I accepts two protons at the electrode surface before the first electron uptake. Polarographic curves are complicated by the presence of three waves of catalytic hydrogen evolution. Wave i_{1, cata} appears at pH < 5, waves i_2,cata at ?1.5 V and i_3,cata at ?1.7 V at pH > 5. Citrate buffers pH 1.5–3 or Britton-Robinson buffers at pH 2.6–3.6 are most suitable for quantitative work with eitehr d.c. polarography or differential pulse polarography.     

High-performance liquid chromatography of the coordination isomers of triphenylphosphine-substituted homo- and hetero-bimetallic carbonyl complexes of manganese and rhenium

The isocratic normal-phase high-performance liquid chromatography of a series of triphenylphosphine (PPh₃)-substituted homo- and hetero-dinuclear metal carbonyl complexes [MM′ (CO)_10−n(PPh₃)_n, where M,M′ = Mn, Re; N = 1,2] is reported. A column packed with silica bonded with phenyl groups was used after preliminary experiments showed that columns packed with conventional silica, and with silica bonded with amion-cyano groups were unsatisfactory for separation. The mobile phases used were hexane-toluene (8:2) and hexane-dichloromethane (90:10). The results suggest that besides the symmetry-imposed polarity of the complexes, the nature of the metal and substituent ligand also determine their retention characteristics.     

Determination of methylamphetamine and related compounds in human urine by high performance liquid chromatography/electrospray/mass spectrometry

The influence of tetrabutylammonium (TBA) as a hydrophobic charged additive of the mobile phase was investigated in a chromatographic system involving d,l-dansyl amino acids as the test solute enantiomers and immobilized human serum albumin as the chiral stationary phase. By varying the column temperature, van't Hoff plots for solute retention and enantioselectivity were performed and thermodynamic parameters were calculated. An enthalpy-entropy compensation study revealed that the type of interaction between the analyte and stationary phase was independent of TBA concentration in the eluent. The counterion dependence on retention indicated that the coulombic interactions between dansyl amino acid and the site II binding cavity were of crucial importance in this association process. Also, the increasing variations of chiral discrimination with a TBA addition were attributed, by an analysis of the thermodynamic parameter trends, to a great facilitation of enantioselective H-bonding between solute and polar residues at the cavity rim.     

Polymer dispersed liquid crystal display device for projection high definition television application

Polymer dispersed liquid crystal (PDLC) is a light scattering material that operates on the principle of electrically modulating the refractive index of the liquid crystal in an optical isotropic, transparent solid. The principle of operation of the PDLC device, the interface requirements between PDLC material and its driving circuit are studied. For high definition television (HDTV) application, a detailed comparison of PDLC vs. twisted nematic/super twisted nematic (TN/STN) display devices will be discussed. It was found that single crystal metal oxide semiconductor field effect transistor (MOSFET) is better than conventionally used thin film transistor (TFT) in driving these PDLC light valves.     

Errors assessment for spectral emissivity measurements collected from a SiNC ceramic matrix composite material using a 1.6 μm single wavelength pyrometer

The effective spectral emissivities for a SiNC ceramic matrix composite material are measured as a function of temperature and duration of the heat cycle. After several heat cycles an increase in the value of the average spectral emissivity was observed. The increase in the value of the effective spectral emissivity was attributed to the formation of SiO₂ layer on the surface area of the SiNC sample.     

Determination of organochlorine pesticides in water using dynamic hook-type liquid-phase microextraction

We developed a simple and efficient headspace liquid-phase microextraction (LPME) technique named dynamic hook-type liquid-phase microextraction (DHT-LPME) and used it in combination with gas chromatography-mass spectrometry (GC-MS) and an electron capture detector (ECD). Aqueous specimens of organochlorine pesticides (OCPs) were used as model compounds to demonstrate the effectiveness of the technique. In the present study, the calibration curves were linear over at least 2 orders of magnitude with R² values of 0.997. The method detection limits (MDLs) varied from 2 to 44.0 ng L⁻¹. The precision of DHT-LPME ranged from 6.5 to 14.4%. The relative recoveries of OCPs in rainwater were more than 84.2%. Enrichment factors (EF) in the range 275-1127 were obtained using DHT-LPME.     

Efficient di-bromination of 5-pyrazolones and 5-hydroxypyrazoles by N-bromobenzamide

An efficient and convenient method for the bromination of pyrazolones and 5-hydroxypyrazoles was developed by using N-bromobenzamide in THF at room temperature. This new method provided di-bromimated pyrazolones in excellent yields (≥90%).