On the stabilizer subgroup of a fair of matrices

Let (F,G) be a pair of matrices defined over an arbitrary field, Fn × n, Gn × m. Consider the natural action of GL_n x GL_m on this pair given by (F,G) ? (gFg^-1,gGh^-1), where (g,h) ∈ GL_n × GL_m. This action is of interest in system theory as well as the representation theory of quivers. In this paper we study the stabilizer subgroup of this action stab(F,G), i.e.

$\text{{(g,h) ∈ GL}{}_{\mathrm{n}}\text{x GL}{}_{\mathrm{m}}\text{|gFg}{}^{-1}\text{= F,gGh}{}^{-1}\text{= G}}$

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Photoinduced intramolecular electron transfer and triplet energy transfer in a steroid-linked norbornadiene-carbazole dyad

Bichromophoric compound 3 beta-((2-(methoxycarbonyl)bicyclo[2.2.1]hepta-2,5-diene-3-yl)carboxy)androst-5-en-17 beta-yl-[2-(N-carbazolyl)acetate] (NBD-S-CZ) was synthesized and its photochemistry was examined by fluorescence quenching, flash photolysis, and chemically induced dynamic nuclear polarization (CIDNP) methods. Fluorescence quenching measurements show that intramolecular electron transfer from the singlet excited state of the carbazole to the norbornadiene group in NBD-S-CZ occurs with an efficiency (Phi SET) of about 14 % and rate constant (kSET) of about 1.6 x 10(7) s-1. Phosphorescence and flash photolysis studies reveal that intramolecular triplet energy transfer and electron transfer from the triplet carbazole to the norbornadiene group proceed with an efficiency (TET + TT) of about 52 % and rate constant (kTET + kTT) of about 3.3 x 10(5) s-1. Upon selective excitation of the carbazole chromophore, nuclear polarization is detected for protons of the norbornadiene group (emission) and its quadricyclane isomer (enhanced absorption); this suggests that the isomerization of the norbornadiene group to the quadricyclane proceeds by a radical-ion pair recombination mechanism in addition to intramolecular triplet sensitization. The long-distance intramolecular triplet energy transfer and electron transfers starting both from the singlet and triplet excited states are proposed to proceed by a through-bond mechanism.     

Gas-Chromatographic Studies of the Interaction between Water and Methanol Molecules and the Surface of Carbon Materials

The gas-chromatographic method is used to study the interaction of water and methanol molecules with active hydrophilic centres existing at the surface of thermally exfoliated graphite and graphitized thermal carbon black. The concentration of carboxyl and phenol hydroxyl groups at the surface of these sorbents is determined, and heats of adsorption of the studied molecules are shown to be and 28−25 kJ/mol, respectively. It is also shown that adsorption of water at the hydrophilic centres at lowest relative pressure values takes place with formation of clusters consisting of n = 2 water molecules.     

Thermochemistry of the solid complex Gd(Et<Subscript>2</Subscript>dtc)<Subscript>3</Subscript>(phen)

Summary A ternary solid complex Gd(Et₂dtc)₃(phen) has been obtained from reactions of sodium diethyldithiocarbamate (NaEt₂dtc), 1,10-phenanthroline (phen) and hydrated gadolinium chloride in absolute ethanol. The title complex was described by chemical and elemental analyses, TG-DTG and IR spectrum. The enthalpy change of liquid-phase reaction of formation of the complex, Δ_rH^Θ_m(l), was determined as (-11.628±0.0204) kJ mol^-1 at 298.15 K by a RD-496 III heat conduction microcalorimeter. The enthalpy change of the solid-phase reaction of formation of the complex, Δ_rH^Θ_m(s), was calculated as (145.306±0.519) kJ mol^-1 on the basis of a designed thermochemical cycle. The thermodynamics of reaction of formation of the complex was investigated by changing the temperature of liquid-phase reaction. Fundamental parameters, the apparent reaction rate constant (k), the apparent activation energy (E), the pre-exponential constant (A), the reaction order (n), the activation enthalpy (Δ_rH^Θ_≠), the activation entropy (Δ_rS^Θ_≠), the activation free energy (Δ_rG^Θ_≠) and the enthalpy (Δ_rH^Θ_≠), were obtained by combination of the thermodynamic and kinetic equations for the reaction with the data of thermokinetic experiments. The constant-volume combustion energy of the complex, Δ_cU, was determined as (-18673.71±8.15) kJ mol^-1 by a RBC-II rotating-bomb calorimeter at 298.15 K. Its standard enthalpy of combustion, Δ_cH^Θ_m, and standard enthalpy of formation, Δ_fH^Θ_m, were calculated to be (-18692.92±8.15) kJ mol^-1 and (-51.28±9.17) kJ mol^-1, respectively.     

Understanding the conformational dependence of spin-spin coupling constants: through-bond and through-space J(31P,31P) coupling in tetraphosphane-1,4-diides [M(L)x]2[P4R4

The characteristic dependence of J(31P,31P) spin-spin coupling constants of alkali metal tetraphosphane-1,4-diides on structure and composition has been analyzed by density functional methods. The computations confirm that the structure of the contact ion pairs is conserved in solution. Calculations on model systems M2P4H4, on naked P4H4(2-) anions, and on models including point charges, show that the role of the cations is mainly structural and to a smaller extent electrostatic. Three of the four J(P,P) coupling constants depend characteristically on the conformation of the anion, which in turn is determined by the substituents R and by cation-anion interactions. Several couplings exhibit a large through-space component and are thus strongly dependent on the relative orientation of nonbonding electron pairs on the phosphorus atoms involved. This is shown by visualization of coupling pathways using the recently introduced coupling energy density (CED), in combination with the electron localization function (ELF).     

Random walk properties of lattices and correlation factors for diffusion via the vacancy mechanism in crystals

Random walk properties and correlation factors for diffusion via the vacancy mechanism are calculated and compared for various three-dimensional lattices. By applying the theory of random walks on an imperfect lattice, the correlation factor for impurity diffusion is calculated rigorously for the five jump frequency model in the fee lattice.Presented at the Symposium on Random Walks, Gaithersburg, MD, June 1982.     

RATE OF INTRA-MOLECULAR CONTACT FORMATION IN SHORT TWO-DIMENSIONAL COMPACT POLYMERS CHAINS

It is important to know the rate of intra-molecular contact formation in proteins in order to understand how proteins fold clearly. Here we investigate the rate of intra-molecular contact formation in short two-dimensional compact polymer chains by calculating the probability distribution p(r) of end-to-end distance r using the enumeration calculation method and HP model on two-dimensional square lattice. The probability distribution of end-to-end distance p(r) of short two-dimensional compact polymers chains may consist of two parts, i.e. p(r) = p1(r) p2(r), where p1(r) and p2(r) are different for small r. The rate of contact formation decreases monotonically with the number of bonds N, and the rate approximately conforms to the scaling relation of k(N) ∝ N-α. Here the value of α increases with the contact radius a and it also depends on the percentage of H (hydrophobic) residues in the sequences of compact chains and the energy parameters of εHH, εHP and εPP . Some comparisons of theoretical predictions with experimental results are also made. This investigation may help us to understand the protein folding.     

Continuous chemiluminescence determination of formaldehyde in air based on Trautz-Schorigin reaction

A new continuous method for the determination of formaldehyde in air is described. A cylindrical wet effluent diffusion denuder is used for the collection of formaldehyde from air into a thin film of absorption liquid (distilled-deionized water). Formaldehyde in the denuder concentrate is on-line detected employing a chemiluminescence flow method based on a reaction of formaldehyde and gallic acid with hydrogen peroxide in an alkaline solution. The collection efficiency of formaldehyde is quantitative at the air flow rate of 0.5 L min⁻¹ (absorption liquid flow rate of 336 μL min⁻¹). The limit of detection (S/N = 3) is 0.60 μg m⁻³ HCHO (0.49 ppb). The calibration graph is linear up to 300 μg m⁻³ HCHO (244 ppb). The relative standard deviations of chemiluminescence method for 1 × 10⁻⁶ and 5 × 10⁻⁶ M HCHO are 2.87% and 1.49%, respectively. Acetaldehyde interferes negligible, other compounds do not interfere. The method was employed for formaldehyde measurement in ambient air. The comparison measurement illustrates the good agreement of results obtained by proposed method with those obtained by reference fluorimetric method.     

Modeling of asymmetric membrane formation by dry-casting method

Many polymeric membranes are produced by phase inversion technique invented by Loeb and Sourirajan in 1962. The dry-casting method is one of the major phase inversion techniques in which a homogeneous polymer solution consisting of solvent(s) and nonsolvent(s) is cast on a support and then evaporation of the casting solution takes place under convective conditions. In this paper, we model membrane formation by the dry-casting method. The model takes into account film shrinkage, evaporative cooling, coupled heat, and mass transfer and incorporates practical and reliable diffusion theory as well as complex boundary conditions especially at the polymer solution/air interface. The predictions from the model provide composition paths, temperature, and thickness of the solution. By plotting the composition paths on the ternary phase diagram, we ascertain the general structural characteristics of the membranes prepared from particular casting conditions. The predictive ability of the model was evaluated by comparing the results with the experimental data obtained from gravimetric measurements for cellulose acetate (CA)–acetone–water system. In an attempt to illustrate the importance of diffusion formalism on the predictions, recently proposed multicomponent diffusion theory and its simplified forms were utilized in the model. The computational results show that the critical factor for capturing the accurate behavior of membrane formation is the diffusion formalism utilized in the model.     

SrO—Al2O3—SiO2：Eu^3＋,Bi^3＋发光体的溶胶—凝胶法合成

制备无机固体材料大都采用高温固相反应,1971年Dislich报导了用溶胶-凝胶法制备多组份固体材料。近年来,有报导利用此法研制玻璃、玻璃陶瓷和陶瓷。我们在过去工作的基础上,合成了SrO-Al_2O_3-SiO_2:Eu~(3 ),Bi~(3 )发光体,研究了从凝胶至发光晶体的转变过程、Eu~(3 )和Bi~(3 )在SrO-Al_2O_3-SiO_2基质中的发光性质以及Bi~(3 )对 EU~(3 )的能量传递。