Asymptotic properties of the growth curve model with covariance components

We consider a multivariate regression (growth curve) model of the form , where and are unknown scalar covariance components. In the case of replicated observations, we derive the explicit form of the locally best estimators of the covariance components under normality and asymptotic confidence ellipsoids for certain linear functions of the first order parameters {B _ij} estimating simultaneously the first and the second order parameters.     

Luminescence of poly(N-vinylcarbazole) in the solution and solid state

Fluorescence spectra of poly(N-vinylcarbazole) have been studied as a function of various environments and temperature. Fluorescence spectra have been excited with UV light from 200 W Xenon lamp or with second-harmonics of a pulsed ruby laser. Polymer films and powders show exclusively excimer fluorescence at room temperature. At high intensities of excitation the observed fluorescence spectra have a weak quasiperiodic structure.     

Crystal structure of tetrahydrocortisol

The crystal structure of tetrahydrocortisol (3, 11, 17,21-tetrahydroxy-5-pregnan-20-one), C₂₁H₃₄O₅, has been determined by X-ray diffraction using CuK radiation. The crystals are orthorhombic, P2₁2₁2₁ witha=7.696(5),b=10.227(2),c=23.688(5) Å and Z=4. The structure was solved by direct methods and refined to a finalR-value of 0.053 with 1714 observed reflections. The rings A, B, C, D arecis, trans, andtrans fused, respectively. The rings, A, B, C, have almost perfect chair conformations and D has a distorted envelope conformation. The steroid skeleton as a whole is somewhat convex toward the -side. The molecules are held together by a three-dimensional network of hydrogen bonds. Despite the similar cell constants and common space group of the title compound with cortisone and 17-hydroxyprogesterone, they are not isostructural.     

Stability of Alkali Metal Halide Polymorphs as a Function of Pressure

We investigated the regions of thermodynamic stability of possible modifications of the alkali metal halides as a function of pressure and type of alkali metal and halogen. Both Hartree–Fock and density functional calculations (for six different functionals) were performed. The results are in good agreement with experiment, and the trends in the computed quantities such as transition pressures and lattice parameters as a function of the ab initio method are similar to those found in earlier studies of the alkali metal sulfides. We predict that in most of these systems the so‐called 5–5 modification should be metastable at standard pressure and be thermodynamically stable at slightly negative pressures. The sizes of the pressure ranges over which the various modifications are stable showed characteristic trends as a function of the type of the constituent elements, thus generalizing the traditional pressure–homologue rule for transition pressures and stable phases in ionic solids.     

Interaction of a finite quantum system with an infinite quantum system that contains a single one-parameter eigenvalue band

Interaction of a finite quantum system that contains ρ eigenvalues and eigenstates with an infinite quantum system that contains a single one-parameter eigenvalue band is considered. A new approach for the treatment of the combined system is developed. This system contains embedded eigenstates with continuous eigenvalues , and, in addition, it may contain isolated eigenstates with discrete eigenvalues . Two ρ × ρ eigenvalue equations, a generic eigenvalue equation and a fractional shift eigenvalue equation are derived. It is shown that all properties of the system that interacts with the system can be expressed in terms of the solutions to those two equations. The suggested method produces correct results, however strong the interaction between quantum systems and . In the case of the weak interaction this method reproduces results that are usually obtained within the formalism of the perturbation expansion approach. However, if the interaction is strong one may encounter new phenomena with much more complex behavior. This is also the region where standard perturbation expansion fails. The method is illustrated with an example of a two-dimensional system that interacts with the infinite system that contains a single one-parameter eigenvalue band. It is shown that all relevant completeness relations are satisfied, however strong the interaction between those two systems. This provides a strong verification of the suggested method.     

Use of Different Salt Solutions in Salting-Out TLC of Co(III) Complexes on Silica Gel

Saturated aqueous solutions of 28 different salts have been studied as a potential mobile phases for salting-out thin-layer chromatography, on silica gel, of a series of four mixed bis-aminocarboxylato cobalt(III) complexes. In addition, by linear regression analysis of chromatographic data obtained for fifteen mixed aminocarboxylato Co(III) complexes (four series) with solutions of ammonium chloride, three alkali metal chlorides, and four alkaline earth metal chlorides, four linear dependences previously established on different adsorbents with (NH₄)₂SO₄ solutions were confirmed. The qualities of the separations achieved with the salts were compared and Li⁺, Mg²⁺, and Ca²⁺ chlorides are proposed as the most suitable.     

Electrochemical sensors for the simultaneous determination of zinc,cadmium and lead using a Nafion/ionic liquid/graphene composite modified screen-printed carbon electrode

A simple, low cost, and highly sensitive electrochemical sensor, based on a Nafion/ionic liquid/graphene composite modified screen-printed carbon electrode (N/IL/G/SPCE) was developed to determine zinc (Zn(II)), cadmium (Cd(II)), and lead (Pb(II)) simultaneously. This disposable electrode shows excellent conductivity and fast electron transfer kinetics. By in situ plating with a bismuth film (BiF), the developed electrode exhibited well-defined and separate peaks for Zn(II), Cd(II), and Pb(II) by square wave anodic stripping voltammetry (SWASV). Analytical characteristics of the BiF/N/IL/G/SPCE were explored with calibration curves which were found to be linear for Zn(II), Cd(II), and Pb(II) concentrations over the range from 0.1 to 100.0 ng L⁻¹. With an accumulation period of 120 s detection limits of 0.09 ng mL⁻¹, 0.06 ng L⁻¹ and 0.08 ng L⁻¹ were obtained for Zn(II), Cd(II) and Pb(II), respectively using the BiF/N/IL/G/SPCE sensor, calculated as 3σ value of the blank. In addition, the developed electrode displayed a good repeatability and reproducibility. The interference from other common ions associated with Zn(II), Cd(II) and Pb(II) detection could be effectively avoided. Finally, the proposed analytical procedure was applied to detect the trace metal ions in drinking water samples with satisfactory results which demonstrates the suitability of the BiF/N/IL/G/SPCE to detect heavy metals in water samples and the results agreed well with those obtained by inductively coupled plasma mass spectrometry.     

Existence of equilibrium for infinite system of interacting diffusions

We develop and implement new probabilistic strategy for proving basic results about long-time behavior for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as a solution to suitable infinite-dimensional martingale problem. However, the techniques allow us to consider cases where the generator of the particle is degenerate elliptic operator. As a model example, we present the situation where the operator arises from Heisenberg group. In the last section, we provide further examples that can be handled using our methods.     

The viscosity cross-section for elastic electron-xenon collisions including electron spin polarization

The results of the evaluation of the viscosity cross-section for elastic electron-xenon collisions, taking into account the spin-orbit interaction of the continuum electron, in the energy interval from 0.1 eV to 50 eV are presented and discussed. The calculations are performed on the basis of three theoretically derived sets of phase shift data obtained by different authors and on the deduced relativistic expression for the viscosity cross-section in terms of phase shifts discerning the spin-up and spin-down states of the scattered electrons. Comparison with viscosity cross-sections, as evaluated from non-relativistic phase shifts extracted from experiments, strongly favours the relativistic results. The assumption of isotropic scattering is critically examined and the error induced by its use is shown to persist to the same extent as in non-relativistic calculations, at least in the energy region considered. Received: 22 April 1998 / Received in final form: 16 December 1998     

Chemometrically Assisted Development and Validation of LC for Simultaneous Determination of Carbamazepine and Its Impurities Iminostilbene and Iminodibenzyl in Solid Dosage Form

A chemometrical approach was applied to develop a reversed-phase liquid chromatographic method for simultaneous determination of carbamazepine and its impurities iminostilbene and iminodibenzyl in solid dosage form. According to contemporary literature, no method was developed for simultaneous determination of carbamazepine and these impurities by chemometrical approach. The fractional factorial design was used for selection of variables significantly influencing the chromatographic separation of the investigated substances. The investigated variables were: temperature of the column, the percentage of organic modifier, the acetate buffer concentration and pH of water phase. The first three variables were proved to be significant and were optimized by face centered, central composite design. Investigation was performed using C18 XBridge Shield analytical column (50 mm × 4.6 mm i.d., particle size 3.5 µm). The optimal conditions for the separation were established with the mobile phase composition of methanol–10 mM acetate buffer (pH adjusted to 2.21 with glacial acetic acid) (50:50, v/v) at a flow rate of 1.5 mL min^?1, 25 °C column temperature and detection at 260 nm. Total analysis time was shortened to about 8 min. Finally, the method was successfully validated and subsequently applied to the analysis of commercially available carbamazepine tablets.