Extreme statistics of complex random and quantum chaotic states

Complex random states have the statistical properties of the Gaussian and circular unitary ensemble eigenstates of random matrix theory. Even though their components are correlated by the normalization constraint, it is nevertheless possible to derive compact analytic formulas for their extreme values' statistical properties for all dimensionalities. The maximum intensity result slowly approaches the Gumbel distribution even though the variables are bounded, whereas the minimum intensity result rapidly approaches the Weibull distribution. Since random matrix theory is conjectured to be applicable to chaotic quantum systems, we calculate the extreme eigenfunction statistics for the standard map with parameters at which its classical map is fully chaotic. The statistical behaviors are consistent with the finite-N formulas.     

Spin-orbit splitting in theN-Δ spectra and the deformed baryon model

The absence of appreciable spin-orbit splitting in the low-lying even and odd parity states of the nucleon and delta is puzzling in conventional quark models. A constitutent quark model, in which the quarks interact through gluon as well as pion exchange, and the baryon is allowed to deform in the excited states, may provide a solution to the problem.     

An interactive decision support system for the bank courier routing problem

In this paper, we present an interactive decision support system for collecting and processing financial transit material for the Southeast Bank N.A. The underlying model is a bicriteria shortest path problem. The system provides a feasible solution in a matter of minutes, which provides the decision maker with an opportunity to perform “what if” analysis. The system can be extended to other vehicle routing problems with inventory components.     

Persistence of manifolds in nonequilibrium critical dynamics

We study the persistence probability P(t) that, starting from a random initial condition, the magnetization of a d'-dimensional manifold of a d-dimensional spin system at its critical point does not change sign up to time t. For d'>0 we find three distinct late-time decay forms for P(t): exponential, stretched exponential, and power law, depending on a single parameter zeta=(D-2+eta)/z, where D=d-d' and eta,z are standard critical exponents. In particular, we predict that for a line magnetization in the critical d=2 Ising model, P(t) decays as a power law while, for d=3, P(t) decays as a power of t for a plane magnetization but as a stretched exponential for a line magnetization. Numerical results are consistent with these predictions.     

The solution behavior of poly(vinylpyrrolidone): its clouding in salt solution, solvation by water and isopropanol, and interaction with sodium dodecyl sulfate

This article deals with the solution properties of poly(vinylpyrrolidone) (PVP) in salt and surfactant environment. The cloud point (CP) of PVP has been found to be induced by the salts NaCl, KCl, KBr, Na2SO4, MgSO4, and Na3PO4. On the basis of CP values for a salt at different [PVP], the energetics of the clouding process have been estimated. The effect of the surfactant, sodium dodecyl sulfate (SDS), on the salt-induced CP has also been studied, and reduction in CP at low [SDS] and increase in CP at high [SDS] have been observed. The water vapor adsorption of PVP has been determined by isopiestic method. The results display a BET Type III isotherm whose analysis has helped to obtain the monolayer capacity of PVP and formation of multilayer on it. The solvation of PVP in a solution of water and a water-isopropanol mixture has been determined by conductometry from which contribution of the individual components were estimated. The interaction of PVP with SDS in solution led to formation of a complex entity, which has been studied also by conductometry adopting a binding-equilibrium scheme. SDS has been found to undergo two types of binding as monomers in the pre- critical aggregation concentration (CAC) range and as small clusters in the post CAC region. The stoichiometries of binding and binding constant were evaluated.     

Removal of Cu(II) and Zn(II) from industrial wastewater by acid-activated montmorillonite-illite type of clay

An acid-activated montmorillonite-illite type of clay collected from the Gulbarga region of Karnataka, India was examined for removing copper and zinc ions from industrial wastewater containing Cu(II), Zn(II) and minor amounts of Pb(II). Langmuir, Freundlich, Brunauer-Emmett-Teller (BET), and competitive Langmuir (two competing ions) isotherms were fitted to experimental data and the goodness of their fit for adsorption was compared. The shapes of isotherms obtained indicated multilayer adsorption of Cu(II) and monolayer adsorption of Zn(II) on the acid-activated clay. Competitive adsorption was found to be significant due to the presence of Cu(II) in the wastewater.     

Supramolecular self-assembly and nanoencapsulation of [60]fullerene by bis-β-cyclodextrin

Bis-β-cyclodextrin connected via ethylene diamine on the primary side of the β-cyclodextrin was synthesized and used for the supramolecular non-covalent inclusion complex with C₆₀ in a mixed solvent system at room temperature. The apparent association constant of the 2:2 inclusion complex determined by combination of UV–Vis absorbance and Benesi–Hildebrand equation was found to be 1.78 × 10⁶ M^?1. The product obtained was highly water-soluble and superior in stability in aqueous medium as compared to previously known β-cyclodextrin/C₆₀ complex. The non-covalent self-assembly of bis-β-cyclodextrin and C₆₀ was characterized and confirmed from FT-IR, UV–Vis, XRD and TGA. The supramolecular aggregation behavior and particle size of the inclusion complex was found from transmission electron microscope and static light scattering measurements. The size of the inclusion complex was found to be ~30 ± 5 nm.     

Reactions of titanium(IV) isopropoxide with aliphatic and aromatic hydroxy esters,part I. 5-, 6-, 7- and 8-coordinate titanium(IV) complexes

Summary Reactions of titanium(IV) isopropoxide with ethyl 1-hydroxycyclohexylacetate, ethyl 2-hydroxy-2-arylpropionate, ethyl 2-hydroxy-2-arylbutyrate and ethyl 2-hydroxy-2-arylhydrocinnamate have been studied in dry benzene in different molar ratios under strictly anhydrous conditions. The Ti(OPr-i)₄-_nL_n type compounds, where L = hydroxy ester and n = 1 to 4, have been isolated and characterised by elemental analysis, molecular weight, i.r. and n.m.r. spectral studies. These products may be distilled unchanged under reduced pressure.Reprints of this are not available.     

Separation of thorium from rare earths

Summary A method for separation of thorium from rare earths in monazite based on the difference of stability of EDTA complexes towards oxine is described.