Analytic calculation of scaling dimensions: Tricritical hard squares and critical hard hexagons

The finite-size corrections, central chargesc, and scaling dimensionsx of tricritical hard squares and critical hard hexagons are calculated analytically. This is achieved by solving the special functional equation or inversion identity satisfied by the commuting row transfer matrices of these lattice models at criticality. The results are expressed in terms of Rogers dilogarithms. For tricritical hard squares we obtainc=7/10,x=3/40, 1/5, 7/8, 6/5 and for hard hexagons we obtainc=4/5,x=2/15, 4/5, 17/15, 4/3, 9/5, in accord with the predictions of conformal and modular invariance.     

Intercalation of Dyes Containing SO3H Groups into Zn–Al Layered Double Hydroxide

The intercalates of Naphthol Yellow S, Tropaeolin 000, and Tropaeolin 00 were prepared by heating [Zn_0.67Al_0.33(OH)₂](CO₃)_0.165 · 0.5H₂O with acidic forms of the dye solutions in an open reaction vessel. The intercalates were characterized by chemical and thermal analysis, X-ray powder diffraction and UV–VIS spectroscopy. A possible arrangement of the dye molecules in the intercalates was suggested on the basis of their chemical compositions and interlayer distances, by taking into account van der Waals dimensions of the guest molecules and by assuming that the structure of the host layers is not changed during the intercalation process.     

Intercalation of 1,2-Alkanediols into α-Zirconium Hydrogenphosphate

Intercalation compounds of α-Zr(HPO₄)₂ · H₂O with 1,2-alkanediols (from C3 to C16) have been prepared by replacing 1-propanol in α-Zr(HPO₄)₂ · 2C₃H₇OH with the desired 1,2-alkanediols by a treatment in a microwave field. It was found that the intercalates contain 1.5 molecules of diol per formula unit. The diol molecules are placed between the host layers in a bimolecular way with their aliphatic chains tilted at an angle of 51°. The diol molecules are anchored in the interlayer space by H-bonds. A mixed intercalate, containing 1,2-butanediol and 1,2-decanediol in a roughly equimolar ratio, is formed when the α-Zr(HPO₄)₂ · 2C₃H₇OH intercalate, suspended in a mixture of 1,2-butanediol and 1,2-decanediol, is exposed to microwave radiation. No new phase containing both types of the guest molecules was observed when the 1-propanol intercalate, suspended in a mixture of 1-propanol and 1,2-octanediol, is exposed to microwave radiation.     

Luminescent groups in very weakly degraded polystyrene

Unstabilized polystyrene samples from various producers, as well as carefully purified laboratory polymers, have been investigated by u.v.-absorption, fluorescence, phosphorescence and i.r. spectroscopy. The emission spectra of all samples indicate fluorescent and phosphorescent chromophores. In u.v.-absorption, the chromophores give rise to a long wavelength tail below the absorption edge of the phenyl groups. The phosphorescence spectrum is due to acetophenone-type end-groups of degraded polymer chains. Ultra-violet-fluorescence is due to monomeric styrene and trans-stilbene groups which probably can be formed at head-to-head sites of the polymer. Fluorescence in the blue spectral region may be due to chromophores formed by conjugated double bonds and phenyl groups. The chromophores are present in all commercial samples investigated and, at smaller concentrations, in the laboratory products also.     

Evidence for quasi-intramolecular acid-base reactions in solutions of transition metal ammine complexes

We have investigated the effect of temperature on the postulated quasi-intramolecular acid-base reactions in aqueous solutions of Cu(NH₃)₄(MnO₄)₂ and Ag(NH₃)₂ClO₄. Pure ammonium permanganate and perchlorate were obtained above 5 C and at room temperature, respectively, due to quasi-intramolecular acid-base reactions.     

Simplified ab initio calculations on small molecules with an extended balanced approximate MO formalism

Based on a test of different known simplified ab initio methods an approximate LCAO MO formalism is proposed which gives reasonable results in a minimal STO basis in comparison with ab initio calculations.     

Possible Mechanisms of Intercalation

Recent knowledge of the kinetics and intercalation mechanisms are summarized and accompanied by examples of intercalation reactions of water and ethanol into anhydrous vanadyl phosphate and redox intercalation of alkali metal cations into vanadyl phosphate dihydrate. Three possible mechanisms of intercalation are presented which are based on: (i) a concept of exfoliation of layers; (ii) the formation of stages and randomly stacked layers; (iii) co-existence of intercalated and non-intercalated parts of crystals of the host separated by an advancing phase boundary. The corresponding kinetic curves are ascribed to mechanisms (ii) and (iii).     

Parameter estimation for a misspecified arma model with infinite variance innovations

We consider a general linear model , where the innovations Z_t belong to the domain of attraction of an α-stable law for α<2, so that neither Z_t nor X_t have a finite variance. We do not assume that (X_t) is a standardARMA process of the form φ(B)X_t=ϕ(B)Z_t, but we fit anARMA process of a given order to the data X₁,...,X_n by estimating the coefficients of φ and ϕ. Given that (X_t) is anARMA process, it has been proved that the Whittle estimator is a consistent estimator of the true coefficients of ϕ and φ. Moreover, it then has a heavytailed limit distribution and the rate of convergence is (n/logn)^1/α, which compares favorably with the L² situation with rate . In this note we study the limit properties of the Whittle estimator when the underlying model is not necessarily anARMA process. Under general conditions we show that the Whittle estimate converges in probability. It converges weakly to a distribution which does not have a finite moment of order a and the rate of convergence is again (n/logn)^1/α. We also give an analytic expression for the limit distribution. Proceedings of the XVI Seminar on Stability Problems for Stochastic Models, Part II, Eger, Hungary, 1994.