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.     

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.     

Interaction of neutrons with zinc and its isotopes

Coherent neutron scattering lengths and total cross sections have been measured for elemental Zn,Zn-compounds and on isotopicly enriched samples for neutron energies from 0.5 meV up to 143 keV using different techniques. From the experimental data the following quantities were obtained:

the coherent scattering lengths (b in fm) of Zn (5.689±0.014);⁶⁴Zn (5.23±0.04);⁶⁶Zn (5.98±0.05);⁶⁷Zn (7.58±0.08;b ₊=9.4±0.5/5.8±0.5;b _?=5.0±0.7/10.1±0.7);⁶⁸Zn (6.04 ±0.03);

the potential scattering radii (R′ in fm) of Zn (6.2±0.2),⁶⁴Zn (6.0±0.3) and⁶⁶Zn (6.2 ±0.3);

the absorption cross sections (σ _γ at 0.025 eV in barn) of Zn (1.11±0.02);⁶⁴Zn (1.1 ±0.1) and⁶⁶Zn (0.62±0.06).

Derived quantities are the “zero energy” scattering cross sections (σ ₀ in barn) for Zn (4.128±0.010) and⁶⁷Zn (7.8±0.3) and the incoherent bound cross sections of Zn (0.061 ±0.023) and⁶⁷Zn (0.6±0.4). In the epithermal region the Zn-cross section can be described by introduction of two strong bound levels of⁶⁷Zn+n for which estimated parameters are given.     

Palladium(II) complexes of the reducing sugars D-arabinose,D-ribose,rac-mannose,and D-galactose

The cellulose solvent Pd-en, an aqueous solution of [(en)Pd(II)(OH)(2)] (en=ethylenediamine), reacts with the monosaccharides D-arabinose (D-Ara), D-ribose (D-Rib), rac-mannose (rac-Man), and D-galactose (D-Gal) under formation of dimetalated aldose complexes, if the molar ratio of Pd and sugar is 2:1 or larger. In the Pd(2) complexes, the aldoses are tetra-deprotonated and act as bisdiolato ligands. Two crystalline pentose complexes were isolated: [(en)(2)Pd(2)(beta-D-Arap1,2,3,4 H(-4))].5 H(2)O (1) and [(en)(2)Pd(2)(beta-D-Ribp1,2,3,4 H(-4))].6.5 H(2)O (2), along with two hexose complexes. With rac-Man, the major solution species is crystallized as the 9.4-hydrate [(en)(2)Pd(2)(beta-rac-Manp1,2,3,4 H(-4))].9.4 H(2)O (3). From the respective D-Gal solutions, [(en)(2)Pd(2)(beta-D-Galf1,3,5,6 H(-4))].5 H(2)O.C(2)H(5)OH (4), with the sugar tetraanion in its furanose form, is crystallized though it is not the major species, rather the second most abundant in purely aqueous solutions. The Galf species is enriched in the mother liquors to the extent of 25 % of total sugar content. Substitution of the en ligand by two molecules of ammonia, methylamine, or isopropylamine, respectively, results in the formation of different solution species. With the bulkiest ligand, isopropylamine, monometalation of the aldoses in the 1,2-position is exclusively observed.     

Synthesis and supramolecular properties of trimethylene-bridged clips

The novel trimethylene-bridged clips 3 and 4 have been synthesized by using repetitive stereoselective Diels-Alder reactions of the benzo- and naphthobismethylenenorbornenes 8 and 19 as dienes and norbornadiene 9 as bisdienophile, and subsequent dehydrogenation of the primary cyclobisadducts 10 and 20 by using 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ). Clips 3 and 4 serve as receptors for a variety of electron-deficient neutral and cationic aromatic substrates, comparable to the molecular tweezers 1 and 2. The thermodynamic parameters of the complex formation, K(a) and DeltaG, were determined by (1)H NMR titration experiments and, in the case of the highly stable complex TCNB 32@4, by the use of isothermal titration microcalorimetry. The finding that clip 4 forms more stable complexes than 3 can be explained by the larger van der Waals contact surfaces of the naphthalene sidewalls in 4 compared to the corresponding benzene systems in 3. In the complexes with 4 as receptor, the plane of each aromatic substrate molecule is calculated to be oriented almost parallel to the naphthalene sidewalls. However, in the complexes of tweezers 2, the substrate is usually oriented parallel to the central naphthalene spacer unit. Due to the more open topology of 4, most complexes were calculated to consist of two or more equilibrating noncovalent conformers.     

Neue Sulfonamide, 12. Mitt. 5-Halogen-substituierte Sulfanilamido-methoxy-pyrimidine

Zusammenfassung Es wird die Darstellung von 2-Sulfanilamido-4-methoxy-5-chlorpyrimidin, 2-Sulfanilamido-4-methoxy-5-jodpyrimidin sowie 4-Sulfanilamido-2-methoxy-5-chlorpyrimidin beschrieben. Die erste Verbindung wurde auf zwei voneinander unabhängigen Synthesewegen erhalten. W. Klötzer undJ. Schantl, Mh. chem.94, 1178 (1963).