Intermittency and the central limit theorem

Central limit theorem estimates of anomalous fractal dimensions of self-similar random cascades are studied. It is found that, in general, the normal approximation fails badly. A systematic series of approximations which converges to the exact result (both for the fractal dimensions and for the distribution itself) is derived for the -model. Consequences for the empty bin effect are indicated.Supported by the World Laboratory/HED and the CERN/LAA Projects     

Phase diagram of the ANNNI model in the Hamiltonian limit

The Hamiltonian limit of the ANNNI model in (1+1) dimensions is studied by using the Quantum Statistical Monte Carlo method. Even if recent results suggest that Monte Carlo calculations may prove unreliable in the study of this system, the phase diagram of the quantum version of the model was successfully obtained. In particular, the clusive transitions between the disordered, the floating incommensurate and the degenerate 2, 2 are determined by analysing the correlation length behaviour in finite lattices.Partially supported by CONICET Argentina     

The bestL 2-approximation by finite sums of functions with separable variables

Summary We consider the problem of the best approximation of a given functionh L ² (X × Y) by sums _k=1 ⁿ f _k f _k, with a prescribed numbern of products of arbitrary functionsf _k L ² (X) andg _k L ² (Y). As a co-product we develop a new proof of the Hilbert—Schmidt decomposition theorem for functions lying inL ² (X × Y).     

Blaschke-Süss type theorems for closed plane curves

A C¹-class of plane closed curves is considered, which contains all ovals and rosettes. This class is divided into some subclasses for which greatest lower bounds of numbers of antipodal and arc-antipodal sets are determined.     

水中3-甲基-6-氨基-5-氰基-4-芳基-1-苯基-1，4-二氢吡喃[2，3-c]吡唑的洁净合成

在水溶剂中并有三乙基苄基氯化铵（TEBA）存在下，取代芳亚甲基丙二腈与3- 甲基-1-苯基-2-吡唑啉-5-酮缩合成为3-甲基-6-氨基-5-氰基-4-芳基-1-苯基-1， 4-二氢吡喃[2,3-c]吡唑，此法为相应化合物的合成提供了一种快速、方便、高效 和洁净的方法。     

Reactivity of thienopyrroles. Synthesis of isomeric nitro and bromothienopyrroles

The preparation of ethyl 2-bromothieno[2,3-b]pyrrole-5-carboxylate, ethyl 2-bromothieno[3,2-b]pyrrole-5-carboxylate, ethyl 2-nitrothieno[2,3-b]pyrrole-5-carboxylate and ethyl 2-nitrothieno[3,2-b]pyrrole-5-carboxylate are described.     

Adams methods for neutral functional differential equations

Summary In this paper Adams type methods for the special case of neutral functional differential equations are examined. It is shown thatk-step methods maintain orderk+1 for sufficiently small step size in a sufficiently smooth situation. However, when these methods are applied to an equation with a non-smooth solution the order of convergence is only one. Some computational considerations are given and numerical experiments are presented.     

Kinetics of the hydrogen electrode reactions of platinum in the NaHSO4 + KHSO4 eutectic melt

The kinetics of the hydrogen electrode reactions on Pt in the NaHSO₄ + KHSO₄ melt at ca. 185°C is studied. Under potentiodynamic conditions both the anodic and cathodic processes can be interpreted with the hydrogen electrode reaction mechanism already known. At potentials more negative than 0.1 V (vs. Ag/Ag⁺ (0.06 M)) the mechanism of the cathodic reaction changes because of a sulphide species formed on the electrode which is produced by a reduction of the melt components.     

Dichloro and alkylchloro gallium derivatives of dichalcogenoimidodiphosphinate ligands: isolation of a spirogallium cation

Dichloro and chloromethyl Ga(III) complexes of general formulae [XClGa-eta2-{R2P(E)NP(E'R'2-E,E'}](X = Cl, R, R'= Ph, E, E'= O (1), S (2), Se (3); R = Ph, R'= OEt, E = O, E'= S (4); R = Me, R'= Ph, E, E'= S (5) and X = Me, E, E'= O (6), S (7), Se (8)) were synthesised by either metathesis reactions between GaCl3 and the potassium salt of the ligand (X = Cl) or by methane eliminations from in situ prepared GaMe2Cl and the protonated ligands LH (X = Me). Redistribution reaction of (3) in either CDCl3 or THF afforded the solvent-free tetracoordinate gallium spirocycle cation [Ga-{eta2-{Ph2P(Se)NP(Se)Ph2-Se,Se'})2]+ (9+). The molecular structures of complexes 2, 4, 5, 7 and 9(+) show non-planar gallacycle rings.