Ring-opening reactions of benzotriazoles with Wittig reagents

Nonafluorobutanesulfonyl-1H-benzotriazole affords phenylazomethylenetriphenylphosphoranes upon treatment with in situ generated alkyl triphenylphosphoranylidenes. Methylenetriphenylphosphorylidene yields the corresponding bis-phenylazomethylene-triphenylphosphorane.     

Agglutination kinetics of F(ab′)2 coated polymer colloids

In a previous publication we have described a simple quantitative model describing the agglutination process due to antigen–antibody interactions in IgG–latex immuno-assays. To achieve colloidal stability, however, some additives had to be used. In this paper we study the immunoreactivity of F(ab′)₂ antibody physical and chemically adsorbed onto sulphonate polystyrene and chloromethylstyrene particles, respectively. This kind of latex immuno-assay does not show stability problems under physiological condi-tions. The influence on the agglutination kinetics of the protein coating level has been now studied for the whole coverage range. Also the influence of coupling procedure, storage time and ionic strength of the reaction medium have been investigated.     

Separation properties of Θ-modifications of topologies

The author examines separation properties of the modification Θ(τ) of a topology τ connected with the concept of Θ-cluster points in the sense of N. V. Veli?ko.     

The correlation coefficient attacks again

The use of the correlation coefficient for testing the linearity of calibration curves is performed according to the ANOVA checking of the lack-of-fit. The procedure is illustrated from a case study.Papers published in this section do not necessarily reflect the opinion of the Editors,the Editorial Board and the Publisher. Apart from exceptional circumstances, they are not submitted to the usual referee procedure and go essentially unaltered.     

The danger model: application to a competitive market

The behavior of the firm in a competitive market based on the idea of the human system, i.e., using a danger activator and a defence system, is modelled. The proposed model uses three variables: market share ratio, danger index and the ratio of relative investment between the firm and the total investments including the competition. The danger activator, the defence and the market reaction functions, which explain how the danger index becomes activated, how the firm reacts to a danger signal, and the market reaction to the firm’s actions, respectively, are carefully constructed. This leads to a parametric dynamic system that governs the behavior of the competitive market. The following five classical behaviors of a firm result: monopoly, below aimed market share, aimed market share, above aimed market share and out of market. Formulas for a sensitivity analysis are derived to determine how and how much the equilibrium points of the dynamic system change when the parameters change. All the concepts are illustrated by graphs that show the equilibrium points and the trajectories of the system.     

Thermodynamic and kinetic considerations in the chemoselective O-acylation by mixed anhydrides. A semiempirical MO approach

A simple methodology to achieve high chemoselective O-acylation of primary hydroxy groups, in the presence of secondary ones, was performed by means of the quick generation of a mixed anhydride using mild and inexpensive conditions. Steric and electronic factors are involved in this preference. As far as the geometries are concerned, semiempirical calculations were carried out in order to determine the nature of the contribution to the thermodynamics and kinetics. From a qualitative point of view, it was found that the thermodynamics are sugar dependent whereas the kinetics are mixed anhydride dependent. These conclusions fit quite well with the experimental results allowing the use of semiempirical MO calculations as a tool for modulating the selectivity ratio for this process since different systems may be modeled in the same way.     

Boundary value problems for Dirac operators and Maxwell's equations in fractal domains

Some boundary value problems are solved for time‐harmonic electromagnetic fields on fractal domains, in the framework of exploiting hypercomplex function theory. Copyright © 2014 John Wiley & Sons, Ltd.     

On ‐Cocyclic Hadamard Matrices

A characterization of ‐cocyclic Hadamard matrices is described, depending on the notions of distributions, ingredients, and recipes. In particular, these notions lead to the establishment of some bounds on the number and distribution of 2‐coboundaries over to use and the way in which they have to be combined in order to obtain a ‐cocyclic Hadamard matrix. Exhaustive searches have been performed, so that the table in p. 132 in A. Baliga, K. J. Horadam, Australas. J. Combin., 11 (1995), 123–134 is corrected and completed. Furthermore, we identify four different operations on the set of coboundaries defining ‐cocyclic matrices, which preserve orthogonality. We split the set of Hadamard matrices into disjoint orbits, define representatives for them, and take advantage of this fact to compute them in an easier way than the usual purely exhaustive way, in terms of diagrams. Let be the set of cocyclic Hadamard matrices over having a symmetric diagram. We also prove that the set of Williamson‐type matrices is a subset of of size .     

Vanillin (1) As Starting Material for the Synthesis of Isomeric Phthalides

Phthalides have bcen employed as useful intcriucdiates in tic sqrnthcsis of my condcnscld aromatic carbocyclic and heterocyclic compounds, including several natural products In this paper we report two alternative synthetic pathways for the preparation of phthalides as shown for the synthesis of the isomeric pairs of compounds 5a-d and 7a-d.