On the geometries of the rational unfoldings of X k

With a view to applications to self-regulating dynamical processes in biology, we determine the geometric structure of what we call isotangent curves, i.e. curves parametrized by the slopes of their points. They come up naturally as bifurcation curves of rational unfoldings of X ^k, and we classify them according to degree and number of cusps. They, as well as their isotangent involute curves, turn up in simulations of these processes.     

Pair formation in age-structured populations

The modelling problems associated with pair formation in age-structured populations are discussed in this paper. The author also formulates a class of models for pair formation in human populations and derives some results on persistent distributions.     

Some inequalities for partial orders

We establish some inequalities connecting natural parameters of a partial order P. For example, if every interval [a,b] contains at most maximal chains, if some antichain has cardinality v, and if there are ₁ chains whose union is cofinal and coinitial in P, then the chain decomposition number for P is ₁v (Theorem 2.2), and the inequality is sharp in a certain sense (Section 3).This paper was written while the authors were visitors at the Laboratoire d'algèbre ordinale, Département de Mathématiques, Université Claude Bernard, Lyon 1, France.Research supported by NSERC grant # A5198.     

Why is space three-dimensional and how may groups be seen?

First we propose a model of visual perception essentially based on the Keldysh-Chernavsky-Sossinsky three-channel theorem, from which three-dimensionality of space follows. Second, we associate with a system of subgroups H ₁, ..., H_s of a given group G a geometric object, called a group crystal, in order to visualize G. How this notion works is illustrated via the Burnside problem.     

A priori-Schranken für diskrete Lösungen monotoner Operatorgleichungen und Anwendungen

Summary Operator equationsTu=f are approximated by Galerkin's method, whereT is a monotone operator in the sense of Browder and Minty, so that existence results are available in a reflexive Banach spaceX. In a normed spaceY error estimates are established, which require a priori bounds for the discrete solutionsu _h in the norm of a suitable space . Sufficient conditions for the uniform boundedness u _{h Z} =O(1) ash0 are proved. Well-known error estimates in [3] for the special caseX=Y=Z are generalized by this. The theory is applied to quasilinear elliptic boundary value problems of order 2m in a bounded domain . The approximating subspaces are finite element spaces. Especially the caseX=W ₀ ^{m, p} (), 1<p<,Y=W ₀ ^{m. 2} (),Z=W ₀ ^{m. max (2,p)} ()W^m, () is treated. Some examples for 1<p<2 are considered. Forp2 a refined technique is introduced in the author's paper [7].

     

A novel synthetic route to substituted pyranoanthocyanins with unique colour properties

Anthocyanins, isolated from natural sources by countercurrent chromatography, were reacted with cinnamic acids bearing at least one electron-donating substituent at the para-position. The resulting pyranoanthocyanins obtained by this simple one-step reaction were much less susceptible to pH shifts and retained their original colour over a wide pH-range. Through reaction with p-dimethylamino cinnamic acid, synthetic malvidin- and cyanidin-based anthocyanins with a unique violet hue were prepared.     

Preparation of Y2Ba4Cu7O15-δ Superconductor without High Oxygen Pressure

The synthesis of bulk Y₂Ba₄Cu₇O_15-δ superconductor at atmospheric oxygen pressure via solid state sintering is reported. Temperature ranging from 860 to 890 °C as well as time interval over 2 to 15 days were used to investigate the formation of the Y₂Ba₄Cu₇O_15-δ phase. A time-temperature profile characterizing the conditions for the preparation of Y₂Ba₄Cu₇O_15-δ phase suggests the optimal condition to be sintering at 890 °C for over 10 days. Detailed results of X-ray diffraction, electrical resistivity, iodometric titration and magnetization measurements are described.     

The use of fluorescence in determining formation constants of complexes : Part II. Complexes which fluoresce

Four different methods for the calculation of the formation constants of fluorescing complexes are discussed. The methods were used to determine constants for the complexes of aluminum(III), gallium(III) and indium(III) with 8-quinolinol-5-sulfonate anion.     

Molecular structure and pseudopolymorphism of squamtin A from Annona squamosa

The cyclopeptide, squamtin A (1, formula: C₃₉H₆₀O₁₁N₈S), was found to crystallized in two pseudopolymorphisms, i.e. 1·(H₂O)_3.5 and 1·(H₂O)_3.9. The composition of the amino acids and their linkage sequences are the same. The main differences between the two kinds of crystals lie in the positions and occupancies of the water molecules, the positions of the sulfur atoms and the conformation of the side chains. The absolute configuration of 1 is established by X-ray analysis in combination with the Marfey's analysis of its hydrolysates.