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.     

Disordered charge distributions and dielectric loss in extra dense flint glasses

The complex permittivities of some extra dense flint glasses (EDF glasses) have been studied. The dielectric features of the samples are dominated by their PbO content. Both refractive indices and dielectric losses exhibit a close relation to the concentration of Pb ions. The latter are located either at sites of the network atoms or filling the potential minima interstitially. They can be identified by their different relaxation mechanisms. The dispersion in the submillimeter wave and FIR area is characterized by a very broad distribution of comparably sharp resonant states. Thermal lens — or hysteresis effects can be excluded.     

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.     

A remark on partial linear spaces of girth 5 with an application to strongly regular graphs

We derive a lower bound on the number of points of a partial linear space of girth 5. As an application, certain strongly regular graphs with=2 are ruled out by observing that the first subconstituents are partial linear spaces.     

含嘧啶环的双冠醚(Ⅳ)

前文已报道由啶环桥联两个苯并冠醚的双冠醚的合成与性质。由于嘧啶环的刚性较大,能把两个冠醚单元固定在有效地协同作用位置,因此以它们作中性载体的离子选择性电极具有较好的选择性。为了进一步研究这类双冠醚的性质,我们合成了四种嘧啶环桥联两个脂肪族冠醚的双冠醚,并经元素分析、IR、′HNMR鉴定。     

Fermi and Coulomb correlations in the 21 S state of the helium isoelectronic sequence

The Fermi and Coulomb holes of the 2¹ S state of the helium isoelectronic sequence are investigated. Several interesting differences between the results obtained and those which might be expected on the basis of the corresponding 2³ S state are pointed out and discussed.     

Photochemical properties and structures ofN-amino andN-azomethine derivatives of 2,4,6-triphenylpyridinium perchlorates

The molecular structures of the initial compounds and the products of photocyclization involving amino and azomethine groups in perchlorates ofN-amino (1) andN-azomethine (2) derivatives of 2,4,6-triphenylpyridinium cations were studied. Cations1 and2 have an essentially non-coplanar arrangement of the -Ph rings, and the product of photocyclization of2, cation3, is characterized by a flattened structure. It was found that the orientation of the lone electron pair of the N atom with respect to one of the planes of the -Ph rings in molecule1 is more favorable for monocyclization involving the amino group. The structure of molecule2 allows two routes of the photoreaction,viz., O N proton transfer and monocyclization with an -Ph ring. However, the structural features of molecule2 are more favorable for photocyclization.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 296–301, February, 1995.     

Photoelectron spectroscopy of mono and binuclear iron and chromium cyclooctatetraene complexes

The ultraviolet photoelectron spectra of mono and binuclear cyclooctatetraene (COT) complexes (CO)₃FeCOT (I) [(CO)₃Fe]₂COT (II), CpCrCOT (Cp: 1,3 cyclopentadienyl) (III) and (CpCr)₂COT (IV) are reported. The interpretation of the low energy part of the spectra is followed by a discussion concerning the metal–ligand (COT) and metal–metal interactions. The calculated gas phase structure of CpCrCOT is presented and its main features are discussed.     

Synthesis of the first stable carborane containing simple enol

A carborane-containing stable simple enol — 1-2-isopropyl-o-carboran-I-yl)-1-phenyl2-mesityl-2-lrydroxyctlrylcne — has been synthesized. This enol does not isomerize to the starting ketone or keto-enol mixture even after prolonged heating in benzene in the presence of CF₃COOH.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 6, pp. 1561–1563, June, 1996.     

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.