Bounded sets structure of CpX and quasi‐(DF)‐spaces

For wide classes of locally convex spaces, in particular, for the space $C_p(X)$ of continuous real‐valued functions on a Tychonoff space X equipped with the pointwise topology, we characterize the existence of a fundamental bounded resolution (i.e., an increasing family of bounded sets indexed by the irrationals which swallows the bounded sets). These facts together with some results from Grothendieck's theory of $(DF)$‐spaces have led us to introduce quasi‐ $(DF)$‐spaces, a class of locally convex spaces containing $(DF)$‐spaces that preserves subspaces, countable direct sums and countable products. Regular $(LM)$‐spaces as well as their strong duals are quasi‐ $(DF)$‐spaces. Hence the space of distributions $D^{\prime }(\mathrm{\Omega })$ provides a concrete example of a quasi‐ $(DF)$‐space not being a $(DF)$‐space. We show that $C_p(X)$ has a fundamental bounded resolution if and only if $C_p(X)$ is a quasi‐ $(DF)$‐space if and only if the strong dual of $C_p(X)$ is a quasi‐ $(DF)$‐space if and only if X is countable. If X is metrizable, then $C_k(X)$ is a quasi‐ $(DF)$‐space if and only if X is a σ‐compact Polish space.     

Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation

Nonlinear Dynamics - This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the...     

Structure and Physical Properties of Coordination Compounds of 2-Aminoindan-2-Phosphonic Acid with Some D-Electron Elements

Abstract

Many complexes of 1-aminoakylphosphonic acids have been obtained and their structures have been studied [1–3]. On the other hand, 2-aminoindan-2-phosphonic acid (2-AIP), the phosphonic conformationally restricted cyclic analogue of phenylalanine, has been recently obtained [4]. We undertook a study of interaction of cobalt(II), nickel(II), and copper(II) with 2-AIP, to learn how the rigid Iigand structure influences the complexes structure.     

Synthesis and Pesticidal Properties of Thio and Seleno Analogs of Some Common Urea Herbicides

Thio and seleno analogs of fenuron, isoproturon, chlorotoluron, metoxuron, monuron, and diuron were synthesized from the corresponding aryl amines. Their reaction with thiophosgene leads to isothiocyanates. Aryl amines were also converted (via isocyanides) to isoselenocyanates. The reaction of both isothio- and isoselenocyanates with dimethylamine affords the corresponding thio and seleno analogs of the above-mentioned urea herbicides. Herbicidal activity of the synthesized compounds was slightly lower than the activity of the parent urea herbicides. The thio and seleno analogs as well as the parent ureas showed good fungicidal activity at a concentration of 200 ppm against selected fungi.