Discrete dynamical equations in Minkowski space

Discrete difference equations in Minkowski space are obtained and the discrete Minkowski force is shown to be a four-vector. A transformation from a discrete dynamical equation in Minkowski space to a Lorentz-invariant difference equation in one-dimensional space is given.     

High-spin levels in138Ce and140Nd Observed in the (α, 4n γ) reactions

Levels of¹³⁸Ce and¹⁴⁰Nd have been studied using the¹³⁸Ba(α,4nγ)¹³⁸Ce and¹⁴⁰Ce(α, 4nγ)¹⁴⁰Nd reactions. Singleγ-ray spectra,γ-γ coincidence spectra, angular and time distributions with respect to the beam bursts have been measured. A number of higher excited states with excitation energies up to about 5 MeV and with spin value up to 12 are populated in both nuclei. The lower states with spins and parities 7^?, 5^?, 6^? and 10⁺ can be explained by two-quasiparticle neutron configurations of the types (h _11/2 ^?1 ,d _3/2 ^?1 ) 7^? , (h _11/2 ^?1 ,S _1/2 ^?1 ) 5^?, 6^? and (h _11/2 ^?2 ) 10⁺. Several high-spin states observed in¹³⁸Ce and¹⁴⁰Nd can be explained qualitatively as four-quasiparticle states with two-proton-two-neutron configurations. The 3^? state at an energy of 2,137.4 keV is observed in¹³⁸Ce. The evidence for the existence of the low-lying 3^? states in¹⁴⁰Nd at 2,124.0 keV is discussed. Beside the known 9.6 ms (7^?) isomeric state in¹³⁸Ce another state at 3,538.5keV (10⁺) with a half life of about 200 ns has been observed. The observed levels in the¹³⁸Ce and¹⁴⁰Nd nuclei are compared with theoretical predictions using delta force interaction.     

A Simple Method for the Synthesis of the Sterically Hindered Chloramines

A simple route to the hindered chloramines, starting from the corresponding hindered amines is reported. Sodium dichlorisocyanurate is the chlorinating agent.     

Synthesis and Reactivity of Metallophosphanes

Abstract

Aspects of the reactivity of metallophosphanes are presented along with the synthesis and structure determinations for new aluminophosphanes.     

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.     

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.