Complete assignment of the 1H and 13C NMR spectra of four 2‐substituted 4a,8a‐cis‐endo‐5,8‐methano‐4a,5,8,8a‐tetrahydronaphthalene‐1,4‐diones

The complete assignment of the ¹H and ¹³C NMR spectra of the title enediones, bearing as substituents N‐aziridinyl (a novel compound), methoxy, chloro and methylsulfanyl, is reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Single access hashing with overflow separators for dynamic files

The dynamic external hashing proposed in this paper allocates records according to the spiral storage technique. Separators derived from the signature technique are used for distinguishing primary from overflow records and for subdividing overflow chains into segments allocated into the primary file. Single access retrieval is obtained by means of a main memory index with an entry per bucket and containing separators and pointers. While this method uses a larger index than other recent proposals, it is much more convenient regarding load factor and insertion cost. Furthermore, file expansion is directed by various control parameters, thus allowing the user to choose the most suitable policy for his application.     

Measurement of Hartmann-Hahn cross-polarization dynamics with quenching of proton T1ρ relaxation dependence

A simple modification of the standard cross-polarization method designed for quenching the proton T_1ρ dependence when studying polarization transfer is presented. It is demonstrated that by using this simple procedure, new and subtle details of cross-polarization dynamics, previously hidden by the T_1ρ(¹H) effect, can be observed in dipolar-coupled spin systems.     

Proof of a conjecture on the supports of Wigner distributions

In this note we prove that the Wigner distribution of an f ∈ L₂(ℝ_n) cannot be supported by a set of finite measure in ℝ_2n unless f=0. We prove a corresponding statement for cross-ambiguity functions. As a strengthening of the conjecture we show that for an f ∈ L₂(ℝ_n) its Wigner distribution has a support of measure 0 or ∞ in any half-space of ℝ_2n.     

An asymmetric Ellis theorem

In 1957 Robert Ellis proved that a group with a locally compact Hausdorff topology T making all translations continuous also has jointly continuous multiplication and continuous inversion, and is thus a topological group. The theorem does not apply to locally compact asymmetric spaces such as the reals with addition and the topology of upper open rays. We first show a bitopological Ellis theorem, and then introduce a generalization of locally compact Hausdorff, called locally skew compact, and a topological dual, Tk, to obtain the following asymmetric Ellis theorem which applies to the example above:Whenever (X,⋅,T) is a group with a locally skew compact topology making all translations continuous, then multiplication is jointly continuous in both (X,⋅,T) and (X,⋅,Tk), and inversion is a homeomorphism between (X,T) and (X,Tk).This generalizes the classical Ellis theorem, because T=Tk when (X,T) is locally compact Hausdorff.     

Bounded sets in topological groups and embeddings

We show that the existence of a non-metrizable compact subspace of a topological group G often implies that G contains an uncountable supersequence (a copy of the one-point compactification of an uncountable discrete space). The existence of uncountable supersequences in a topological group has a strong impact on bounded subsets of the group. For example, if a topological group G contains an uncountable supersequence and K is a closed bounded subset of G which does not contain uncountable supersequences, then any subset A of K is bounded in G?(K?A). We also show that every precompact Abelian topological group H can be embedded as a closed subgroup into a precompact Abelian topological group G such that H is bounded in G and all bounded subsets of the quotient group G/H are finite. This complements Ursul's result on closed embeddings of precompact groups to pseudocompact groups.     

On a theorem of Shchepin and Repovš concerning the smoothness of compacta

We show that a theorem of Shchepin and Repovš concerning the smoothness of compacta follows from the theory of semicontinuous relations.     

Preperfect graphs

We say that a vertexx of a graph is predominant if there exists another vertexy ofG such that either every maximum clique ofG containingy containsx or every maximum stable set containingx containsy. A graph is then called preperfect if every induced subgraph has a predominant vertex. We show that preperfect graphs are perfect, and that several well-known classes of perfect graphs are preperfect. We also derive a new characterization of perfect graphs.