Studies on stable free radicals. XIX. Copolymerization of N-oxyl biradical with α-chloro-p-xylylene

Copolymerization of N-oxyl biradical with α-chloro-p-xylylene was carried out by varying the feed ratio of α,α′-dichloro-p-xylene which was the precursor of α-chloro-p-xylylene. The structures of the obtained copolymers were determined spectroscopically. The results that the N-oxyl attacked the carbon-bearing chlorine atom of α-chloro-p-xylylene suggest a nucleophilic reactivity of N-oxyl radical. The copolymerization process was also discussed.     

Small-Angle electron scattering and electron density in carbon dioxide

The total (elastic and inelastic) intensity of electrons scattered by CO₂ was measured in the s range of 1 to 12 Å^?1 and compared with the theoretical intensity calculated from the Hartree-Fock molecular wave function and those calculated for the independent-atom-model (IAM ) molecule. In the range of s ? 4 Å^?1 the electron correlation effect on the total scattered intensity was found to be represented by that for the IAM molecule.     

Multi-poly-Bernoulli numbers and polynomials with a <Emphasis Type="Italic">q</Emphasis> parameter

We introduce themulti-poly-Bernoulli numbers and polynomialswith a q parameter, which are generalizations of the poly-Bernoulli numbers and polynomials with a q parameter, respectively.We give several combinatorial identities and properties of these new numbers and polynomials.     

On the residue classes of integer sequences satisfying a linear three term recurrence formula

In this paper we investigate linear three-term recurrence formulae with sequences of integers (T(n))_n?0 and (U(n))_n?0, which are ultimately periodic modulo m, e.g.

     

On the image of the Burau representation of the IA-automorphism group of a free group

In this paper we study the graded quotients of the lower central series of the image of the IA-automorphism group of a free group by the Burau representation. In particular, we determine their structures for degrees 1 and 2.     

Extremal solutions for stochastic equations indexed by negative integers and taking values in compact groups

Stochastic equations indexed by negative integers and taking values in compact groups are studied. Extremal solutions of the equations are characterized in terms of infinite products of independent random variables. This result is applied to characterize several properties of the set of all solutions in terms of the law of the driving noise.     

Lower bounds on the cardinality of the maximum matchings of planar graphs

Lower bounds on the cardinality of the maximum matchings of planar graphs, with a constraint on the minimum degree, are established in terms of a linear polynomial of the number of vertices. The bounds depend upon the minimum degree and the connectivity of graphs. Some examples are given which show that all the lower bounds are best possible in the sense that neither the coefficients nor the constant terms can be improved.