On extendable planes of order ten

It is well known that the only way of extending a projective plane of order n (conceivable orders are 2, 4 and 10) is adjoining a set of hyperovals to the given projective plane. A converse is proved in this note. It is shown as a corollary that the existence of an extendable plane of order 10 is equivalent to the existence of a quasi-symmetric 2-(111, 12, 10)-design.     

Auxiliary sets of matrices with new step parameter sequences

Constructions are given for auxiliary sets of matrices which have the previously unknown step parameter sequences (3,11,3), (2,2,8,11), (2,2,8,13), (2,2,9,11). As a consequence one obtains a projective Hjelmslev plane for each of the preceding four step parameter sequences.     

Evaluation of Successive Fractions for Optimum Quantification of Bergenin and Gallic Acid in Three Industrially Important Bergenia species by High-Performance Thin-Layer Chromatography

JPC – Journal of Planar Chromatography – Modern TLC -     

An Efficient Straightforward Synthesis of (-)-Bulgecinine

(-)-Bulgecinine 1, a component of the antibiotic bulgecins, was efficiently synthesized from (S)-pyroglutaminol2.     

Classification of (16,6,2)-designs by ovals

Using the triangular graph T(6) it is shown that up to isomorphism any (16,6,2)-design is uniquely determined by the number of ovals in it, which is 12, 28 or 60. It is shown that the (16,6,2)-design with precisely 60 ovals is embeddable in a 3-(22,6,1)-design. As a consequence the uniqueness of the 3-(22,6,1)-design is obtained.     

Some new invariant pairs (t,3) for projective hjelmslev planes

Associated with every finite projective Hjelmslev plane is an invariant pair (t,r): t is the number of neighbours of a given point on a given line passing through it and r is the order of the underlying projective plane. The Drake-Lenz method [2],[3] of using auxiliary matrices for the constructions of projective Hjelmslev planes has become standard by now. This paper is intended to give some new constructions of projective Hjelmslev planes with invariant pairs (t,3) by making use of the generalization and improvement of the Drake-Lenz theorem [3] obtained by the author in [6] and [7]. The results of this paper add 8 new values to the list ([5], example 3.7(ii)) of invariant pairs (t,3) with t 1,000 for projective Hjelmslev planes.     

A successful algorithm for the undirected Hamiltonian path problem

In this paper a polynomial algorithm called the Minram algorithm is presented which finds a Hamiltonian Path in an undirected graph with high frequency of success for graphs up to 1000 nodes. It first reintroduces the concept described in [13] and then explains the algorithm. Computational comparison with the algorithm by Posa [10] is given.It is shown that a Hamiltonian Path is a spanning arborescence with zero ramification index. Given an undirected graph, the Minram algorithm starts by finding a spanning tree which defines a unique spanning arborescence. By suitable pivots it locates a locally minimal value of the ramification index. If this local minima corresponds to zero ramification index then the algorithm is considered to have ended successfully, else a failure is reported.Computational performance of the algorithm on randomly generated Hamiltonian graphs is given. The random graphs used as test problems were generated using the procedure explained in Section 6.1. Comparison with our version of the Posa algorithm which we call Posa-ran algorithm [10] is also made.     

Intramolekulare Cycloadditionen Mit Azomethin-Yliden: Synthese und NMR-Untersuchungen einiger Paracyclophan-Derivate vom Makrolid-Typ

Intramolecular Cycloaddition Reactions with Azomethine Ylides: Synthesis and NMR Investigations of Some Macrolide-Type Paracyclophanes Several aziridine derivatives bearing a para-substituted phenyl group have been prepared as precursors of azomethine ylides for intramolecular 1,3-dipolar cycloadditions. Upon heating in refluxing toluene, the expected reactions take place resulting in the regioselective formations of the pairs of diastereoisomers 14 / 15 and 16 / 17 , respectively. As indicated by the sharply decreasing yield in the a -series (< 5%), a useful application of this method for preparing paracyclophane compounds is restricted to derivatives with more than 11 bridging atoms. The results of detailed ¹H- and ¹³C-NMR investigations with the pyrrolidino-annulated cyclophanes are discussed with respect to the configuration at the five-membered heterocycles and to the conformational flexibility of the bridges.     

Kinetic investigations on interaction of carbon monoxide with RuIICl2(PPh3)3 in mixed aqueous medium

Kinetics, equilibrium and thermodynamics of interaction of CO with RuCl₂(PPh₃)₃ (1) have been investigated in 1:1(v/v) water — 1,4-dioxan mixture in which 1 dissociates to RuCl₂(PPh₃)₂ (1a), by losing a coordinated PPh₃. The kinetics of complexation of (1a) with CO to form RuCl₂(CO)(PPh₃)₂ (2) indicated first order dependence in [1a] and [CO]. The thermodynamic parameters for the formation of 2 were determined.This revised version was published online in December 2005 with corrections to the Cover Date.