Intramolecular monodealkylation during the attempted synthesis of diethylphosphonoacetohydroxamic acid

The reaction of diethyl methyl phosphonoacetate ( 1 ) with hydroxylamine in NaOH solution resulted in the loss of one of the phosphorus ethyl groups, and yielded monoethylphosphonoacetohydroxamic acid ( 2 ) as the major product (79%) and diethylphosphonoacetic acid ( 3 ) as the minor product (21%). A series of control experiments were carried out to elucidate the sequence of the reactions leading to 2 . When the reaction of 1 with NH₂OH was carried out in NaHCO₃ solution, a transient product 4 was also observed, which slowly transformed to 2 . Compound 4 was assigned the structure diethylphosphonoacetohydroxamic acid. There was no dealkylation observed at the phosphorus when 1 was reacted with methoxylamine or when O‐methyl diethylphosphonoacetohydroxamate ( 7 ) was placed in alkaline solution. The dealkylation at phosphorus was interpreted in terms of intramolecular nucleophilic catalysis by the hydroxamic OH group attacking the phosphorus in 4 , involving cyclic 1,2,5‐oxazaphospholidine intermediates. © 2003 Wiley Periodicals, Inc. Heteroatom Chem 14:67–71, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/hc.10082     

Monotone paths on polytopes

We investigate the vertex-connectivity of the graph of f-monotone paths on a d-polytopeP with respect to a generic functionalf. The third author has conjectured that this graph is always (d )-connected. We resolve this conjecture positively for simple polytopes and show that the graph is 2-connected for any d-polytope with . However, we disprove the conjecture in general by exhibiting counterexamples for each in which the graph has a vertex of degree two. We also re-examine the Baues problem for cellular strings on polytopes, solved by Billera, Kapranov and Sturmfels. Our analysis shows that their positive result is a direct consequence of shellability of polytopes and is therefore less related to convexity than is at first apparent. Received April 6, 1999 / in final form October 1, 1999 / Published online July 20, 2000     

Sum Multicoloring of Graphs

Scheduling dependent jobs on multiple machines is modeled by the graph multicoloring problem. In this paper we consider the problem of minimizing the average completion time of all jobs. This is formalized as the sum multicoloring problem: Given a graph and the number of colors required by each vertex, find a multicoloring which minimizes the sum of the largest colors assigned to the vertices. It reduces to the known sum coloring problem when each vertex requires exactly one color.This paper reports a comprehensive study of the sum multicoloring problem, treating three models: with and without preemptions, as well as co-scheduling where jobs cannot start while others are running. We establish a linear relation between the approximability of the maximum independent set problem and the approximability of the sum multicoloring problem in all three models, via a link to the sum coloring problem. Thus, for classes of graphs for which the independent set problem is ρ-approximable, we obtain O(ρ)-approximations for preemptive and co-scheduling sum multicoloring and O(ρ log n)-approximation for nonpreemptive sum multicoloring. In addition, we give constant ratio approximations for a number of fundamental classes of graphs, including bipartite, line, bounded degree, and planar graphs.     

Novel podands and macrocycles with diacetal (tetraoxadecalin) cores: synthesis, structure, stereochemistry and cation inclusion

A series of functionalized 2,6-dialkyl-cis-1,3,5,7-tetraoxadecalin podands (3-10, alkyl = hydroxy-, mesyloxy-, halo-, azido- and aminomethyl and -ethyl) were prepared, characterized, and used as precursors for a new and interesting class of macrocycles and cryptands (12-21), with the aim to use these as host-guest inclusion systems. Extensive spectroscopic work was performed, structural endorsement was obtained from X-ray diffraction analyses and further insight into the structures was obtained from theoretical/computational studies. A number of macrocycles in the series exhibited good complexation with alkaline-earth metal ions.     

Magnetooptics and magnetic ordering in ferrite nanoparticles in glass doped with iron and rare-earth elements

Magnetic circular dichroism and X-ray diffraction were used to investigate the structure and magnetooptical properties of nanoparticles formed in potassium-aluminum-germanium-boron glass doped with iron and rare-earth elements. It is demonstrated that in thermally processed glass, the main magnetic phase of the formed nanoparticles is γ-Fe₂O₃ maghemite.     

Hierarchical structures in the phase space and fractional kinetics: I. Classical systems

Hamiltonian chaotic dynamics is not ergodic due to the infinite number of islands imbedded in the stochastic sea. Stickiness of the islands' boundaries makes the wandering process very erratic with multifractal space-time structure. This complication of the chaotic process can be described on the basis of fractional kinetics. Anomalous properties of the chaotic transport become more transparent when there exists a set of islands with a hierarchical structure. Different consequences of the described phenomenon are discussed: a distribution of Poincare recurrences, characteristic exponents of transport, nonuniversality of transport, log periodicity, and chaos erasing. (c) 2000 American Institute of Physics.     

A counterexample to a hadamard matrix pivot conjecture

In the study of the growth factor of completely pivoted Hadamard matrices, it becomes natural to study the possible pivots. Very little is known or provable about these pivots other than a few cases at the beginning and end. For example it is known that the first four pivots must be 1,2,2 and 4 and the last three pivots in backwards order must be n/2, and n/2. Based on computational experiments, it was conjectured by Day and Peterson, that the n—3rd pivot must always be n/4. This conjecture would have suggested a kind of symmetry with the first four pivots. In this note we demonstrate a matrix whose n-3rd pivot is n/2 showing that the conjecture is false.