Independence and graph homomorphisms graph homomorphisms

A graph with n vertices that contains no triangle and no 5-cycle and minimum degree exceeding n/4 contains an independent set with at least (3n)/7 vertices. This is best possible. The proof proceeds by producing a homomorphism to the 7-cycle and invoking the No Homomorphism Lemma. For k ≥ 4, a graph with n vertices, odd girth 2k+1, and minimum degree exceeding n/(k+1) contains an independent set with at least kn/(2k+1) vertices; however, we suspect this is not best possible. © 1993 John Wiley & Sons, Inc.     

On Improvements to the Analytic Center Cutting Plane Method

In this paper, we explore a weakness of a specific implementation of the analytic center cutting plane method applied to convex optimization problems, which may lead to weaker results than Kelley's cutting plane method. Improvements to the analytic center cutting plane method are suggested, and tested on some example problems.     

Synthesis of 4H-pyrans by O-cyclization of 1,5-diketones

Substituted 4H-pyrans were obtained in high preparative yields by the reaction of 1,5-diketones with acetic anhydride and boron trifluoride etherate in diethyl ether. It is assumed that the heterocyclization of 1,5-diketones includes a step involving the formation and transformations of an acyloxy carbonium ion.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 320–322, March, 1992.     

Nitroazines. 20. Simple syntheses of nitropyrazolopyridines from aliphatic nitrosynthons and aminopyrazoles

Two variants of a synthesis for nitropyrazolopyridines from aminopyrazoles and two- or three-carbon nitrosynthons are examined.For Communication 19 see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1560–1564, November, 1992.     

Mg 2p shallow core-level and local atomic structure of i-ZnMgRE quasicrystals

We present a detailed analysis of the Mg 2p shallow core-levels measured on icosahedral single-grain ZnMgY, ZnMgHo, and ZnMgEr quasicrystals during a photoelectron microscopy study. The synchrotron radiation photoemission measurements were performed on in situ cleaved samples at a pressure of 10⁻¹⁰ mbar and at low temperature, typically 90-150 K. The Mg 2p photoemission lines are essentially broadened as compared to those of the Mg 2p spin-orbit doublet recorded on the Zn₂Mg crystalline Laves phase. The broadening is associated to the coordination shifts of the Mg 2p level due to the inequivalent magnesium sites in the quasicrystalline lattice. The coordination shifts are calculated on the basis of i-ZnMg(Ho, Y) atomic structure data, recently determined from the pair distribution function analysis. The coordination shifts obtained are up to 0.2 eV. The Mg 2p experimental spectral intensity is nicely reproduced by a superposition of coordination-shifted Mg 2p spin-orbit doublets.     

Taylor-Galerkin algorithms for viscoelastic flow: Application to a model problem

Coupled and decoupled Taylor-Galerkin algorithms are considered for viscoelastic flow and a model problem—transient startup Poiseuille flow in a channel under a fixed pressure gradient. All algorithms reproduce the steady-state solutions and are stable at high elasticity numbers (E). For a fixed mesh, the coupled and decoupled versions (TGC and TGD) give exceptional time-accuracy at low elasticity numbers [to within O(1%) at E = 1] and reasonable accuracy at high elasticity numbers [to within O(10%) at E = 10, 100]. By definition, the decoupled false-transient scheme (TGF), which uses different time scales for velocity and stress time stepping, provides a poor transient history. Where the main requirement is to compute a steady-state algorithm efficiency is crucial. The TGF scheme attains a steady state between six to eight times faster than does the TGC scheme, and the latter is over twice as fast as the TGD form. © 1994 John Wiley & Sons, Inc.