Joint flight experiment UK/1977. Report no. 1: Planning and execution

There are no author-identified significant results in this report

TELLUS newsletter 1

There are no author-identified significant results in this report

Coloring and constructing (hyper)graphs with restrictions

We consider questions regarding the existence of graphs and hypergraphs with certain coloring properties and other structural properties. In Chapter 2 we consider color-critical graphs that are nearly bipartite and have few edges. We prove a conjecture of Chen, Erdős, Gyárfás, and Schelp concerning the minimum number of edges in a “nearly bipartite” 4-critical graph. In Chapter 3 we consider coloring and list-coloring graphs and hypergraphs with few edges and no small cycles. We prove two main results. If a bipartite graph has maximum average degree at most 2(k−1), then it is colorable from lists of size k; we prove that this is sharp, even with an additional girth requirement. Using the same approach, we also provide a simple construction of graphs with arbitrarily large girth and chromatic number (first proved to exist by Erdős). In Chapter 4 we consider list-coloring the family of kth power graphs. Kostochka and Woodall conjectured that graph squares are chromatic-choosable, as a strengthening of the Total List Coloring Conjecture. Kim and Park disproved this stronger conjecture, and Zhu asked whether graph kth powers are chromatic-choosable for any k. We show that this is not true: we construct families of graphs based on affine planes whose choice number exceeds their chromatic number by a logarithmic factor. In Chapter 5 we consider the existence of uniform hypergraphs with prescribed degrees and codegrees. In Section 5.2, we show that a generalization of the graphic 2-switch is insufficient to connect realizations of a given degree sequence. In Section 5.3, we consider an operation on 3-graphs related to the octahedron that preserves codegrees; this leads to an inductive definition for 2-colorable triangulations of the sphere. In Section 5.4, we discuss the notion of fractional realizations of degree sequences, in particular noting the equivalence of the existence of a realization and the existence of a fractional realization in the graph and multihypergraph cases. In Chapter 6 we consider a question concerning poset dimension. Dorais asked for the maximum guaranteed size of a subposet with dimension at most d of an n-element poset. A lower bound of sqrt(dn) was observed by Goodwillie. We provide a sublinear upper bound

Theory of chromatography and its application to cation exchange in soils.

Different types of solutions of the differential equation describing the process of cation exchange chromatography are compared and evaluated for their applicability to soil conditions. In cases where divalent cations replace monovalent ions, the exchange front assumes a stationary profile at an early stage which then yields an analytical solution provided a fairly simple exchange equation like that of Gapon or Vanselow is applicable. Where monovalent ions replace divalent ions, a non-stationary front arises, which is strongly dominated by the exchange equation. A good approximation of the front can be obtained by an analytical solution taking no account of diffusion or dispersion. Knowledge of the total electrolyte in the soil column is often the limiting factor in predicting the location and shape of the exchange front.[112.23.07]. (Abstract retrieved from CAB Abstracts by CABI’s permission