Completeness of the SO(4) Extended Bethe Ansatz for the One-Dimensional Hubbard Model

We show how to construct a complete set of eigenstates of the hamiltonian of the one-dimensional Hubbard model on a lattice of even length $L$. This is done by using the nested Bethe Ansatz {\it and} the $SO(4)$ symmetry of the model. We discuss in detail how the counting of independent eigenstates is carried out.Comment: 33 pages, using latex, to appear in Nucl.Phys. B (FS

On the pathwidth of almost semicomplete digraphs

We call a digraph {\em $h$-semicomplete} if each vertex of the digraph has at most $h$ non-neighbors, where a non-neighbor of a vertex $v$ is a vertex $u \neq v$ such that there is no edge between $u$ and $v$ in either direction. This notion generalizes that of semicomplete digraphs which are $0$-semicomplete and tournaments which are semicomplete and have no anti-parallel pairs of edges. Our results in this paper are as follows. (1) We give an algorithm which, given an $h$-semicomplete digraph $G$ on $n$ vertices and a positive integer $k$, in $(h + 2k + 1)^{2k} n^{O(1)}$ time either constructs a path-decomposition of $G$ of width at most $k$ or concludes correctly that the pathwidth of $G$ is larger than $k$. (2) We show that there is a function $f(k, h)$ such that every $h$-semicomplete digraph of pathwidth at least $f(k, h)$ has a semicomplete subgraph of pathwidth at least $k$. One consequence of these results is that the problem of deciding if a fixed digraph $H$ is topologically contained in a given $h$-semicomplete digraph $G$ admits a polynomial-time algorithm for fixed $h$.Comment: 33pages, a shorter version to appear in ESA 201

A study of milling of pure polymers and a structural transformation of polyethylene

We investigated possible physical and chemical changes in inert polymers by means of mechanical milling. No chemical changes were observed. However, in polystyrene we found two glass temperatures after milling, in contrast to one glass temperature in the original material. Under certain conditions crystalline polyethylene transformed almost completely from the orthorhombic to the monoclinic structure

Parton Distributions in the Valon Model

The parton distribution functions determined by CTEQ at low $Q^2$ are used as inputs to test the validity of the valon model. The valon distributions in a nucleon are first found to be nearly $Q$ independent. The parton distribution in a valon are shown to be consistent with being universal, independent of the valon type. The momentum fractions of the partons in the valon add up separately to one. These properties affirm the validity of the valon model. The various distributions are parameterized for convenient application of the model.Comment: 9 pages + 9 figures in ep

Novel fungal genera and species associated with the sooty blotch and flyspeck complex on apple in China and the USA

Fungi in the sooty blotch and flyspeck (SBFS) complex cause blemishes on apple and pear fruit that result in economic losses for growers. The SBFS fungi colonise the epicuticular wax layer of pomaceous fruit but do not invade the cuticle. Fungi causing fuliginous and punctate mycelial types on apple are particularly difficult to identify based on morphological criteria because many species in the SBFS complex share the same mycelial phenotypes. We compared the morphology and nuclear ribosomal DNA phylogeny (ITS, LSU) of 11 fungal strains isolated from SBFS blemishes on apple obtained from two provinces in China and five states in the USA. Parsimony analysis, supported by cultural characteristics and morphology in vitro, provided support to delimit the isolates into three novel genera, representing five new species. Phaeothecoidiella, with two species, P. missouriensis and P. illinoisensis, is introduced as a new genus with pigmented endoconidia in the Dothideomycetes. Houjia (Capnodiales) is introduced for H. pomigena and H. yanglingensis. Although morphologically similar to Stanjehughesia (Chaetosphaeriaceae), Houjia is distinct in having solitary conidiogenous cells. Sporidesmajora (Capnodiales), based on S. pennsylvaniensis, is distinguished from Sporidesmium (Sordariomycetes) in having long, multiseptate conidiophores that frequently have a subconical, darkly pigmented apical cell, and very long, multi-euseptate conidia

SU(2)xSU(2) Invariant Scattering Matrix of the Hubbard Model

We consider the one-dimensional half-filled Hubbard model. We show that the excitation spectrum is given by the scattering states of four elementary excitations, which form the fundamental representation of $SU(2)\times SU(2)$. We determine the exact two-particle Scattering matrix, which a solution of the Yang-Baxter equation and reflects the $SO(4)$ symmetry of the model. The results for repulsive and attractive Hubbard model are related by an interchange of spin and charge degrees of freedom.Comment: 29 pages, jyTeX (macro included - just TeX the file) ITP-SB-93-45, BONN-HE-93-3