Partial differential equations from integrable vertex models

In this work we propose a mechanism for converting the spectral problem of vertex models transfer matrices into the solution of certain linear partial differential equations. This mechanism is illustrated for the $U_q[\widehat{\mathfrak{sl}}(2)]$ invariant six-vertex model and the resulting partial differential equation is studied for particular values of the lattice length.Comment: 19 pages. v2: affiliation and references updated, minor changes, accepted for publication in J. Math. Phy

Refined functional relations for the elliptic SOS model

In this work we refine the method of [1] and obtain a novel kind of functional equation determining the partition function of the elliptic SOS model with domain wall boundaries. This functional relation is originated from the dynamical Yang-Baxter algebra and its solution is given in terms of multiple contour integrals.Comment: v2: details of derivations and reference added, typos fixed, accepted for publication in NP

Multiple integral representation for the trigonometric SOS model with domain wall boundaries

Using the dynamical Yang-Baxter algebra we derive a functional equation for the partition function of the trigonometric SOS model with domain wall boundary conditions. The solution of the equation is given in terms of a multiple contour integral.Comment: 28 pages, v2: comments and references added, typos fixed, to appear in NP

Water quality monitor

The preprototype water quality monitor (WQM) subsystem was designed based on a breadboard monitor for pH, specific conductance, and total organic carbon (TOC). The breadboard equipment demonstrated the feasibility of continuous on-line analysis of potable water for a spacecraft. The WQM subsystem incorporated these breadboard features and, in addition, measures ammonia and includes a failure detection system. The sample, reagent, and standard solutions are delivered to the WQM sensing manifold where chemical operations and measurements are performed using flow through sensors for conductance, pH, TOC, and NH3. Fault monitoring flow detection is also accomplished in this manifold assembly. The WQM is designed to operate automatically using a hardwired electronic controller. In addition, automatic shutdown is incorporated which is keyed to four flow sensors strategically located within the fluid system

On kernel engineering via Paley–Wiener

A radial basis function approximation takes the form $$s(x)=\sum_{k=1}^na_k\phi(x-b_k),\quad x\in {\mathbb{R}}^d,$$ where the coefficients a 1,…,a n are real numbers, the centres b 1,…,b n are distinct points in ℝ d , and the function φ:ℝ d →ℝ is radially symmetric. Such functions are highly useful in practice and enjoy many beautiful theoretical properties. In particular, much work has been devoted to the polyharmonic radial basis functions, for which φ is the fundamental solution of some iterate of the Laplacian. In this note, we consider the construction of a rotation-invariant signed (Borel) measure μ for which the convolution ψ=μ φ is a function of compact support, and when φ is polyharmonic. The novelty of this construction is its use of the Paley–Wiener theorem to identify compact support via analysis of the Fourier transform of the new kernel ψ, so providing a new form of kernel engineering

Selfduality for coupled Potts models on the triangular lattice

We present selfdual manifolds for coupled Potts models on the triangular lattice. We exploit two different techniques: duality followed by decimation, and mapping to a related loop model. The latter technique is found to be superior, and it allows to include three-spin couplings. Starting from three coupled models, such couplings are necessary for generating selfdual solutions. A numerical study of the case of two coupled models leads to the identification of novel critical points

Sphenopteris sellardsii, a problematical pteridosperm from the Permian of Kansas

8 p., 4 fig.http://paleo.ku.edu/contributions.htm

New critical frontiers for the Potts and percolation models

We obtain the critical threshold for a host of Potts and percolation models on lattices having a structure which permits a duality consideration. The consideration generalizes the recently obtained thresholds of Scullard and Ziff for bond and site percolation on the martini and related lattices to the Potts model and to other lattices.Comment: 9 pages, 5 figure

Fungi at the Field Station

The UWM Field Station now has a mycological reference collection, for use in identifying fungi of the area. Botanists and zoologists doing research at the Field Station will find the collection useful. It can also be used by visiting groups who have some interest in identifying the more conspicuous fungi that are likely to be seen during a tour of the area