Hopf-algebraic structure of combinatorial objects and differential operators

A Hopf-algebraic structure on a vector space which has as basis a family of trees is described, and we survey some applications of this structure to combinatorics and to differential operators. Some possible future directions for this work are indicated. Supported in part by NASA Grant NAG 2-513. Supported in part by NSF Grant DMS 870-1085.     

Plasma isotope separation methods

Six major types of isotope separation methods which involve plasma phenomena are discussed. These methods are: plasma centrifuge, AVLIS (atomic vapor laser isotope separation), ion wave, ICR (ion cyclotron resonance), calutron, and gas discharge. The plasma phenomena in these major categories are described. An attempt is made to include enough references so that a more detailed study or evaluation of a particular method could readily be pursued. A brief discussion of isotope separation using mass balance concepts is also included     

Capillary electrophoresis of DNA in entangled polymer solutions.

Electrophoretic separations of DNA restriction fragments were performed in solutions of hydroxyethylcellulose (HEC) using capillary electrophoresis. Rheological studies confirmed that the entanglement threshold (phi*) for the solution is ca. 0.003 g/ml, in good agreement with theoretical predictions. A mesh size an order of magnitude smaller than that found in agarose gels was calculated using polymer-entanglement theory and was confirmed by electrophoretic measurements. Electrophoretic migration was shown to follow the Ogston regime under most conditions. An approach for obtaining smaller mesh sizes is presented.     

Correlated ejection of electron-hole drops from a continuously generated electron-hole liquid in Ge

The photocurrent power spectra were measured in a Ge photodiode as a function of the incident optical intensity at 1.8 K and 4.3 K. The observed spectra showed a peak at low frequencies superimposed on a continuum which has a cut-off at high frequency. The interpretation of the results implies that the electron-hole drops coming from a same region of the photoexcited liquid are ejected periodically.     

Model of a microwave beam coupling to CO2 laser plasma

We have designed a transmission line model of the microwave coupling mechanism for a microwave pumped CO₂ laser. The model is a total loss ridge waveguide transmission line having nonuniform impedance. The laser plasma is modeled as a frequency-dependent lossy dielectric and acts as a distributed resistance in the length of the microwave cavity. The coupling structure of the microwaves is designed not to be resonant at the microwave source frequency of 2.45 GHz at 1 kW and propagating the total microwave field energy to be absorbed without internal reflection. An exact solution to this general transmission line propagation constant for a shunt resistance along length of the guide is found. The measurements and predictions of the parameters of the plasma conductivity as a function of the attenuation constant agree closely.     

Gradient-constrained discounted Steiner trees II: optimally locating a discounted Steiner point

A gradient-constrained discounted Steiner tree is a network interconnecting given set of nodes in Euclidean space where the gradients of the edges are all no more than an upper bound which defines the maximum gradient. In such a tree, the costs are associated with its edges and values are associated with nodes and are discounted over time. In this paper, we study the problem of optimally locating a single Steiner point in the presence of the gradient constraint in a tree so as to maximize the sum of all the discounted cash flows, known as the net present value (NPV). An edge in the tree is labelled as a b edge, or a m edge, or an f edge if the gradient between its endpoints is greater than, or equal to, or less than the maximum gradient respectively. The set of edge labels at a discounted Steiner point is called its labelling. The optimal location of the discounted Steiner point is obtained for the labellings that can occur in a gradient-constrained discounted Steiner tree. In this paper, we propose the gradient-constrained discounted Steiner point algorithm to optimally locate the discounted Steiner point in the presence of a gradient constraint in a network. This algorithm is applied to a case study. This problem occurs in underground mining, where we focus on the optimization of underground mine access to obtain maximum NPV in the presence of a gradient constraint. The gradient constraint defines the navigability conditions for trucks along the underground tunnels.     

Intermediate subfactors with no extra structure

If are type II factors with and we show that restrictions on the standard invariants of the elementary inclusions , , and imply drastic restrictions on the indices and angles between the subfactors. In particular we show that if these standard invariants are trivial and the conditional expectations onto and do not commute, then is or . In the former case is the fixed point algebra for an outer action of on and the angle is , and in the latter case the angle is and an example may be found in the GHJ subfactor family. The techniques of proof rely heavily on planar algebras.