Transitions in geometric minimum spanning trees

We study some combinatorial and algorithmic problems associated with an arbitrary motion of input points in space. The motivation for such an investigation comes from two different sources:computer modeling andsensitivity analysis. In modeling, the dynamics enters the picture since geometric objects often model physical entities whose positions can change over time. In sensitivity analysis, the motion of the input points might represent uncertainties in the precise location of objects. The main results of the paper deal with state transitions in the minimum spanning tree when one or more of the input points move arbitrarily in space. In particular, questions of the following form are addressed: (i) How many different minimum spanning trees can arise if one point moves while the others remain fixed? (ii) When does the minimum spanning tree change its topology if all points are allowed to move arbitrarily?     

Decoupling approximations for structural acoustic interactions

The model problem of acoustic scattering by a baffled membrane is formally cast as a dual integral equation. A class of approximations are made to the equation's kernel and each gives rise to an analytically solvable problem. Each of these approximate problems corresponds to an existing physical theory which was derived in a complete by different manner. The present method of analysis systematically deduces these theories, suggests potentially useful new ones, and indicates where more theoretical studies are required.     

Evaluation of thermal analysis equipment for the determination of vapor pressure and heat of vaporization

A rapid, relatively simple method for determining vapor pressure and heat of vaporization on small amounts of organic compounds is described. A DuPont 900 differential thermal analyzer (DTA), a Perkin—Elmer Model DSC-1B differential scanning calorimeter (DSC), and a Thomas—Hoover (TH) melting point apparatus were evaluated in this work. Vapor pressure data for a wide variety of organic liquids were obtained by measuring the boiling points of the liquids at pressures ranging from 20 to 735 torr. A computer was used to rapidly plot the experimental data. The average deviations of boiling points from the literature values were 2.3°C for the DTA 1.2°C for the DSC, and 1.5°C for the TH. The vapor pressure data were used to solve the Haggenmacher equation for heat of vaporization (ΔH_v). The deviations of the experimental values for ΔH_v. from the literature values were 5.5%, 8.3%. and 3.3% for the DTA, DSC, and TH methods, respectively.     

Innovations and Wold decompositions of stable sequences

Summary For symmetric stable sequences, notions of innovation and Wold decomposition are introduced, characterized, and their ramifications in prediction theory are discussed. As the usual covariance orthogonality is inapplicable, the non-symmetric James orthogonality is used. This leads to right and left innovations and Wold decompositions, which are related to regression prediction and least p ^th moment prediction, respectively. Independent innovations and Wold decompositions are also characterized; and several examples illustrating the various decompositions are presented.Research supported by the Air Force Office of Scientific Research Contract F49620 82 C 0009     

Generating a Random Signed Permutation with Random Reversals

Signed permutations form a group known as the hyperoctahedral group. We bound the rate of convergence to uniformity for a certain random walk on the hyperoctahedral group that is generated by random reversals. Specifically, we determine that O(n log n) steps are both necessary and sufficient for total variation distance and ℓ² distance to become small. This random walk arose as the result of an effort in molecular biology to model certain types of genome rearrangements.     

On-line affinity selection of histidine-containing peptides using a polymeric monolithic support for capillary electrophoresis

An on-line affinity selection method using a polymeric monolithic support is proposed for the retention of histidine-containing peptides and their subsequent separation by capillary zone electrophoresis (CZE). Monolithic capillary columns were prepared in fused-silica capillaries of 150 mum inner diameter (ID) by ionizing radiation-initiated in situ polymerization and cross-linking of diethylene glycol dimethacrylate and glycidyl methacrylate, and chemically modified with iminodiacetic acid (IDA) and copper ion. Monolithic microextractors were coupled on-line near the inlet of the separation capillary (fused-silica capillary, 75 mum ID x 28 cm from the microextractor to the detector). Model peptide mixtures of histidine-containing and histidine-noncontaining peptides were assessed. Peptides were released from the sorbent by a 5 mM imidazole solution and then separated by CZE with ultraviolet detection. Relative standard deviation values for migration times and corrected peak areas were found to be lower than 5.8 and 10.5%, respectively. IDA-Cu(II) ion modified monolithic microextractors showed a chromatographic behavior and could be reused at least 25 times. The use of monolithic supports proved to be an advantageous alternative to packed particles for the preparation of microextractors.