Hull-Volume with Applications to Convergence Analysis

We introduce and study decompositions of finite sets as well as coverings of their convex hulls, and use these objects to develop various estimates of and formulas for the “hull-volume” of the sets (i.e., the volume of their convex hull). We apply our results to the convergence analysis of the “iterate-sets” associated with each iteration of a reduce-or-retreat optimization method (including pattern-search methods like Nelder–Mead as well as model-based methods).     

Inverse Gas Chromatographic Characterization of Aluminosilicates as Fillers for Abrasive Articles

The surface properties of aluminosilicates (perlites and zeolites)—potential fillers in abrasive articles—have been examined by inverse gas chromatography. The dispersive component of the surface free energy ( $ \gamma_{\text{S}}^{\text{D}} $ ) and K _A and K _D describing the acidity and basicity, respectively, of the fillers were used to express the surface activity of examined materials. The Flory–Huggins parameter, $ \chi_{23}^{'} , $ characterized the interactions between polymer and filler, i.e., interactions between phenolic resin and filler. Zeolites were found to be materials with an active surface layer and relatively high ability to participate in filler–resin interactions. Therefore, they might be considered as potential “replacement material” for standard fillers. The IGC-derived values mentioned above provided useful information about the behavior of fillers during the manufacture and use of abrasive articles.     

Immunoextraction of zinc proteins from human plasma using chicken yolk antibodies immobilized onto paramagnetic particles and their electrophoretic analysis

Zinc(II) as the only transition metal lacking redox activity is an essential part of approximately 10% proteins as a cofactor of these proteins. Considering the fact that there are numerous zinc(II) containing proteins, proteomics and metallomics studies aimed on them require accurate methods for preparation of real biological samples prior to their subsequent analysis using 2DE and MS. For this purpose, we suggested a new method based on chicken anti-zinc antibodies and magnetizable particles. Antibodies were covalently immobilized to the surface of paramagnetic beads activated with tosyl group. Binding of the antibody to the beads was confirmed by secondary anti-chicken antibody conjugated with horseradish peroxidase. The immunoextraction conditions, such as concentration of the beads (6-18 μg/mL of the sample), time of immunoextraction (6-34 min), pH and composition of the elution buffer, and time of extraction (48-300 s) were optimized. Subsequently, zinc proteins were extracted from human plasma and total concentration of zinc was monitored by electrochemical detection in the extracts. Under optimal conditions it was possible to monitor the proteins and zinc removal from the sample by chip CE, SDS-PAGE, and indirectly using electrochemistry.     

Three-dimensional temporally resolved measurements of turbulence–flame interactions using orthogonal-plane cinema-stereoscopic PIV

A new orthogonal-plane cinema-stereoscopic particle image velocimetry (OPCS-PIV) diagnostic has been used to measure the dynamics of three-dimensional turbulence–flame interactions. The diagnostic employed two orthogonal PIV planes, with one aligned perpendicular and one aligned parallel to the streamwise flow direction. In the plane normal to the flow, temporally resolved slices of the nine-component velocity gradient tensor were determined using Taylor’s hypothesis. Volumetric reconstruction of the 3D turbulence was performed using these slices. The PIV plane parallel to the streamwise flow direction was then used to measure the evolution of the turbulence; the path and strength of 3D turbulent structures as they interacted with the flame were determined from their image in this second plane. Structures of both vorticity and strain-rate magnitude were extracted from the flow. The geometry of these structures agreed well with predictions from direct numerical simulations. The interaction of turbulent structures with the flame also was observed. In three dimensions, these interactions had complex geometries that could not be reflected in either planar measurements or simple flame–vortex configurations.     

Rectangular Tiling in Multidimensional Arrays

We study the following tiling problem in d dimensions: given a d-dimensional rectangular array of nonnegative numbers and an integer p, partition the array into at most p rectangular subarrays so that the maximum weight of any subarray is minimized; the weight of a subarray is the sum of its elements. The rectangular tiling problem is motivated by applications in data mining, data partitioning, and video compression. Recently, Khanna, Muthukrishnan, and Paterson [SODA '98], showed that the tiling problem is NP-complete and gave a 2.5-approximation algorithm for d = 2.In this paper, we extend their result to multidimensional arrays and give an algorithm with approximation ratio , for d ≥ 2. The algorithm can be implemented to run in worst-case time O(N + p log N) time, where N is the size of the array, and the constant is of the order d!. We also obtain a similar algorithm for the dual tiling problem, where the goal is to compute a tiling of weight at most W using as few tiles as possible. Our algorithm yields an approximation factor (2d + 1).We implemented our algorithm and ran simulation tests on multidimensional arrays with random data. In our limited experiments, the algorithm always produced approximations that were no worse than factor two from the optimal.     

Influence of the Bulk and Donor-Acceptor Properties of Solvent on Ligand Field Spectra

The influence of solvents on the electronic absorption spectra of chromium (III) complexes was investigated. The dependence of the crystal field parameter Dq on dielectric constant as well as Gutmann donor number DN of solvent was found and described. By using the proposed model, unknown in the literature donor numbers for a few alcohols were estimated.