A representation of acoustic waves in unbounded domains

Compact, time‐harmonic, acoustic sources produce waves that decay too slowly to be square‐integrable on a line away from the sources. We introduce an inner product, arising directly from Green's second theorem, to form a Hilbert space of these waves and present examples of its computation.¹ © 2005 Wiley Periodicals, Inc.     

Resolution of Some Open Problems Concerning Multiple Zeta Evaluations of Arbitrary Depth

We prove some new evaluations for multiple polylogarithms of arbitrary depth. The simplest of our results is a multiple zeta evaluation one order of complexity beyond the well-known Broadhurst–Zagier formula. Other results we provide settle three of the remaining outstanding conjectures of Borwein, Bradley, and Broadhurst. A complete treatment of a certain arbitrary depth class of periodic alternating unit Euler sums is also given.     

Experimental design and the optimization of a polymer supported palladium complex for use in the Heck reaction

Optimization of the Heck reaction of 4-bromoacetophenone with styrene by a polymer supported, sulfur-containing palladacycle, varying 6 factors at a total of 28 different levels, corresponding to 5760 different possibilities was undertaken. Conversion improved from 34%, with large observable leaching to 88% with no leaching. This was accomplished using a Design of Experiments approach facilitated by the Statistical Design Package, MODDE 7.0^TM.     

Algorithm for Optimal Triangulations in Scattered Data Representation and Implementation

Scattered data collected at sample points may be used to determine simple functions to best fit the data. An ideal choice for these simple functions is bivariate splines. Triangulation of the sample points creates partitions over which the bivariate splines may be defined. But the optimality of the approximation is dependent on the choice of triangulation. An algorithm, referred to as an Edge Swapping Algorithm, has been developed to transform an arbitrary triangulation of the sample points into an optimal triangulation for representation of the scattered data. A Matlab package has been completed that implements this algorithm for any triangulation on a given set of sample points.     

Image Formation in Low Vacuum SEM

The role of positive gaseous ions in the formation of secondary electron images in low vacuum scanning electron microscopes is discussed. This paper describes the charging processes and related effects that occur during high vacuum imaging of insulators and then discusses the influence of ions on those processes. The ions are responsible for a number of phenomena, including distortion of the electric field above and below the specimen surface due to space charge, removal of excess negative charge from the specimen, alteration of the specimen surface barrier, and scavenging/filtering of the secondary electron emission. The resulting electron-specimen-ion interactions can give rise to interesting contrast effects that are unique to this class of instruments.     

Analyzing the effect of the inventory policy on order and inventory variability with linear control theory

In this paper we apply linear control theory to study the effect of various inventory policies on order and inventory variability, which are key drivers of supply chain performance. In particular, we study a two-echelon supply chain with a stationary demand pattern under the influence of three inventory policies: an inventory-on-hand policy that bases orders on the visible inventory at an installation, an installation-stock policy that bases orders on the inventory position (on-hand plus on-order inventory) at an installation, and an echelon-stock policy that bases orders on the inventory position at that installation and all downstream installations. We prove analytically that the inventory-on-hand policy is unstable in practical settings, confirming analytically what has been observed in experimental settings and in practice. We also prove that the installation-stock and echelon-stock policies are stable and analyze their effect on order and inventory fluctuation. Specifically, we show the general superiority of the echelon-stock in our setting and demonstrate analytically the effect of forecasting parameters on order and inventory fluctuations, confirming the results in other research.     

Representing the mean residual life in terms of the failure rate

In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Whereas the failure rate can be expressed quite simply in terms of the mean residual life and its derivative, the inverse problem—namely that of expressing the mean residual life in terms of the failure rate—typically involves an integral of a complicated expression. In this paper, we obtain simple expressions for the mean residual life in terms of the failure rate for certain classes of distributions which subsume many of the standard cases. Several results in the literature can be obtained using our approach. Additionally, we develop an expansion for the mean residual life in terms of Gaussian probability functions for a broad class of ultimately increasing failure rate distributions. Some examples are provided to illustrate the procedure.     

Photodynamic Therapy of 9L Gliosarcoma with Liposome-Delivered Photofrin

Abstract— The effect of Photofrin encapsulated in a liposome delivery vehicle for photodynamic therapy (PDT) of the 9L gliosarcoma and normal rat brain was tested. We hypothesized that the liposome vehicle enhances therapeutic efficacy, possibly by increasing tumor tissue concentration of Photofrin. Male Fisher rats bearing a 9L gliosarcoma were treated 16 days after intracerebral tumor implantation with either Photofrin in dextrose (n = 5) or Photofrin in liposome (n = 6). Nontumor-bearing animals were treated with Photofrin delivered either in dextrose (n = 4) or liposome (n = 4) vehicle. Tissue concentrations of Photofrin delivered either in dextrose (n = 4) or liposome (n = 4) vehicle were measured in tumor, brain adjacent to tumor and in normal brain tissue. Photofrin was administered (intraperitoneally) at a dose of 12.5 mg/kg and PDT (17 J/cm₂ of 632 nm light at 100 mW/cm₂) was performed 24 h after Photofrin administration. Brains were removed 24 h after PDT and stained with hematoxylin and eosin for analysis of cellular damage. The PDT using Photofrin in the liposome vehicle caused significantly more damage to the tumor ( P < 0.001) than did PDT with Photofrin in dextrose. The PDT of tumor with Photofrin delivered in liposomes caused a 22% volume of cellular necrosis, while PDT of tumor with Photofrin delivered in dextrose caused only scattered cellular damage. Photofrin concentration in tumors was significantly higher ( P = 0.021) using liposome (33.8 ± 18.9 μg/g) compared to dextrose delivery (5.5 ± 1.5 μg/g). Normal brain was affected similarly in both groups, with only scattered cellular necrosis. Our data suggest that the liposome vehicle enhances the therapeutic efficacy of PDT treatment of 9L tumors.