A modified Frank–Wolfe algorithm for computing minimum-area enclosing ellipsoidal cylinders: Theory and algorithms

We study a first-order method to find the minimum cross-sectional area ellipsoidal cylinder containing a finite set of points. This problem arises in optimal design in statistics when one is interested in a subset of the parameters. We provide convex formulations of this problem and its dual, and analyze a method based on the Frank–Wolfe algorithm for their solution. Under suitable conditions on the behavior of the method, we establish global and local convergence properties. However, difficulties may arise when a certain submatrix loses rank, and we describe a technique for dealing with this situation.     

Weak measurements are universal

It is well known that any projective measurement can be decomposed into a sequence of weak measurements, which cause only small changes to the state. Similar constructions for generalized measurements, however, have relied on the use of an ancilla system. We show that any generalized measurement can be decomposed into a sequence of weak measurements without the use of an ancilla, and give an explicit construction for these weak measurements. The measurement procedure has the structure of a random walk along a curve in state space, with the measurement ending when one of the end points is reached. This shows that any measurement can be generated by weak measurements, and hence that weak measurements are universal. This may have important applications to the theory of entanglement.     

Application of mid-infrared cavity-ringdown spectroscopy to trace explosives vapor detection using a broadly tunable (6–8 μm) optical parametric oscillator

A novel instrument, based on cavity-ringdown spectroscopy (CRDS), has been developed for trace gas detection. The new instrument utilizes a widely tunable optical parametric oscillator (OPO), which incorporates a zinc–germanium–phosphide (ZGP) crystal that is pumped at 2.8 μm by a 25-Hz Er,Cr:YSGG laser. The resultant mid-IR beam profile is nearly Gaussian, with energies exceeding 200 μJ/pulse between 6 and 8 μm, corresponding to a quantum conversion efficiency of approximately 35%. Vapor-phase mid-infrared spectra of common explosives (TNT, TATP, RDX, PETN and Tetryl) were acquired using the CRDS technique. Parts-per-billion concentration levels were readily detected with no sample preconcentration. A collection/flash-heating sequence was implemented in order to enhance detection limits for ambient air sampling. Detection limits as low as 75 ppt for TNT are expected, with similar concentration levels for the other explosives. Received: 1 April 2002 / Revised version: 13 June 2002 / Published online: 12 September 2002 RID="*" ID="*"Corresponding author. Fax: +1-408/524-0551, E-mail: mtodd@picarro.com     

Gaps between integers with the same prime factors

We give numerical and theoretical evidence in support of the conjecture of Dressler that between any two positive integers having the same prime factors there is a prime. In particular, it is shown that the abc conjecture implies that the gap between two consecutive such numbers is , and it is shown that this lower bound is best possible. Dressler's conjecture is verified for values of and up to .

     

Selective ultrafilters and

Mathias (Happy families, Ann. Math. Logic. 12 (1977), 59-111) proved that, assuming the existence of a Mahlo cardinal, it is consistent that CH holds and every set of reals in is -Ramsey with respect to every selective ultrafilter . In this paper, we show that the large cardinal assumption cannot be weakened.

     

Measurement of total Zn and Zn isotope ratios by quadrupole ICP-MS for evaluation of Zn uptake in gills of brown trout (Salmo trutta) and rainbow trout (Oncorhynchus mykiss)

This study evaluates the potential use of stable zinc isotopes in toxicity studies measuring zinc uptake by the gills of brown trout (Salmo trutta) and rainbow trout (Oncorhynchus mykiss). The use of stable isotopes in such studies has several advantages over the use of radioisotopes, including cost, ease of handling, elimination of permit requirements, and waste disposal. A pilot study using brown trout was performed to evaluate sample preparation methods and the ability of a quadrupole inductively coupled plasma mass spectrometer (ICP-MS) system to successfully measure changes in the ⁶⁷Zn/⁶⁶Zn ratios for planned exposure levels and duration. After completion of the pilot study, a full-scale zinc exposure study using rainbow trout was performed. The results of these studies indicate that there are several factors that affect the precision of the measured ⁶⁷Zn/⁶⁶Zn ratios in the sample digests, including variations in sample size, endogenous zinc levels, and zinc uptake rates by individual fish. However, since these factors were incorporated in the calculation of the total zinc accumulated by the gills during the exposures, the data obtained were adequate for their intended use in calculating zinc binding and evaluating the influences of differences in water quality parameters.     

Sequential and localized grafting on aliphatic polyester diblock copolymers using alkyne deprotection and click cycloaddition

Diblock copolymers, in which both blocks are composed of aliphatic polyesters, were synthesized from two different alkyne‐functionalized δ‐valerolactone monomers by ring opening polymerization and subsequent click cycloaddition. Trimethylsilyl protection of the alkyne functionality of one block was instrumental to the success of the synthesis. These novel aliphatic polyester diblock copolymers were characterized by ¹H and ¹³C NMR spectroscopy, gel permeation chromatography (GPC), and infrared (IR) spectroscopy. Sequential functionalization of the diblock copolymers with hydrophobic groups on one block, and hydrophilic groups on the other block, provides access to amphiphilic structures. Micellar structures generated from these polyester amphiphiles were characterized by fluorescence spectroscopy and transition electron microscopy (TEM). © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2009     

Analytical Solution for Multi-Species Contaminant Transport Subject to Sequential First-Order Decay Reactions in Finite Media

Transport equations governing the movement of multiple solutes undergoing sequential first-order decay reactions have relevance in analyzing a variety of subsurface contaminant transport problems. In this study, a one-dimensional analytical solution for multi-species transport is obtained for finite porous media and constant boundary conditions. The solution permits different retardation factors for the various species. The solution procedure involves a classic algebraic substitution that transforms the advection-dispersion partial differential equation for each species into an equation that is purely diffusive. The new system of partial differential equations is solved analytically using the Classic Integral Transform Technique (CITT). Results for a classic test case involving a three-species nitrification chain are shown to agree with previously reported literature values. Because the new solution was obtained for a finite domain, it should be especially useful for testing numerical solution procedures.     

Development and validation of a cost-effective,efficient, and robust liquid chromatographic method for the simultaneous determination of the acetyl and succinoyl content in hydroxypropyl methylcellulose acetate succinate polymer

A reversed-phase liquid chromatographic method was developed and validated for the determination of the content of free acetic acid, free succinic acid, acetyl substituents, and succinoyl substituents in hydroxypropyl methylcellulose acetate succinate (HPMCAS; Chemical Abstracts Service Registry No. 71138-97-1) polymer. This single new method gave accurate and precise measurement of both acetyl and succinoyl substituents, which had previously required 3 Japanese Pharmaceutical Excipients (JPE) methods to accomplish. Consequently, analysis time and turnaround time are decreased significantly. Furthermore, this method can also separate and determine the free acetic and succinic acids in HPMCAS polymer, a task that the corresponding JPE method cannot achieve. The values for accuracy (average recovery from 12 standard samples) were 99.9% for acetic acid and 99.8% for succinic acid. The values for injection precision (relative standard deviation [RSD]) were 0.11% for acetic acid and 0.28% for succinic acid. The values for intermediate precision (RSD) were 1.25% for determination of the acetyl content at the 8.78% (w/w) level and 1.33% for determination of the succinoyl content at the 10.9% (w/w) level. The values for intermediate precision (RSD) were 5.98% for determination of free acetic acid at the 0.12% (w/w) level and 5.13% for determination of free succinic acid at the 0.029% (w/w) level. The method was proven to be robust with respect to variation in the pH of the mobile phase, the concentration of potassium dihydrogen phosphate, and the flow rate. The method is well suited for quality control in today's fast-paced pharmaceutical laboratories.     

Halophilic reactions of a stable silylene with chloro and bromocarbons

A number of disilanes have been synthesized from a stable silylene, 1 (N,N'-di-tert-butyl-1,3-diaza-2-silacyclopent-4-en-2-ylidene), and a variety of halocarbons. It is proposed that disilane formation is a result of an initial halophilic interaction between the silylene and halocarbon. Formation of disilanes from 1 and CCl4, 2a, CHCl3, 2b, CH2Cl2, 2c, benzyl chloride, 2d, and bromobenzene, 5, are described here. An X-ray crystal structure of 2b was determined.