A characterization of discrete unimodality with applications to variance upper bounds

Bertin and Theodorescu (1984,Statist. Probab. Lett.,2, 23–30) developed a characterization of discrete unimodality based on convexity properties of a discretization of distribution functions. We offer a new characterization of discrete unimodality based on convexity properties of a piecewise linear extension of distribution functions. This reliance on functional convexity, as in Khintchine's classic definition, leads to variance dilations and upper bounds on variance for a large class of discrete unimodal distributions. These bounds are compared to existing inequalities due to Muilwijk (1966,Sankhy, Ser. B,28, p. 183), Moors and Muilwijk (1971,Sankhy, Ser. B,33, 385–388), and Rayner (1975,Sankhy, Ser. B,37, 135–138), and are found to be generally tighter, thus illustrating the power of unimodality assumptions.     

Asymptotic behavior of eigenvalues and random updating schemes

For a stochastic matrix (Q _ij ^T ) _i,j=1 ^M withQ _ij ^T exp(–U(ij)/T) at the off-diagonal positions, we develop an algorithm to evaluate the asymptotic convergence rate of all eigenvalues ofQ _ij ^T asT 0 using Ventcel's optimal graphs. As an application we can compare the convergence rates of some random updating schemes used in image processing.This research was partially supported by the National Science Council, Taiwan and Air Force Office of Scientific Research Contract No. F49620 S5C 0144, and was completed while Tzuu-Shuh Chiang was visiting the Center for Stochastic Processes, Department of Statistics, University of North Carolina, Chapel Hill, NC 27599-3260, USA.     

The separation of tellurium and selenium by polyurethane foam sorbents

Tellurium and selenium can be sorbed from hydrochloric acid and hydrobromic acid solution by both polyether and polyester-based polyurethane foam. Although some acid is needed, the substitution of sodium chloride or sodium bromide increases the extraction significantly. Tellurium is extracted rapidly with > 99% sorbed in 2 min from 1.0/5.0M and 2.0/4.0M hydrochloric acid/sodium bromide. Selenium can also be sorbed quantitatively but much more slowly so that a separation is possible based on the relative rates of extraction. The capacity of polyether foam is 3% by weight of tellurium.     

Utilization of 1-oxa-2,2-(dimesityl)silacyclopentane acetals in the stereoselective synthesis of polyols

We have developed a route for the stereoselective synthesis of 1-oxa-2,2-(dimesityl)silacyclopentane acetals, intermediates in the synthesis of highly functionalized 1,3-diols. This route involves a diastereoselective conjugate addition reaction of a hydrosilyl anion, a subsequent diastereoselective enolate alkylation, and a fluoride-catalyzed intramolecular hydrosilylation reaction to afford the oxasilacyclopentane acetal. A highly selective nucleophilic substitution reaction, followed by oxidation of the C-Si bond, leads to the desired polyol.     

The Reaction of Triplet State Benzophenone with Acetylacetone

Irradiation of benzophenone in acetic acid containing acetylacetone resulted in regiospecific addition to form cis-2,2-dihpenyl-3-hydroxy-3-methyl-4-acetyloxetane and the rearrangement products therefrom. In the co-presence of copper ions, the regiospecificity is scrambled to give these products and a small amount of 1,1-diphenyl-1-buten-3-one, the secondary decomposition product of the other oxetane arising from the alternative orientation of the addition.     

Evaluation and validation of the ABI 3700, ABI 3100, and the MegaBACE 1000 capillary array electrophoresis instruments for use with short tandem repeat microsatellite typing in a forensic environment

The demand for high-throughput DNA profiling has increased with the introduction of national DNA databases and has led to the development of automated methods of short tandem repeat (STR) profile production; however, a potential bottleneck still exists at the gel electrophoresis stage. Capillary electrophoresis sequencers capable of processing 96 samples with considerably reduced manual intervention are now available. In this paper, we compare the ABI Prism 377 slab-gel sequencer currently used by the Forensic Science Service with three leading capillary array electrophoresis instruments: the ABI Prism 3700, the Amersham MegaBACE 1000 and the 16-capillary ABI Prism 3100. We describe the experiments used to evaluate and validate these platforms for forensic use with the STR multiplex Ampf/STR SGMplus [1, 2], along with comparative data from the ABI Prism 377 sequencer.     

Magnetoelectric compounds with two sets of magnetic sublattices: UCrO4 and NdCrTiO5

Using magnetic and magnetoelectric (ME) powder susceptibility measurements, the low temperature magnetic properties of antiferromagnetic UCrO₄ and NdCrTiO₅ have been studied. Their Néel temperatures T_N are 44.5 and 20.5°K, respectively, the Cr³⁺ spin systems of both materials ordering cooperatively at T_N. Below T_N, the U⁵⁺ and Nd³⁺ moments are polarized due to their exchange interaction with the ordered Cr³⁺ spins. It is argued that, for both compounds, each of the two spin systems contributes to the ME susceptibilities. They are thus the first known ME materials possessing two distinct magnetic sublattices. The effective magnetic moments calculated from the magnetic susceptibilities are in good agreement with those previously reported by neutron diffraction studies.