Alternatives for testing total dual integrality

In this paper we provide characterizing properties of totally dual integral (TDI) systems, among others the following: a system of linear inequalities is TDI if and only if its coefficient vectors form a Hilbert basis, and there exists a test-set for the system’s dual integer programs where all test vectors have positive entries equal to 1. Reformulations of this provide relations between computational algebra and integer programming and they contain Applegate, Cook and McCormick’s sufficient condition for the TDI property and Sturmfels’ theorem relating toric initial ideals generated by square-free monomials to unimodular triangulations. We also study the theoretical and practical efficiency and limits of the characterizations of the TDI property presented here. In the particular case of set packing polyhedra our results correspond to endowing the weak perfect graph theorem with an additional, computationally interesting, geometric feature: the normal fan of the stable set polytope of a perfect graph can be refined into a regular triangulation consisting only of unimodular cones.     

On Multiple Points of Meromorphic Functions

Lower bounds are established for the number of zeros of thelogarithmic derivative of a meromorphic function of small growthwith few poles.     

非醚合氢化铝的制备及性质研究

本文论述了大晶粒α-AlH_3的合成条件,从而制得高纯度产品;对α-AlH_3和α′-AlH_3的稳定性进行比较研究表明,α′-AlH_3也是一种相当稳定的非醚合氢化铝;提出了α-AlH_3与α′-AlH_3的分离方法。     

A ring expansion-annulation strategy for the synthesis of substituted azulenes. Preparation and Suzuki coupling reactions of 1-azulenyl triflates

[structure: see text]. A new strategy for the synthesis of substituted azulenes is reported, based on the reaction of beta'-bromo-alpha-diazo ketones with rhodium carboxylates. The key transformation involves intramolecular addition of a rhodium carbenoid to an arene pi-bond, electrocyclic ring opening, beta-elimination, tautomerization, and trapping to produce 1-hydroxyazulene derivatives. The synthetic utility of the method is enhanced by the ability of the triflate derivatives to participate in Suzuki coupling reactions, as illustrated in a synthesis of the antiulcer drug egualen sodium (KT1-32).     

Synthesis and preliminary cytotoxicity studies of achiral pyrrolyl-substituted titanocenes

From the reaction of various 6-pyrrolylfulvenes (3a–3d) with Super Hydride (LiBEt₃H), lithiated cyclopentadienide intermediates (4a–4d) were synthesised. These intermediates were then transmetallated with titanium tetrachloride TiCl₄ to yield the pyrrolyl-substituted titanocenes bis-[((1-(4-methoxybenzyl)-pyrrole)2-)cyclopentadienyl]titanium(IV) dichloride (5a), bis-[((1-(4-methoxyphenyl)-pyrrole)2-)cyclopentadienyl]titanium(IV) dichloride (5b), bis-[((2,4-bis(4-methoxyphenyl)-1-methyl-pyrrole)2-)cyclopentadienyl]titanium(IV) dichloride (5c), bis-[((2-(4-methoxyphenyl)-1-methyl-pyrrole)2-)cyclopentadienyl]titanium(IV) dichloride (5d). Titanocene 5b crystallised and was characterised by X-ray crystallography. The four titanocenes 5a–5d were tested for their cytotoxicity through MTT-based in vitro tests on CAKI-1 cell lines in order to determine their IC₅₀ values. Titanocenes 5a–5d were found to have IC₅₀ values of 440 (±35), 68 (±14), 105 (±30), and 36 (±7) μM.     

Contrast-enhanced microwave imaging of breast tumors: a computational study using 3-D realistic numerical phantoms

The detection of early-stage tumors in the breast by microwave imaging is challenged by both the moderate endogenous dielectric contrast between healthy and malignant glandular tissues and the spatial resolution available from illumination at microwave frequencies. The high endogenous dielectric contrast between adipose and fibroglandular tissue structures increases the difficulty of tumor detection due to the high dynamic range of the contrast function to be imaged and the low level of signal scattered from a tumor relative to the clutter scattered by normal tissue structures. Microwave inverse scattering techniques, used to estimate the complete spatial profile of the dielectric properties within the breast, have the potential to reconstruct both normal and cancerous tissue structures. However, the ill-posedness of the associated inverse problem often limits the frequency of microwave illumination to the UHF band within which early-stage cancers have sub-wavelength dimensions. In this computational study, we examine the reconstruction of small, compact tumors in three-dimensional numerical breast phantoms by a multiple-frequency inverse scattering solution. Computer models are also employed to investigate the use of exogenous contrast agents for enhancing tumor detection. Simulated array measurements are acquired before and after the introduction of the assumed contrast effects for two specific agents currently under consideration for breast imaging: microbubbles and carbon nanotubes. Differential images of the applied contrast demonstrate the potential of the approach for detecting the preferential uptake of contrast agents by malignant tissues.     

Development of a method for the determination of heavy metals in calcified tissues by inductively coupled plasma-mass spectrometry

Calcified tissues are good indicators of exposure to environmental pollution since the mineral phase incorporates heavy metals to which it is exposed during development. Analysis of these specimens is difficult due to the low concentration of the elements of interest compared with the high concentration of the matrix elements. ICP-MS allows rapid multielement determination of samples and a method for the determination of trace elements in calcified tissues is presented with reference to an SRM of Bone Ash (NIST 1400). Received: 2 October 1998 / Revised: 30 November 1998 / Accepted: 4 December 1998