The Polynomial Behavior of Weight Multiplicities for the Affine Kac–Moody Algebras A(1)r

We prove that the multiplicity of an arbitrary dominant weight for an irreducible highest weight representation of the affine Kac–Moody algebra A ⁽¹⁾ _r is a polynomial in the rank r. In the process we show that the degree of this polynomial is less than or equal to the depth of the weight with respect to the highest weight. These results allow weight multiplicity information for small ranks to be transferred to arbitrary ranks.     

cis‐Dichloro(dimethyl sulfoxide‐S)(2‐methoxypyridine‐N)platinum(II)

The title complex, [PtCl₂(C₆H₇NO)(C₂H₆OS)], exhibits square‐planar geometry. The plane of the pyridine ring makes a dihedral angle of 67.2 (3)° with the square plane of the metal center. The S—O bond is nearly aligned with the adjacent Pt—N bond, leaving the methyl groups of the di­methyl sulfoxide ligand to stagger the Pt—Cl bond.     

Efficient formulations for pricing under attraction demand models

We propose a modeling and optimization framework to cast a broad range of fundamental multi-product pricing problems as tractable convex optimization problems. We consider a retailer offering an assortment of differentiated substitutable products to a population of customers that are price-sensitive. The retailer selects prices to maximize profits, subject to constraints on sales arising from inventory and capacity availability, market share goals, bounds on allowable prices and other considerations. Consumers’ response to price changes is represented by attraction demand models, which subsume the well known multinomial logit (MNL) and multiplicative competitive interaction demand models. Our approach transforms seemingly non-convex pricing problems (both in the objective function and constraints) into convex optimization problems that can be solved efficiently with commercial software. We establish a condition which ensures that the resulting problem is convex, prove that it can be solved in polynomial time under MNL demand, and show computationally that our new formulations reduce the solution time from days to seconds. We also propose an approximation of demand models with multiple overlapping customer segments, and show that it falls within the class of demand models we are able to solve. Such mixed demand models are highly desirable in practice, but yield a pricing problem which appears computationally challenging to solve exactly.     

Max and min limiters

 If and the function is partial recursive, it is easily seen that A is recursive. In this paper, we weaken this hypothesis in various ways (and similarly for ``min' in place of ``max') and investigate what effect this has on the complexity of A. We discover a sharp contrast between retraceable and co-retraceable sets, and we characterize sets which are the union of a recursive set and a co-r.e., retraceable set. Most of our proofs are noneffective. Several open questions are raised. Received: 28 November 1999 / Published online: 31 May 2002     

Validation of a fully automated high throughput liquid chromatographic/tandem mass spectrometric method for roxithromycin quantification in human plasma. Application to a bioequivalence study

A fully automated high-throughput liquid chromatography/tandem mass spectrometry (LC-MS/MS) method was developed for the determination of roxithromycin in human plasma. The plasma samples were treated by liquid-liquid extraction (LLE) in 2.2 mL 96-deep-well plates. Roxithromycin and the internal standard clarithromycin were extracted from 100 microL of human plasma by LLE, using methyl t-butyl ether as the organic solvent. All liquid transfer steps were performed automatically using robotic liquid handling workstations. After vortexing, centrifugation and freezing, the supernatant organic solvent was evaporated and reconstituted. Sample analysis was performed by reversed-phase LC-MS/MS, with positive ion electrospray ionization, using multiple-reaction monitoring. The method had a very short chromatographic run time of 1.6 min. The calibration curve was linear for the range of concentrations 50.0-20.0x10(3) ng mL(-1). The proposed method was fully validated and it was proven to be selective, accurate, precise, reproducible and suitable for the determination of roxithromycin in human plasma. Therefore, it was applied to the rapid and reliable determination of roxithromycin in a bioequivalence study after per os administration of 300 mg tablet formulations of roxithromycin.     

Polyhalite and its analogous triple salts

Polyhalite (K₂SO₄ · MgSO₄ · 2CaSO₄ · 2H₂O) and analogue triple salts, where Mg²⁺ is substituted by Mn²⁺, Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺ and Zn²⁺, have been synthesized. The salts were characterized by thermal analysis, Raman spectroscopy and X-ray powder diffraction. Diffraction patterns and Raman spectra resemble those of natural polyhalite, except K₂SO₄ · CuSO₄ · 2CaSO₄ · 2H₂O. The latter corresponds to the mineral leightonite, which is structurally different. For polyhalite analogues the cell parameters of the triclinic unit cell have been determined from the powder diffraction patterns. The length of the unit cell vectors varies regularly with the ionic radius of the substituted ion M ²⁺ and is explained by changes in the extension of the coordination octahedron of M ²⁺. Thereby increasing distances of the coordinated water molecules at M ²⁺ parallel with decreasing dehydration temperatures of the corresponding polyhalite. Correspondence: Daniela Freyer, Institut für Anorganische Chemie, TU Bergakademie Freiberg, 09599 Freiberg, Germany.     

Development of an Electrochemical Biosensor for the Rapid Detection of Carbofuran Based on Air Stable Lipid Films with Incorporated Calix[4]arene Phosphoryl Receptor

This work describes the preparation of a selective receptor for the rapid, selective and sensitive electrochemical flow injection analysis of carbofuran in foods using air stable lipid films supported on a methacrylate polymer on a glass fiber filter with incorporated artificial receptor. The selective receptor was synthesized by transformation of the ? OH groups of resorcin[4]arene receptor into phosphoryl groups. These lipid films were supported on a methylacrylate polymer (i.e., methacrylic acid was the functional monomer for the polymerization, ethylene glycol dimethacrylate was used as the crosslinker and 2,2′‐azobis‐2‐methylpropionitrile as an initiator). A minisensor device was constructed for the electrochemical flow injection analysis of toxicants based on air stabilized lipid films supported on a polymer. The device can sense the analyte in a drop (50 μL) of sample. Carbofuran was injected into flowing streams of a carrier electrolyte solution. A host‐guest complex formation between the calix[4]arene phosphoryl receptor and carbofuran takes place through hydrogen bonding. This enhances the preconcentration of carbofuran at the lipid membrane surface which in turn causes dynamic alterations of the electrostatic fields and phase structure of membranes; as a result ion current transients were obtained and the magnitude of these signals was correlated to the substrate concentration. The response times were ca. 80 s and carbofuran was determined at concentration levels of nM. The effect of potent interferences included a wide range of compounds and other insecticides. The effect of interference of proteins and lipids was also examined. The reproducibility of the method was checked by recovery experiments in fruit and vegetable samples with satisfactory results.     

Synthesis of 2D Germanane (GeH): a New,Fast, and Facile Approach

Germanane (GeH), a germanium analogue of graphane, has recently attracted considerable interest because its remarkable combination of properties makes it an extremely suitable candidate to be used as 2D material for field effect devices, photovoltaics, and photocatalysis. Up to now, the synthesis of GeH has been conducted by substituting Ca by H in a β‐CaGe₂ layered Zintl phase through topochemical deintercalation in aqueous HCl. This reaction is generally slow and takes place over 6 to 14 days. The new and facile protocol presented here allows to synthesize GeH at room temperature in a significantly shorter time (a few minutes), which renders this method highly attractive for technological applications. The GeH produced with this method is highly pure and has a band gap (E_g) close to 1.4 eV, a lower value than that reported for germanane synthesized using HCl, which is promising for incorporation of GeH in solar cells.     

Reversed phase StrataTM-X resin as sorbent for automatic on-line solid phase extraction atomic absorption spectrometric determination of trace metals: comparison of polymeric-based sorbent materials

A novel on-line flow injection solid phase extraction method for the preconcentration of trace toxic metals prior determination by flame atomic absorption spectrometry (FI-SPE-FAAS) was developed. The potential application of the hydrophobic reversed phase co-polymer sorbent Strata^TM-X packed into an on-line microcolumn for the quantification of Cd(II), Pb(II), Cu(II) and Cr(VI) was demonstrated for the first time. The method was based on the on-line formation of metal complexes using sodium diethyl-dithiocarbamate (DDTC) and on the subsequent retention of them onto the sorbent material. The target analytes were completely eluted by methanol and, subsequently, directed to FAAS for quantification. All chemical and flow variables affecting the performance of the developed method were thoroughly studied and optimised. For a preconcentration time of 90 s and a sampling frequency of 28 h^?1, enhancement factors of 72, 140, 185, 63 and detection limits of 0.18, 1.6, 0.20 and 1.2 μg L ^?1 were obtained for Cd(II), Pb(II), Cu(II) and Cr(VI), respectively. The accuracy of the FI-SPE-FAAS method was evaluated by analysing certified reference materials as well as spiked environmental water samples. Furthermore, a comparative study of the analytical characteristics, the properties as well as the chemical structures of commercial polymeric based sorbent materials was employed. Strata-X sorbent was compared against Hypersep^TM SCX, Bond Elut® Plexa^TM PCX, Oasis-HLB^TM and Nobias^TM PA-1, regarding the adaptation in on-line FI-SPE-FAAS systems for metal determination, and herein presented.