Bin packing can be solved within 1 + ε in linear time

For any listL ofn numbers in (0, 1) letL* denote the minimum number of unit capacity bins needed to pack the elements ofL. We prove that, for every positive ε, there exists anO(n)-time algorithmS such that, ifS(L) denotes the number of bins used byS forL, thenS(L)/L*≦1+ε for anyL providedL* is sufficiently large. The work of this author was supported by NSF Grant MCS 70-04997.     

Mineralization procedure for use with the fluorometric determination of zinc in biological samples

Several minerelization procedures have been evaluated for use in conjunction with a method to determine zinc in milk, eggs, water and whole diets, based on the formation and extraction into diethyl ether, of Zn-5,7-dibromo-8-quinolinol. The results were compared with the known contents of standard samples or those obtained by flame atomic-absorption spectrometry. The most satisfactory procedure employed digestion with acid mixtures to destroy organic matter, and yielded a detection limit of 0.3 mg/kg for Zn.     

Quantitation of 35S promoter in maize DNA extracts from genetically modified organisms using real-time polymerase chain reaction, part 2: interlaboratory study

The European Committee for Standardization (CEN) and the European Network of GMO Working Laboratories have proposed development of a modular strategy for stepwise validation of complex analytical techniques. When applied to the quantitation of genetically modified organisms (GMOs) in food products, the instrumental quantitation step of the technique is separately validated from the DNA extraction step to better control the sources of uncertainty and facilitate the validation of GMO-specific polymerase chain reaction (PCR) tests. This paper presents the results of an interlaboratory study on the quantitation step of the method standardized by CEN for the detection of a regulatory element commonly inserted in GMO maize-based foods. This is focused on the quantitation of P35S promoter through using the quantitative real-time PCR (QRT-PCR). Fifteen French laboratories participated in the interlaboratory study of the P35S quantitation operating procedure on DNA extract samples using either the thermal cycler ABI Prism 7700 (Applied Biosystems, Foster City, CA) or Light Cycler (Roche Diagnostics, Indianapolis, IN). Attention was focused on DNA extract samples used to calibrate the method and unknown extract samples. Data were processed according to the recommendations of ISO 5725 standard. Performance criteria, obtained using the robust algorithm, were compared to the classic data processing after rejection of outliers by the Cochran and Grubbs tests. Two laboratories were detected as outliers by the Grubbs test. The robust precision criteria gave values between the classical values estimated before and after rejection of the outliers. Using the robust method, the relative expanded uncertainty by the quantitation method is about 20% for a 1% Bt176 content, whereas it can reach 40% for a 0.1% Bt176. The performances of the quantitation assay are relevant to the application of the European regulation, which has an accepted tolerance interval of about +/-50%. These data were fitted to a power model (r2 = 0.96). Thanks to this model, it is possible to propose an estimation of uncertainty of the QRT-PCR quantitation step and an uncertainty budget depending on the analytical conditions.     

A Model for Community Nursing in a Rural County

A model for the working day of the community nurse is proposed. This takes into account the attachment of the nurse to the patients registered with assigned general practices and the effect that this will have on her travelling time, visiting time and administrative duties. It also leads to a method of dividing the country into nursing team regions, assessing the level of nursing service thereby provided.     

Jahn-Teller distortion in the SnH4+ ion

The extension of the Jahn-Teller distortion of the SnH₄⁺ structure is estimated from ab initio SCF CI calculations using pseudopotential atomic approximation with and without relativistic correction. These calculations show the lowest minima of SnH₄⁺ to have C_2v symmetry and are very close to the C_3v minima. The calculated photoelectron spectrum of SnH₄ is in good agreement with the experimental values.     

Effect of the temperature on the synthesis of (K,Na)NbO<Subscript>3</Subscript>-modified nanoparticles by a solid state reaction route

(Na_0.5K_0.5)NbO₃ (KNN)-modified nano-particulated powders, based on variations of sodium–potassium niobate, were synthesised by solid state reaction from carbonate starting materials. The nanoparticles were attained by an optimization of the raw materials particle size and particle refinement of the carbonates during their decomposition. Particle sizes between 50 and 200 nm have been obtained as a function of calcination (decomposition) temperature. The obtained powders showed a co-existence between a tetragonal phase and an orthorhombic phase. The optimization of the raw materials particle size and the particle refinement of the carbonates during their decomposition play a key role in the formation of the KNN-modified nano particles. The developed method is well suited for the production of KNN-modified nano powders at low cost for mass production.     

Single facility location on a network under mill and delivered pricing

^** E-mail: pelegrin{at}um.es Firms normally use either a mill price or a delivered pricepolicy, depending on market conditions (type of good, transportationway, customers location, costs, etc). In this paper, the problemof selecting the best location for an entering firm in competitionwith some pre-existing firms, under each price policy, is studiedon a network for the first time. With mill pricing, an equilibriumin price rarely exists and it is assumed that all competingfirms set a common mill price for all customers. With deliveredpricing, there exists a Nash equilibrium in price and it isassumed that the equilibrium price in each area is offered tothe customers in that area. In both cases, we consider thatcustomers buy from the cheapest facility and the same rulesare used for tie breaking in the lowest cost. While the profitmaximization problem for the entering firm always has optimalsolutions under mill pricing, this problem might not have anoptimal solution under delivered pricing. We show some discretizationresults and give procedures to find the full set of optimal,or -optimal, solutions to the problem under the two price policies.A comparison of results with the two price policies is givenby using an illustrative example.     

Structural characterization and oxidative dehydrogenation activity of V2O5/Ce(x)Zr(1-x)O2/SiO2 catalysts

The thermal stability of a nanosized Ce(x)Zr(1-x)O2 solid solution on a silica surface and the dispersion behavior of V2O5 over Ce(x)Zr(1-x)O2/SiO2 have been investigated using XRD, Raman spectroscopy, XPS, HREM, and BET surface area techniques. Oxidative dehydrogenation of ethylbenzene to styrene was performed as a test reaction to assess the usefulness of the VOx/Ce(x)Zr(1-x)O2/SiO2 catalyst. Ce(x)Zr(1-x)O2/SiO2 (1:1:2 mol ratio based on oxides) was synthesized through a soft-chemical route from ultrahigh dilute solutions by adopting a deposition coprecipitation technique. A theoretical monolayer equivalent to 10 wt % V2O5 was impregnated over the calcined Ce(x)Zr(1-x)O2/SiO2 sample (773 K) by an aqueous wet impregnation technique. The prepared V2O5/Ce(x)Zr(1-x)O2/SiO2 sample was subjected to thermal treatments from 773 to 1073 K. The XRD measurements indicate the presence of cubic Ce0.75Zr0.25O2 in the case of Ce(x)Zr(1-x)O2/SiO2, while cubic Ce0.5Zr0.5O2 and tetragonal Ce0.16Zr0.84O2 in the case of V2O5/Ce(x)Zr(1-x)O2/SiO2 when calcined at various temperatures. Dispersed vanadium oxide induces more incorporation of zirconium into the ceria lattice, thereby decreasing its lattice size and also accelerating the crystallization of Ce-Zr-O solid solutions at higher calcination temperatures. Further, it interacts selectively with the ceria portion of the composite oxide to form CeVO4. The RS measurements provide good evidence about the dispersed form of vanadium oxide and the CeVO4 compound. The HREM studies show the presence of small Ce-Zr-oxide particles of approximately 5 nm size over the surface of amorphous silica and corroborate with the results obtained from other techniques. The catalytic activity studies reveal the ability of vanadium oxide supported on Ce(x)Zr(1-x)O2/SiO2 to efficiently catalyze the ODH of ethylbenzene at normal atmospheric pressure. The remarkable ability of Ce(x)Zr(1-x)O2 to prevent the deactivation of supported vanadium oxide leading to stable activity in the time-on-stream experiments and high selectivity to styrene are other important observations.