The nontriviality of certain Zl-extensions

Let k be a J-field, K the basic Z_l-extension of k, and A₀, A the l-class groups of k, K respectively. It is known that if A₀^1?J is nontrivial, then $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>J</mtext><mtext>?</mtext>}}$ is infinite. It is shown that this result is still true if the classes represented by the primes lying over l are factored out from both groups. This is applied to $\text{k = Q((?m)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ and A₀ = (0) for information on the invariants λ and μ. There are such k for which λ ≥ 2.     

Local mixture injection to extend the lean limit of spark-ignition engines

 The effect of charge stratification by direct, in-cylinder injection of a small quantity of propane-air mixture in a single-cylinder, propane-fuelled, spart-ignition engine, has been determined in terms of in-cylinder pressure, flame visualisation and exhaust emissions. The operating conditions ranged from low load to wide open throttle at 1000 and 1500 rpm, and with quiescent and swirling in-cylinder flows. The effects of injection-driven flow and turbulence on combustion have been considered independently of mixture strength by assessing the consequences of injecting a local mixture of an equivalence ratio equal to that of the port-induced charge. The results provide further evidence to support the concept of direct in-cylinder mixture injection. At 1000 rpm and low load, faster development of the flame kernel and subsequent enflamed area were observed, together with a 60% increase in peak cylinder combustion pressure at an overall equivalence ratio of 0.7 (A/F of 22.5). The relative effect of local-charge stratification increased with reduction in equivalence ratio at this engine speed and without increase in emissions; at 1500 rpm, stable combustion was achieved even at an equivalence ratio of 0.61 (A/F of 25.8), which was below the flammability limit of the homogeneous port-only propane/ air mixture. Unthrottled engine operation produced similar results so that at an equivalence ratio of 0.55 (A/F of 28.5), for example, the Coefficient of variation of the indicated mean effective pressure was reduced from 0.4 to less than 0.1 by mixture local injection. With a shrouded inlet valve generating mean gas velocities of 6 m/s at the time of ignition in the vicinity of the spark plug, control of rich mixture injection both with and against the bulk in-cylinder flow, resulted in stable combustion with Coefficient of variation of the indicated mean effective pressure of less than 0.1 at an equivalence ratio of 0.55 (A/F of 28.5). Received: 28 October 1997/Accepted: 23 March 1998     

Complete reducibility and Steinberg endomorphisms

Let G be a connected reductive algebraic group defined over an algebraically closed field of positive characteristic. We study a generalization of the notion of G-complete reducibility in the context of Steinberg endomorphisms of G. Our main theorem extends a special case of a rationality result in this setting.     

Single-particle relaxation time of the two-dimensional electron gas in Si/SiGe: Many-body effects

The single-particle relaxation time of the two-dimensional electron gas in SiGe/Si/SiGe quantum wells is calculated. Many-body effects beyond the random-phase approximation become important at low electron density. For charged impurity scattering (remote doped), the importance of these many-body effects as functions of the electron density and spacer width is analyzed. Induced by many-body effects, a strong reduction of the single-particle relaxation time at low electron densities is predicted. The relation with the transport scattering time is described, multiple-scattering effects are commented, and the determination of many-body effects in existing samples is discussed.     

Home to School: Numeracy Practices and Mathematical Identities

Drawing on a perspective of mathematics as situated social practice, we focus on 4 children in an urban preschool classroom and follow those children between home and school sites to shed light on urban children's persistent underachievement in mathematics. In this article, we describe the ways in which numeracy practices travel with children between home and school and, within those contexts, shape complex and sometimes limited social identities for children. We found that school imperatives, such as assessments and socialization curricula, often obscure teachers' views of children's mathematical practices. Deficit assumptions about family and community support for children, and limited interaction between caregivers and teachers, further contribute to the tendency of school personnel to overlook the mathematical practices that children bring with them to school. We further suggest that vignettes drawn from ethnographic-type research such as this have potential for professional development for classroom teachers.     

Identification of tyrosine nitration in UCH-L1 and GAPDH

Protein tyrosine nitration is a post-translational modification commonly used as a marker of cellular oxidative stress associated with numerous pathophysiological conditions. We focused on ubiquitin carboxyl terminal hydrolase-L1 (UCH-L1) and glyceraldehyde-3-phosphate (GAPDH) which are high-abundant brain proteins that have been identified to be highly susceptible to oxidative modification. Both UCH-L1 and GAPDH have been linked to the pathogenesis of Alzheimer's and Parkinson's disease, however specific nitration sites have not been elucidated. Identification of specific nitration sites and quantitation of endogenous nitrated proteins are important in correlating this modification to disease pathology. In this study, purified UCH-L1 and GAPDH were nitrated in vitro with peroxynitrite and the presence of nitrated proteins was confirmed by anti-3-nitrotyrosine Western blots. Data-dependent LC-MS/MS analysis identified several distinct tyrosine nitration sites in UCH-L1 (Tyr-80) and GAPDH (Tyr-47, Tyr-92, and Tyr-312). Subsequent validation with synthetic peptides was conducted for selected nitropeptides. An LC-MS/MS method was developed for semi-quantitative determination of the synthetic nitropeptides: KGQEVSPKVY(*) (UCH-L1) and mFQY(*) DSTHGKF (GAPDH). The nitropeptides were detectable in the mid-attomole range and the peak area response was linear over three orders of magnitude. Targeted analysis of endogenous UCH-L1 and GAPDH nitration was then conducted in an in vivo second-hand smoke rat model to evaluate the utility of this approach.     

Cayley-Bacharach and evaluation codes on complete intersections

Hansen (Appl. Algebra Eng. Comm. Comput. 14 (2003) 175) uses cohomological methods to find a lower bound for the minimum distance of an evaluation code determined by a reduced complete intersection in P². In this paper, we generalize Hansen's results from P² to P^m; we also show that the hypotheses of Hansen (2003) may be weakened. The proof is succinct and follows by combining the Cayley-Bacharach Theorem and the bounds on evaluation codes obtained in Hansen (Zero-Dimensional Schemes (Ravello, 1992), de Gruyter, Berlin, 1994, pp. 205-211).     

Performance analysis of a batch service queue arising out of manufacturing system modelling

In this paper, we present an exact analysis of a queueing system with Poisson arrivals and batch service. The system has a finite numberS of waiting places and a batch service capacityb. A service period is initialized when a service starting thresholda of waiting customers has been reached. The model is denoted accordingly byM/G ^[a,b] /1–S. The motivation for this model arises from manufacturing environments with batch service work stations, e.g. in machines for computer components and chip productions. The method of embedded Markov chain is used for the analysis, whereby a representation of the general service time is obtained via a moment matching approach. Numerical results are shown in order to illustrate the dependency of performance measures on special sets of system parameters. Furthermore, attention is devoted to the issues of starting rules, where performance objectives like short waiting time, small blocking probability and minimal amount of work in progress are taken into account.     

A 100-kW three-phase AC plasma furnace for spheroidization of aluminum silicate particles

A 100-kW three-phase ac plasma furnace with sheathed copper electrodes (sheathing gas: air) is presented. It is used for spheroidizing chamotte (refractory-fired clay) particles having a smooth, pore-free surface. A simple, one-dimensional numerical model for the heat transfer to the particles explains the maximum processing rate and the detrimental influence of an inhomogeneous particle size distribution.     

Productivity Analysis and System Coherence

Productivity analyses have been undertaken by such a variety of specialists and in such differing contexts that few can cope with the broadly dispersed literature. It is not surprising, therefore, that the same problems are rediscovered time and again, that faulty concepts remain in use and that empirical findings are often misinterpreted. Such shortcomings will continue to hamper the development of this field until past advances are more effectively consolidated and the current frontiers more clearly delineated. In this paper, therefore, certain past findings will be used as points of departure for considering the problems and means of effecting further gains.One comprehensive exploration of productivity analysis suggested four general conclusions, along with their analytical foundations, which seem to have withstood subsequent consideration well enough to serve as bases for this undertaking:

1. 1)
   That productivity analysis serves a variety of purposes and hence requires a corresponding variety of appropriately designed measures:
    
2. 2)
   That the productivity of any activity system should refer not to any single input-output ratio, but to an integrated network of such measures;
    
3. 3)
   That the effects of productivity adjustments depend not only on their magnitudes, but also on the sources responsible for them, on the nature of the changes in input-output relationships involved, and on managerial choices among alternative means of harnessing their potential benefits;
    
4. 4)
   That evaluating such effects requires supplementing physical with cost measures and then with successively broader criteria until these come to reflect the guiding objectives of the system under study.
    

Such conclusions imply that productivity adjustments may assume many forms, that apparent increases in productivity levels need not always be beneficial, that the very same pattern of productivity changes may have quite different effects in dissimilar circumstances and, finally, that productivity increases are not ends in themselves but merely one means of promoting more fundamental ends. Further development may seek to extend the original analysis beyond standardized commodity production to other economic activities, beyond a plant or firm to larger aggregates, and beyond short periods. But such elaborations of this framework require the strengthening of its conceptual foundations. Hence, it is to these that primary attention will be given.