Constitutional Aspects of the Covenant

Studier och granskningar har visat på en fokusering på imitativt resonemang i skolsammanhang där eleverna många gånger inte bedöms utifrån samtliga kunskapskrav. Syftet med denna studie är att få fördjupad kunskap kring vilket resonemangskrav som ställs på elever vid skriftliga prov i Matematik 1. I studien har provuppgifter från en lärarhandledning analyserats och klassificerats utifrån ett ramverk för matematiska resonemang. Genom att jämföra resultatet med tidigare forskning om resonemangskrav i nationella prov har även en slutsats kunnat dras huruvida resonemangskraven i lärarhandledningens provuppgifter är tillräckligt höga för att generellt sett kunna följa styrdokumentens riktlinjer. Resultatet visade att 26 % av de analyserade uppgifterna krävde globalt kreativt resonemang medan 26 % fordrade lokalt kreativt resonemang och 47 % var lösbara med någon typ av imitativt resonemang. Utifrån jämförelsen med resonemangskraven för de nationella proven drogs slutsatsen att resonemangskraven i lärarhandledningens provuppgifter överlag inte var tillräckligt höga för att i tillräcklig utsträckning testa alla kunskapskrav. Resultatet indikerar att centrala förmågor, i första hand problemlösnings-, resonemangsförmågan och förmågan att använda matematiska begrepp, inte testas i tillräckligt hög grad

Additive noise effects in active nonlinear spatially extended systems

We examine the effects of pure additive noise on spatially extended systems with quadratic nonlinearities. We develop a general multiscale theory for such systems and apply it to the Kuramoto-Sivashinsky equation as a case study. We first focus on a regime close to the instability onset (primary bifurcation), where the system can be described by a single dominant mode. We show analytically that the resulting noise in the equation describing the amplitude of the dominant mode largely depends on the nature of the stochastic forcing. For a highly degenerate noise, in the sense that it is acting on the first stable mode only, the amplitude equation is dominated by a pure multiplicative noise, which in turn induces the dominant mode to undergo several critical state transitions and complex phenomena, including intermittency and stabilisation, as the noise strength is increased. The intermittent behaviour is characterised by a power-law probability density and the corresponding critical exponent is calculated rigorously by making use of the first-passage properties of the amplitude equation. On the other hand, when the noise is acting on the whole subspace of stable modes, the multiplicative noise is corrected by an additive-like term, with the eventual loss of any stabilised state. We also show that the stochastic forcing has no effect on the dominant mode dynamics when it is acting on the second stable mode. Finally, in a regime which is relatively far from the instability onset, so that there are two unstable modes, we observe numerically that when the noise is acting on the first stable mode, both dominant modes show noise-induced complex phenomena similar to the single-mode case

Comment on ``Density Matrix Renormalization Group Study of the Haldane Phase in Random One-Dimensional Antiferromagnets"

In a recent Letter (PRL 83, 3297 (1999)), Hida presented numerical results indicating that the Haldane phase of the Heisenberg antiferromagnetic spin-1 chain is stable against bond randomness, for box distributions of the bond strength, even when the box distribution stretches to zero bond strength. The author thus concluded that the Haldane phase is stable against bond randomness for any distribution of the bond strength, no matter how broad. In this Comment, we (i) point out that the randomness distributions studied in this Letter do not represent the broadest possible distributions, and therefore these numerical results do not lead to the conclusion that the Haldane phase is stable against any randomness; and (ii) provide a semiquantitative estimate of the critical randomness beyond which the Haldane phase yields to the Random Singlet phase, in a specific class of random distribution functions for the bond strength.Comment: A comment on PRL 83, 3297 (1999). One pag

Hydrogen thermal conductivity at temperatures from 2000 to 4000 deg F Final report

Hydrogen thermal conductivity at temperatures from 2000 to 4600 deg

LM cathode thruster system Quarterly progress report, 4 Oct. 1969 - 4 Jan. 1970

Optimization testing of thermally integrated liquid mercury cathode thruster syste