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Stephen Pankavich 《Mathematical Methods in the Applied Sciences》2007,30(5):529-548
A collisionless plasma is modelled by the Vlasov–Poisson system in one dimension. We consider the situation in which mobile negative ions balance a fixed background of positive charge, which is independent of space and time, as ∣x∣ → ∞. Thus, the total positive charge and the total negative charge are both infinite. Smooth solutions with appropriate asymptotic behaviour are shown to exist locally in time, and criteria for the continuation of these solutions are established. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
23.
Lee Stephen; Harrison Martin C.; Robinson Carol L. 《Teaching Mathematics and its Applications》2007,26(3):111-118
In the past 6 years changes have occurred in GCE A-levels. Inparticular, there have been several major changes in A-levelMathematics courses. As engineering students are usually requiredto have studied A-level Mathematics, or its equivalent, thesechanges have had an effect on their prior mathematical knowledge.Moreover, engineering students traditionally obtained a goodgrounding in mechanics as part of their A-level Mathematicsqualification. However, mechanics, which was once included inthe core syllabus, is now optional. This article investigatesthe current availability and uptake of mechanics modules withinA-level Mathematics courses in schools. Comparisons are drawnbetween these results and results of a survey of schools in2004 and surveys of first year engineering students conductedin 2004 and 2005. It is found that there is a decline in theavailability of mechanics modules and the uptake of more thanone mechanics module has also decreased. The implications ofthese findings for engineering educators are discussed. 相似文献
24.
Using a combinatorial approach that avoids geometry, this paper studies the structure of KT(G/B), the T-equivariant K-theory of the generalized flag variety G/B. This ring has a natural basis
(the double Grothendieck polynomials), where
is the structure sheaf of the Schubert variety Xw. For rank two cases we compute the corresponding structure constants of the ring KT(G/B) and, based on this data, make a positivity conjecture for general G which generalizes the theorems of M. Brion (for K(G/B)) and W. Graham (for HT*(G/B)). Let [Xλ]KT(G/B) be the class of the homogeneous line bundle on G/B corresponding to the character of T indexed by λ. For general G we prove “Pieri–Chevalley formulas” for the products
,
,
, and
, where λ is dominant. By using the Chern character and comparing lowest degree terms the products which are computed in this paper also give results for the Grothendieck polynomials, double Schubert polynomials, and ordinary Schubert polynomials in, respectively K(G/B), HT*(G/B) and H*(G/B). 相似文献
25.
Luis Anchordoqui María Teresa Dova Thomas McCauley Stephen Reucroft 《Annals of Physics》2004,314(1):145-207
The properties of cosmic rays with energies above 106 GeV have to be deduced from the spacetime structure and particle content of the air showers which they initiate. In this review we summarize the phenomenology of these giant air showers. We describe the hadronic interaction models used to extrapolate results from collider data to ultra high energies, and discuss the prospects for insights into forward physics at the LHC. We also describe the main electromagnetic processes that govern the longitudinal shower evolution, as well as the lateral spread of particles. Armed with these two principal shower ingredients and motivation from the underlying physics, we provide an overview of some of the different methods proposed to distinguish primary species. The properties of neutrino interactions and the potential of forthcoming experiments to isolate deeply penetrating showers from baryonic cascades are also discussed. We finally venture into a terra incognita endowed with TeV-scale gravity and explore anomalous neutrino-induced showers. 相似文献
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We develop the theory of the nonadiabatic geometric phase, in both the Abelian and non-Abelian cases, in quaternionic Hilbert space. 相似文献
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