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be an elliptic curve over a field
. There is a functor
from the category of finitely presented torsion-free left
-modules to the category of abelian varieties isogenous to a power of
, and a functor
in the opposite direction. We prove necessary and sufficient conditions on
for these functors to be equivalences of categories. We also prove a partial generalization in which
is replaced by a suitable higher-dimensional abelian variety over
For almost four decades Carole Rawcliffe has been a towering figure among historians of the later Middle Ages. Although now best known for her pioneering contributions to medical history, including major studies of hospitals, leprosy and public health, her published works range far more broadly to encompass among other subjects the English nobility, Members of Parliament, the regional history of East Anglia and myriad aspects of political and social interaction. The essays collected in this festschrift, written by a selection of her colleagues, friends and former students, cover a wide spectrum of themes and introduce such diverse characters as an estranged queen, a bankrupt aristocrat, a female apothecary, a flute-playing Turkish doctor and a medieval "Dad's Army" conscripted to defend England's coasts.
Linda Clark is Editor of the 1422-1504 section of the History of Parliament; Elizabeth Danbury is an Honorary Senior Research Fellow at the Institute of English Studies, School of Advanced Study, University of London, and Honorary Research Fellow at the Department of Information Studies, University College London.
Contributors: Jean Agnew, John Alban, Brian Ayers, Caroline Barron, Christopher Bonfield, Carole Hill, Peregrine Horden, Hannes Kleineke, Nicholas Vincent.
Diatoms provide the chief Cenozoic biostratigraphic tool in marine sediments beneath high primary productivity zones, especially where calcareous fossils are rare or poorly preserved. Diatom biostratigraphy, which is based on originations and extinctions of unique taxa, is especially useful in circum-Antarctic, equatorial Pacific, and high latitude North Pacific marine successions, which are available largely from ocean drilling. Oligocene to Holocene diatom biostratigraphic zonations are correlated with the geopaleomagnetic timescale, resulting in age control of million-year to as little as hundred-thousand year resolution. Paleocene and Eocene zonations are less well developed and have lower chronostratigraphic control, but are more widely applicable, because planktonic diatom assemblages of the globally warm early Paleogene were less provincial. We review the principals and methods of biostratigraphy and the application of diatoms to age control in stratigraphic successions worldwide. Distinct biostratigraphic zonations defined for the low latitudes, the North Pacific and the Antarctic, are reviewed, and Atlantic records and Antarctic coastal records are discussed. New biostratigraphic tools are introduced, including multidimensional graphic correlation of published diatom ranges.
Objective: Intraoperative ultrasound was introduced to evaluate the adequacy of repair after surgical repair of congenital cardiac malformations. Our purpose was to review the evolution of this technique at our centre. Methods: We evaluated all intraoperative ultrasound studies undertaken between 1997 and 2002, reviewing the data from 1997 through 2001 retrospectively, but undertaking a prospective audit of studies undertaken from 2002 onwards. In all, we carried out a total number of 639 intraoperative ultrasound studies, from a possible 2737 cardiac operations (23.3%), using the epicardal approach in 580 (90.7%), and transoesophageal ultrasound in the other 59 patients (9.3%). Median age was 0.6 years, with an interquartile range from 0.06 to 3.6 years. Results: The findings obtained using intraoperative ultrasound influenced the surgical management in 63 of the 639 patients (9.9%), suggesting the need for additional surgery in 26, adjustment of the band placed round the pulmonary trunk in 16, preoperative assessment of the cardiac malformation in 5, and confirming the need for prolonged support with cardiopulmonary bypass for impaired ventricular function in 16. There were 18 early reoperations, 5 of which may have been predicted by intraoperative ultrasound. Of the 183 studies reviewed prospectively in 2002, it was not possible to obtain the complete range of views in 8 (4.4%), while in 27 patients (14.7%), the postoperative findings using transthoracic interrogation differed from the findings obtained immediately following bypass. Conclusion: Intraoperative ultrasound is an important technique for monitoring the results of complex congenital cardiac surgery. The immediate recognition of significant lesions, together with multidisciplinary discussion, allows for improved management and prevention of early surgical reintervention.
In this chapter, we argue that the learning sciences are poised for a “decade of synergy.” We focus on several key traditions of theory and research with the potential for mutually influencing one another in ways that can transform how we think about the science of learning, as well as how future educators and scientists are trained.
The three major strands of research that we focus on are: (1) implicit learning and the brain, (2) informal learning, and (3) designs for formal learning and beyond. As Figure 2.1A illustrates, these three areas have mainly operated independently, with researchers attempting to apply their thinking and findings directly to education, and with the links between theory and well-grounded implications for practice often proving tenuous at best.
The goal of integrating insights from these strands in order to create a transformative theory of learning is illustrated in Figure 2.1B. Successful efforts to understand and advance human learning require a simultaneous emphasis on informal and formal learning environments, and on the implicit ways in which people learn in whatever situations they find themselves.
We explore examples of research from each of these three strands. We then suggest ways that the learning sciences might draw on these traditions for creating a more robust understanding of learning, which can inform the design of learning environments that allow all students to succeed in the fast changing world of the twenty-first century (e.g., Darling-Hammond & Bransford, 2005; Vaill, 1996).
Diatoms, golden brown algae, are present in most aqueous environments. Within the marine environment marine diatoms occupy the photic zone and represent the lowest level of the marine food chain. Diatoms are either planktonic or benthic and possess an external siliceous skeleton or frustule, that is boxlike in structure. The size of diatom frustules ranges from less than 1 μm to more than 1,000 μm, but most frustules range in size from 10 to 100 μm. Diatoms are present in the geological record from at least the Cretaceous (Harwood and Nikolaev, this volume) and have numerous advantages for biostratigraphic correlation and paleoenvironmental reconstruction of marine sedimentary sequences. This chapter summarizes the current state of marine diatom biostratigraphy for the Cenozoic and provides examples of how marine diatoms are used in paleoenvironmental reconstructions. No attempt is made to illustrate the various diatom taxa discussed; the reader is referred to published references such as the syntheses of Fenner (1985) and Barron (1985).
Individuals of Perilissus nudus sp.nov. of the Perilissus anatinus species group are described. This species, which occurs in the mountain ranges of southern Mexico and Costa Rica, is compared with the closely related species P. anatinus Barron. Locality data on additional specimens of P. anatinus, found in mountain ranges in Mexico, are included. Study of characteristics of P. nudus in relation to P. anatinus clarifies further the relationship of this species group with the other species groups of Perilissus.