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Iterative Conceptions of Set
Many philosophers are aware of the paradoxes of set theory (e.g.Russell's paradox). For many people, these were solved by the iterative conception of set which holds that sets are formed in stages by collecting sets available at previous stages.This Element will examine possibilities for articulating this solution.In particular, the author argues that there are different kinds of iterative conception, and it's open which of them (if any) is the best.Along the way, the author hopes to make some of the underlying mathematical and philosophical ideas behind tricky bits of the philosophy of set theory clear for philosophers more widely and make their relationships to some other questions in philosophy perspicuous.
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Iterative Optimization in Inverse Problems
Iterative Optimization in Inverse Problems brings together a number of important iterative algorithms for medical imaging, optimization, and statistical estimation.It incorporates recent work that has not appeared in other books and draws on the author’s considerable research in the field, including his recently developed class of SUMMA algorithms.Related to sequential unconstrained minimization methods, the SUMMA class includes a wide range of iterative algorithms well known to researchers in various areas, such as statistics and image processing. Organizing the topics from general to more specific, the book first gives an overview of sequential optimization, the subclasses of auxiliary-function methods, and the SUMMA algorithms.The next three chapters present particular examples in more detail, including barrier- and penalty-function methods, proximal minimization, and forward-backward splitting.The author also focuses on fixed-point algorithms for operators on Euclidean space and then extends the discussion to include distance measures other than the usual Euclidean distance.In the final chapters, specific problems illustrate the use of iterative methods previously discussed.Most chapters contain exercises that introduce new ideas and make the book suitable for self-study. Unifying a variety of seemingly disparate algorithms, the book shows how to derive new properties of algorithms by comparing known properties of other algorithms.This unifying approach also helps researchers—from statisticians working on parameter estimation to image scientists processing scanning data to mathematicians involved in theoretical and applied optimization—discover useful related algorithms in areas outside of their expertise.
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Scotland Mountain Biking : The Wild Trails
Revised reprint 2019Scotland Mountain Biking – The Wild Trails features 24 of the best and more adventurous mountain bike rides in Scotland.The routes range from 6.5 to 290 kilometres in length, and are suitable for all levels of mountain bikers.Split into three sections, Southern & Central Scotland, North-West Scotland & Highlands, and North-East Scotland & Cairngorms, this book includes challenging mountain passes, magical woodland singletrack, Munro peaks and idyllic spins past ancient lochs.The routes include a classic Torridon Circuit, Glen Sligachan on Skye, man-made and natural trails around the Minch Moor at Innerleithen, Munro Mount Keen, the end-to-end Corrieyairack Pass, and a big-mountain loop around Ben Alder.A Bonus Section includes the Fort William to Montrose Coast to Coast route. The book is written by Scottish mountain bike guide Phil McKane and includes stunning photography by Andy McCandlish.It features Ordnance Survey 1:50,000 maps; easy-to-follow directions; details of distance, times and difficulty; and refreshment stops and local knowledge. Reprinted in 2019 with updated mapping and revisions.
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Lake District Mountain Biking : Essential Trails
Lake District Mountain Biking – Essential Trails is the full third edition of the bestselling guide to some of the finest mountain bike riding in the UK. Featured are over 20 of the best mountain bike rides in the Lake District, between 12 and 60 kilometres in length, suitable for all levels of mountain bikers. Explore classic rides around Walna Scar, High Street and Borrowdale, and discover several lesser-known gems.Ride moorland singletrack, tackle massive climbs and rattle along some of the rockiest trails you’ll ever encounter on two wheels.Enjoy lakeside cruises, picturesque valleys and 360-degree panoramas. Researched, ridden and written by local riders Richard Staton and Chris Gore, each route features clear and easy to use Ordnance Survey 1:50,000 maps; easy-to-follow directions; details of distance, timings and difficulty gradings; and refreshment stops and local knowledge.A Bonus Section includes information about the man-made trails at Whinlatter and Grizedale, Top Tens and a detailed Appendix.Also includes downloadable GPX files.
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Peak District Mountain Biking : Dark Peak Trails
Peak District Mountain Biking - Dark Peak Trails is the full second edition of the groundbreaking mountain bike guidebook Dark Peak Mountain Biking - True Grit Trails, described by leading mountain biking website Bikemagic.com as 'far and away the best Peak guide we've come across.'All route information has been thoroughly checked for this new edition, to give the most up-to-date and comprehensive guidebook to some of the finest and most popular riding in the country.As with all new Vertebrate MTB guidebooks, this new edition features industry-standard Ordnance Survey mapping, and is illustrated with stunning action photography. Featured within the book are 26 of the best mountain bike rides in the Dark Peak, between 11.5 and 105 (!) kilometres in length, suitable for all levels of mountain bikers.Researched, ridden and written by a local rider, each route features easy-to-follow directions; details of distance, timings and difficulty gradings; refreshment stops and local knowledge; and clear and easy to use Ordnance Survey 1:50,000 maps.A Bonus Section includes Top Ten Climbs, Downhills and Singletracks, Sheffield City Links and a detailed Appendix.
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Yorkshire Dales Mountain Biking : Classic Pennine Trails
Yorkshire Dales Mountain Biking features 26 rides between 10 and 43 kilometres in length in one of the UK’s most MTB-friendly national parks. The routes make the most of the Dales’ superb network of stone-based trails, rideable in all seasons.Classic loops take in the best of Swaledale, a tour of Ingleborough, big days around Whernside and Pen-y-ghent, quintessential Dales scenery near Malham and Kilnsey, and moorland riding above Pateley Bridge. A Bonus Section includes information about the Howgills, the easy-going Swale Trail and the Pennine Bridleway, as well as the riding at Gisburn Forest and Stainburn which lies just outside the national park.There are also top tens and a detailed appendix. Written by Dales local and experienced author Nick Cotton, each ride is described with easy-to-follow directions and is plotted on clear and easy-to-use Ordnance Survey 1:50,000 mapping.Also included with each ride are details of distance, timings and difficulty gradings, plus refreshment stops and local knowledge.
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West Yorkshire Mountain Biking - South Pennine Trails
West Yorkshire Mountain Biking - South Pennine Trails features 23 of the best mountain bike rides in West Yorkshire, between 10.5km and 32km in length, suitable for all levels of mountain bikers. The routes are split into four sections: Calderdale, Bradford, Kirklees and City of Leeds.Explore wild moorland, plunge into steep and deep wooded valleys, cruise through the heart of industrial Yorkshire and speed along some of the best singletrack in the country. As with all new Vertebrate MTB guidebooks, this title features industry-standard Ordnance Survey mapping, and is illustrated with stunning action photography. Researched, ridden and written by local expert and MTB journalist Benjamin Haworth, each route features clear and easy to use Ordnance Survey 1:50,000 maps, easy-to-follow directions, details of distance, timings and difficulty gradings, and refreshment stops and local knowledge.Also included is a detailed Appendix.
Price: 14.95 £ | Shipping*: 3.99 £ -
Scotland Mountain Biking : Wild Trails Vol.2
Scotland Mountain Biking – Wild Trails Vol.2 features 24 new and classic mountain bike rides across Scotland.Like the original Wild Trails guidebook, this book includes challenging mountain passes, endless singletrack, lochside cruises and more, all in a country named a 'Global Superstar' by the International Mountain Biking Association. Split into three sections – Southern & Central Scotland, North West Scotland & Islands, and North East Scotland – Wild Trails Vol.2 has been researched, ridden and written by Scottish Mountain Bike Guide Phil McKane, and each route features clear and easy to use Ordnance Survey 1:50,000 maps, easy-to-follow directions, details of distance, timings and difficulty gradings, and refreshment stops and local knowledge. The book is illustrated with stunning action photography from top pro photographer Andy McCandlish, and also features a detailed Appendix.
Price: 15.95 £ | Shipping*: 3.99 £
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