Quadratic Differentials

Quadratic Differentials

Author: K. Strebel

Publisher: Springer Science & Business Media

Published: 1984-04-02

Total Pages: 204

ISBN-13: 9783540130352

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A quadratic differential on aRiemann surface is locally represented by a ho lomorphic function element wh ich transforms like the square of a derivative under a conformal change of the parameter. More generally, one also allows for meromorphic function elements; however, in many considerations it is con venient to puncture the surface at the poles of the differential. One is then back at the holomorphic case. A quadratic differential defines, in a natural way, a field of line elements on the surface, with singularities at the critical points, i.e. the zeros and poles of the differential. The integral curves of this field are called the trajectories of the differential. A large part of this book is about the trajectory structure of quadratic differentials. There are of course local and global aspects to this structure. Be sides, there is the behaviour of an individual trajectory and the structure deter mined by entire subfamilies of trajectories. An Abelian or first order differential has an integral or primitive function is in general not single-valued. In the case of a quadratic on the surface, which differential, one first has to take the square root and then integrate. The local integrals are only determined up to their sign and arbitrary additive constants. However, it is this multivalued function which plays an important role in the theory; the trajectories are the images of the horizontals by single valued branches of its inverse.


Quadratic Differentials

Quadratic Differentials

Author: K. Strebel

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 197

ISBN-13: 3662024144

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A quadratic differential on aRiemann surface is locally represented by a ho lomorphic function element wh ich transforms like the square of a derivative under a conformal change of the parameter. More generally, one also allows for meromorphic function elements; however, in many considerations it is con venient to puncture the surface at the poles of the differential. One is then back at the holomorphic case. A quadratic differential defines, in a natural way, a field of line elements on the surface, with singularities at the critical points, i.e. the zeros and poles of the differential. The integral curves of this field are called the trajectories of the differential. A large part of this book is about the trajectory structure of quadratic differentials. There are of course local and global aspects to this structure. Be sides, there is the behaviour of an individual trajectory and the structure deter mined by entire subfamilies of trajectories. An Abelian or first order differential has an integral or primitive function is in general not single-valued. In the case of a quadratic on the surface, which differential, one first has to take the square root and then integrate. The local integrals are only determined up to their sign and arbitrary additive constants. However, it is this multivalued function which plays an important role in the theory; the trajectories are the images of the horizontals by single valued branches of its inverse.


Ford Differentials

Ford Differentials

Author: Joe Palazzolo

Publisher: CarTech Inc

Published: 2013

Total Pages: 146

ISBN-13: 161325038X

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A driveline expert guides you through each step of the rebuild process for 8.8- and 9-inch axle assemblies, so you can confidently complete the work yourself. He explains in detail limited-slip and open differential disassembly, inspection, assembly, final calibration, and break-in. He also shows you how to identify worn ring-and-pinion gears, rebuild clutch packs, set the correct contact pattern for pinion and ring gears as well as the backlash, and much more.


Small Animal Medical Differential Diagnosis

Small Animal Medical Differential Diagnosis

Author: Mark S. Thompson

Publisher: Elsevier Health Sciences

Published: 2014

Total Pages: 379

ISBN-13: 1455744549

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Small Animal Medical Differential Diagnosis, 2nd Edition is a practical, concise guide to the differential diagnosis, etiology, laboratory abnormalities, and classification of clinical signs and medical disorders in dogs and cats. By covering nearly every possible sign and clinical disorder relevant to small animal medical practice, this pocket-sized, rapid reference helps you make more reliable on-the-scene decisions. More than 400 lists bring the most important medical diagnostic information from multiple resources into a single rapid reference. An organized presentation of differential diagnoses by sign and symptom, disorder, and body system, facilitates quick and flexible access to information at many stages of the diagnostic work-up. Alphabetical listing of all relevant laboratory tests makes information easy to find for students and experienced practitioners alike. Easily identify the likeliest diagnosis by reviewing the possibilities listed in order of incidence. Pocket-sized for portability, practicality, and quick reference. NEW! Coverage of new disorders and syndromes expands the span of differential diagnoses to help you effectively evaluate more signs and symptoms. NEW! Addition of new and more widely used diagnostic and laboratory tests keeps you up-to-date as lab tests become more specialized and sophisticated.


Top 3 Differentials in Radiology

Top 3 Differentials in Radiology

Author: William T. O'Brien

Publisher: Thieme

Published: 2011-01-01

Total Pages: 726

ISBN-13: 1604062282

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Praise for this book:Innovative...the descriptions are accurate and concise - exactly what the examiner wants to hear...it would be difficult to find a better high-yield, high-quality textbook covering every subsection of the radiology oral board examination.--JAMAyExtremely useful...This review book is not only rewarding but also a resource radiologists can continue to refer to throughout their careers.--Academic RadiologyProvides an excellent selection of cases for sharpening diagnostic radiology considerations...useful for board preparation and review.--Doody's ReviewTop 3 Differentials in Radiology: A Case Review is a practical case-based reference that will enable radiologists and radiology residents to hone their skills in developing differential diagnoses for common imaging findings. Presented as unknowns, the cases are arranged into twelve main sections based on radiology subspecialties. The book presents each case as a two-page unit. The left page features clinical images and a brief description of the clinical presentation. The right page provides the key imaging finding, Top 3 differential diagnoses, additional differential diagnoses, the final diagnosis, and imaging pearls. The final section of the book contains selected cases from all radiology subspecialties with distinctive imaging findings that should lead definitively to a single diagnosis. Features: 325 cases presented as unknowns to facilitate exam preparation Valuable high-yield review of all disease entities on the list of differential diagnoses for each case More than 700 high-quality images, including 74 in full color, depicting key radiographic findings Imaging pearls at the end of each case that highlight key teaching points With its emphasis on gaining a solid foundation in differential diagnoses for the full range of key imaging findings encountered in clinical practice, this book is ideal for individuals preparing for the initial American Board of Radiology examination as well as more experienced radiologists preparing for recertification examinations.


High-Performance Differentials, Axels, and Drivelines

High-Performance Differentials, Axels, and Drivelines

Author: Joe Palazzolo

Publisher: CarTech Inc

Published: 2009

Total Pages: 146

ISBN-13: 1934709026

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Covers everything you need to know about selecting the most desirable gear ratio, rebuilding differentials and other driveline components, and most importantly, matching the correct driveline components to engine power output.


Nominal Exchange Rates and Nominal Interest Rate Differentials

Nominal Exchange Rates and Nominal Interest Rate Differentials

Author: Mr.Francisco Nadal De Simone

Publisher: International Monetary Fund

Published: 1999-10-01

Total Pages: 42

ISBN-13: 1451856164

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This paper reexamines some unsettled theoretical and empirical issues regarding the relationship between nominal exchange rates and interest rate differentials and provides a model for the behavior of exchange rates in the long run, where interest rates are determined in the bond market. The model predicts that an increase in the interest rate differential appreciates the home currency. We test the model for the U.S. dollar against the Deutsche mark, the British pound, the Japanese yen, and the Canadian dollar. The first two pairs of exchange rates—for which purchasing power parity seems to hold—display a strong relationship with interest rate differentials.


Interest-Growth Differentials and Debt Limits in Advanced Economies

Interest-Growth Differentials and Debt Limits in Advanced Economies

Author: Philip Barrett

Publisher: International Monetary Fund

Published: 2018-04-11

Total Pages: 55

ISBN-13: 148435205X

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Do persistently low nominal interest rates mean that governments can safely borrow more? To addresses this question, I extend the model of Ghosh et al. [2013] to allow for persistent stochastic changes in nominal interest and growth rates. The key model parameter is the long-run difference between nominal interest and growth rates; if negative, maximum sustainable debts (debt limits) are unbounded. I show how both VAR- and spectral-based methods produce negative point estimates of this long-run differential, but cannot reject positive values at standard significance levels. I calibrate the model to the UK using positive but statistically plausible average interest-growth differentials. This produces debt limits which increase by only around 5% GDP as interest rates fall after 2008. In contrast, only a tiny change in the long-run average interest-growth differential – from the 95th to the 97.5th percentile of the distribution – is required to move average debt limits by the same amount.