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Books on the topic 'Bounded variation'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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1

author, Banas Jozef 1950, and Merentes Díaz, Nelson José, author, eds. Bounded variation and around. Berlin: Walter de Gruyter GmbH & Co. KG, 2013.

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2

Nicola, Fusco, and Pallara Diego, eds. Functions of bounded variation and free discontinuity problems. Oxford: Clarendon Press, 2000.

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3

Liflyand, Elijah. Functions of Bounded Variation and Their Fourier Transforms. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-04429-9.

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4

Ziemer, William P. Weakly differentiable functions: Sobolev spaces and functions of bounded variation. New York: Springer-Verlag, 1989.

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5

Braides, Andrea. Approximation of free-discontinuity problems. Berlin: Springer-Verlag, 1998.

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6

On the algebraic foundation of bounded cohomology. Providence, R.I: American Mathematical Society, 2011.

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7

Giuseppe, Buttazzo, and Michaille Gérard, eds. Variational analysis in Sobolev and BV spaces: Applications to PDEs and optimization. Philadelphia: Society for Industrial and Applied Mathematics, 2005.

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8

Dudley, R. M. Differentiability of six operators on nonsmooth functions and p-variation. Berlin: Springer, 1999.

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9

Cheverry, Christophe. Systèmes de lois de conservation et stabilité BV. [Paris, France]: Société mathématique de France, 1998.

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10

Verrill, S. P. Confidence bounds and hypothesis tests for normal distribution coefficients of variation. Madison, WI: USDA, Forest Service, Forest Products Laboratory, 2007.

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11

service), SpringerLink (Online, ed. Exterior Billiards: Systems with Impacts Outside Bounded Domains. New York, NY: Springer New York, 2012.

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12

Appell, J., and J. Banas. Bounded Variation and Around. De Gruyter, Inc., 2013.

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13

Fusco, Nicola, Luigi Ambrosio, and Diego Pallara. Functions of Bounded Variation and Free Discontinuity Problems (Oxford Mathematical Monographs). Oxford University Press, USA, 2000.

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14

Ziemer, William P. Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation. Springer, 2012.

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15

Koleva, Maria K. Boundedness and self-organized semantics: Theory and applications. 2012.

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16

Appell, Jürgen, Józef Banas, and Nelson José Merentes Díaz. Bounded Variation and Around (De Gruyter Series in Nonlinear Analysis and Applications Book 17). De Gruyter, 2013.

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17

Attouch, Hedy, Giuseppe Buttazzo, and Gérard Michaille. Variational Analysis in Sobolev and BV Spaces: Applications to PDEs and Optimization, Second Edition. SIAM-Society for Industrial and Applied Mathematics, 2014.

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18

Forest Products Laboratory (U.S.), ed. Confidence bounds for normal and lognormal distribution coefficients of variation. [Madison, Wis.]: U.S. Dept. of Agriculture, Forest Service, Forest Products Laboratory, 2003.

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19

Pedagogy Out of Bounds: Untamed Variations of Democratic Education. Springer, 2014.

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20

Plakhov, Alexander. Exterior Billiards: Systems with Impacts Outside Bounded Domains. Springer, 2014.

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21

Plakhov, Alexander. Exterior Billiards: Systems with Impacts Outside Bounded Domains. Springer, 2012.

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22

Edmunds, D. E., and W. D. Evans. Sesquilinear Forms in Hilbert Spaces. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0004.

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The centre-pieces of this chapter are the Lax–Milgram Theorem and the existence of weak or variational solutions to problems involving sesquilinear forms. An important application is to Kato’s First Representation Theorem, which associates a unique m-sectorial operator with a closed, densely defined sesquilinear form, thus extending the Friedrichs extension for a lower bounded symmetric operator. Stampacchia’s generalization of the Lax–Milgram Theorem to variational inequalities is also discussed.
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23

Murphy, Dominic. Description and explanation of the culture-bound syndromes. Edited by Kenneth S. Kendler and Josef Parnas. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780198796022.003.0020.

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Recent attempts to deal with cultural variation have adopted one of two approaches: Particularization tries to understand mental illness as the outgrowth of local forms of life, and universalization sees it as a disorder to be understood as the malfunctioning of a common human endowment. What does it means for a syndrome to be bound up with a particular culture? The issues here concern the viability of social constructionist models in cases where the individual minds that are altered by social forces are presumed to work in untypical ways. So this chapter is more broadly about integrating social theory and cognitive theory into a framework for explaining mental illness. This should be applicable to all psychopathology, but has been most fully articulated for culture-bound syndromes, where boundaries between the normal and the pathological are often hardest for psychiatry to distinguish.
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24

Al-Wer, Enam. Sociolinguistics. Edited by Jonathan Owens. Oxford University Press, 2013. http://dx.doi.org/10.1093/oxfordhb/9780199764136.013.0010.

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This article provides a critical overview of the application of sociolinguistic principles, methods, and analysis to Arabic data with reference to research conducted over the past three decades or so in various Arabic-speaking societies. It focuses on linguistic variation and change, the major concerns of (variationist) sociolinguistics. The article begins with an outline of the relationship between traditional dialectology and sociolinguistics, the ways dialectological data are incorporated into sociolinguistic analysis, and the benefits of maintaining the link between the two disciplines. Then an outline is presented of the basic principles of the variationist paradigm, which are intricately bound up with sociolinguistic methodology and theory; where relevant, research practices in studies on Arabic are cited. The article then critically reviews the “diglossia” model as an approach to analyzing variation in Arabic. Finally, an alternative and up-to-date model of analysis is given, with case studies from recent research used as illustration.
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25

Isett, Philip. Energy Approximation. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691174822.003.0023.

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This chapter presents the equations and calculations for energy approximation. It establishes the estimates (261) and (262) of the Main Lemma (10.1) for continuous solutions; these estimates state that we are able to accurately prescribe the energy that the correction adds to the solution, as well as bound the difference between the time derivatives of these two quantities. The chapter also introduces the proposition for prescribing energy, followed by the relevant computations. Each integral contributing to the other term can be estimated. Another proposition for estimating control over the rate of energy variation is given. Finally, the coarse scale material derivative is considered.
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26

Limebeer, D. J. N., and Matteo Massaro. Dynamics and Optimal Control of Road Vehicles. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198825715.001.0001.

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The broad aim of this book is to provide a comprehensive coverage of the modelling and optimal control of both two‐ and four‐wheeled road vehicles. The first focus of this book is a review of classical mechanics and its use in building vehicle and tyre dynamic models. The second is nonlinear optimal control, which is used to solve a range of minimum‐time, minimum‐fuel, and track curvature reconstruction problems. As is known classically, all thismaterial is bound together by the calculus of variations and stationary principles. The treatment of this material is supplemented with a large number of examples that highlight obscurities and subtleties in the theory. A particular strength of the book is its unified treatment of tyre, car, and motorcycle dynamics and the application of nonlinear optimal control to vehicle‐related problems within a single text. These topics are usually treated independently, and can only be found in disparate texts and journal articles. It is our contention that presentday vehicle dynamicists should be familiar with all of these topic areas. The aim in writing this book is to provide a comprehensive and yet accessible text that emphasizes particularly the theoretical aspects of vehicular modelling and control.
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27

Murer, Heini, Jürg Biber, and Carsten A. Wagner. Phosphate homeostasis. Edited by Robert Unwin. Oxford University Press, 2015. http://dx.doi.org/10.1093/med/9780199592548.003.0025.

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Inorganic phosphate ions (H2PO4−/ HPO42−) (abbreviated as Pi) are involved in formation of bone and generation of high-energy bonds (e.g. ATP), metabolic pathways, and regulation of cellular functions. In addition, Pi is a component of biological membranes and nucleic acids. Only about 1% of total body Pi content is present in extracellular fluids, at a plasma concentration in adults within the range 0.8–1.4 mMol/L (at pH 7.4 mostly as HPO42−), with diurnal variations of approximately 0.2 mM. A small amount of plasma Pi is bound to proteins or forms complexes with calcium. Under normal, balanced conditions, absorption of dietary Pi along the small intestine equals the output of Pi via kidney and faeces. Renal excretion of Pi represents the key determinant for the adjustment of normal Pi plasma concentrations. Renal reabsorption of Pi occurs along the proximal tubules by sodium-dependent Pi cotransporters that are strictly localized at the apical brush border membrane. Parathyroid hormone (PTH) and FGF23 are key regulators amongst a myriad of factors controlling excretion of Pi in urine, mostly by changes of the apical abundance of Na/Pi cotransporters. Hypophosphataemia may result in osteomalacia, rickets, muscle weakness, and haemolysis. Hyperphosphataemia can lead to hyperparathyroidism and severe calcifications in different tissues.
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28

Sharpless, Brian A., ed. Unusual and Rare Psychological Disorders. Oxford University Press, 2017. http://dx.doi.org/10.1093/med:psych/9780190245863.001.0001.

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Many fascinating and important psychological disorders are either omitted from our current diagnostic systems or rarely covered during graduate or medical training. As a result, most mental health students and trainees are never taught to identify, diagnose, or treat them. This lack of attention has real-world consequences not only for patients, but for basic science as well.This volume collects and usefully synthesizes the scientific and clinical literatures of 21 lesser-known, but nonetheless important, psychological disorders. The chapters are broadly grouped into (a) disorders of sleep, (b) variations in psychosis, (c) sexual disorders/disorders of arousal, (d) culture-bound disorders, and (e) miscellaneous syndromes. All chapters follow a uniform structure and begin with a vivid clinical vignette. After discussing the historical context of each disorder, consideration is given to the typical presentation, the current roles in diagnostic systems (if any), and the main etiological theories. Next, clinically relevant information on assessment and differential diagnosis is provided. Finally, specific treatment recommendations are made and future directions for research are discussed. This unique and engaging volume will not only be a useful resource for researchers and clinicians who already possess expertise in the more well-known manifestations of psychopathology, but it will also be of interest to students and trainees in the mental health professions.
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29

Oqubay, Arkebe, and Justin Yifu Lin, eds. China-Africa and an Economic Transformation. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198830504.001.0001.

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Progress in Africa’s economic growth in the new millennium has been uneven across countries, and has not translated into structural transformation. The same can be said about the evolving China–Africa economic relations. Although economic ties between China and Africa have made a positive contribution, the impact of this dynamic engagement has been uneven, shaped by variations in strategic approach, policy ownership, and implementation capacity among African governments. As China undergoes major economic rebalancing to upgrade to an innovation-driven economy, this is bound to affect China–Africa relations, offering both opportunities and challenges. Authored by leading scholars on Africa, China, and China–Africa relations, this volume brings together stimulating and thought-provoking perspectives, and deeper analyses on the evolving China–Africa relations. Focusing on Africa’s economic development, the volume looks at core areas of structural transformation: productive investment and industrialization, international trade, infrastructure development, and financing. China–Africa relations are considered in the context of the global division of labour and power, and the particular role of both China and the continent of Africa in the evolving global hierarchy. This volume seeks to fill the gap in the existing literature, steer policy and scholarly debate on the progress and trajectory of China–Africa cooperation, and analyse China’s development path as a source of learning for Africa.
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30

Horing, Norman J. Morgenstern. Superfluidity and Superconductivity. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198791942.003.0013.

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Chapter 13 addresses Bose condensation in superfluids (and superconductors), which involves the field operator ψ‎ having a c-number component (<ψ(x,t)>≠0), challenging number conservation. The nonlinear Gross-Pitaevskii equation is derived for this condensate wave function<ψ>=ψ−ψ˜, facilitating identification of the coherence length and the core region of vortex motion. The noncondensate Green’s function G˜1(1,1′)=−i<(ψ˜(1)ψ˜+(1′))+> and the nonvanishing anomalous correlation function F˜∗(2,1′)=−i<(ψ˜+(2)ψ˜+(1′))+> describe the dynamics and elementary excitations of the non-condensate states and are discussed in conjunction with Landau’s criterion for viscosity. Associated concepts of off-diagonal long-range order and the interpretation of <ψ> as a superfluid order parameter are also introduced. Anderson’s Bose-condensed state, as a phase-coherent wave packet superposition of number states, resolves issues of number conservation. Superconductivity involves bound Cooper pairs of electrons capable of Bose condensation and superfluid behavior. Correspondingly, the two-particle Green’s function has a term involving a product of anomalous bound-Cooper-pair condensate wave functions of the type F(1,2)=−i<(ψ(1)ψ(2))+>≠0, such that G2(1,2;1′,2′)=F(1,2)F+(1′,2′)+G˜2(1,2;1′,2′). Here, G˜2 describes the dynamics/excitations of the non-superfluid-condensate states, while nonvanishing F,F+ represent a phase-coherent wave packet superposition of Cooper-pair number states and off-diagonal long range order. Employing this form of G2 in the G1-equation couples the condensed state with the non-condensate excitations. Taken jointly with the dynamical equation for F(1,2), this leads to the Gorkov equations, encompassing the Bardeen–Cooper–Schrieffer (BCS) energy gap, critical temperature, and Bogoliubov-de Gennes eigenfunction Bogoliubons. Superconductor thermodynamics and critical magnetic field are discussed. For a weak magnetic field, the Gorkov-equations lead to Ginzburg–Landau theory and a nonlinear Schrödinger-like equation for the pair wave function and the associated supercurrent, along with identification of the Cooper pair density. Furthermore, Chapter 13 addresses the apparent lack of gauge invariance of London theory with an elegant variational analysis involving re-gauging the potentials, yielding a manifestly gauge invariant generalization of the London equation. Consistency with the equation of continuity implies the existence of Anderson’s acoustic normal mode, which is supplanted by the plasmon for Coulomb interaction. Type II superconductors and the penetration (and interaction) of quantized magnetic flux lines are also discussed. Finally, Chapter 13 addresses Josephson tunneling between superconductors.
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31

Benestad, Rasmus. Climate in the Barents Region. Oxford University Press, 2018. http://dx.doi.org/10.1093/acrefore/9780190228620.013.655.

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The Barents Sea is a region of the Arctic Ocean named after one of its first known explorers (1594–1597), Willem Barentsz from the Netherlands, although there are accounts of earlier explorations: the Norwegian seafarer Ottar rounded the northern tip of Europe and explored the Barents and White Seas between 870 and 890 ce, a journey followed by a number of Norsemen; Pomors hunted seals and walruses in the region; and Novgorodian merchants engaged in the fur trade. These seafarers were probably the first to accumulate knowledge about the nature of sea ice in the Barents region; however, scientific expeditions and the exploration of the climate of the region had to wait until the invention and employment of scientific instruments such as the thermometer and barometer. Most of the early exploration involved mapping the land and the sea ice and making geographical observations. There were also many unsuccessful attempts to use the Northeast Passage to reach the Bering Strait. The first scientific expeditions involved F. P. Litke (1821±1824), P. K. Pakhtusov (1834±1835), A. K. Tsivol’ka (1837±1839), and Henrik Mohn (1876–1878), who recorded oceanographic, ice, and meteorological conditions.The scientific study of the Barents region and its climate has been spearheaded by a number of campaigns. There were four generations of the International Polar Year (IPY): 1882–1883, 1932–1933, 1957–1958, and 2007–2008. A British polar campaign was launched in July 1945 with Antarctic operations administered by the Colonial Office, renamed as the Falkland Islands Dependencies Survey (FIDS); it included a scientific bureau by 1950. It was rebranded as the British Antarctic Survey (BAS) in 1962 (British Antarctic Survey History leaflet). While BAS had its initial emphasis on the Antarctic, it has also been involved in science projects in the Barents region. The most dedicated mission to the Arctic and the Barents region has been the Arctic Monitoring and Assessment Programme (AMAP), which has commissioned a series of reports on the Arctic climate: the Arctic Climate Impact Assessment (ACIA) report, the Snow Water Ice and Permafrost in the Arctic (SWIPA) report, and the Adaptive Actions in a Changing Arctic (AACA) report.The climate of the Barents Sea is strongly influenced by the warm waters from the Norwegian current bringing heat from the subtropical North Atlantic. The region is 10°C–15°C warmer than the average temperature on the same latitude, and a large part of the Barents Sea is open water even in winter. It is roughly bounded by the Svalbard archipelago, northern Fennoscandia, the Kanin Peninsula, Kolguyev Island, Novaya Zemlya, and Franz Josef Land, and is a shallow ocean basin which constrains physical processes such as currents and convection. To the west, the Greenland Sea forms a buffer region with some of the strongest temperature gradients on earth between Iceland and Greenland. The combination of a strong temperature gradient and westerlies influences air pressure, wind patterns, and storm tracks. The strong temperature contrast between sea ice and open water in the northern part sets the stage for polar lows, as well as heat and moisture exchange between ocean and atmosphere. Glaciers on the Arctic islands generate icebergs, which may drift in the Barents Sea subject to wind and ocean currents.The land encircling the Barents Sea includes regions with permafrost and tundra. Precipitation comes mainly from synoptic storms and weather fronts; it falls as snow in the winter and rain in the summer. The land area is snow-covered in winter, and rivers in the region drain the rainwater and meltwater into the Barents Sea. Pronounced natural variations in the seasonal weather statistics can be linked to variations in the polar jet stream and Rossby waves, which result in a clustering of storm activity, blocking high-pressure systems. The Barents region is subject to rapid climate change due to a “polar amplification,” and observations from Svalbard suggest that the past warming trend ranks among the strongest recorded on earth. The regional change is reinforced by a number of feedback effects, such as receding sea-ice cover and influx of mild moist air from the south.
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