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Author: John R. Shackell
Publisher: Springer Science & Business Media
ISBN: 3662101769
Category : Mathematics
Languages : en
Pages : 249
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Book Description
Accessible to anyone with a good general background in mathematics, but it nonetheless gets right to the cutting edge of active research. Some results appear here for the first time, while others have hitherto only been given in preprints.
Author: John R. Shackell
Publisher: Springer Science & Business Media
ISBN: 3662101769
Category : Mathematics
Languages : en
Pages : 249
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Book Description
Accessible to anyone with a good general background in mathematics, but it nonetheless gets right to the cutting edge of active research. Some results appear here for the first time, while others have hitherto only been given in preprints.
Author: A. R. Brazzale
Publisher: Cambridge University Press
ISBN: 1139463837
Category : Mathematics
Languages : en
Pages : 211
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Book Description
In fields such as biology, medical sciences, sociology, and economics researchers often face the situation where the number of available observations, or the amount of available information, is sufficiently small that approximations based on the normal distribution may be unreliable. Theoretical work over the last quarter-century has led to new likelihood-based methods that lead to very accurate approximations in finite samples, but this work has had limited impact on statistical practice. This book illustrates by means of realistic examples and case studies how to use the new theory, and investigates how and when it makes a difference to the resulting inference. The treatment is oriented towards practice and comes with code in the R language (available from the web) which enables the methods to be applied in a range of situations of interest to practitioners. The analysis includes some comparisons of higher order likelihood inference with bootstrap or Bayesian methods.
Author: Matthias Aschenbrenner
Publisher: Princeton University Press
ISBN: 1400885418
Category : Mathematics
Languages : en
Pages : 880
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Book Description
Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems. This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity. Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.
Author: B. Salvy
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
Author: Rudrapatna V. Ramnath
Publisher: Springer Science & Business Media
ISBN: 3642257496
Category : Technology & Engineering
Languages : en
Pages : 126
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Book Description
This book addresses the task of computation from the standpoint of asymptotic analysis and multiple scales that may be inherent in the system dynamics being studied. This is in contrast to the usual methods of numerical analysis and computation. The technical literature is replete with numerical methods such as Runge-Kutta approach and its variations, finite element methods, and so on. However, not much attention has been given to asymptotic methods for computation, although such approaches have been widely applied with great success in the analysis of dynamic systems. The presence of different scales in a dynamic phenomenon enable us to make judicious use of them in developing computational approaches which are highly efficient. Many such applications have been developed in such areas as astrodynamics, fluid mechanics and so on. This book presents a novel approach to make use of the different time constants inherent in the system to develop rapid computational methods. First, the fundamental notions of asymptotic analysis are presented with classical examples. Next, the novel systematic and rigorous approaches of system decomposition and reduced order models are presented. Next, the technique of multiple scales is discussed. Finally application to rapid computation of several aerospace systems is discussed, demonstrating the high efficiency of such methods.
Author: Ulises Xolocotzin
Publisher: Academic Press
ISBN: 0128024895
Category : Psychology
Languages : en
Pages : 474
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Book Description
Emotions play a critical role in mathematical cognition and learning. Understanding Emotions in Mathematical Thinking and Learning offers a multidisciplinary approach to the role of emotions in numerical cognition, mathematics education, learning sciences, and affective sciences. It addresses ways in which emotions relate to cognitive processes involved in learning and doing mathematics, including processing of numerical and physical magnitudes (e.g. time and space), performance in arithmetic and algebra, problem solving and reasoning attitudes, learning technologies, and mathematics achievement. Additionally, it covers social and affective issues such as identity and attitudes toward mathematics. Covers methodologies in studying emotion in mathematical knowledge Reflects the diverse and innovative nature of the methodological approaches and theoretical frameworks proposed by current investigations of emotions and mathematical cognition Includes perspectives from cognitive experimental psychology, neuroscience, and from sociocultural, semiotic, and discursive approaches Explores the role of anxiety in mathematical learning Synthesizes unifies the work of multiple sub-disciplines in one place
Author: Helene Kirchner
Publisher: Springer
ISBN: 3540464212
Category : Mathematics
Languages : en
Pages : 300
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Book Description
This book constitutes the refereed proceedings of the Third International Workshop on Frontiers of Combining Systems, FroCoS 2000, held in Nancy, France, in March 2000. The 14 revised full papers presented together with four invited papers were carefully reviewed and selected from a total of 31 submissions. Among the topics covered are constraint processing, interval narrowing, rewriting systems, proof planning, sequent calculus, type systems, model checking, theorem proving, declarative programming, logic programming, and equational theories.
Author: Gary L. Mullen
Publisher: Springer
ISBN: 3540246339
Category : Mathematics
Languages : en
Pages : 271
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Book Description
Thisvolumerepresentstherefereedproceedingsofthe7thInternationalC- ference on Finite Fields and Applications (F 7) held during May 5-9, q 2003, in Toulouse, France. The conference was hosted by the Pierre Baudis C- gress Center, downtown, and held at the excellent conference facility. This event continued a series of biennial international conferences on Finite Fields and - plications, following earlier meetings at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University of Glasgow (UK) in July 1995, the University of Waterloo (Canada) in August 1997, the Univ- sity of Augsburg (Germany) in August 1999, and the Universidad Aut ́ onoma Metropolitana-Iztapalapa, in Oaxaca (Mexico) in 2001. The Organizing Committee of F 7 consisted of Claude Carlet (INRIA, Paris, q France), Dieter Jungnickel (University of Augsburg, Germany), Gary Mullen (Pennsylvania State University, USA), Harald Niederreiter (National University of Singapore, Singapore), Alain Poli, Chair (Paul Sabatier University, Toulouse, France), Henning Stichtenoth (Essen University, Germany), and Horacio Tapia- Recillas (Universidad Aut ́ onoma Metropolitan-Iztapalapa, Mexico). The program of the conference consisted of four full days and one half day of sessions, with eight invited plenary talks, and close to 60 contributed talks.
Author: Christopher G. Small
Publisher: CRC Press
ISBN: 1420011022
Category : Mathematics
Languages : en
Pages : 359
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Book Description
Asymptotic methods provide important tools for approximating and analysing functions that arise in probability and statistics. Moreover, the conclusions of asymptotic analysis often supplement the conclusions obtained by numerical methods. Providing a broad toolkit of analytical methods, Expansions and Asymptotics for Statistics shows how asymptoti
Author: Michael Demuth
Publisher: John Wiley & Sons
ISBN: 9783055017698
Category : Mathematics
Languages : en
Pages : 436
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Book Description
This volume contains a collection of original papers, associated with the International Conference on Partial Differential Equations, held in Potsdam, July 29 to August 2, 1996. The conference has taken place every year on a high scientific level since 1991; this event is connected with the activities of the Max Planck Research Group for Partial Differential Equations at Potsdam. Outstanding researchers and specialists from Armenia, Belarus, Belgium, Bulgaria, Canada, China, France, Germany, Great Britain, India, Israel, Italy, Japan, Poland, Romania, Russia, Spain, Sweden, Switzerland, Ukraine, and the USA contribute to this volume. The main topics concern recent progress in partial differential equations, microlocal analysis, pseudo-differential operators on manifolds with singularities, aspects in differential geometry and index theory, operator theory and operator algebras, stochastic spectral analysis, semigroups, Dirichlet forms, Schrodinger operators, semiclassical analysis, and scattering theory.
