scispace - formally typeset
Search or ask a question
Topic

Asymptotology

About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, it was shown that (1.3) is necessary and sufficient for the boundedness of all solutions of the Ricatti equation with initial conditions in the first quadrant (third quadrant) will intersect the positive (negative) x-axis.
Abstract: is necessary and sufficient for the global asymptotic stability of the equilibrium point (0, 0) of (1.2). The idea of the proof is to show that (1.3) is necessary and sufficient for the boundedness of all solutions of (1.2). In doing this the crucial step is determining whether a solution with initial conditions in the first quadrant (third quadrant) will intersect the positive (negative) x-axis. In this paper we investigate global asymptotic stability of the origin (0, 0) of (1.2) for the case when a ? 1. In addition to the above idea, the main feature of our approach is to reduce (1.2) to a first order generalized Ricatti equation and then determine conditions under which it has and does not have positive solutions for large values of the independent variable. Using a different method, Willet and Wong [4] have considered this same problem. Their approach is more general and (1.2) is considered as a special case. If a _ 1, they obtain a necessary and sufficient condition (which is the same as Burton's for cx 1, however, it will be shown here that their condition is included in one of those obtained here.

25 citations

Journal ArticleDOI
TL;DR: In this paper, a method is presented for modeling bonding processes and interfaces on thin layers, where the contact and pseudo-friction conditions between the adhesive and the adherents are also taken into account.

25 citations

Book
30 Nov 2002
TL;DR: Asymptotic Methods and Physical Theories as mentioned in this paper have been studied in a wide range of applications in physics, from Harmonic Waves to Solitons to scaling transformations.
Abstract: Foreword. Preface. Acknowledgments. Synopsis. 1. Introduction. 2. What Are Asymptotic Methods? 3. A Little Mathematics. 4. How Asymptotic Methods Work. 5. Asymptotic Methods and Physical Theories. 6. Phenomenology and First Principles. 7. A Little History. 8. Fathers of Asymptotic Methods. 9. Conclusion. Appendices: A. Linear and Nonlinear Mathematical Physics: from Harmonic Waves to Solitons. B. Certain Mathematical Notions of Catastrophe Theory. C. Asymptotics and Scaling Transformations. D. Asymptotic Approaches: Attempt af a Definition. E. Some Web-pages. References. About the Authors. Author Index. Topic Index.

25 citations

Journal ArticleDOI
Sadao Ikeda1
TL;DR: In this paper, the basic concepts of asymptotic equivalence of probability distributions, which are fundamental to the study of approximation problems, are established precisely and useful criterions for the asymPTE are given.
Abstract: The problem of asymptotic approximation is formulated in a generalized form, and the basic concepts of asymptotic equivalence of probability distributions, which are fundamental to the study of asymptotic approximation problems, are established precisely. For the purpose of practical applications, some useful criterions for the asymptotic equivalence are given.

24 citations

Journal ArticleDOI
TL;DR: In this paper, the authors presented a systematic derivation of a refined engineering theory governing the response of elastic beams using asymptotic expansion that combines dimensional analysis with the expansion in powers of a small parameter of the solution of the linear elasticity theory.
Abstract: A systematic derivation of a refined engineering theory governing the response of elastic beams is presented. The method employed to accomplish this is that of asymptotic expansion that combines dimensional analysis with the expansion in powers of a small parameter of the solution of the three-dimensional linear elasticity theory. The present beam theory contains more information than the classical Timoshenko theory. A new shear coefficient is defined and compared with existing ones.

24 citations


Network Information
Related Topics (5)
Stochastic partial differential equation
21.1K papers, 707.2K citations
84% related
Differential equation
88K papers, 2M citations
83% related
Numerical partial differential equations
20.1K papers, 703.7K citations
82% related
Bounded function
77.2K papers, 1.3M citations
81% related
Partial differential equation
70.8K papers, 1.6M citations
81% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526