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the Lindstedt–Poincare technique (LP) that is developed by the astronomers to understand the orbital motion of the planets and small perturbations in the trajectories. Next, the recently developed multiple scales Lindstedt–Poincare technique (MSLP) [3–6] is employed in search of approximate analytical solutions. The method combines the elimination mechanisms of secular terms of both the classical Lindstedt–Poincare technique and the classical multiple scales technique and increases the possibility of success for obtaining uniform solutions for the nonlinear

-transformed morphometric variables can be considered as symmetric and with heavy tails, the assumption of elliptical contours may be rather restrictive, with heavy-tailed distributions accounting for alternative symmetric shapes providing a better fit. To describe these shapes, we consider the family of multiple scaled symmetric (MSS) distributions proposed by Forbes and Wraith [ 13 ]. MSS distributions can be roughly considered as an extension of the MN scale mixture based on two key elements: the decomposition of the scale matrix Σ by eigenvalues and eigenvectors matrices Λ and Γ

) equation is an example of a universal nonlinear model that describes many physical nonlinear systems. The equation can be applied to hydrodynamics, nonlinear optics, nonlinear acoustics, quantum condensates, plasma physics, heat pulses in solids, and various other nonlinear instability phenomena [ 5 ]. It is well known that a multiple scales analysis of the KdV equation (and, indeed a wide variety of equations) leads to the NLS equation for the modulated amplitude [ 6 ], [ 7 ], [ 8 ], [ 9 ], [ 10 ]. In [ 6 ], Zakharov and Kuznetsov showed a much deeper correspondence

Multiple Skalierung nach dem Kristallisationsprinzip Eine Alternative zur explorativen Faktorenanalyse Multiple Scaling According to the Principle of Crystallization An Alternative Method to Exploratory Factor Analysis Thomas Müller-Schneider Herzog-Max-Straße 38, D-96047 Bamberg Zusammenfassung: In diesem Beitrag geht es um eines der zentralen methodischen Probleme, die bei der sozialwissen- schaftlichen Skalierung auftreten: das Erkennen mehrdimensionaler Datenstrukturen. In der Forschungspraxis setzt man dazu in aller Regel die Faktorenanalyse ein. Dieses

CHAPTER 9 Applications of multiple scaling Thus far we have only considered situations in which essentially one known dimension, political efficacy, could be discovered by means of our technique with a scale of adequately chosen items. Such neat uni- dimensional cases do not abound in social research. We often have to face the possibility that more dimensions may be involved with respect to a given set of items. In section 5.2.3 we mentioned that our set of procedures included a version of multiple scaling,* by which a given set of items may be divided up

©Freund Publishing House Ltd., International Journal of Nonlinear Sciences & Numerical Simulation 11(8): 603-609, 2010 Multiple - scale Expansion for Nonlinear Ion-acoustic Waves Hilmi Demiray Department of Mathematics, Faculty of Arts and Sciences, Isik University, Kumbaba Mevkii 34980 Sile, Istanbul-Turkey Email Abstract By employing the multiple-scale expansion method, the present work examines non-linear waves in a cold collisionless plasma, in the long-wave limit, and obtains a set of KdV equations governing various order terms

INTRODUCTION AIHWA ONG An Analytics of Biotechnology and Ethics at Multiple Scales The dispersal of genetic science across the world raises questions about the interactions of biotechnologies and bioethics in diverse global loca- tions. Yet the tendency has been to think in terms of general rules for governing the proliferation of scientific and commercial uses of biolog- ical resources. For instance, at the 2008 meeting of the World Eco- nomic Forum in Davos, a panel proposing ‘‘Rules for the Genomic Age’’ issued this statement: Genetic data about specific

, working at multiple scales. I focus on the “multi-level” character of ceji’s practice as “local,” “national,” and “global,” and on how it was conceptu- alized and operationalized. This multi-scale spatial framework was consti- NINE | Toward a Movement of Multiple Scales 205 BV79_RevOfNat_060116.qxp 1/16/06 11:48 AM Page 205 tutive of ceji’s politics and represents an example of innovation in social movement practice in response to the political transformations wrought by globalization. “Globalization” has involved multiple and contradictory processes of the rescaling

slower rates to maximize efficiency over longer time scales or when resources are scarce. This principle leads to several hypotheses and predictions about how biological systems will behave over particular time scales and exergy regimes. In the following sections we highlight several empirical studies which serve as illustrative examples of how this principle explains the behavior of biological processes across multiple scales (Figures 1 and 2 ), including ontogeny, succession, and evolution. 5.1 Ontogeny and aging Prigogine and Wiame [ 101 ] hypothesized that the

Variance- Explicit Ecol ogy a Call for Holistic study of the Consequences of Variability at multiple scales Marcel Holyoak and William C. Wetzel Variability or heterogeneity is everywhere in ecol ogy and evolution. For instance, Levins (1968) introduces his classic work “Evolution in Chang- ing Environments: Some Theoretical Explorations” as “a series of explo- rations . . .  around the common theme of the consequences of environmen- tal heterogeneity.” We have many reasons for studying variability at diff er ent levels, including within- individual variation