scholarly journals The application of centre-manifold theory to the evolution of system which vary slowly in space

1988 ◽  
Vol 29 (4) ◽  
pp. 480-500 ◽  
Author(s):  
A. J. Roberts
Keyword(s):  
Multiple Scales ◽  
Limited Range ◽  
Future Research ◽  
Centre Manifold ◽  
Space And Time ◽  
Physical Problems ◽  
Formal Procedure ◽  
Slow Evolution ◽  
Manifold Theory ◽  
Correction Terms

AbstractIn many physical problems, the system tends quickly to a particular structure, which then evolves relatively slowly in space and time. Various methods exist to derive equations describing the slow evolution of the particular structure; for example, the method of multiple scales. However, the resulting equations are typically valid only for a limited range of the parameters. In order to extend the range of validity and to improve the accuracy, correction terms must be found for the equations. Here we describe a procedure, inspired by centre-manifold theory, which provides a systematic approach to calculating a sequence of successively more accurate approximations to the evolution of the principal structure in space and time.The formal procedure described here raises a number of questions for future research. For example: what sort of error bounds can be obtained, do the approximations converge or are they strictly asymptotic, and what sort of boundary conditions are appropriate in a given problem?

scholarly journals Conclusion

2021 ◽  
pp. 93-98
Author(s):  
Rosita Fibbi ◽  
Arnfinn H. Midtbøen ◽  
Patrick Simon
Keyword(s):  
Racial Discrimination ◽  
Future Research ◽  
Space And Time ◽  
The Relationship

AbstractThis chapter briefly summarizes the content of the book, emphasizing how the impressive breadth of research reveal a worrying picture of enduring discrimination in immigrant-receiving societies across space and time, suggesting the contour of troubling “three P’s” in contemporary European societies: that ethno-racial discrimination appears to be pervasive, perpetuating, and persistent. The chapter also revisits the relationship between theories of integration and discrimination, and it concludes by pointing out promising for future research on discrimination.

Conclusions

2021 ◽  
pp. 295-300
Author(s):  
Diego Pescarini
Keyword(s):  
Cluster Formation ◽  
Future Research ◽  
Chronological Order ◽  
Yield Variation ◽  
Space And Time

My intentions in writing this book were (i) to collect phenomena and put them in logical/chronological order and (ii) to engage with the analysis of some (syntactic) phenomena that yield variation across space and time such as enclisis/proclisis alternations, clitic climbing, and cluster formation. Concluding remarks are organized in two lists. The first mainly restates known empirical conclusions, refines previous analyses, or establishes very general theoretical anchors that may provide some guidelines for future research. The second focuses on more specific conclusions relating to generative theorizing.

scholarly journals Seasonal survival and migratory connectivity of the Eurasian Oystercatcher revealed by citizen science

The Auk ◽  
2019 ◽  
Vol 136 (1) ◽  
Author(s):  
Andrew M Allen ◽  
Bruno J Ens ◽  
Martijn Van de Pol ◽  
Henk Van der Jeugd ◽  
Magali Frauendorf ◽  
...  
Keyword(s):  
Citizen Science ◽  
Avian Species ◽  
Future Research ◽  
Migratory Connectivity ◽  
Space And Time ◽  
Demographic Rates ◽  
Breeding Populations ◽  
Spatio Temporal ◽  
Using Data ◽  
Model Structures

Abstract Migratory connectivity describes linkages between breeding and non-breeding areas. An ongoing challenge is tracking avian species between breeding and non-breeding areas and hence estimating migratory connectivity and seasonal survival. Collaborative color-ringing projects between researchers and citizen scientists provide opportunities for tracking the annual movements of avian species. Our study describes seasonal survival and migratory connectivity using data from more than 4,600 individuals with over 51,000 observations, predominantly collected by citizen scientists. Our study focuses on the Eurasian Oystercatcher (Haematopus ostralegus), a species that has experienced a substantial and ongoing decline in recent decades. Multiple threats have been described, and given that these threats vary in space and time, there is an urgent need to estimate demographic rates at the appropriate spatio-temporal scale. We performed a seasonal multi-state (5 geographical areas within The Netherlands) live- and dead-recoveries analysis under varying model structures to account for biological and data complexity. Coastal breeding populations were largely sedentary, while inland breeding populations were migratory and the direction of migration varied among areas, which has not been described previously. Our results indicated that survival was lower during winter than summer and that survival was lower in inland areas compared with coastal areas. A concerning result was that seasonal survival of individuals over-wintering in the Wadden Sea, an internationally important site for over-wintering shorebirds, appeared to decline during the study period. We discuss the outcomes of our study, and how citizen science was integral for conducting this study. Our findings identify how the demographic rates of the oystercatcher vary in space and time, knowledge that is vital for generating hypotheses and prioritizing future research into the causes of decline.

A centre theorem for two-dimensional complex holomorphic systems and its generalization

1995 ◽  
Vol 450 (1939) ◽  
pp. 225-232 ◽  
Keyword(s):  
Singular Point ◽  
Equilibrium Point ◽  
Point Theory ◽  
Two Dimensional ◽  
Imaginary Eigenvalue ◽  
Centre Manifold ◽  
Manifold Theory

We consider a two-dimensional complex holomorphic system. In particular, we use the centre manifold theory together with the singular point theory of C. H. Briot & J. C. Bouquet ( J . Éc . imp . Polyt . 21, 133 (1856)) to establish a centre theorem concerning the behaviour of the phase paths of the system in the neighbourhood of an equilibrium point having a single purely imaginary eigenvalue. An extended centre theorem is established for the corresponding N -dimensional complex holomorphic system ( N ≥ 3).

scholarly journals APPLICATION OF CENTRE MANIFOLD THEORY IN GENERALIZED MAXWELL-BLOCH LASER EQUATIONS

1996 ◽  
Vol 45 (1) ◽  
pp. 46
Author(s):  
WANG KAI-GE ◽  
WANG YU-LONG ◽  
SUN YIN-GUAN
Keyword(s):  
Centre Manifold ◽  
Manifold Theory

Weakly Nonlinear and High Speed Propagation of Quasi-Monochromatic High Frequency Waves in Compressible Bubbly Liquids

2019 ◽  
Author(s):  
Takanori Yoshimoto ◽  
Tetsuya Kanagawa
Keyword(s):  
High Speed ◽  
Bubble Dynamics ◽  
Multiple Scales ◽  
Compressible Liquid ◽  
Governing Equations ◽  
Nls Equation ◽  
Weakly Nonlinear ◽  
Bubbly Liquids ◽  
High Frequency Waves ◽  
Correction Terms

Abstract This study theoretically investigates plane progressive quasi-monochromatic waves in an initially quiescent compressible liquid containing many spherical gas bubbles, on the basis of the derivation of a nonlinear wave equation that represents waves propagating at a high phase velocity induced by taking the effect of liquid compressibility in consideration. The governing equations for bubbly flows are composed of the conservation equations of mass and momentum, the equation of bubble dynamics as radial oscillations, and so on. By using the method of multiple scales with an appropriate choice of set of scaling relations of nondimensional parameters, the nonlinear Schrödinger (NLS) equation with an attenuation term and some correction terms can be derived from the governing equations. The decrease in the group velocity in a far field is then clarified. The dependence of waveform on wavenumber is implied.

Language, Race, and Reflexivity

2020 ◽  
pp. 23-46
Author(s):  
Adrienne Lo ◽  
Elaine Chun
Keyword(s):  
United States ◽  
Racial Discrimination ◽  
Multiple Scales ◽  
The United States ◽  
Linguistic Differences ◽  
Space And Time

This chapter reviews research on language and race in the United States, concentrating on two paradigms of research: research focused on linguistic differences and racial discrimination and research focused on ideologies and racialization. It examines several thorny conceptual issues that arise in the first paradigm and that specifically relate to the notion of the ‘ethnolect’, including their labeling, distinctiveness, authenticity, and multidimensionality. It also argues for the importance of a reflexive approach that entails looking at racialized language as an ideological construct and situating processes of racialization across multiple scales of space and time and within structures of power. Such an approach recognizes how processes of racialization, which take place in both scholarly and everyday contexts, often prioritize the perspectives and interests of certain people over those of others.

scholarly journals Estimation of Chlorophyll Fluorescence at Different Scales: A Review

Sensors ◽  
2019 ◽  
Vol 19 (13) ◽  
pp. 3000 ◽  
Author(s):  
Zhuoya Ni ◽  
Qifeng Lu ◽  
Hongyuan Huo ◽  
Huili Zhang
Keyword(s):  
Remote Sensing ◽  
Chlorophyll Fluorescence ◽  
Multiple Scales ◽  
Future Research ◽  
Passive Remote Sensing ◽  
Advantages And Disadvantages ◽  
Remote Sensing Technology ◽  
Sensing Technology ◽  
Key Issues ◽  
Non Destructive

Measuring chlorophyll fluorescence is a direct and non-destructive way to monitor vegetation. In this paper, the fluorescence retrieval methods from multiple scales, ranging from near the ground to the use of space-borne sensors, are analyzed and summarized in detail. At the leaf-scale, the chlorophyll fluorescence is measured using active and passive technology. Active remote sensing technology uses a fluorimeter to measure the chlorophyll fluorescence, and passive remote sensing technology mainly depends on the sun-induced chlorophyll fluorescence filling in the Fraunhofer lines or oxygen absorptions bands. Based on these retrieval principles, many retrieval methods have been developed, including the radiance-based methods and the reflectance-based methods near the ground, as well as physically and statistically-based methods that make use of satellite data. The advantages and disadvantages of different approaches for sun-induced chlorophyll fluorescence retrieval are compared and the key issues of the current sun-induced chlorophyll fluorescence retrieval algorithms are discussed. Finally, conclusions and key problems are proposed for the future research.

scholarly journals Modeling Spatiotemporal Rainfall Variability in Paraíba, Brazil

Water ◽  
2019 ◽  
Vol 11 (9) ◽  
pp. 1843
Author(s):  
Elias Silva de Medeiros ◽  
Renato Ribeiro de Lima ◽  
Ricardo Alves de Olinda ◽  
Carlos Antonio Costa dos Santos
Keyword(s):  
Rainfall Variability ◽  
Rain Gauge ◽  
Rainfall Data ◽  
Future Research ◽  
Time Variability ◽  
Total Rainfall ◽  
Space And Time ◽  
Variable Distribution ◽  
Monthly Total ◽  
The Mean

The purpose of this study was to provide a detailed framework to use the spatiotemporal kriging to model the space-time variability of precipitation data in Paraíba, which is located in the northeastern region of Brazil (NEB). The NEB is characterized by an irregular, highly variable distribution of rainfall in space and time. In this region, it is common to find high rates of rainfall at locations adjacent to those with no record of rain. Paraíba experiences localized periods of drought within rainy seasons and distinct precipitation patterns among the state’s mesoregions. The mean precipitation values observed at several irregularly spaced rain gauge stations from 1994 to 2014 showed remarkable variations among the mesoregions in Paraíba throughout the year. As a consequence of this behavior, there is a need to model the rainfall distribution jointly with space and time. A spatiotemporal geostatistical methodology was applied to monthly total rainfall data from the state of Paraíba. The rainfall data indicate intense spatial and temporal variabilities that directly affect the water resources of the entire region. The results provide a detailed spatial analysis of sectors experiencing precipitation conditions ranging from a scarcity to an excess of rainfall. The present study should help drive future research into spatiotemporal rainfall patterns across all of NEB.

MMPI Discrimination between Violent and Nonviolent State Hospital Adult Male Inpatients

1979 ◽  
Vol 7 (2) ◽  
pp. 199-209 ◽  
Author(s):  
Antonio M. Betancourt ◽  
William L. Albott
Keyword(s):  
State Hospital ◽  
Discriminant Function ◽  
Adult Male ◽  
Discriminant Function Analysis ◽  
Multiple Scales ◽  
Function Analysis ◽  
Future Research ◽  
Research Needs ◽  
Literature Analysis ◽  
Prediction Of Violence

In this investigation comparisons between 24 violent and 24 nonviolent male psychiatric inpatients indicated that the possibilities of accurate prediction of violence by means of the MMPI are higher than previously noted in the literature. Analysis of MMPI profiles indicated that single and 2-point coding is not as efficient or accurate as use of multiple scales–-i.e. the entire profile. Multiple discriminant function analysis correctly classified 75% of the two groups. Discussion of the results pointed to future research needs and to some theoretical problems that make interpretation difficult at this time.

Sign in / Sign up

Export Citation Format

Share Document