scholarly journals Asymptotics of the Charlier polynomials via difference equation methods

2020 ◽  
pp. 1-35
Author(s):  
Xiao-Min Huang ◽  
Yu Lin ◽  
Yu-Qiu Zhao
Keyword(s):  
Difference Equation ◽  
Asymptotic Approximation ◽  
Turning Point ◽  
Turning Points ◽  
Point Theory ◽  
Uniform Asymptotics ◽  
Intermediate Region ◽  
Local Transformation ◽  
Charlier Polynomials ◽  
Matching Techniques

We derive uniform and non-uniform asymptotics of the Charlier polynomials by using difference equation methods alone. The Charlier polynomials are special in that they do not fit into the framework of the turning point theory, despite the fact that they are crucial in the Askey scheme. In this paper, asymptotic approximations are obtained, respectively, in the outside region, an intermediate region, and near the turning points. In particular, we obtain uniform asymptotic approximation at a pair of coalescing turning points with the aid of a local transformation. We also give a uniform approximation at the origin by applying the method of dominant balance and several matching techniques.

Examining context shifts’ effect on relationship trajectories in friendships using Turning Point Theory

2020 ◽  
Vol 37 (6) ◽  
pp. 1892-1909
Author(s):  
Jess Dominguez ◽  
Jeffrey A. Hall
Keyword(s):  
Turning Point ◽  
Turning Points ◽  
Point Theory ◽  
First Year ◽  
First Year Students ◽  
Social Attraction ◽  
Self Disclosure ◽  
Working Adults ◽  
Context Variable ◽  
College Friendships

Drawing from Turning Point Theory, this study explores whether context shifts, which are changes in the location where a friendship is enacted, affect relationship trajectories and friendship closeness. Study 1A ( N = 120) experimentally manipulated invitations for context shifts in college friendships to test their effects on perceived relationship trajectory, social attraction, and closeness. Study 1B ( N = 112) replicated the results of Study 1A with working adults. Both studies’ results suggest that context-variable shifts lead to a change in perceived relationship trajectory but did not influence social attraction or closeness. In Study 2, first-year students ( N = 98) reported on turning points in their friendships twice over 9 weeks. Friendships reporting context-variable shifts as a turning point were associated with higher friendship closeness than relationships that had no turning points and similar closeness as friendships that reported self-disclosure as a turning point.

Fragmenting Feminine-Athletic Identities: Identity Turning Points During Girls’ Transition into High School

2021 ◽  
pp. 216747952110129
Author(s):  
Alaina C. Zanin ◽  
Laura V. Martinez ◽  
Lucy C. Niess
Keyword(s):  
High School ◽  
Identity Development ◽  
Turning Point ◽  
Communication Theory ◽  
Sport Participation ◽  
Female Athletes ◽  
Turning Points ◽  
Athletic Identity ◽  
Communication Theory Of Identity ◽  
And Gender

This study employed a turning point analysis to document events that influence the development of athletic identities in female athletes transitioning into high school. All participants ( N = 28), between the ages of 14–15 years old, belonged to a competitive club soccer team located in the southwestern United States. Through an analysis of pre- and post-season interviews and bi-weekly video journal entries, data revealed several fragmenting turning point events related to participants’ athletic identity development. These fragmenting turning points paired with the communication theory of identity (CTI) framework highlighted three identity gaps: (a) athletic-relational, (b) athletic-communal, and (c) athletic-enacted. Theoretical and practical implications are discussed regarding turning points in relation to athletic identity development and gender disparities in sport participation.

Judging the stance of the business cycle

2021 ◽  
pp. 222-240
Author(s):  
Jesper Rangvid
Keyword(s):  
Business Cycle ◽  
Turning Point ◽  
Turning Points ◽  
Leading Indicators ◽  
Economic Variables ◽  
Near Term ◽  
The Business Cycle

This chapter describes if and how we can detect business-cycle turning points. What variables should we study if we want to say something about the likelihood that the business cycle will change? The chapter discusses business-cycle ‘indicators’. It distinguishes between lagging, coincident, and leading indicators. Lagging indicators refer to economic variables that react to a change in the business cycle, i.e. variables that react after a business-cycle turning point. Coincident indicators tell us something about where we are right now in the business cycle. Leading indicators, which are probably the most important ones, tell us about the near-term outlook for the business cycle, i.e. forecast the business cycle. The chapter emphasizes that business-cycle turning points are hard to predict, but also that some indicators are more informative than others.

scholarly journals Stability, Neimark–Sacker Bifurcation, and Approximation of the Invariant Curve of Certain Homogeneous Second-Order Fractional Difference Equation

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Mirela Garić-Demirović ◽  
Samra Moranjkić ◽  
Mehmed Nurkanović ◽  
Zehra Nurkanović
Keyword(s):  
Difference Equation ◽  
Equilibrium Point ◽  
Asymptotic Approximation ◽  
Second Order ◽  
Invariant Curve ◽  
Unique Equilibrium ◽  
Fractional Difference ◽  
Global Character ◽  
Fractional Difference Equation

We investigate the local and global character of the unique equilibrium point and boundedness of the solutions of certain homogeneous fractional difference equation with quadratic terms. Also, we consider Neimark–Sacker bifurcations and give the asymptotic approximation of the invariant curve.

scholarly journals Periodic and subharmonic solutions for a 2nth-order p-Laplacian difference equation containing both advances and retardations

2018 ◽  
Vol 16 (1) ◽  
pp. 1435-1444 ◽  
Author(s):  
Peng Mei ◽  
Zhan Zhou
Keyword(s):  
Difference Equation ◽  
Critical Point ◽  
Critical Point Theory ◽  
Point Theory ◽  
Nonlinear Difference Equation ◽  
Subharmonic Solutions ◽  
Existence And Multiplicity ◽  
Explicit Criteria

AbstractWe consider a 2nth-order nonlinear difference equation containing both many advances and retardations with p-Laplacian. Using the critical point theory, we obtain some new explicit criteria for the existence and multiplicity of periodic and subharmonic solutions. Our results generalize and improve some known related ones.

scholarly journals Reappraising maturity models in e-Government research: The trajectory-turning point theory

2019 ◽  
Vol 28 (3) ◽  
pp. 310-329 ◽  
Author(s):  
Federico Iannacci ◽  
Aline Pietrix Seepma ◽  
Carolien de Blok ◽  
Andrea Resca
Keyword(s):  
Turning Point ◽  
Point Theory ◽  
Maturity Models ◽  
Government Research

Spectral characteristics of hydromagnetic waves in the magnetosphere

1987 ◽  
Vol 38 (2) ◽  
pp. 235-243 ◽  
Author(s):  
S. P. Kuo ◽  
M. C. Lee ◽  
A. Wolfe
Keyword(s):  
Turning Point ◽  
Spectral Characteristics ◽  
Turning Points ◽  
Resonant Mode ◽  
Period Range ◽  
Plasma Density Profile ◽  
Cavity Modes ◽  
Hydromagnetic Waves ◽  
Radial Axis ◽  
East West

This work is intended to explain why the resonant response of the magnetosphere prefers to have discrete frequencies. Using a cylindrical model for the outer magnetosphere with a plasma density profile proportional to 1/r, we show that the eigenequation characterizing the eigenmodes of the hydromagnetic waves in this model has two turning points along the radial axis. The locations of the turning points depend upon the values of the eigenperiod and the associated east-west wavenumber of the eigenmode. The energy spectrum of the excited cavity modes is seen to have sharp peaks at discrete frequencies when the surface perturbations have a uniform spectrum in the frequency range of interest. We, therefore, have also shown that only the discrete set of the magnetospheric cavity eigenmodes can efficiently couple the perturbations excited on the boundary of the magnetosphere to the field-line resonant mode excited inside the inner turning point of the cavity eigenmode. The most likely values of east-west wavenumbers and wave period range are determined.

(Re)Constructing Relationships with Grandparents: A Turning Point Analysis of Granddaughters' Relational Development with Maternal Grandmothers

1998 ◽  
Vol 46 (4) ◽  
pp. 287-303 ◽  
Author(s):  
Sherry Holladay ◽  
Rita Lackovich ◽  
Margaret Lee ◽  
Mindy Coleman ◽  
David Harding ◽  
...  
Keyword(s):  
Turning Point ◽  
Turning Points ◽  
Transition To College ◽  
Relational Development ◽  
Negative Experiences ◽  
Point Analysis ◽  
The Family ◽  
Relational Closeness ◽  
Geographic Separation ◽  
Interviewing Technique

This study explores how granddaughters account for the development of their relationships with their maternal grandmothers. The retrospective interviewing technique was used to elicit turning points in their relational histories. Analysis of the turning point content revealed several different types of turning points that reflected both normative and idiosyncratic events. Increases in relational closeness resulted from decreases in geographic separation, engaging in shared activities, deaths or serious illnesses in the family, and family disruptions. Decreases in closeness were associated with negative experiences with the grandmother, increases in geographic separation, and the transition to college. Granddaughters reported that turning points related to death or serious illness and participation in shared activities were the most significant ones in their relationships with maternal grandmothers.

Turning Points in Labor Migration: The Case of Hong Kong

1994 ◽  
Vol 3 (1) ◽  
pp. 93-118 ◽  
Author(s):  
Ronald Skeldon
Keyword(s):  
Hong Kong ◽  
Rural Population ◽  
Labor Migration ◽  
Turning Point ◽  
Turning Points ◽  
Emigration And Immigration ◽  
Complex Sequence ◽  
Professional Workers ◽  
Developmental Characteristics ◽  
City State

The Hong Kong experience of emigration and immigration does not fit neatly into models of migration transition. As a city-state with a small rural population, it has exhibited different developmental characteristics from the larger Asian newly industrialized economies. Geopolitical factors have also played a key role in “patterns” of migration, such as restrictive immigration policies in receiving countries. Also significant are individual considerations of political and economic risk, as evidenced by the current rise in the emigration of skilled and professional workers prior to the return of Hong Kong to China. The author concludes that, rather than a simple turning point in labor migration, there may be multiple turning points in a complex sequence of change.

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