Invariant measures for the strong-facilitated exclusion process

Consider a generalized model of the facilitated exclusion process, which is a onedimensional exclusion process with a dynamical constraint that prevents the particle at site x from jumping to x+1 (or x-1) if the sites x-1, x-2 (or x+1, x+2) are empty. It is nongradient and lacks invariant measures of product form. The purpose of this paper is to identify the invariant measures and to show that they satisfy both exponential decay of correlations and equivalence of ensembles. These properties will play a pivotal role in deriving the hydrodynamic limit.

UNIQUENESS, ERGODICITY AND UNIDIMENSIONALITY OF INVARIANT MEASURES UNDER A MARKOV OPERATOR

Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by for any f = （f1,f2,… ,fN）, where （pij） is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T＊-invariant measures where T＊ is the adjoint operator of T.

CONVERGENCE OF INVARIANT MEASURES FOR MULTIVALUED STOCHASTIC DIFFERENTIAL EQUATIONS

This article is concerned with the weak convergence of invariant measures asso- ciated with multivalued stochastic differential equations in the finite dimensional space.

Invariant measures for planar piecewise isometries

In this paper,we discuss the invariant measures for planar piecewise isometries.It is shown that the Hausdorff measure restricted to an almost invariant set with respect to the Hausdorff measure is invariant.

INVARIANT MEASURE,RATIO LIMITS AND MARTIN BOUNDARY

In this article the notion of quasi symmetry is introduced.It is proved that the quasi symmetry is equivalent to the uniqueness of invariant measure of Lévy processes in some sense.Moreover,the relationship between ratio limits and invariant measures is studied.

Invariant Measure for the Markov Process Corresponding to a PDE System

In this paper, we consider the Markov process （X^∈（t）, Z^∈（t）） corresponding to a weakly coupled elliptic PDE system with a small parameter ∈ 〉 0. We first prove that （X^∈（t）, Z^∈（t）） has the Feller continuity by the coupling method, and then prove that （X^∈（t）, Z^∈（t）） has an invariant measure μ^∈（·） by the Foster-Lyapunov inequality. Finally, we establish a large deviations principle for μ^∈（·） as the small parameter e tends to zero.

Invariant Measures for a Random Evolution Equation with Small Perturbations

In this paper we consider a random evolution equation with small perturbations, and show how to construct coupled solutions to the equation. As applications, we prove the Feller continuity of the solutions and the existence and uniqueness of invariant measures. Furthermore, we establish a large deviations principle for the family of invariant measures as the perturbations tend to zero.

Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing

Some recent developments in the analysis of long-time behaviors of stochastic solutions of nonlinear conservation laws driven by stochastic forcing are surveyed.The existence and uniqueness of invariant measures are established for anisotropic degenerate parabolic-hyperbolic conservation laws of second-order driven by white noises.Some further developments,problems,and challenges in this direction are also discussed.

The Structure on Invariant Measures of C^1 Generic Diffeomorphisms

Let Λ be an isolated non-trivial transitive set of a C1 generic diffeomorphism f ∈ Diff（M）. We show that the space of invariant measures supported on A coincides with the space of accumulation measures of time averages on one orbit. Moreover, the set of points having this property is residual in Λ （which implies that the set of irregular＋ points is also residual in Λ）. As an application, we show that the non-uniform hyperbolicity of irregular＋ points in A with totally 0 measure （resp., the non-uniform hyperbolicity of a generic subset in Λ） determines the uniform hyperbolicity of Λ.

Factor Structure and Measurement Invariance of the Japanese Version of the Mother-to-Infant Bonding Scale

Background: Bonding disorders affect the growth and development of infants. In Japan, the Japanese version of the Mother-to-Infant Bonding Scale (MIBS-J) is widely used for early detection of bonding disorders. Repeated use of a questionnaire has problems of reduced validity. In order to correctly detect bonding disorders at multiple time points, it is necessary to confirm the measurement invariance of the scale. Baba et al. reported that invariance of the MIBS-J factor structure could only be obtained by abridging the scale into three items. Purpose: The aim of this study was to 1) confirm the factor structure and measurement invariance of the MIBS-J between two measurement times and 2) to examine factors that can be used without being affected by measurement time in order to identify item that contribute to measure met invariance. Methods: We analysed the data of 1049 and 878 mothers with a neonate collected in two waves: 5 days (Wave 1) and 1 month postpartum (Wave 2). Exploratory and confirmatory factor analyses were conducted on the data randomly divided into two groups in each wave. Results: The three-item model (MIBS-J items 1, 6, and 8) was most accepted. Measurement invariance and structural invariance were confirmed in the model. This was consistent with Baba et al.’s model. Conclusion: The three MIBS-J items showed measurement invariance and structural invariance in Japanese mothers during 1 month postpartum.

A Cross-cultural Examination of the Noise-sensitivity Scale-short Form:Measurement Invariance Testing between the US and Chinese Samples

Unwanted sound that is unpleasant or disruptive to hear, often interpreted as noise, is a widespread environmental pollutant. Similar to other environmental pollutants, this noise incurs a variety of costs to society. Numerous negative health impacts are linked to increases in noise exposure,such as increased cardiovascular risk;and sleep

Factor Structure and Measurement Invariance of the Prenatal Attachment Inventory: A Study among Japanese Pregnant Women

Background: Maternal emotional tie towards a foetus is a predictor of later maternal and child’s mental health. Methods: A questionnaire survey was conducted among 539 first trimester women. It included the Prenatal Attachment Inventory (PAI), Relationship Questionnaire (RQ), and Edinburgh Postnatal Depression Scale (EPDS). The factor structure models derived from exploratory factor analyses were compared by confirmatory factor analyses. Results: A three-factor bifactor model of the PAI was bet fit to the data. The omega coefficients and explained common variance suggested that the influences of three group factors were not negligible. The scores of the three subscales (derived from the three factors) were differently associated with age, gestation week, and adult attachment styles (derived from RQ). They were, however, not correlated with the EPDS scores. Conclusion: The PAI has a model of three groups and one general factor with an excellent fit to the data. The three subscales have construct validity too.

DYNAMICS OF THE STOCHASTIC g-NAVIER-STOKES EQUATIONS DRIVEN BY NONLINEAR NOISE

This paper deals with the asymptotic behavior of solutions of the stochastic g-Navier-Stokes equation driven by nonlinear noise.The existence and uniqueness of weak pullback mean random attractors for the equation in Bochner space is proven for when the diffusion terms are Lipschitz nonlinear functions.Furthermore,we also establish the existence of invariant measures for the equation.

ERGODIC THEOREM FOR INFINITE ITERATED FUNCTION SYSTEMS

A set of contraction maps of a metric space is called an iterated function systems. Iterated function systems with condensation, can be considered infinite iterated function systems. Infinite iterated function systems on compact metric spaces were studied. Using the properties of Banach limit and uniform contractiveness, it was proved that the random iterating algorithms for infinite iterated function systems on compact metric spaces-satisfy ergodicity. So the random iterating algorithms for iterated function systems with condensation satisfy ergodicity, too.

ABUNDANCE OF UNIMODAL MAPS WITH DENSE CRITICAL ORBIT AND PREFIXED CRITICAL ORBIT

For the so-called quadratic family, it is proved that, there exists a positive Lebesgue measure set E in the parameter space such that the corresponding map has a dense critical orbit in the support set of the invariant measure for almost all parameters in E; it is also proved that there is a dense set in E such that the critical orbit of the corresponding map enter the reversed fixed point.

Stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise

The current paper is devoted to the study of the stochastic stability of FitzHugh-Nagumo systems perturbed by Gaussian white noise. First, the dynamics of stochastic FitzHugh-Nagumo systems are studied. Then, the existence and uniqueness of their invariant measures, which mix exponentially are proved. Finally, the asymptotic behaviors of invariant measures when size of noise gets to zero are investigated.

Validation and adaptation of the Physical Activity Enjoyment Scale (PACES) in fitness group exercisers

Background:Recently,Mullen et al.(2011)presented an 8-item version of the Physical Activity Enjoyment Scale(PACES)that provides a valid instrument for assessing enjoyment in physical activity.The present paper investigated the psychometric properties of a Portuguese adaptation of PACES.Methods:After a process of back-to-back translation into Portuguese,395 members of fitness centers who ranged in age from 18 to 66 years(31.11§8.90,mean§SD)completed the translated version of the PACES.On average,participants had 3.2 years of experience in fitness group classes and practiced for approximately 3.3 times per week.Results:An initial exploratory factor analysis(n=139)revealed a unidimensional structure with factor loadings ranging from 0.79 to 0.89.Results also showed acceptable internal consistency.A confirmatory factor analysis in an independent sample(n=256)provided additional support for the unidimensional structure of the questionnaire.In addition,moderate positive correlations between enjoyment and intrinsic and identified regulation,and moderate negative correlations between enjoyment and external and amotivation,demonstrate the convergent validity of the instrument.Finally,measurement invariance between 2 independent samples was also found.Conclusion:The 8-item Portuguese version of PACES is a valid and reliable instrument for measuring enjoyment of physical activity in Portuguese adult fitness exercisers,and it is therefore suitable to use as a measure of affect in exercise adherence interventions studies.

Inverse shadowing and related measures

We study various weaker forms of the inverse shadowing property for discrete dynamical systems on a smooth compact manifold.First,we introduce the so-called ergodic inverse shadowing property(Birkhoff averages of continuous functions along an exact trajectory and the approximating one are close).We demonstrate that this property implies the continuity of the set of invariant measures in the Hausdorff metric.We show that the class of systems with ergodic inverse shadowing is quite broad;it includes all diffeomorphisms with hyperbolic nonwandering sets.Second,we study the so-called individual inverse shadowing(any exact trajectory can be traced by approximate ones,but this shadowing is not uniform with respect to the initial point of the trajectory).We demonstrate that this property is closely related to structural stability andΩ-stability of diffeomorphisms.

Factor Structure and Longitudinal Invariance of the CES-D across Diverse Residential Backgrounds in Chinese Adolescents

Background:Valid and reliable measures of depressive symptoms are crucial for understanding risk factors,outcomes,and interventions across rural and urban settings.Despite this need,the longitudinal invariance of these measures over time remains understudied.This research explores the structural components of the Center for Epidemiological Studies Depression Scale(CES-D)and examines its consistency across various living environments and temporal stability in a cohort of Chinese teenagers.Method:In the initial phase,1,042 adolescents furnished demographic details and undertook the CES-D assessment.After a three-month interval,967 of these participants repeated the CES-D evaluation.The study employed Confirmatory factor analysis(CFA)to scrutinize the scale’s structural integrity.We investigated factorial invariance by conducting a twopronged CFA:one comparing urban vs.rural backgrounds,and another contrasting the results from the initial assessment with those from the follow-up.Results:The CES-D demonstrated adequate reliability in both rural and urban high school student samples.The preliminary four-factor model applied to the CES-D demonstrated a good fit with the collected data.Invariance tests,including multigroup analyses comparing rural and urban samples and longitudinal assessments,confirmed the scale’s invariance.Conclusions:The results suggest that the CES-D serves as a reliable instrument for evaluating depressive symptoms among Chinese adolescents.Its applicability is consistent across different living environments and remains stable over time.

The Spread Speed of Multiple Catalytic Branching Random Walks

In this paper we study the asymptotic behavior of the maximal position of a supercritical multiple catalytic branching random walk(X_(n))on Z.If M_(n) is its maximal position at time n,we prove that there is a constantα>0 such that M_(n)/n converges toαalmost surely on the set of infinite number of visits to the set of catalysts.We also derive the asymptotic law of the centered process M_(n)-αn as n→∞.Our results are similar to those in[13].However,our results are proved under the assumption of finite L log L moment instead of finite second moment.We also study the limit of(X_(n))as a measure-valued Markov process.For any function f with compact support,we prove a strong law of large numbers for the process X_(n)(f).