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 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.

Invariant Measures and Asymptotic Gaussian Bounds for Normal Forms of Stochastic Climate Model

The systematic development of reduced low-dimensional stochastic climate models from observations or comprehensive high dimensional climate models is an important topic for atmospheric low-frequency variability,climate sensitivity,and improved extended range forecasting.Recently,techniques from applied mathematics have been utilized to systematically derive normal forms for reduced stochastic climate models for low-frequency variables.It was shown that dyad and multiplicative triad interactions combine with the climatological linear operator interactions to produce a normal form with both strong nonlinear cubic dissipation and Correlated Additive and Multiplicative(CAM) stochastic noise.The probability distribution functions(PDFs) of low frequency climate variables exhibit small but significant departure from Gaussianity but have asymptotic tails which decay at most like a Gaussian.Here,rigorous upper bounds with Gaussian decay are proved for the invariant measure of general normal form stochastic models.Asymptotic Gaussian lower bounds are also established under suitable hypotheses.

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 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.

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.

Scaling Equation for Invariant Measure

An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.

Centre symmetric quadruple pattern-based illumination invariant measure

A centre symmetric quadruple pattern-based illumination invariant measure(CSQPIM)is proposed to tackle severe illumination variation face recognition.First,the subtraction of the pixel pairs of the centre symmetric quadruple pattern(CSQP)is defined as the CSQPIM unit in the logarithm face local region,which may be positive or negative.The CSQPIM model is obtained by combining the positive and negative CSQPIM units.Then,the CSQPIM model can be used to generate several CSQPIM images by controlling the proportions of positive and negative CSQPIM units.The single CSQPIM image with the saturation function can be used to develop the CSQPIM-face.Multi CSQPIM images employ the extended sparse representation classification(ESRC)as the classifier,which can create the CSQPIM image-based classification(CSQPIMC).Furthermore,the CSQPIM model is integrated with the pre-trained deep learning(PDL)model to construct the CSQPIM-PDL model.Finally,the experimental results on the Extended Yale B,CMU PIE and Driver face databases indicate that the proposed methods are efficient for tackling severe illumination variations.

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.

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 Note on a Misuirewicz's Theorem

In this paper,we improve a Misuirewicz's theorem and give a new proof of small conjecture on topological entropy.

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.

Confirmatory factor analysis of VISA-P scale and measurement invariance across sexes in athletes with patellar tendinopathy

Background:The Victorian Institute of Sport Assessment–Patella(VISA-P) scale is the most condition-specific patient-reported outcome measure used to assess symptom severity in athletes with patellar tendinopathy.Previous exploratory factor analyses have been conducted to evaluate the scale's dimensionality,with inconsistent results,and the factor structure of the scale remains unclear.The aims of the present study were to determine the factorial structure of the VISA-P scale using confirmatory factor analysis(CFA) and test measurement invariance across sexes.Methods:The study included a convenience sample of 249 Spanish athletes with patellar tendinopathy.CFA was performed to assess factorial validity.Hypothesized 1-and 2-factor models were tested.Measurement invariance across sexes was evaluated via multi-group CFA with several fit indices using EQS 6.1 software.Results:The internal consistency coefficient was 0.74.Several CFA models were examined and the 1-factor model in which errors for Items 7 and8 were correlated showed acceptable fit in terms of comparative fit index(CFI) and goodness-of-fit index(GFI) statistics(CFI = 0.93;GFI = 0.94;standardized root mean square residual = 0.06;root mean square error of approximation = 0.10;90% confidence interval:0.08–0.13).This model was invariant across sexes.Conclusion:The 1-factor model of the Spanish version of the VISA-P scale(VISA-P-Sp) in which errors for Items 7 and 8 were correlated demonstrated relative fit in CFA.Scores obtained via VISA-P-Sp can be compared between men and women without sexes bias.Further studies should examine the VISA-P scale and other single-score patient-reported outcome measures concurrently.

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.