A Mixed Finite Element Formulation for the Conservative Fractional Diffusion Equations

We consider a boundary-value problem of one-side conservative elliptic equation involving Riemann-Liouville fractional integral. The appearance of the singular term in the solution leads to lower regularity of the solution of the equation, so to the lower order convergence rate for the numerical solution. In this paper, by the dividing of equation, we drop the lower regularity term in the solution successfully and get a new fractional elliptic equation which has full regularity. We present a theoretical framework of mixed finite element approximation to the new fractional elliptic equation and derive the error estimates for unknown function, its derivative, and fractional-order flux. Some numerical results are illustrated to confirm the optimal error estimates

Approach to health monitoring and assessment of rolling bearing

A bearing is the most common and vital element in the majority of rotating machinery. Condition monitoring and performance assessment of rolling bearing have recently attracted significant attention. This paper proposes a set of methodologies to realize the efficient health monitoring and assessment of rolling bearing. Considering the difficulties and disadvantages in detecting the fault signal of rolling bearing with background noise, this paper presents a method based on the Duffing oscillator and Hu’s moment invariant for health monitoring. The proposed method mainly combines the chaotic oscillator and moment invariant, fully utilizing the sensitivity of the former to detect the fault signal and taking the latter as a quantitative index for fault identification without the need for a qualitative artificial judgment on the Duffing oscillator phase trajectory map. To provide the optimal performance of Hu’s moment invariant in automatic recognition for the phase trajectory map, the influencing principle of different oscillator parameters was analyzed. Therefore, the health state of rolling bearing can be automatically monitored by quantitatively identifying the transition state of the phase trajectory map. A health assessment model was established to evaluate the health state of bearings. Wavelet packet transform was used to extract the features (approximate entropy) of bearing vibration signal, which were input into the self-organizing map (SOM) network. The health state of rolling bearings was then assessed using the SOM network and confidence values. A case study on health monitoring and assessment for rolling bearing was conducted to demonstrate the effectiveness and accuracy of the proposed methods

Age Differences in Stress and Coping: Problem-Focused Strategies Mediate the Relationship between Age and Positive Affect

The present study examined the different types of stressors experienced by adults of different ages, their coping strategies, and positive/negative affect. A mediation hypothesis of coping strategies was tested on the relationships between age and positive/negative affect. One-hundred and ninety-six community-dwelling adults (age range 18-89 years old) reported the most stressful situation they experienced in the past month and coping strategies. Levels of positive and negative affect in the past month were also measured. Content analysis revealed age differences in different types of stressors adults reported. Three types of coping strategies were found: problem-focused, positive emotion-focused, and negative emotion-focused coping. Older adults were less likely than younger adults to use problem-focused coping and reported lower levels of positive affect. Path analysis supported the mediation hypothesis, showing that problem-focused coping mediated the relationship between age and positive affect. Implications are discussed on the importance of promoting problem-focused coping among older adults

On a problem of Henning and Yeo about the transversal number of uniform linear systems whose 2-packing number is fixed

For $r\geq2$, let $(P,\mathcal{L})$ be an $r$-uniform linear system. The transversal number $\tau(P,\mathcal{L})$ of $(P,\mathcal{L})$ is the minimum number of points that intersect every line of $(P,\mathcal{L})$. The 2-packing number $\nu_2(P,\mathcal{L})$ of $(P,\mathcal{L})$ is the maximum number of lines such that the intersection of any three of them is empty. In [Discrete Math. 313 (2013), 959--966] Henning and Yeo posed the following question: Is it true that if $(P,\mathcal{L})$ is a $r$-uniform linear system then $\tau(P,\mathcal{L})\leq\displaystyle\frac{|P|+|\mathcal{L}|}{r+1}$ holds for all $k\geq2$?. In this paper, some results about of $r$-uniform linear systems whose 2-packing number is fixed which satisfies the inequality are given

Numerical Simulation for 2D Sedimentation Model by an Upwind Discontinuous Galerkin Procedure

We reformulate the mathematical model for the 2D sedimentation in an estuary as a coupled nonlinear differential system. Combining the mass-conservation character of the discontinuous Galerkin method and the jump-capturing property of Lesaint-Raviart upwind technique, we design an upwind discontinuous Galerkin finite element method, which obeys the local mass conservation and possesses good stability. Our theoretical analysis shows that there exists a unique solution to the numerical procedure and the discrete solution permits O(hk+Δt) convergence rate. Numerical experiments are conducted to verify our theoretical findings. This may provide a theoretical principle for better understanding of the mechanism and morphological characters of sedimentation at estuaries

Psychological Reactions to COVID-19: Survey Data Assessing Perceived Susceptibility, Distress, Mindfulness, and Preventive Health Behaviors

The COVID-19 pandemic created a complex psychological environment for persons in America. A total of 450 USA MTurk workers completed measures of: (a) basic demographic characteristics; (b) health risk factors for COVID-19; (c) perceived susceptibility variables related to COVID-19; (d) COVID-19 preventive health behaviors; and (e) distress, physical symptoms, and quality of life measures. The surveys were completed between April 9, 2020 and April 18, 2020. This recruitment period corresponded to the first 2-3 weeks of lockdown in most of the USA. Follow-up surveys were completed by 151 of the USA participants between June 19, 2020 and July 11, 2020 (approximately 2 months after the first measurement). These data permit evaluation of relationships among demographic variables, COVID-19 stress and coping, COVID-19 preventive health behavior, and the role of mindfulness as a possible moderator of distress as well as a predictor of preventive health behavior. The availability of follow-up data permit longitudinal analyses that provide a stronger basis for causal inference

Measuring Acculturative Stress of Chinese International Students: Development and Validation of the Unique Stress of Chinese International Students Questionnaire (USCIS)

Over half a million of Chinese international students left their homeland to study abroad in western universities. These students’ unique mental health needs should be addressed. Research has indicated that Chinese international students face unique acculturative stressors and have higher levels of psychological distress compared to their domestic counterparts. Yet, there is a lack of research on the measurement of these stressors. In a previous study, we used data from a focus group study to develop a new acculturative stress measure for Chinese international students and conducted a preliminary analysis with a small sample to further modify the measure. Then, an exploratory factor analysis was conducted using a bigger sample and that resulted in a 9-factor measure. This measure has a total of 40 items and was named the Unique Stress of Chinese International Students Questionnaire (USCIS). The USCIS demonstrated good internal consistencies and criterion-related validity when used to predict psychological distress. In this study, a confirmatory factor analysis (CFA) was conducted with data from 333 Chinese international student participants. This CFA replicated the previously established nine-factor model and this model demonstrated a good model fit. The nine factors in the model are Loneliness, Social Isolation, Academic Stress, Health Care, Language Barrier, Financial Burden, Academic Isolation, Family Distance, and Transportation. The psychometric properties of this new measure were evaluated, including internal consistency and construct validity by using correlational analysis and hierarchical regression. The testing results suggested excellent internal consistency of the USCIS and adequate convergent/discriminant validity and criterion-related validity. The USCIS is one of the first measures devoted to assessing acculturative stress experienced by CIS. We envision this measure to be used as a screening tool for identifying CIS who express acculturation-related distress. Due to its significant predicting power of psychological distress and somatization, this measure would perform well as a predictor of general wellbeing and mental health for CIS. Moreover, the USCIS can be used to detect the effects of racial discrimination and microaggression on acculturation-related wellbeing. In addition, we argue that this culturally sensitive and population-specific measure can serve as an outcome measure for interventions targeting acculturative stress