Simpson’s Second-Type Inequalities for Co-Ordinated Convex Functions and Applications for Cubature Formulas

Inequality theory has attracted considerable attention from scientists because it can be used in many fields. In particular, Hermite–Hadamard and Simpson inequalities based on convex functions have become a cornerstone in pure and applied mathematics. We deal with Simpson’s second-type inequalities based on coordinated convex functions in this work. In this paper, we first introduce Simpson’s second-type integral inequalities for two-variable functions whose second-order partial derivatives in modulus are convex on the coordinates. In addition, similar results are acquired by considering that powers of the absolute value of second-order partial derivatives of these two-variable functions are convex on the coordinates. Finally, some applications for Simpson’s 3/8 cubature formula are given.

Life Course Stressors and Functional Limitations in Later Life Among White, Black, and Hispanic Adults

Although striking racial and ethnic disparities in health are manifest during later life, they may be rooted in early-life exposures. Drawing from cumulative inequality theory, we investigate whether experiencing life course stressors increases the risk of later-life functional limitations and whether this relationship differs by race and ethnicity. This study utilizes longitudinal data from the Health and Retirement Study to test whether six indicators of child stressors and eleven indicators of adult stressors predict trajectories of the onset and severity of functional limitations in later life among a diverse sample of adults. We find that child and adult stressors are associated with earlier onset and greater severity of functional limitations during later life. Mediation analyses reveal the indirect influence of child stressors via adult stressors on onset and severity of functional limitations; however, the indirect effects are slightly stronger for Black and Hispanic adults than their White counterparts (i.e., moderated mediation). In sum, child stressors, in and of themselves, do not increase functional limitations among Black and Hispanic people but are associated with greater adult stress exposure, leading to more functional limitations in later life. Disparities in functional limitations are also partly due to lower education and less wealth among Black and Hispanic adults.

Do Early-Life Social, Behavioral, and Health Exposures Increase Later-Life Arthritis Incidence?

Objectives: This study investigates direct and indirect influences of childhood social, behavioral, and health exposures on later-life osteoarthritis and rheumatoid arthritis development. Methods: Drawing from cumulative inequality theory and six waves of the Health and Retirement Study (2004–2014), we estimate structural equation modeling-based discrete-time survival analysis of the association between six childhood exposure domains and both osteoarthritis and rheumatoid arthritis incidence for men ( n = 2720) and women ( n = 2974). Using the delta method to test for mediation, we examine indirect effects via selected health-related risks and resources. Results: Risky adolescent behavior is associated with rheumatoid arthritis incidence for women (h.O.R. = 1.883, 95% C.I. [1.016, 3.490]), whereas several types of childhood exposures are associated with later-life osteoarthritis development for both men and women. Experiencing two or more childhood socioeconomic disadvantages is indirectly associated with osteoarthritis (men: coef. = 0.024, 95% C.I. [0.003, 0.045]; women: coef. = 0.111, 95% C.I. [0.071, 0.150]) and rheumatoid arthritis (men: coef. = 0.037, 95% C.I. [0.000, 0.074]; women: coef. = 0.097, 95% C.I. [0.035, 0.159]) development through adult body mass index. Discussion: Findings highlight the importance of childhood contexts in understanding the development of later-life osteoarthritis and rheumatoid arthritis.

On New Generalizations of Hermite-Hadamard Type Inequalities via Atangana-Baleanu Fractional Integral Operators

Fractional operators are one of the frequently used tools to obtain new generalizations of clasical inequalities in recent years and many new fractional operators are defined in the literature. This development in the field of fractional analysis has led to a new orientation in various branches of mathematics and in many of the applied sciences. Thanks to this orientation, it has brought a whole new dimension to the field of inequality theory as well as many other disciplines. In this study, a new lemma has been proved for the fractional integral operator defined by Atangana and Baleanu. Later with the help of this lemma and known inequalities such as Young, Jensen, Hölder, new generalizations of Hermite-Hadamard inequality are obtained. Many reduced corollaries about the main findings are presented for classical integrals.

On New Generalized Dunkel Type Integral Inequalities with Applications

In this paper, by applying majorization theory, we study the Schur convexity of functions related to Dunkel integral inequality. We establish some new generalized Dunkel type integral inequalities and their applications to inequality theory.

What You Want Is Not Always What You Get: Gender Differences in Employer-Employee Exchange Relationships during the COVID-19 Pandemic

Relational Inequality Theory (RIT) argues that relational claims-making- the process of employer-employee exchange relationships explicitly regarding negotiations over resources and rewards- is the central mechanism that produces social inequalities at work. Yet, the COVID-19 pandemic has significantly affected employees and employers, possibly altering their behavior in relational claims-making. Hence, this paper aims to explore if long-standing gender inequalities in employer-employee exchange relationships have reproduced or changed during the COVID-19 pandemic. It is examined (1) whether women and men differ in their response to the pandemic regarding expected employer support with further training to work from home (WFH) and (2) whether employers’ decisions on adequate support depend on employees’ gender. The hypotheses were tested using a linked employer-employee dataset (LEEP-B3) with information on German employees’ working conditions before and during COVID-19. OLS regression models predicted no gender differences in training expectations. However, women are more likely to be provided with less training than they expect from their employers. Thus, employers’ decision-making has not been altered, but gender remains an important determinant in relational claims-making, thereby reproducing gender inequalities. Finally, the workforces’ pre-COVID-19 gender ideologies predicted whether mechanisms are mitigated or enhanced. Hence, these findings underline the crucial role of the workplace context in which employer-employee exchange relationships are embedded.

Life Course Stressors and Functional Limitations in Later Life among White, Black, and Hispanic Adults: Deleterious, Hardening, or Benign?

Objectives Although striking racial and ethnic disparities in health are manifest during later life, they may be rooted in early-life exposures. Drawing from cumulative inequality theory, we investigate whether life course stressors are associated with risk of later life functional limitations and whether this relationship differs by race and ethnicity. Methods We utilize longitudinal data from the Health and Retirement Study to test whether child and adult stressors predict trajectories of the occurrence and severity of functional limitations among a diverse sample of older adults. Results Child and adult stressors are associated with greater occurrence and severity of functional limitations during later life. Mediation analyses reveal the indirect influence of child stressors via adult stressors on occurrence and severity of functional limitations; however, the indirect effects are slightly stronger for Black and Hispanic adults than their White counterparts. Discussion Child stressors, in and of themselves, do not increase functional limitations among Black and Hispanic people but are associated with greater adult stress exposure, predisposing them to more functional limitations. Results suggest that childhood stressors are associated with distinct social pathways to functional limitations among Black, White, and Hispanic older adults.

Design and Implementation of Novel LMI-Based Iterative Learning Robust Nonlinear Controller

An iterative learning robust fault-tolerant control algorithm is proposed for a class of uncertain discrete systems with repeated action with nonlinear and actuator faults. First, by defining an actuator fault coefficient matrix, we convert the iterative learning control system into an equivalent unknown nonlinear repetitive process model. Then, based on the mixed Lyapunov function approach, we describe the stability of the nonlinear repetitive mechanism on time and trial indices and have appropriate conditions for the repeated control system’s stability in terms of linear matrix inequality theory. Through LMI techniques, we have obtained satisfactory results and controller stability, and robustness against fault tolerance is also discussed in detail. Finally, the simulation results of the output tracking control of the two exemplary models verify the effectiveness of the proposed algorithm.