Theory Of Inequalities Research Articles

On Multilinear Inequalities of Ho ̈lder-Brascamp-Lieb Type for Torsion-Free Discrete Abelian Groups

Holder-Brascamp-Lieb inequalities provide upper bounds for a class of multilinear expressions, in terms of L^p norms of the functions involved. They have been extensively studied for functions defined on Euclidean spaces. Bennett-Carbery-Christ-Tao have initiated the study of these inequalities for discrete Abelian groups and, in terms of suitable data, have characterized the set of all tuples of exponents for which such an inequality holds for specified data, as the convex polyhedron defined by a particular finite set of affine inequalities. In this paper we advance the theory of such inequalities for torsion-free discrete Abelian groups in three respects.The optimal constant in any such inequality is shown to equal 1 whenever it is finite.An algorithm that computes the admissible polyhedron of exponents is developed. It is shown that nonetheless, existence of an algorithm that computes the full list of inequalitiesin the Bennett-Carbery-Christ-Tao description of the admissible polyhedron for all data,is equivalent to an affirmative solution of Hilbert's Tenth Problem over the rationals.That problem remains open.

New integral inequalities for synchronous functions via Atangana–Baleanu fractional integral operators

Chebyshev’s inequality is a well-known inequality in the field of inequality theory and yields remarkable results for functions that exhibit synchronous behavior. The study, designed to obtain Chebyshev type inequalities with the help of the Atangana–Baleanu fractional integral operator, which has become the most popular concept of fractional analysis in recent years, aims to obtain general forms for synchronous functions. In the process of obtaining results for synchronized functions within the scope of the study, functional tools such as Atangana–Baleanu fractional integral operator, various mathematical analysis operations and induction were used. The most striking aspect of the findings is that for some special values of the parameter of the fractional integral operator, some of the results can be reduced to the Chebyshev inequality. Compared to the studies in the literature, this study has a unique aspect in that the findings obtained with the help of the Atangana–Baleanu fractional integral operator contain general forms, as well as bringing together a popular concept of synchronous functions and fractional analysis.

The gendered character of claims-making: A longitudinal analysis

In this article, we examine the gendered outcomes of career negotiations, which involve employees discussing career advancements with their direct supervisors. We apply relational inequality theory, which conceptualizes career negotiations as instances of relational claims-making, to explain gender differences in returns in terms of hourly wages, occupational status, and subjective perceptions of job advancements. Our empirical approach employs individual fixed-effect models using three waves of unique German linked employer-employee panel data on 2090 employees across 131 workplaces (LEEP-B3; 2012–2019). We find that men discussing career advancements with supervisors, experience pay raises and occupational upward mobility, whereas women do not. Yet, we find only minor gender differences in perceived job advancements following career negotiations. In workplaces with a more balanced gender representation in management and supervisory positions, women’s wage returns from negotiations increase. Although individual negotiations seem to perpetuate gender inequalities, workplace structures can weaken inequality-generating mechanisms.

Inequalities for strongly s-convex functions via Atangana-Baleanu fractional integral operators

It is more convenient to use fractional derivatives and integrals to express and represent rapid changes than to use integer derivatives and integrals. For this reason, fractional analysis has been found worthy of study in many fields. In recent years, fractional derivatives and integrals have been discussed together with inequality theory and the studies have attracted attention. In this article, we discuss new Hermite-Hadamard type approximations for strongly convex functions with the help of Atangana-Baleanu fractional integral operators. Additionally, new upper bounds have been obtained using various auxiliary inequalities with the help of twice differentiable strongly convex functions.

Hidden inequities within universalising primary education in rural Sierra Leone

ABSTRACT Despite great progress, attaining the goal of universal primary education (UPE) has stalled, particularly in sub-Saharan Africa. This study critically examines how UPE is experienced by out-of-school children and families in three rural villages in Sierra Leone. Drawing on data from 101 qualitative interviews, this study applies relational inequality theory to illustrate a benefit of education that is often underemphasised in UPE discourse – that of maintaining human dignity and relational power. Through the widespread cultural acceptance of exploitative teacher stipends, the formation of new lines of social closure, and the inability of out-of-school children and their families to make claims for respect, I argue that out-of-school children are being excluded from a pathway to basic dignity – an effect that can be mitigated by a renewed commitment to delivering on the de jure promise of free access to education through universal teacher remuneration.

Trust in unions drives egalitarianism: Longitudinal evidence

AbstractDespite the fundamental role of unions in reducing economic inequality, social psychology still needs to incorporate the systematic study of unions concerning the contemporary theories of intergroup inequality. In this study, we do so by testing the reciprocal relationship between trust in unions and social‐dominance orientation egalitarianism (SDO‐E) over time. Using data from the Longitudinal Social Survey of Chile, which is a panel study with a representative sample of urban areas, we carried out a Random Intercept Cross‐Lagged Panel Model with four waves (2016–2019, N = 2972–2153). We controlled the main effect by sex, age, political ideology and educational level. The results show a positive relationship between SDO‐E and trust in unions within and between levels. This means that people who trust in unions also tend to have higher SDO‐E (between effect), and an intraindividual increase in trust in labour unions tends to be followed by an increase in SDO‐E (within effect). Trusting unions as an institution that promotes the hierarchy reduction between workers and employers helps increase people's SDO‐E over time. Please refer to the Supplementary Material section to find this article's Community and Social Impact Statement.

A New Class of Coordinated Non-Convex Fuzzy-Number-Valued Mappings with Related Inequalities and Their Applications

Both theoretical and applied mathematics depend heavily on integral inequalities with generalized convexity. Because of its many applications, the theory of integral inequalities is currently one of the areas of mathematics that is evolving at the fastest pace. In this paper, based on fuzzy Aumann’s integral theory, the Hermite–Hadamard’s type inequalities are introduced for a newly defined class of nonconvex functions, which is known as U·D preinvex fuzzy number-valued mappings (U·D preinvex F·N·V·Ms) on coordinates. Some Pachpatte-type inequalities are also established for the product of two U·D preinvex F·N·V·Ms, and some Hermite–Hadamard–Fejér-type inequalities are also acquired via fuzzy Aumann’s integrals. Additionally, several new generalized inequalities are also obtained for the special situations of the parameters. Additionally, some of the interesting remarks are provided to acquire the classical and new exceptional cases that can be considered as applications of the main outcomes. Lastly, a few suggested uses for these inequalities in numerical integration are made.

Von Neumann Inequality and Dilation Theory on Regular $${{\mathcal {U}}}$$-Twisted Polyballs

Von Neumann Inequality and Dilation Theory on Regular $${{\mathcal {U}}}$$-Twisted Polyballs

Fixed Time Synchronization of Stochastic Takagi–Sugeno Fuzzy Recurrent Neural Networks with Distributed Delay under Feedback and Adaptive Controls

In this paper, the stochastic Takagi–Sugeno fuzzy recurrent neural networks (STSFRNNS) with distributed delay is established based on the Takagi–Sugeno (TS) model and the fixed time synchronization problem is investigated. In order to synchronize the networks, we design two kinds of controllers: a feedback controller and an adaptive controller. Then, we obtain the synchronization criteria in a fixed time by combining the Lyapunov method and the related inequality theory of the stochastic differential equation and calculate the stabilization time for the STSFRNNS. In addition, to verify the authenticity of the theoretical results, we use MATLABR2023A to carry out numerical simulation.

Unruh-De Witt detectors, Bell-CHSH inequality and Tomita-Takesaki theory

The interaction between Unruh-De Witt spin 1/2 detectors and a real scalar field is scrutinized by making use of the Tomita-Takesaki modular theory as applied to the Von Neumann algebra of the Weyl operators. The use of the modular theory enables to evaluate in an exact way the trace over the quantum field degrees of freedom. The resulting density matrix is employed to the study of the Bell-CHSH correlator. It turns out that, as a consequence of the interaction with the quantum field, the violation of the Bell-CHSH inequality exhibits a decreasing as compared to the case in which the scalar field is absent.

Health insurance in the United States: A case of effectively maintained inequality?

The theory of Effectively Maintained Inequality (EMI) (Lucas, 2001) posits that goods have both quantitative (how much?) and qualitative (what kind?) dimensions. Coupled with the hypothesized mechanisms of EMI, this simple observation greatly complicates research and policy development concerning inequality. First applied to explain educational inequality in the United States, evidence for the theory has been found in education systems in over 20 countries, including Chile, China, the Czech Republic, Denmark, Egypt, Germany, Greece, Ireland, Nigeria, South Africa, and South Korea. Yet, while EMI was proposed as a general theory of inequality, to date no research has assessed its applicability to domains outside education. This work uses nearly two decades of National Health Interview Survey data (N = 451,161) to provide the first effort to assess whether EMI illuminates patterns of inequality outside education, by taking up the issue of health insurance in the United States.

Control and Stabilization of Chaotic System Based on Linear Feedback Control Method

In this paper, two kinds of chaotic systems are controlled respectively with and without time-delay to eliminate their chaotic behaviors. First of all, according to the first-order approximation method and the stabilization condition of the linear system, one linear feedback controller is structured to control the chaotic system without time-delay, its chaotic behavior is eliminated and stabilized to its equilibrium. After that, based on the first-order approximation method, the Lyapunov stability theorem, and the matrix inequality theory, the other linear feedback controller is structured to control the chaotic system with time-delay and make it stabilized at its equilibrium. Finally, two numerical examples are given to illustrate the correctness and effectiveness of the two linear feedback controllers.

Explaining mobilization for revolts by private interests and kinship relations. A comment on Armandola, Doehne and Rost

The authors study the role of kinship relationships in explaining mobilization for a revolt in Basel, Switzerland, in 1691; rebels consisted of a weaker fraction of the elite and individuals with citizen rights. The empirical section shows that revolts are mainly driven by the elite’s distant kin rather than the rebels’ close kin. Allowing for coalition formation, as in the new theory of corruption, conflict, and inequality proposed in this comment, can give an alternative explanation. In the first formal model, we assume “elite” corresponds to the term “enforcer” in the new theory. This is a nonproductive individual who is the strongest in terms of fighting against peasants over a prize in a contest. In this simple model, there are no other players. Thus, this framework predicts that the only rebels would come from within the elite. Historical evidence shows that the marginal elite got stronger relatively and, thus, excluded the oligarchy from the winning coalition to take over the government. The direct application of this model would imply that non-elite members were not part of the rebellion. However, the historical facts presented by Armandola et al. show that non-elite citizens also participated in the revolt. To match these facts in Armandola et al., we allow informally individuals with citizen rights to participate in the rebellion. Peasants, a term also used in the new theory, and marginalized groups (a term only used in the commented paper) in the cities did not participate. Kinship effects are discussed.

The Brownian transport map

Contraction properties of transport maps between probability measures play an important role in the theory of functional inequalities. The actual construction of such maps, however, is a non-trivial task and, so far, relies mostly on the theory of optimal transport. In this work, we take advantage of the infinite-dimensional nature of the Gaussian measure and construct a new transport map, based on the Föllmer process, which pushes forward the Wiener measure onto probability measures on Euclidean spaces. Utilizing the tools of the Malliavin and stochastic calculus in Wiener space, we show that this Brownian transport map is a contraction in various settings where the analogous questions for optimal transport maps are open. The contraction properties of the Brownian transport map enable us to prove functional inequalities in Euclidean spaces, which are either completely new or improve on current results. Further and related applications of our contraction results are the existence of Stein kernels with desirable properties (which lead to new central limit theorems), as well as new insights into the Kannan–Lovász–Simonovits conjecture. We go beyond the Euclidean setting and address the problem of contractions on the Wiener space itself. We show that optimal transport maps and causal optimal transport maps (which are related to Brownian transport maps) between the Wiener measure and other target measures on Wiener space exhibit very different behaviors.

Path-following control of 4WIS/4WID autonomous vehicles considering vehicle stability based on phase plane

In order to ensure the following accuracy and improve the operational stability of four-wheel independent driving and four-wheel independent steering autonomous vehicles, this paper proposes a path-following control strategy based on the β−[Formula: see text] phase plane. First, based on the kinematic relationship between the vehicle and the reference path, the linear matrix inequality theory is used to design the H∞ controller to obtain the wheel steering angle. Then, the vehicle steering system is subjected to nonlinear analysis according to phase plane theory, and a partition region controller is designed. In the unstable region, the instability degree of the vehicle is predicted by quadratic polynomial extrapolation and the particle swarm optimization PID controller is designed to determine the required yaw moment to restore the vehicle to the stable region. In the stable region, a fuzzy sliding mode controller is adopted to determine the required yaw moment so that the actual state variable of the vehicle follows the ideal state variable. Finally, the optimal tire force distributor is designed such that the required forces are allocated to all four wheels. The simulation results show that the proposed method can obtain excellent path-following performance and stability performance under different driving conditions.

Mobility and the Social Differentiation of Rural Youth in Australia

Geographical mobility has become an integral element of the biographical trajectories of young people from rural areas. In this paper, we contend that theories of rural-urban inequality tend to unduly homogenise rural social groups and are insufficient to understand rural youth out-migration as a selective rather than universal practice. We draw on a statistical analysis of the social differentiation of rural youth mobility in Australia to argue that sociologists gain from further theorising the social differentiation of rural society. Empirically, we find that classed resources and stratified dispositions toward one’s future life are important properties associated with outward mobility. Theoretically, we propose the concept of rural social space to make sense of these patterns. Rural social space describes the material and symbolic hierarchies that structure the social differentiation of rural society. We conclude by suggesting how future research could refine the conceptualisation of rural social space proposed in this paper, by further considering the opportunities, practices and representations that distinguish the lives of different groups of rural young people.

A Novel Method for Stability and Stabilization of Interconnected Descriptor Systems

This paper addresses the issues of stability and stabilization in interconnected descriptor systems. The existing results based on different structures of the Lyapunov equation are not directly applicable to resolving time-varying problems. In this paper, based on the original literature, the stability of the system is re-described and extended, and new results are obtained, these results are extended to encompass time-varying singular systems exhibiting state-space symmetry, which is achieved by introducing a novel Lyapunov functional. The approach in this paper is grounded in the theory of trace inequalities for matrices, establishing a new sufficient condition for the admissibility of interconnected descriptor systems. In the last, an illustrative example demonstrates the feasibility of employing state feedback to render interconnected descriptor systems admissible, affirming the validity of our proposed method.

Responding to consumer environmental awareness: A variational inequality approach to green manufacturing optimization

In response to increasing consumer environmental awareness, our study introduces a sustainable supply chain optimization model that stimulates competition among multiple green manufacturers within an uncertain market context. Each manufacturer crafts a selection of products showcasing various degrees of greenness, purposefully designed to meet the expanding demand of environmentally conscious consumers. This strategic model emphasizes profit maximization for green manufacturers, necessitating the definition of ideal greenness levels and production quantities for an array of product types. By employing variational inequality theory, we transmute the preliminary optimization model into an interconnected variational inequality problem. We propose an improved Euler algorithm, a proficient tool for attaining equilibrium solutions. Empirical scenarios inspired by the electric vehicle industry lend credibility to our model, indicating that the surge in consumer environmental awareness compels manufacturers to diversify their offerings and accentuate their products’ greenness levels. Intriguingly, the research suggests that escalating competition can incentivize manufacturers to elevate their products’ greenness levels, strategically countering potential profit erosion. In addition, the study reveals that intensifying consumers’ green utility sensitivity doesn’t invariably augment demand for manufacturers, even with significant improvements in product greenness. This paradox highlights the necessity for manufacturers to strategically adjust their production approaches in light of varying consumer preferences. Moreover, when the level of consumer environmental awareness achieves a certain level, the fierce competition might not always be harmful to some manufacturers and the industry if they can adopt effective strategies to improve green utility sensitivity.

Disparities in Stress Exposure and Later-Life Disability.

Drawing from cumulative inequality theory and the weathering hypothesis, this study examined the relationship between life-course stress exposure (measured cumulatively and by domains) and the onset of disability in later life among White, Black, U.S.-born Hispanic, and foreign-born Hispanic older adults. Cross-sectional and longitudinal models were estimated using nationally representative data from the Health and Retirement Study (N = 11,483). We used logistic regression models to examine associations between stress exposure and Wave 1 disability (i.e., occurrence), and Weibull-accelerated failure-time models to examine the relationship between stress exposure and age of onset of disability 12-14 years later (i.e., incidence). We tested for moderation between stress and disability by race, ethnicity, and Hispanic nativity. At Wave 1, higher odds of disability occurrence were associated with cumulative stress burden (CSB; odds ratio [OR] = 4.93, 95% confidence interval [CI]: 2.95-8.23). In a model specifying domains of stressors, disability occurrence was associated with childhood financial strain (OR = 1.22, CI: 1.01-1.46), lifetime traumatic events (OR = 1.92, CI: 1.41-2.62), neighborhood disadvantage (OR = 1.32, CI: 1.01-1.73), and major lifetime discrimination (OR = 1.64, CI: 1.12-2.41). Over time, earlier onset of disability was associated with CSB (β = -0.39), childhood traumatic events (β = -0.16), adult financial strain (β = -0.17), everyday discrimination (β = -0.15), and major lifetime discrimination (β = -0.13). The effect of childhood traumatic events on the transition to disability was stronger for U.S.-born Hispanic adults than White adults (occurring 33% earlier). To reduce racial, ethnic, and nativity disparities in disability, it is important to consider the historical and structural disadvantages associated with stress exposure across the life course. It is also important to acknowledge that nativity influences stratification processes associated with disparities in racial and ethnic health trajectories.

Social contact during the COVID-19 pandemic: The role of long-term connectedness and cumulative inequality in later life

Though the COVID-19 crisis put many older adults at sudden risk of social isolation, the pandemic was far from the “great equalizer” some pundits and politicians initially claimed it would be. Drawing from Cumulative Inequality Theory, I consider how long-run patterns of social dis/connectedness contextualize key disparities in social contact that manifested during the pandemic. I incorporate data from four rounds of the National Social Life, Health, and Aging Project (2005–2021), constructing multiple operationalizations of connectedness accumulation across pre-COVID years and examining several types of social contact during the pandemic, both in-person and remote. Results from ordered logistic regression show that those most durably connected were especially likely to incorporate digital tools for maintaining contact with family and friends. On the other hand, people experiencing more bouts of social disconnection were least likely to see friends during the pandemic, and were yet relatively tolerant of that level of engagement. Even while many older people's level of social dis/connectedness fluctuates over the course of 15 years, it was long-run accumulation patterns—not conditions observed most recently—that best explain their experience of social contact during the pandemic. Findings point to the role of crises in perpetuating and exacerbating key axes of inequality, and suggest points of attention and intervention in COVID's aftermath.