Theory Of Inequalities Research Articles

Lognormal (re)distribution: A macrofounded theory of inequality

We study how political competition over redistribution determines income inequality under one macrofounded premise: the income distribution is approximately log-normal before and after any policy intervention. The unique equilibrium features substantial income inequality and less than maximal redistribution, even if the voters’ median income is very low. Fitting our model to the US economy, we argue that either the efficiency cost of redistribution is higher than estimates in the literature, or else US’s redistributive policies are optimal for an agent richer than the median voter.

Bifurcation and stability analysis of a Leslie–Gower diffusion predator–prey model with prey refuge and Beddington–DeAngelis functional response

In this paper, we consider the spatiotemporal dynamics behaviors of a Leslie–Gower diffusion predator–prey system with prey refuge and Beddington–DeAnglis (B‐D) functional response. By using the Poincaré inequality and topological degree theory, we first investigate the Turing instability of the reaction–diffusion system and prove the existence of nonconstant positive steady‐state solutions. Then we discuss the steady‐state bifurcation and the direction to Hopf bifurcation of the PDE model by the local bifurcation theorem and center manifold theory. Finally, some numerical simulations are presented to supplement the analytic results in one dimension which indicates that changes in prey refuge and diffusion coefficient can increase the complexity of the system.

Structural inequality and the protectorate of discrimination law

This article asks whether discrimination law should be symmetrical: whether it should offer the same level of protection to dominant and dominated groups. It articulates a structural inequality theory of the moral foundations of discrimination law and defends it against prominent alternatives, such as the view that discrimination is wrong because it is irrational or disrespectful. The paper then argues that while direct discrimination is symmetrical, indirect discrimination is asymmetrical. It cannot be claimed by those – men, or white persons – who are not at the sharp end of structural inequality. Furthermore, even dominated groups cannot claim to be indirectly discriminated against by just any law that has a disparate impact on them. If the structural inequality view is correct, the protectorate of discrimination law is not as extensive as is commonly assumed.

Income Distribution and the Elasticity of Substitution in the Works of Joan Robinson

ABSTRACT Independently devised by John Hicks and Joan Robinson, the elasticity of substitution (σ) plays an important role in mainstream theories of inequality. This paper examines the role of σ in Robinson's writings, charting the differing ways in which she used it to examine questions of distribution. Robinson initially applied the concept to examine distribution in a Keynesian framework, proceeding to downplay its importance later on in spite of having played a central role in its formulation. Her criticisms of the nature of neoclassical production functions led her to dismiss mainstream theories of distribution as tautological, while seeing σ as an expression of the potential for rising profit shares under full employment. The use of a single parameter such as the substitution elasticity in mainstream frameworks neglected the important role played by investment and institutions, drawing focus away from an understanding of the ‘rules of the game’ that determined distributive shares in capitalist economies. Given the primacy of σ in discussions today — in textbooks and in the works of economists such as Thomas Piketty — her writings offer an important critique of established frameworks, while also advancing alternatives that stress the role of institutions and class conflict in modern economies.

Fractional Reverse Inequalities Involving Generic Interval-Valued Convex Functions and Applications

The relation between fractional calculus and convexity significantly impacts the development of the theory of integral inequalities. In this paper, we explore the reverse of Minkowski and Hölder’s inequality, unified Jensen’s inequality, and Hermite–Hadamard (H-H)-like inequalities using fractional calculus and a generic class of interval-valued convexity. We introduce the concept of I.V-(⋏,ℏ) generic class of convexity, which unifies several existing definitions of convexity. By utilizing Riemann–Liouville (R-L) fractional operators and I.V-(⋏,ℏ) convexity to derive new improvements of the H-H- and Fejer and Pachpatte-like inequalities. Our results are quite unified; by substituting the different values of parameters, we obtain a blend of new and existing inequalities. These results are fruitful for establishing bounds for I.V R-L integral operators. Furthermore, we discuss various implications of our findings, along with numerical examples and simulations to enhance the reliability of our results.

Generalization of the Fuzzy Fejér–Hadamard Inequalities for Non-Convex Functions over a Rectangle Plane

Integral inequalities with generalized convexity play a vital role in both theoretical and applied mathematics. The theory of integral inequalities is one of the branches of mathematics that is now developing at the quickest rate due to its wide range of applications. We define a new Hermite–Hadamard inequality for the novel class of coordinated ƛ-pre-invex fuzzy number-valued mappings (C-ƛ-pre-invex 𝘍 𝘕 𝘝 𝘔s) and examine the idea of C-ƛ-pre-invex 𝘍 𝘕 𝘝 𝘔s in this paper. Furthermore, using C-ƛ-pre-invex 𝘍 𝘕 𝘝 𝘔s, we construct several new integral inequalities for fuzzy double Riemann integrals. Several well-known results, as well as recently discovered results, are included in these findings as special circumstances. We think that the findings in this work are new and will help to stimulate more research in this area in the future. Additionally, unique choices lead to new outcomes.

Unveiling the evolving educational inequality from upper secondary to higher education in South Korea: from effectively maintained inequality theory perspective

Unveiling the evolving educational inequality from upper secondary to higher education in South Korea: from effectively maintained inequality theory perspective

Navigating online perils: Socioeconomic status, online activity lifestyles, and online fraud targeting and victimization of old adults in China

Online fraud poses a growing threat to the well-being of old adults. This study examines the causes and correlates of online fraud targeting and victimization among old adults in China. Drawing insights from the digital inequality theory and lifestyle routine activity theory and utilizing a nationally representative survey of Chinese old adults (N = 4293), this study examines how socioeconomic status and online lifestyle patterns affect their susceptibility to online fraud. The results show that old adults of better socioeconomic status are more likely to be targeted by online frauds, though not necessarily experiencing financial loss. Latent class analysis identifies four online activity lifestyles among old adults: basic, entertainment, risky, and advanced users. Subsequent analysis demonstrates that these lifestyle types predict different risks of online fraud targeting and victimization. Basic users face a heightened risk of being targeted but not necessarily monetary loss. Risky users, while not exhibiting elevated targeting risks compared to basic users, are more susceptible to financial loss once targeted. Advanced users, in contrast to basic users, face elevated risks of being targeted and monetary loss. This study offers new insights into the risk factors for online fraud targeting and victimization among old adults in China, informing the development of effective online fraud prevention programs.

Loneliness and pain among community-dwelling middle-aged and older Black, Latino, and White adults in the United States.

Prior research has demonstrated a strong and independent association between loneliness and pain, but few studies to date have explored this relationship in racially and ethnically diverse groups of midlife and older adults. We drew on the diathesis stress model of chronic pain and cumulative inequality theory to examine the relationship of loneliness and the presence and intensity of pain in a nationally representative sample of Black, Latino, and White adults aged 50 or older in the United States. Data were from Wave 3 of the National Social Life, Health, and Aging Project (n = 2,706). We used weighted logistic and ordinary least squares regression analyses to explore main and interactive effects of loneliness and race and ethnicity while adjusting for well-documented risk and protective factors (e.g., educational attainment, perceived relative income, inadequate health insurance, perceived discrimination) and salient social and health factors. Almost half (46%) of the participants reported feeling lonely and 70% reported the presence of pain. Among those who reported pain (n = 1,910), the mean intensity score was 2.89 (range = 1-6) and 22% reported severe or stronger pain. Greater loneliness was associated with increased odds of pain presence (AOR = 1.154, 95% CI [1.072, 1.242]) and higher pain intensity (β = 0.039, p < 0.01). We found no significant interaction effects involving Black participants. However, Latino participants who reported greater loneliness had significantly higher levels of pain (β = 0.187, p < 0.001) than their White counterparts with similar levels of loneliness. Loneliness is an important correlate of pain presence and intensity and may have a stronger effect on pain intensity among Latino adults aged 50 or older. We discuss clinical and research implications of these findings, including the need for more fine-grained analyses of different types of loneliness (e.g., social, emotional, existential) and their impact on these and other pain-related outcomes (e.g., interference). Our findings suggest a need for interventions to prevent and manage pain by targeting loneliness among middle-aged and older adults, particularly Latino persons.

LMI-based state observer design for supercavitating vehicles with time delay

Due to the existence of the planing force, the control of the supercavitating vehicle is difficult, and the vertical velocity which has a great influence on the planing force cannot be directly measured. Therefore, considering the time-delay effect of the planing force and the external disturbance, the state observer and controller based on linear matrix inequality (LMI) have been designed. By decomposing the planing force into two parts of time delay and non-time delay, and a longitudinal plane Linear Parameter Varying (LPV) time-delay model for supercavitating vehicles is derived. In addition, the controller and state observer for the supercavitating vehicle system with time-delay characteristics and external disturbances are simultaneously designed. The gains of the controller and observer are obtained by combining the theory of linear matrix inequalities and convex polytopes, ensuring the convergence of estimation error. At the same time, taking into account the possibility of exceeding the physical limits of the actuator when the input value is too large, the compensator has been added. Finally, the simulation results demonstrate that the designed controller exhibits good stability and tracking performance.

Mind the gap: causes and consequences of the racial gap in music funding organizations

ABSTRACT This article explores the challenges of applying for and receiving music funding for Canadian music workers identifying as Indigenous, Black, or as a person of colour (IBPOC). Using survey data from the Canadian Live Music Association we find evidence of a racialized gap in music funding. Interviews with IBPOC music workers reveal the causes and consequences of the racial funding gap: there are limitations to worker agency wrought by gaps in knowledge of funding opportunities; perceived bias in favour of majority White-racialized music genres; and bureaucratic contradictions in funding applications that disadvantage IBPOC applicants. We argue that the conceptual tenets of racialized organizations and theories of racial inequality in cultural policy and creative organizations explain why gaps in funding persist, despite stated efforts to the contrary. We conclude by outlining a model of how music funding organizations exemplify racializing processes and offer policy implications for scholars and practitioners of arts funding.

Mixed finite element method for multi-layer elastic contact systems

With the development of multi-layer elastic systems in the field of engineering mechanics, the corresponding variational inequality theory and algorithm design have received more attention and research. In this study, a class of equivalent saddle point problems with interlayer Tresca friction conditions and the mixed finite element method are proposed and analyzed. Then, the convergence of the numerical solution of the mixed finite element method is theoretically proven, and the corresponding algebraic dual algorithm is provided. Finally, through numerical experiments, the mixed finite element method is not only compared with the layer decomposition method, but also its convergence relationship with respect to the spatial discretization parameter H is verified.

Fractional Hermite–Hadamard, Newton–Milne, and Convexity Involving Arithmetic–Geometric Mean-Type Inequalities in Hilbert and Mixed-Norm Morrey Spaces ℓq(·)(Mp(·),v(·)) with Variable Exponents

Function spaces play a crucial role in the study and application of mathematical inequalities. They provide a structured framework within which inequalities can be formulated, analyzed, and applied. They allow for the extension of inequalities from finite-dimensional spaces to infinite-dimensional contexts, which is crucial in mathematical analysis. In this note, we develop various new bounds and refinements of different well-known inequalities involving Hilbert spaces in a tensor framework as well as mixed Moore norm spaces with variable exponents. The article begins with Newton–Milne-type inequalities for differentiable convex mappings. Our next step is to take advantage of convexity involving arithmetic–geometric means and build various new bounds by utilizing self-adjoint operators of Hilbert spaces in tensorial frameworks for different types of generalized convex mappings. To obtain all these results, we use Riemann–Liouville fractional integrals and develop several new identities for these operator inequalities. Furthermore, we present some examples and consequences for transcendental functions. Moreover, we developed the Hermite–Hadamard inequality in a new and significant way by using mixed-norm Moore spaces with variable exponent functions that have not been developed previously with any other type of function space apart from classical Lebesgue space. Mathematical inequalities supporting tensor Hilbert spaces are rarely examined in the literature, so we believe that this work opens up a whole new avenue in mathematical inequality theory.

A Ramsey-Type Equilibrium Model with Spatially Dispersed Agents

AbstractWe present a spatial and time-continuous Ramsey-type equilibrium model for households and firms that interact on a spatial domain to model labor mobility in the presence of commuting costs. After discretization in space and time, we obtain a mixed complementarity problem that represents the spatial equilibrium model. We prove existence of equilibria using the theory of finite-dimensional variational inequalities and derive a tailored diagonalization method to solve the resulting large-scale instances. Finally, we present a case study that highlights the influence of commuting costs and show that the model allows to analyze transitory effects of industrial agglomeration that emerge and vanish over time as in the real economy.

Parental Involvement to Promote the Social-Emotional Well-Being of Asian Immigrant Youth: A Cultural Mismatch of Teachers and Parents’ Perspectives

This conceptual paper applies the theory adaptation approach to integrate the literature concerning barriers experienced by Asian immigrant families in parental involvement, with a specific focus on comparative analysis of perspectives from Asian immigrant families and their teachers in the United States. The mismatch in the perceptions of parental involvement held by teachers and Asian immigrant parents supports the refinement and applications of the cultural mismatch theory of inequality. The theory provides a comprehensive understanding of how the misalignment between the prevailing school culture and the cultural background of practices of Asian immigrant families contribute to the barriers of parental involvement experienced by Asian immigrant families. The paper outlines implications for reducing the barriers in the communication and collaboration between schools and Asian immigrant families, improving parental involvement in schools, and promoting the social and emotional well-being of Asian immigrant youth. Impact Statement The conceptual paper is one of the first applications of the cultural mismatch theory of inequality in conceptualizing the barriers of parental involvement faced by Asian immigrant youth’s parents and teachers. It provides research and practical implications for school psychologists and other educators on improving their practices to address parental engagement barriers to promote social-emotional well-being of youth in communities of immigrants and other marginalized groups.

Analysis of a dynamic contact problem with long memory

We examine a mathematical framework detailing a dynamic frictional contact involving thermo-viscoelastic materials characterized by long memory and damage. The contact is modeled by the normal compliance condition with Coulomb's friction law, while surface wear is also factored in. The model was in the form of a coupled system which includes an evolution equation written in inclusion form for the frictional contact, parabolic variational inequality for the damage field, nonlinear differential equation for the temperature field and an equation for the wear particles and an evolution. A variational formulation for the model was derived and the existence of the unique weak solution established, under smallness assumptions on a part of the problem data. The proof used various results from the theory of evolution inequalities and repeated fixed-point arguments.

“I don’t believe that I have been wanted”: Processes of Overinclusion and Exclusion in Racialized and Gendered Organizations

Abstract Many studies document that faculty of color, and particularly women of color, find the academy unwelcoming. Yet research that centers intersectional understanding of the mechanisms leading to these inequalities is underdeveloped. We identify three context-dependent mechanisms of racial and gender disadvantage among faculty: active exclusion, overinclusion, and passive exclusion. Taking an explicitly intersectional approach that builds on relational inequality theory, our study focuses on 32 faculty of color, including 18 women and 14 men, comparing their experiences to 30 same-rank white departmental colleagues. Comparing the experiences of faculty who share the same rank and department but differ by race and gender provides a deeper understanding of how race and gender inequalities intersect and are shaped by organizational processes. Active exclusion involves the devaluation of BIPOC faculty’s research, as well the barring of access to resources and positions. Overinclusion is characterized by the overreliance of the university on the labor of faculty of color, particularly women of color, without appropriate compensation. Finally, we conceptualize a more passive kind of exclusion, where BIPOC faculty are left out of collaborations, mentoring, and decision-making relative to white colleagues. Moving beyond rhetoric to disrupting racism in the academy requires addressing overinclusion, and both active and passive forms of exclusion.

Heat and Organization Studies: Organizing in a world approaching 50°C

As a symptom of the current global climate emergency, rising temperatures pervade organizational lives. Yet organization studies have hardly investigated the everyday organizing necessary to cope and adapt, here and now, to life in a world approaching and even surpassing 50°C. This article seeks to open spaces of collective inquiry to grapple with practices of organizational co-evolution with heat. I apply Barad’s post-humanist notion of diffraction—patterns of interference in entangled agency—through warming organizations, as rising temperatures intra-act with the matter, materials, bodies, and discourses that co-constitute them. Diffractive inquiry helps organization studies understand how rising heat alters and amplifies bodily differences across families, communities, firms, societies, and ecologies. This post-humanist view forces us to rethink theories of organizational resilience, inequality, and identity in co-evolution with heat and other ecological phenomena as part of a relational whole.

Generalized uniform optimization for robust adaptive Buck converter with uncertain perturbations

This paper presents an event-triggered impulse (ETI) control mechanism with generalized uniform optimization, endowing robust adaptive for various uncertain Buck converter perturbations. An impulse compensates for the state fluctuation error, and the event triggering mechanism (ETM) is introduced into the control process of the stochastic model of the Buck converter. The mean square stability theory of linear matrix inequality (LMI) stochastic systems is provided, wherein the cost function incorporates uncertain perturbation-induced state feedback impulses and adaptive system tuning. Unlike traditional event-triggered control with manually determined triggering times, ETI is activated only when events conform to the optimal design, significantly enhancing error-tracking accuracy and adaptive capability. Moreover, the parameters of the optimal controller remain independent of the statistical characteristics of uncertain noise, ensuring globally optimal operational control and model generality. Namely, the proposed method demonstrates versatility by extending its application to DC motor control, addressing various perturbations Buck converters encounter. Finally, the designed controller can closely track the required angular velocity trajectory across sudden changes in system uncertain perturbation.

Mapping the imaginary of Information Communication Technologies (ICTs) in education: the case of Botswana

ABSTRACT This article investigates policy-as-discourse and policy-as-technology with specific focus on how the deployment of Information and Communication Technology (ICT) in education is positioned as a redemptive force in the case of Botswana. Therborn's theory of inequalities was adopted to catalogue ways in which supranational organisations and the national government of Botswana consider the potential of ICT and/ICT in education to address (in)equalities in Botswana. A deductive Directed Qualitative Content Analysis (DQICA) was adopted focusing on how the national government and supranational organisations view and present ICT in education in Botswana with regards to being an equaliser. The analysis of the evidence points to ICT in education being seen and operationalised to ameliorate existing inequalities in education and broader society, without, necessarily, questioning broader socioeconomic structural arrangements and factors sustaining inequalities.