Role-Reversible Judgments and Related Democratic Objections to AI Judges

In a recent article published by this journal, Kiel Brennan-Marquez and Stephen E. Henderson argue that replacing human judges with AI would violate the role-reversibility ideal of democratic governance. Unlike human judges, they argue, AI judges are not reciprocally vulnerable to the process and effects of their own decisions. I argue that role-reversibility, though a formal ideal of democratic governance, is in the service of substantive ends that may be independently achieved under AI judges. Thus, although role-reversibility is necessary for democratic governance when human judges are on the job, it may not be so when AI judges replace them. One broader implication for normative evaluation of disruptive technologies follows: formal and substantive ideals that often align must be independently examined in the evaluation of disruptive technologies. This is because these formal and substantive ideals may no longer align under the factual circumstances that come to govern when such technologies are deployed

Existence results for a class of (p,q) Laplacian systems

We establish the existence of a nontrivial solution for inhomogeneous quasilinear elliptic systems:−∆pu = λ a(x) u |u|γ−2 + α (α + β)–1 b(x) u |u|α−2 |v|β + f    in Ω,−∆qv = µ d(x) v |v|γ−2 + β (α + β)–1 b(x) |u|α v |v|β−2 + g    in Ω,(u,v) ∈ W01,p(Ω) × W01,q(Ω).Our result depending on the local minimization

On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value

This study concerns the existence of positive solutions to classes of boundary value problems of the form−∆u = g(x,u), x ∈ Ω,u(x) = 0, x ∈ ∂Ω,where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u)

On a Nonlinear System of Reaction-Diffusion Equations

The aim of this article is to study the existence of positive weak solution for a quasilinear reaction-diffusion system with Dirichlet boundary conditions,− div(|∇u1|p1−2∇u1) = λu1α11u2α12... unα1n,   x ∈ Ω,− div(|∇u2|p2−2∇u2) = λu1α21u2α22... unα2n,   x ∈ Ω, ... , − div(|∇un|pn−2∇un) = λu1αn1u2αn2... unαnn,   x ∈ Ω,ui = 0,   x ∈ ∂Ω,   i = 1, 2, ..., n,  where λ is a positive parameter, Ω is a bounded domain in RN (N > 1) with smooth boundary ∂Ω. In addition, we assume that 1 < pi < N for i = 1, 2, ..., n. For λ large by applying the method of sub-super solutions the existence of a large positive weak solution is established for the above nonlinear elliptic system

The Nehari manifold approach for p(x)p(x)-Laplacian problem with Neumann boundary condition

In this paper, we consider the system \begin{eqnarray*} \left\{\begin{array}{ll} -\Delta_{p(x)} u + |u|^{p(x)-2}u = \lambda a(x)|u|^{r_1(x)-2}u + \frac{\alpha(x)}{\alpha(x) + \beta(x)} c(x)|u|^{\alpha(x)-2}u|v|^{\beta(x)} &~\textrm{in}~\Omega\\ -\Delta_{q(x)} v+|v|^{q(x)-2}v = \mu b(x)|v|^{r_2(x)-2}v + \frac{\beta(x)}{\alpha(x) + \beta(x)} c(x)|v|^{\beta(x)-2}v|u|^{\alpha(x)} & ~\textrm{in}~\Omega\\ \frac{\partial u}{\partial \gamma} = \frac{\partial v}{\partial \gamma}= 0 & \textrm{on}~ \partial \Omega \end{array}\right. \end{eqnarray*} where $\Omega \subset R^N$ is a bounded domain with smooth boundary and $\lambda, \mu > 0,~\gamma$ is the outer unit normal to $\partial\Omega$. Under suitable assumptions, we prove the existence of positive solutions by using the Nehari manifold and some variational techniques

On a class of nonuniformly nonlinear systems with Dirichlet boundary conditions

The existence and multiplicity of weak solutions for some nonuniformly nonlinear elliptic systems are obtained by using the minimum principle and the Mountain-pass theorem.Існування та кратність слабких розв'язків деяких нерівномірно нєлінійних еліптичних систем досліджено за допомогою принципу мінімуму та теореми про гірський перевал

The Nehari Manifold for p-Laplacian Equation with Dirichlet Boundary Condition

The Nehari manifold for the equation −∆pu(x) = λu(x)|u(x)|p−2 + b(x)|u(x)|γ−2u(x) for x ∈ Ω together with Dirichlet boundary condition is investigated in the case where 0 < γ < p. Exploiting the relationship between the Nehari manifold and fibrering maps (i.e., maps of the form of t → J(tu) where J is the Euler functional associated with the equation), we discuss how the Nehari manifold changes as λ changes, and show how existence results for positive solutions of the equation are linked to the properties of Nehari manifold

Cultural perceptions of ethical leadership and its effect on intention to leave in the independent hotel industry

Purpose Studies have shown that due to the high direct and indirect costs of staff-turnover there is a need for managers to use approaches which engender a feeling that the organisation is fair to its employees and consequently reduce intention-to-leave. However, to understand how to apply research findings and theories from different parts of the world, we need to understand how employees’ perceptions of such factors as ethical leadership and organisational justice are affected by national culture. Therefore, we compared the impact of ethical leadership on intention-to-leave through justice, loyalty and satisfaction among employees of independent12 hotels from two GLOBE cultural clusters. Design/methodology/approach A total of 1561 questionnaires were received from independent hotel employees, which were analysed using SEM. Data were collected in the USA, UK, Italy and Spain whose national cultures fall into two different GLOBE regional clusters. Findings Our results show similarities and differences between countries and within and between clusters. No relationship was found between procedural justice and intention to leave in any of the four countries. Ethical leadership had no significant impact on job satisfaction and organisational justice in the UK, which contrasts with results in the other three countries. Our findings also show that distributive justice has a significant relationship with intention to leave in the US and UK (Anglo cluster), whereas no specific relationship was found between these two variables in Italy and Spain (Latin European cluster). Originality/value This study contributes to the literature of ethical leadership and its application to the hotel industry in two culturally different GLOBE clusters. This study shows how the relationships between organisational variables are affected by national culture and emphasises the importance for hotel managers of being aware of the specific characteristics of the culture of the country in which they are operating