Theory Of Inequalities Research Articles

Analysis and Numerical Approach of a Coupled Thermo-Electro-Mechanical System for Nonlinear Hencky-Type Materials with Nonlocal Coulomb’s Friction

The effects of an included temperature field in the contact process between a piezoelectric body and a rigid foundation with thermal and electrical conductivity are discussed. The constitutive relation of the material is assumed to be thermo-electro-elastic and involves the nonlinear elastic constitutive Hencky’s law. The frictional contact is modeled with Signorini’s conditions, the regularized Coulomb law, and the regularized electrical and thermal conductivity conditions. The resulting thermo-electromechanical model includes the temperature field as an additional state variable to take into account thermal effects alongside with those of the piezoelectric. The existence of the unique weak solution to the problem is established by using Schauder’s fixed point theorem combined with arguments from the theory of variational inequalities involving nonlinear strongly monotone Lipschitz continuous operators. A successive iteration technique to solve the problem numerically is proposed, and its convergence is established. A variant of the Augmented Lagrangian, the so-called Alternating Direction Method of multipliers (ADMM), is used to decompose the original problem into two sub-problems, solve them sequentially and update the dual variables at each iteration. The influence of the thermal boundary condition on the behavior of contact forces and electrical potential is shown through graphical illustrations.

Some New Fractional Hadamard and Pachpatte-Type Inequalities with Applications via Generalized Preinvexity

The term convexity associated with the theory of inequality in the sense of fractional analysis has a broad range of different and remarkable applications in the domain of applied sciences. The prime objective of this article is to investigate some new variants of Hermite–Hadamard and Pachpatte-type integral inequalities involving the idea of the preinvex function in the frame of a fractional integral operator, namely the Caputo–Fabrizio fractional operator. By employing our approach, a new fractional integral identity that correlates with preinvex functions for first-order differentiable mappings is presented. Moreover, we derive some refinements of the Hermite–Hadamard-type inequality for mappings, whose first-order derivatives are generalized preinvex functions in the Caputo–Fabrizio fractional sense. From an application viewpoint, to represent the usability of the concerning results, we presented several inequalities by using special means of real numbers. Integral inequalities in association with convexity in the frame of fractional calculus have a strong relationship with symmetry. Our investigation provides a better image of convex analysis in the frame of fractional calculus.

New finite-time stability result for a class of Itô-Doob stochastic fractional order systems

In this article, we study the Finite-Time Stability (FTS) of Linear Stochastic Fractional Differential Equations of Itô-Doob Type with Delay (LSFDEIDTwD) for a derivative order ρ∈(0,1). In fact, the (FTS) here consists in studying the stability of the (LSFDEIDTwD) in a finite-time domain [0,T]. To our knowledge, this work represents the first successful attempt to study the (FTS) for the (LSFDEIDTwD), where the fractional order ρ∈(0,1). According to the generalized Gronwall Inequality (GWI) and stochastic calculus theory, the (FTS) of (LSFDEIDTwD) is investigated. We illustrate the main results by two numerical examples.

Finding and improving bounds of real functions by thermodynamic arguments

The possibility of stating the second law of thermodynamics in terms of the increasing behaviour of a physical property establishes a connection between that branch of physics and the theory of algebraic inequalities. We use this connection to show how some well-known inequalities, such as the standard bounds for the logarithmic function or generalizations of Bernoulli's inequality, can be derived by thermodynamic methods. Additionally, we show that by comparing the global entropy production in processes implemented with decreasing levels of irreversibility but subject to the same change of state of one particular system, we can find progressively better bounds for the real function that represents the entropy variation of the system. As an application, some new families of bounds for the function log (1+x) are obtained by this method.

Intermittent Exponential Synchronization for Memristor-Based Neural Networks With Inertial Items and Mixed Time-Varying Delays

This article investigates the exponential synchronization problem for a class of memristor-based neural networks with mixed time-varying delays and parameter perturbations, and inertial items are considered (MINNs). A periodically intermittent control protocol is designed to guarantee the exponential synchronization between two MINNs. Then, by adopting nonsmooth analysis, Halanay inequality, and Lyapunov theory, the exponential synchronization criteria for MINNs under the proposed controller are obtained. Furthermore, instead of the reduced-order method, the synchronization of MINNs is considered under the framework of the second-order system directly, which is different from existing literature. Some numerical simulations are presented to show the validity of the proposed criteria in the end.

Preference Shifts During Health Shocks: Foreign Tourists’ Expenditure–Price Elasticity Throughout the Pandemic

This study evaluates the changes in the expenditure–price elasticities of foreign tourists in the summer periods of 2019, 2020, and 2021. We first develop a theoretical characterization that combines microeconomic, loss aversion, price inequality and precautionary savings theories. Next, exploiting microdata for more than 34,000 foreign tourists visiting Spain, we estimate OLS and quantile regressions to empirically examine the expenditure elasticities with respect to the prices of transport services, leisure activities and bars and restaurants at the destination (17 regions). We find that (i) the expenditure–price elasticity of transportation (leisure activities) increases (decreases) during the pandemic, whereas that of bars and restaurants remains unchanged, (ii) foreign tourists are comparatively less expenditure–price elastic at high expenditure levels in transportation and bars and restaurants, and (iii) expenditure–price elasticities are highly heterogeneous depending on the origin country. Managerial and theoretical implications of the findings for firms’ pricing strategies are discussed.

Theoretical models of inequality: Examples from rational choice theory and behavioural economics

AbstractUsing illustrations from research on inequality, this essay makes a case for ‘behavioural synthesis’, that is the reconciliation between neo‐classical and behavioural economics. Focusing on selected theories of absolute and relative inequality, we first give a brief critique of utilitarian models that emphasize self‐interested income maximization. Their assumptions are then compared to status‐seeking models of competition where income differences are maximized. These are then contrasted to altruism models that consider other‐regarding preferences that encourage less inequality. We emphasize the value of behavioural economic experiments in testing the competing predictions of these models. We conclude that consolidation among assumptions from neo‐classical and behavioural economics is necessary when it comes to understanding inequality and propose strategies on how it can be done. We specifically identify some empirical shortcomings of these key economic theories of inequality: context‐dependency in the Global South, specificity of reference groups and consistency of measurement. We propose several ways forward, including the relaxation of assumptions of rationality in theoretical models and further fieldwork in developing countries.

Semi-active fuzzy cooperative control of vehicle suspension with a magnetorheological damper

This study attempts to improve the vibration isolation performance of a vehicle suspension system with a magnetorheological damper (MRD) under complex driving conditions. Structure parameter uncertainty, disturbance of the driving process, and response time delay of MRD are all addressed. Firstly, experiments of MRD were carried out in a damping force testing machine to identify the parameters of the MRD adjustable Sigmoid model by the Levenberg-Marquardt optimization algorithm. Then, the parameter identification is verified by comparing experimental and simulation data. Secondly, the state space equations of the suspension system are derived by Newton’s second law. The transfer function from the bounded disturbance input to the control output is obtained based on H∞ control theory. To make the Infinite norm of the system transfer function less than a certain value, three control strategies are proposed: variable structure control (VSC), disturbance rejection control (DRC), and delay tolerance control (DTC). Thirdly, considering these issues together to weaken the effect of disturbances on vehicle driving conditions, a fuzzy cooperative control (FCC) strategy is proposed based on the linear matrix inequality (LMI) theory. Simulation results demonstrate that FCC semi-active vehicle suspension systems conduct effective vibration isolation performance while responding to multiple external disturbances.

Equilibrium pricing mechanism of low-carbon supply chain considering carbon cap-and-trade policy

In the low-carbon supply chain (LSC) network, because of the different carbon emission reduction investment costs and product exhibition costs, members of the same level will show certain competitive behavior. This paper aims to realize the low-carbon development of the supply chain network based on the carbon quota trading system and the risk aversion characteristics of retailers and uses variational inequality theory to construct the network equilibrium model under the constraint of inventory capacity, and designs an improved projection contraction algorithm to solve the model. The results mean that when the retailer is risk averse, the improvement of the risk aversion coefficient (RAC) reduces the manufacturer's carbon emission rate and profit and increases the product sales price and retailer's profit. When the retailer has an inventory capacity constraint, the enhancement of the inventory capacity constraint increases the profit of the manufacturer and the retailer but reduces the emission reduction rate of the manufacturer. If the retailer has risk aversion characteristics and inventory capacity constraints, the manufacturers' profits will increase as RAC increases, while retailers' profits will decrease as RAC increases. In addition, the carbon trading mechanism can promote enterprises to invest in carbon emission reduction and raise the low-carbon level of products.

New stochastic fractional integral and related inequalities of Jensen–Mercer and Hermite–Hadamard–Mercer type for convex stochastic processes

In this investigation, we unfold the Jensen–Mercer (mathtt{J-M}) inequality for convex stochastic processes via a new fractional integral operator. The incorporation of convex stochastic processes, the mathtt{J-M} inequality and a fractional integral operator having an exponential kernel brings a new direction to the theory of inequalities. With this in mind, estimations of Hermite–Hadamard–Mercer (mathtt{H-H-M})-type fractional inequalities involving convex stochastic processes are presented. In the context of the new fractional integral operator, we also investigate a novel identity for differentiable mappings. Then, a new related mathtt{H-H-M}-type inequality is presented using this identity as an auxiliary result. Applications to special means and matrices are also presented. These findings are particularly appealing from the perspective of optimization, as they provide a larger context to analyze optimization and mathematical programming problems.

The views on distributive justice and economic inequality revisited: the political philosophy and the economic perspectives on (in)equality

This review attempts to provide pointers to some of the parallel evolution of the concept of distributive justice put forward by philosophers, political scientists, sociologists, historians, and economists. In political philosophy, debates originating in the 17th century have primarily focused on the conditions for redistribution, the definition of justice, and how to make society more just. These debates have evolved from discussions between egalitarians and utilitarians to modern theories of capabilities and inequality of opportunity. Economic inequality from the economists perspective is often linked to the measurement of socioeconomic conditions at a specific point in time (although initial conditions or future income may also be considered), and often does not include considerations of fairness or institutional guarantees of liberty, equal opportunity, or fair distribution. This review emphasizes that distributive justice and inequality are separate concepts with separate discussions. Political philosophers debate distributive justice along multiple axes, including utilitarian and egalitarian perspectives, as well as theories of ex ante inequality of opportunity and capabilities. In contrast, economists focus on issues such as measurement, the existence of an efficiency/inequality trade-off, and the endogeneity of inequality.

An urban myth? Government involvement in the economy and left–right politics

People frequently assume that attitudes towards the government’s involvement in the economy differentiate left- from right-wing politics. This paper compares this idea to a version of acceptance of inequality theory, where acceptance of inequality is the principal element of left–right competition, but the specific inequality motivating individuals’ left–right choice may differ. Using multilevel regression models with survey data from the World Values Survey, as well as two case studies, this paper finds that: (a) acceptance of inequality is a better context-independent predictor of left-right self-placements around the world; and (b) in the Netherlands and Denmark, the correlation between acceptance of an inequality (regarding class or immigration) and right-wing self-placement is stronger when the specific issue dimension is salient to citizens. However, the paper finds no equivalent interaction effect for attitudes towards economic statism. The evidence thus supports the view that the left–right dimension concerns acceptance of inequality, rather than economic interventionism.

A Fractional-Order Density-Dependent Mathematical Model to Find the Better Strain of Wolbachia

The primary objective of the current study was to create a mathematical model utilizing fractional-order calculus for the purpose of analyzing the symmetrical characteristics of Wolbachia dissemination among Aedesaegypti mosquitoes. We investigated various strains of Wolbachia to determine the most sustainable one through predicting their dynamics. Wolbachia is an effective tool for controlling mosquito-borne diseases, and several strains have been tested in laboratories and released into outbreak locations. This study aimed to determine the symmetrical features of the most efficient strain from a mathematical perspective. This was accomplished by integrating a density-dependent death rate and the rate of cytoplasmic incompatibility (CI) into the model to examine the spread of Wolbachia and non-Wolbachia mosquitoes. The fractional-order mathematical model developed here is physically meaningful and was assessed for equilibrium points in the presence and absence of disease. Eight equilibrium points were determined, and their local and global stability were determined using the Routh–Hurwitz criterion and linear matrix inequality theory. The basic reproduction number was calculated using the next-generation matrix method. The research also involved conducting numerical simulations to evaluate the behavior of the basic reproduction number for different equilibrium points and identify the optimal CI value for reducing disease spread.

Online Learning for Rate-Adaptive Task Offloading Under Latency Constraints in Serverless Edge Computing

We consider the interplay between latency constrained applications and function-level resource management in a serverless edge computing environment. We develop a game theoretic model of the interaction between rate adaptive applications and a load balancing operator under a function-oriented pay-as-you-go pricing model. We show that under perfect information, the strategic interaction between the applications can be formulated as a generalized Nash equilibrium problem, and use variational inequality theory to prove that the game admits an equilibrium. For the case of imperfect information, we propose an online learning algorithm for applications to maximize their utility through rate adaptation and resource reservation. We show that the proposed algorithm can converge to equilibria and achieves zero regret asymptotically, and our simulation results show that the algorithm achieves good system performance at equilibrium, ensures fast convergence, and enables applications to meet their latency constraints.

New Bounds for the Jensen-Dragomir Functional with Applications in Analysis

The normalised Jensen functional is an important functional in theory of inequalities and it has been a subject of study in its own right. In this paper, we establish new bounds for Jensen’s discrete inequality. Also, we improve the basic result of Dragomir through a stronger refinement of Jensens inequality which is then applied to analysis and information theory.

Some new integral inequalities for higher-order strongly exponentially convex functions

Integral inequalities with generalized convexity play an important role in both applied and theoretical mathematics. The theory of integral inequalities is currently one of the most rapidly developing areas of mathematics due to its wide range of applications. In this paper, we study the concept of higher-order strongly exponentially convex functions and establish a new Hermite–Hadamard inequality for the class of strongly exponentially convex functions of higher order. Further, we derive some new integral inequalities for Riemann–Liouville fractional integrals via higher-order strongly exponentially convex functions. These findings include several well-known results and newly obtained results as special cases. We believe that the results presented in this paper are novel and will be beneficial in encouraging future research in this field.

On the parameterized fractal integral inequalities and related applications

The utilization of local fractional calculus to investigate inequalities has become a widespread research method, which has enriched the theory of inequalities. The current study, inspired by this methodology and combined with the parameterized approach, explores a series of novel inequalities in the fractal spaces. Firstly, a fractal Bullen-type inequality with one parameter is presented. Secondly, the integral identity involving two parameters is established in the fractal domains. As an effect of this outcome, we derive a series of parameterized inequalities related to local fractional differentiable functions that are generalized (s,P)-convex and generalized (s,P)-concave at absolute values, respectively. Several special cases are discussed in depth as well. Certain applications concerning the special means, the quadrature formulas and the probability density functions are delivered in the end.

Aggregative Variational Inequalities

We enrich the theory of variational inequalities in the case of an aggregative structure by implementing recent results obtained by using the Selten–Szidarovszky technique. We derive existence, semi-uniqueness and uniqueness results for solutions and provide a computational method. As an application we derive very powerful practical equilibrium results for Nash equilibria of sum-aggregative games and illustrate with Cournot oligopolies.

Matching Candidates to Culture: How Assessments of Organisational Fit Shape the Hiring Process

Organisational fit represents a crucial criterion in the hiring process. This article aims to understand how employers and external recruitment consultants define and apply organisational fit in professional labour markets, such as engineering, marketing and finance. It also investigates how the use of organisational fit in hiring can lead to social bias within these labour markets. It relies on semi-structured interviews with 47 external recruitment consultants who assist employers in these sectors. The article draws on Relational Inequality Theory to demonstrate how hiring managers and consultants use organisational fit to create and justify boundaries between acceptable and unacceptable candidates. Claim-making supports the rationalisation and legitimisation in the exclusion of groups of candidates. The article critically informs human resource management, business and psychology literature that perceive organisational fit as a largely benign criterion for recruitment. It also extends sociological and critical management literature by delineating three main exclusionary mechanisms in matching candidates for organisational fit.

Finite-time bipartite lag synchronization of coupled memristive neural networks with uncertain disturbances via hybrid control

This article is concerned about the finite-time bipartite lag synchronization of coupled memristive neural networks with time-varying delay and uncertain disturbances. To deal with the same and the different transmission lags in practical applications, some appropriate control strategies including two different phases are designed. Compared with some existing literatures of this subject, the restriction of the switching value is relaxed. Then, with the help of stability theory, matrix theory and algebra inequality theory, some Lyapunov-based synchronization criteria are derived. In addition, the settling time is given as a function of the initial values. Finally, the efficacy and accuracy of the suggested theoretical results are demonstrated through numerical examples and their simulations.