A generalized system of triple fractional stochastic differential variational inequalities with Lévy jumps

Fourier-Motzkin elimination is a fundamental operation in polyhedral geometry. It can be performed by several equivalent procedures, and can be regarded as an adaptation of Gaussian elimination to systems of linear inequalities. These procedures tend to generate large numbers of redundant inequalities. Efficiently detecting these redundancies is essential for obtaining software implementation of practical interest. In this paper, we propose a novel detection technique. We demonstrate its benefits over alternative approaches. A detailed experimentation is reported.

This paper presents an optimal -induced control problem for systems with multiple sector-bounded nonlinearities. Sufficient boundedness conditions for the -induced norm are derived in terms of a specific system of linear matrix inequalities (LMIs). Based on these conditions, an optimal state feedback control problem is then formulated and solved for the considered class of nonlinear systems. A procedure to reduce the conservatism of the derived conditions is also provided. The proposed formulation, which explicitly considers multiple sector-bounded nonlinearities, is useful because it enables optimal -control problems for a much wider class of nonlinearities. Indeed, by invoking the universal approximation theorem, one may represent nonlinearities that do not satisfy sector-bounded conditions as a weighted sum of sector-bounded sigmoid functions. The theoretical and procedural developments are illustrated by a numerical example consisting of the state feedback optimal -induced control of a forced van der Pol oscillator.

Optimal $L^{\infty }$-error analysis for parabolic systems of quasi-variational inequalities with nonlinear source terms

The essay summarizes the data collected in a research, which is still in progress, conducted by the Tempi Moderni study centre on the condition of the Rom communities in Italy. It is based on two fundamental theses. First of all, on the fact that the system of inequalities experienced by Rom people is multidimensional. These dimensions influence each other on a material level and turn the relationship between cause and effect, legitimising widespread prejudice and discrimination against the Rom community. These prejudices are reconstructed also from a historical point of view, and the essay focuses mainly on employment and housing inequality. The second thesis analyzes the system of complex disparities affecting Rom communities within the system of inequalities and discriminations typical of Italian and global society. Inequality, poverty and work segregation are therefore the consequences of political choices aimed at marginalizing the numerous Rom communities and legitimizing widespread and dangerous commonplaces and prejudices.

Approximating Inequality Systems Within Probability Functions: Studying Implications for Problems and Consistency of First-Order Information

Abstract Program verification using abstract interpretation involves the symbolic calculation of fixpoints over lattices. Integral to these fixpoint calculations is widening, an operation that trades precision for guarantees of termination. Abstract interpretation often works with lattices of convex sets of points in n-dimensional space, represented by sets of linear inequalities. When the form of these inequalities is restricted these are known as weakly relational domains. This paper addresses weakly relational domains, the detail of their representation and the way in which widening is applied, including study of how the closure operators used in weakly relational domains interact with widening, and considers how sequences of constraints might be widened. Satisfiability checking for numeric constraints is one tool used in this work.

Mixed finite element method for a system of hemivariational inequalities of Navier-Stokes equations coupled with the heat equation

This paper examines the concept of power as a dynamic force shaped by physical strength, emotional intelligence, and socio-cultural structures, with a particular focus on the theoretical framework of New Historicism. Drawing on the ideas of Stephen Greenblatt and Catherine Gallagher, the study explores how power operates not only through political authority and institutional dominance but also through subtle cultural practices, empathy, and narrative control. Historically, power has evolved from basic survival needs such as food and shelter to complex systems of domination, including colonialism, caste, class hierarchies, and gender inequalities. Although the modern era claims progress, traditional structures continue to shape social relations, especially in areas such as feminism, and social justice, revealing the persistence of power in everyday life. The research applies Greenblatt’s three modes of power empathy, displacement, and narrative identity to Flights by Olga Tokarczuk, particularly through the biographical narrative of Philip Verheyen. The study demonstrates how empathy functions as a strategic and transformative tool in both personal and historical contexts. Through the relationship between Verheyen and his mentor Baruch Spinoza, the paper highlights how emotional understanding can enable access to education, social mobility, and intellectual authority. The role of caregivers, mentors, and institutions further illustrates the ethical dimension of power when it is used for social and individual development. Ultimately, this paper argues that power is not merely coercive but also constructive when mediated through compassion, knowledge, and narrative agency. By situating Tokarczuk’s work within a New Historicist framework, the study reveals how historical consciousness and literary imagination intersect to produce alternative understandings of authority, identity, and human resilience. The research concludes that empathy remains a crucial mode through which individuals negotiate power and reshape both personal and collective histories in contemporary society.

In [Croatian Oper. Res. Rev. 13 (2022), 131–135], it was shown that the Lipschitz continuity condition with respect to the first and/or second variable has been misapplied in prior literature on systems of variational inequalities. This paper corrects errors in previous work by M. A. Noor and K. I. Noor by introducing a new iterative method.

Abstract This paper investigates the approximation of fixed points for quasi-nonexpansive mappings in Banach spaces using the general Picard-Mann (GPM) algorithm. Under mild conditions such as the demiclosedness of $$I - \digamma $$ I - ϝ at zero and the Opial property, we derive weak and strong convergence theorems for the iterative sequences generated by the GPM method. We establish several stability results for the GPM scheme, including summably almost stability property for quasi-contractive mappings. The theoretical findings are applied to the classical relaxation method for solving systems of linear inequalities, demonstrating the practical relevance of our approach. Numerical examples in $$\mathbb {R}^4$$ R 4 and $$\ell ^2$$ ℓ 2 are provided to illustrate the efficiency and convergence behavior of the proposed algorithm. The results presented herein extend and complement existing work in fixed point theory and iterative approximation methods.

A note on the error bound at infinity for nonconvex inequality systems via asymptotic analysis

Mathematics learning at the high school level still shows various problems, especially in students' mathematical problem-solving abilities on the material of two-variable linear inequality systems, which is characterized by many student errors in solving problems in the form of problem solving. This study aims to identify the types of errors made by class X students of SMA and the factors causing errors in solving mathematical problems on the material. This study uses a qualitative approach with a descriptive method, with the research subjects being class X students of. Data collection was conducted through written tests and interviews, while data analysis included data reduction, data presentation, and conclusion drawing. Analysis of student errors was based on Polya's problem-solving stages combined with the Newman Procedure. The results showed that students made four types of errors: errors in understanding the problem, errors in creating a solution plan, errors in implementing the plan, and errors in rechecking the final answer. The most dominant error occurred at the stage of implementing the plan with a percentage of 59.1%, while the least error occurred at the stage of understanding the problem at 17%. Factors causing errors included a lack of understanding of the basic concepts of two-variable linear inequality systems, an inability to transform contextual problems into mathematical models, weak skills in drawing graphs and determining the solution region, and students' low habit of rechecking their answers. Based on these findings, it can be concluded that student errors are conceptual and procedural in nature, so mathematics learning is recommended to emphasize conceptual understanding, strengthening procedural skills, and the habit of reflection and rechecking in the process of mathematical problem solving.

Abstract Compared with monostatic active sonar, multistatic active sonar employs multiple spatially distributed nodes for transmitting and receiving detection signals, which has excellent spatial diversity gain. To overcome the limitations of monostatic sonar systems in low signal-to-noise ratio (SNR) environments, this paper proposes a multistatic active detection framework based on Doppler feature extraction and fusion. First, a Doppler feature extraction method is proposed using Robust Adaptive Chirp Mode Decomposition combined with Wigner–Ville Distribution (RACMD–WVD). Adaptive Chirp Mode Decomposition (ACMD) is introduced to effectively suppress cross-term interference in echoes containing multiple highlights, while a robust pre-estimation strategy for frequency significantly improves the accuracy of Doppler factor estimation under low SNR. Second, a multi-perspective Doppler feature fusion method is developed. By exploiting the spatial consistency constraints among the observed angles and Doppler features from multiple nodes, a system of inequalities is constructed. The presence of a target is determined and its true motion parameters are recovered by solving the common feasible region of these constraints. Finally, both simulations and the south China sea experiment validate the effectiveness and robustness of the proposed method in low-SNR environments. The experimental results further confirm that the proposed framework not only attains optimal detection stability but also achieves a substantial enhancement in motion-parameter reconstruction—specifically, it reduces heading error by 25.1% and speed error by 15.6% relative to compared methods. Although the proposed framework is developed and validated within a multistatic sonar context, it’s core methodology could be potentially extended to other multi-sensor systems, such as radar or seismic arrays, for moving target detection.

A New Differential Variational-Hemivariational Inequality System and Its Applications

Liouville-Type Results for a System of Parabolic Inequalities on Locally Finite Graphs

The present paper is focused on the computation of the Lipschitz upper semicontinuity modulus of the feasible set mapping in the context of fully perturbed linear inequality systems, i.e. where all coefficients are allowed to be perturbed. The direct antecedent comes from the framework of right-hand side (RHS, for short) perturbations. The difference between both parametric contexts, full versus RHS perturbations, is emphasized. In particular, the polyhedral structure of the graph of the feasible set mapping in the latter framework enables us to apply classical results as those of Hoffman [On approximate solutions of systems of linear inequalities. J Res Natl Bur Stand. 1952;49:263–265] and Robinson [Some continuity properties of polyhedral multifunctions. Math Progr Study. 1981;14:206–214]. In contrast, the graph of the feasible set mapping under full perturbations is no longer polyhedral (not even convex). This fact requires ad hoc techniques to analyse the Lipschitz upper semicontinuity property and its corresponding modulus.

ABSTRACT This article examines how workplace fertility governance operates as a system of control, consent, and inequality shaped by organizational, cultural, and institutional forces. Drawing on feminist theory, we develop a multilevel framework of cascading accountability that integrates symbolic violence, biopolitics, chrononormativity, and postfeminist agency to analyze how corporate fertility benefits simultaneously expand and constrain reproductive autonomy. Using feminist thematic analysis of media coverage, corporate materials, digital lived experiences, and independent reports, we show how fertility support schemes reinforce normative timelines, managerial control, and affective expectations, particularly for structurally marginalized groups such as migrants, LGBTQ+ workers, and racialized minorities. Throughout this paper, fertility governance is treated not as a women's issue per se but as a system regulating reproductive capacity across differently gendered bodies, including cisgender, transgender, and nonbinary workers. Theoretically, we synthesize Bourdieu's and Foucault's insights with feminist critiques to demonstrate how reproductive governance unfolds across macro, meso, and micro levels. Practically, we argue for a shift from discretionary benefits to rights‐based policies grounded in reproductive justice, centering the lived experiences of those whose reproductive needs fall outside normative models.

An Adaptive Inverse-Free Robust DZNN for Solving Future Linear Equation and Inequality Systems With Manipulator Application

A novel penalty approach for a system of quasivariational-hemivariational inequalities