This study focuses on the analysis of $C$-class functions, with particular attention given to the development of fixed-point theorems for mappings that satisfy $H$-$(\psi, \phi)$-contractive conditions. The principal aim is to extend fixed-point results to the broader framework of $G_{\mathcal{F}}$-complete metric spaces. This generalized setting provides greater flexibility of contractive mappings, covering cases not addressed by traditional fixed-point theory.
This paper studies the particular class of second order functional differential equations involving casual operators on a function space $L^p_{\mathrm{loc}}(\mathbb{R}_+, \mathbb{R}^n)$. Previous studies\cite{Corduneanu2008,Mahdavi2008} discussed this equations in the following different function spaces$C(\mathbb{R}_+,\mathbb{R}^n)$ and $L^2_{\mathrm{loc}}(\mathbb{R}_+,\mathbb{R}^n)$. We establish the existence and uniqueness of solutions for both linear and nonlinear cases. Our worked based on the resolvent kernel method, Hölder's inequality, and successive approximation techniques. Finally, We provide examples to illustrate our results.
Socialism and egalitarianism in the United States drew, among their principal sources of inspiration, on the work of the novelist Edward Bellamy. His utopian project, articulated in Looking Backward (1888) and Equality (1897), can be read as the outcome of prior experiences of intentional communities-mystical, Fourierist, and especially Owenite-combined with elements taken from republicanism and the North American democratic tradition. Recent theoretical developments in socialist republicanism make it possible to recast Bellamy's anticipations, particularly in a text of agitation and propaganda known as "The Parable of the Water Tank". This piece presents capitalism as a system of impersonal, objective, and political domination, while at the same time positing the self-emancipation of the working class and pointing toward a society-founded on cooperatives and radical democracy-which may be described as a social republic following the model set by the Paris Commune. After a succinct description of some original utopian experiments in the United States, Bellamy's parable is analyzed as well as some of the very early criticisms launched against it within the socialist field. Lastly, a reply-that intends to be a defense-is presented drawing from contemporary socialist republicanism.
The following paper aims to reflect on the exclusionary character of the Renaissance Republic of Venice. Famous for its great longevity, and stability-which earned it the title of serenissima-we argue that the perspectives of Niccol & ograve; Machiavelli and William Shakespeare allow us to elucidate its segregatory and expulsive character. Thus, through the works of the Florentine thinker and the English poet's comedy The Merchant of Venice, we seek to problematize the image of a Venice serenissima and the impossibility of a republic-whether more popular or more aristocratic-that would allow for a perfect ordering without exclusions or latent conflicts.
The relationship between Machiavelli and Lucretius is one of the most intriguing topics in contemporary interpretations of the Florentine thinker. Beginning with a brief overview of this encounter, we propose to follow Lucretius's lead to address-in discussion with J. G. A. Pocock's interpretation-the problem of political temporality in Machiavelli. Considering Machiavelli's analysis of the difference between the temporalities of the principality and the republic, we will propose a materialist reading of republican temporality to argue why this mode of political life is in better conditions to respond to the movement, mutation, and-more radically-the finitude of all political order. We will conclude with an analysis of the status of novelty, in which transformative forces and hopes for renewal enter into a critical tension in times of crisis.
In this article, we revisit republican interpretations of Niccol & ograve; Machiavelli and his work in order to reflect on the current political situation in Argentina. The starting point for this piece was a speech given by the current Argentine president, Javier Milei, at the annual meeting of the World Economic Forum in Davos. It was on that occasion that Milei uttered the phrase "Machiavelli is dead," which we take as an excuse to analyze libertarian politics from a republican perspective. The aim of this article is to contribute to the characterization of contemporary radical right-wing movements, while decoding the meanings of Machiavelli's work in relation to libertarian political practices.
This article adopts Hannah Arendt's theory to reflect on two opposing conceptions of freedom: one depoliticized and possibly anti-political,and the other political,republican, and democratic. In particular, it reconstructs her arguments regarding the depoliticization of freedom, her critique of liberalism, and her defense of "political freedom." This analysis is part of a diagnosis of the current Argentine political scenario linked to the fragility of republican institutions and the crisis of democratic representation. Using Arendt's concept of freedom, it will be possible to delve into ways of understanding some of the contemporary tensions between liberalism, republicanism, and democracy. Furthermore, this interpretative framework will allow us to address certain dimensions of the question of "republican temporality".
The aim of this article is to reconstruct the different forms assumed by the concept of the "national-popular" in the work of the Argentine intellectual Juan Carlos Portantiero. The article traces the uses of this concept in his early writings, where it served as a basis for a critique of the positions of Argentine communism; in his works of the 1960s and 1970s, in which it fostered an approximation between Marxism and Peronism; and in his writings of the 1980s, where the concept was ultimately closed off within the horizon of democratic socialism.
In this study, the stochastic Kakutani-Matsuuchi equation (SKME) forced by a multiplicative stochastic term is considered. The Kakutani-Matsuuchi equation is a fundamental tool for analyzing internal gravity waves in fluid dynamics, particularly in geophysical contexts such as oceanography and meteorology. Internal gravity waves occur in stratified fluids where density variations are influenced by gravity, leading to fascinating phenomena among different layers of fluid. Due to the importance of the Kakutani-Matsuuchi equation in examining the waves of internal gravity in the oceans and atmosphere, the solutions of the SKME can help us comprehend a variety of exciting scientific phenomena. Utilizing two distinct techniques, namely the Sardar sub equation technique and the Jacobi elliptic function method, we derive novel bright and dark solitons, periodic solitons, as well as kink and anti-kink soliton solutions for the SKME. Moreover, we show many 3D and 2D graphs illustrating the influence of noise on SKME solutions.
This paper presents a methodological approach where students are provided with erroneous or non-rational solutions to problems to enhance their learning process. Specifically, the study focuses on equations and inequalities with absolute value. The proposed incorrect or non-rational solutions to equations and inequalities involving absolute value help students to identify mistakes, analyze them, and correct their misconceptions, thereby facilitating deeper understanding of the material. After presenting each erroneous solution, an analysis and explanation follow, guiding students toward the correct and rational solution. This study demonstrates the significant advantages of using erroneous solutions to engage students in deeper reflection, foster self-correction, and develop a critical attitude towards problem-solving in mathematics education.
Medical diagnosis systems frequently rely on structured information collected during physician-patient interviews. These data naturally follow a hierarchical organization, where general questions are followed by more specific sub-questions. Such a structure should be explicitly incorporated into similarity measures used in classification algorithms, as it reflects dependencies between symptoms and contributes essential diagnostic information. In this work, we introduce a kernel that simultaneously accounts for (i) the hierarchical structure linking main questions to their subordinate items and (ii) interactions among sub-variables. The kernel is integrated into the pgpDA classification framework, allowing the method to embed prior knowledge on how variables are organized and how symptoms interact. The proposed kernel is designed for binary data arranged in two-level tree structures and supports interaction modeling of any given order. Experiments conducted on simulated data and a real verbal autopsy dataset from Senegal demonstrate consistent improvements over classical kernels, and a deep-learning benchmark confirms that the structured kernel retains strong predictive power even in modern architectures. The methodology may be extended to mixed data types or adapted to graph-structured symptom networks.
This study focuses on the analysis of C-class functions, with particular attention given to the development of fixed-point theorems for mappings that satisfy H-( psi, phi)-contractive conditions. The principal aim is to extend fixed-point results to the broader framework of GF-complete metric spaces. This generalized setting provides greater flexibility of contractive mappings, covering cases not addressed by traditional fixed-point theory.
This paper introduces strong fuzzy planar graphs (SFPLGs), extending fuzzy graph theory with a quantitative planarity measure theta(ohm) = 1/1+Sigma(n)(i=1) Lambda(theta(i)) that classifies networks as strong or weak based on controlled edge crossings. Formal definitions establish fuzzy strong-weak arcs, face memberships, dual graph constructions, and key theorems, including the 0.67 threshold that prohibits strong-strong intersections and maintains planarity values through isomorphism. Theoretical results reconcile classical Kuratowski's graphs with fuzzy gradations. The framework proves effective in the planning of the traffic network, modelling a 10 urban core intersections with vertex memberships of 0.70 - 0.90 and edge strengths revealing connectivity bottlenecks CONN limited by weak segments 5 - 10, 9 - 10 at 0.70. Strong edges form reliable backbones, while weak links identify upgrade priorities, balancing costs with necessary intersections in environments with uncertain capacities. SFPLGs provide transportation engineers with interpretable tools for durable infrastructure design, with zero-crossing embeddings verifying planarity and edge analysis guiding investments. Future work will investigate dynamic traffic data, multi-layer networks, and intuitionistic variants.
In this paper, we consider the concepts of uni-soft left and uni-soft right ideals, uni-soft quasi-ideals, and uni-soft bi-ideals within the context of ordered semigroups. We demonstrate that in ordered semigroups, both uni-soft right and uni-soft left ideals exhibit properties of uni-soft quasi-ideals. Similarly, uni-soft quasi-ideals possess characteristics of uni-soft bi-ideals. Furthermore, our analysis establishes that the definitions of uni-soft quasi-ideals and uni-soft bi-ideals align, indicating their equivalence within this specific class of semigroups. Additionally, we prove that in an ordered semigroup, uni-soft quasi-ideals can be understood simply as the unions of unisoft right and uni-soft left ideals. This elucidates the relationship between these concepts, shedding light on their fundamental role in the structure of ordered semigroups.
A subset S of the vertex set V(G) of a graph G is called an equitable fair dominating set of G if S is an equitable dominating set of G and for any v, w is an element of V(G) \ S, NG(v) f1 S = NG(w) f1S >= 1. The equitable fair domination number of G, denoted by gamma efd(G), is the minimum cardinality of an EFD-set of G. The set S is called an equitable k-fair dominating set (abbreviated EkFD-set) of G if NG(v) f1S = k for any v is an element of V(G)\S, where k is a positive integer. The equitable k-fair domination number of G, denoted by gamma kefd(G), is the minimum cardinality of an EkFD-set. An equitable k-fair dominating set of cardinality gamma kefd(G) is called a gamma kefd-set of G. In this paper, we characterize the notions of equitable k-fair domination in graphs, study the EkFD-sets under some binary operations of graphs, and determine exact values or bounds for this domination variant.
Performing a thought study of fractional inequalities by means of convexity and fractional operators has conspicuous work in the field of analysis. The main object of this paper is to discuss the coordinated convexity, pre-invexity, and also establish fractional double integral operators (FDIO) having generalized Bessel-Maitland function as its kernel. We develop a new generation of Hermite-Hadamard (H-H) and trapezoid-type inequalities through different types of coordinated convexities and pre-invexities with successful implementation of newly designed fractional double integral operators. Moreover, we extract some corollaries, which are generalizations of well-known inequalities for different coordinated convexities that show a strong consolidation of our main results.
The present study develops a generalised version of the exponential Lord-Shulman thermoelasticity theory that takes into account the combined effects of body forces and time-harmonic thermal sources. The appropriate governing equations are generated and analytically solved by means of the harmonic wave technique, assuming that the medium under discussion is traction-free. Displacements, dilatation, temperature distribution, and stress components are among the non-dimensional findings for field variables. Comprehensive numerical evaluations are used to support the explicit analytical formulas developed for these variables. Examining how the operator expansion order and temporal evolution affect the physical fields' behaviour is assumed particular attention. The significance of higher-order modelling in capturing complex dynamic thermo elastic responses is highlighted by graphical representations that unequivocally show that the operator expansion order plays a crucial role in influencing all thermo elastic parameters.
This paper studies the particular class of second order functional differential equations involving casual operators on a function space Lploc(I[8+, I[8n). Previous studies [1, 2] discussed this equations in the following different function spaces C(I[8+, I[8n) and L2loc(I[8+, I[8n). We establish the existence and uniqueness of solutions for both linear and nonlinear cases. Our worked based on the resolvent kernel method, Ho & uml;lder's inequality, and successive approximation techniques. Finally, we provide examples to illustrate our results.
Conditional distribution estimation (CDE) is central in nonparametric forecasting and risk analysis. While considerable progress has been made for finite-dimensional and stationary settings, functional data and nonstationary settings pose new challenges. We propose a Nadaraya-Watson (NW) conditional quantile estimator for regularly mixing locally stationary functional time series (LSFTS). It incorporates three kernel functions: one for time rescaling, another for functional covariates, and an integrated kernel that serves as the cumulative distribution function (CDF) of the response variable. A theoretical framework and the estimator's uniform convergence were provided. To demonstrate the estimator's consistency, a numerical experiment was conducted. Finally, we apply the method to financial data, specifically the Nikkei 225.
