This article examines the political and philosophical legacy of the American conservative thinker Irving Babbitt (1865–1933), his approach to social conflicts and social policy. Irving Babbitt taught history of literature at Harvard, and his philosophy was built on the idea of emulating the best examples of self-discipline of the past. According to Babbitt, self-restraint by the strong strengthens the ethical union that underlies social relations. Self-restraint of the powerful strengthened the ethical union that serves as foundation for social relations. Without self-restraint according to role models, human aspirations become limitless, leading to conflict. To overcome the social conflicts created by the competitive market, it was necessary to develop education, educate the elites with examples of virtue, and teach them self-restraint and fairness, so that other members of society would follow their example and achieve social peace. The problem of inequality is solved by equalizing desires, not property. Babbitt’s ideas can be useful for adapting modern social policy systems to new challenges and preventing social conflicts.

The article is devoted to the analysis of feminine nominations in the narratives of military media communication in the linguistic and gender aspect. The research focuses on the identification and interpretation of linguistic means that reflect the change in gender roles and the representation of women’s experience in the realities of the Russo-Ukrainian war. Particular attention is paid to the formation of a female narrative of heroism, which affirms the image of a woman as an active participant in armed resistance, equal to men in the performance of military duty. The representative, identification, mobilization, and symbolic functions of feminine lexemes, which are increasingly used in journalistic discourse to name women serving in the Armed Forces of Ukraine or performing other roles in the war, are noted. The active presence of names for female persons in the headlines and texts of various genres of journalistic materials – news, reports, interviews, articles, – is observed. This is due to a number of factors: linguistic economy, attracting the audience’s attention, demonstrating editorial policy, gender differentiation, ensuring social visibility. Differentiation of the most common thematic groups of feminine media nominations (names by military positions and ranks, combat functions, technical or special training, medical and humanitarian role of women, status of participation in the war) showed that gender narratives of wartime demonstrate a gradual departure from traditional stereotypes, where women appear mainly as a symbol of motherhood, care or logistical support. At the same time, certain gender stereotypes still persist in military media communication. Quite often, the image of a female soldier is presented through the prism of a double standard: she “breaks the perception”, “impresses”, “proves” that she can be no worse than men. Such discourse, despite its positive connotation, hides a shade of comparison and the need for women to “assert themselves” in a traditionally male sphere (Santoniccolo et al., 2023). Modern Ukrainian media increasingly raise the issue of gender prejudices and manifestations of sexism that women face at the front, which indicates the growing sensitivity of society to the problems of gender equality. The most common word-forming models of feminine nominations have been identified: -к-а (воячка, воїнка, снайперка, піхотинка, волонтерка, солдатка, командирка); -иц-я (військовослужбовиця, захисниця, розвідниця, кулеметниця, гранатометниця); -ин-я (бійчиня, медикиня), two-component names (операторка БПЛА, військова ЗСУ). The results obtained show that the active functioning of feminine lexemes in military media communication not only linguistically reflects sociocultural transformations, but also contributes to the formation of a new, more balanced gender narrative of heroism, free from stereotyping.

Abstract The purpose of this paper is to extend the definition of quasi-arithmetic means by taking a strictly monotone generating function instead of a strictly monotone and continuous one. We establish the properties of such means and compare them to the analogous properties of standard quasi-arithmetic means. The comparability and equality problems of generalized quasi-arithmetic are also solved. We also provide an example of a mean which, depending on the underlying interval or on the number of variables, could be or could not be represented as a generalized quasi-arithmetic mean.

CQ-algorithms for the related problems of split equality problem in Hilbert spaces

We initiate the focused study of constant-cost randomized communication, with emphasis on its connection to graph representations. We observe that constant-cost randomized communication problems are equivalent to hereditary (i.e. closed under taking induced subgraphs) graph classes which admit constant-size adjacency sketches and probabilistic universal graphs (PUGs), which are randomized versions of the well-studied adjacency labeling schemes and induced-universal graphs. This gives a new perspective on long-standing questions about the existence of these objects, including new methods of constructing adjacency labeling schemes. We ask three main questions about constant-cost communication, or equivalently, constant-size PUGs: (1) Are there any natural, non-trivial problems aside from Equality and k-Hamming Distance which have constant-cost communication? We provide a number of new examples, including deciding whether two vertices have path-distance at most k in a planar graph, and showing that constant-size PUGs are preserved by the Cartesian product operation. (2) What structures of a problem explain the existence or non-existence of a constant-cost protocol? We show that in many cases a Greater-Than subproblem is such a structure. (3) Is the Equality problem complete for constant-cost randomized communication? We show that it is not: there are constant-cost problems which do not reduce to Equality.81 pages. This is the TheoretiCS journal version

The split equality problem has gained significant recognition due to its widespread applicability across various applied mathematical fields. In this present paper, a hyperplane projection algorithm is introduced for solving the split equality problem in Hilbert spaces. This algorithm integrates the hyperplane projection technique with the gradient projection method, utilising Polyak's step sizes for efficient convergence. The weak convergence of our proposed algorithm is demonstrated as well as its relaxed version. Under mild conditions, the strong and linear convergence of the algorithms is established. Numerical experiments conducted on signal recovery problems reveal that our algorithm accelerates the convergence rate and outperforms some existing algorithms.

This study focuses on the equalization problem of the filter bank multicarrier system based on offset quadrature amplitude modulation (FBMC/OQAM) in underwater acoustics and proposes an innovative joint time–frequency-domain equalization (JTFDE) algorithm. The algorithm combines frequency-domain Minimum Mean Square Error (MMSE) equalization with time-domain adaptive decision feedback equalization, effectively addressing the shortcomings of traditional single-domain equalization methods in terms of multipath interference suppression and time-varying channel tracking. By first using frequency-domain linear equalization to preliminarily eliminate multipath interference, and then combining it with time-domain Recursive Least Squares (RLS) adaptive decision feedback to further suppress residual interference, the system performance is significantly improved. The experimental results show that compared with existing single-domain equalization methods, this scheme reduces the bit error rate at the system receiver and enhances the system’s interference resistance.

Neurodynamic optimization algorithm for split equality problems and application to sparse signal recovery

Inertial projection-type algorithms for systems of split equality problems in Hilbert spaces

This research discusses the concept of justice according to Syed Muhammad Naquib Al-Attas as an alternative solution to the problem of contemporary gender equality. The aim is to describe the meaning of justice ('adl) according to Al-Attas and examine its relevance in responding to demands for absolute equality between men and women. The method used is a literature study with a qualitative approach and content analysis of Al-Attas' works related to the concept of justice and human nature. The results show that justice, in Al-Attas' view, is a harmonious condition when everything is in its place and function in accordance with the nature and purpose of creation. In the context of gender, justice does not mean uniformity of roles, but rather fair placement based on the rights, responsibilities, and natures of each. The novelty of this research lies in offering a paradigm of fitrah-based justice as a critique of the Western concept of gender equality. The implication is that this approach can prevent misunderstanding of gender differences while emphasising the importance of the Islamic worldview in building fair and harmonious gender relations.

We introduce an unconstrained optimization approach to solving mixed split feasibility problems in Hilbert spaces. We use a method of selecting the control parameters so that the implementation of our algorithms does not require prior information on the transfer mapping norms. This avoids the difficult task of estimating these norms. Besides, we also present applications to solving the split feasibility problem with multiple output sets and to solving split equality problems. Finally, we exhibit three numerical examples which bring out the efficiency of our proposed algorithms when compared with some existing ones.

The level of arithmetic knowledge of a high school student was explored when solving additive word problems considering the semantic structure and syntactic component. The methodology was qualitative and developed in four stages: the first is the selection of the participant, the second is the design of a questionnaire with twenty additive problems, the third is the application of the semi-structured interview and questionnaire for the student to solve, and the fourth is the analysis of the data to identify the arithmetic knowledge. The results show that the student is at level 4 (directional relations level) solving comparison and equalization problems. However, he had difficulty in one of the comparison problems (incorrect application of the operation), but successfully solved the change, combination and equalization problems. It is concluded that the student can reinforce the comparison structure to have arithmetic knowledge of level 4 in its entirety.

This paper tracks Indian EV growth from 2013 to 2024. It covers important trends, government actions, infrastructure upgrades, and stakeholder impacts. The statistics show strong increase, especially in two and three-wheelers. This is due to rising petrol prices, urban mobility demand, and cost effectiveness. Fourwheeled electric automobiles are still in development, but they have made progress. This growth shows consumer confidence and technology advancement. The National Electric Mobility Plan (NEMMP), FAME I and FAME II, and Production Linked Incentive (PLI) programs have helped India buy and make electric vehicles. The uneven distribution of Public Charging Stations among states raises equality problems. Urban areas like Delhi and Maharashtra have the most infrastructure, while northeastern and remote areas lack it. The analysis shows that India is moving towards electric vehicles, but a collaborative, inclusive, and fair strategy is needed to ensure stakeholder acceptance and sustainability

The article is devoted to the analysis of the category of “justice” through the prism of the problem of social equality. It is noted that in the pre-modern naturalistic paradigm of philosophizing, where the main narratives were the correspondence of the social order to the eternal natural law, justice was associated with inequality and the principle of hierar-chy. Moreover, just hierarchy concerned both the internal spiritual qualities of the person himself, where reason should rule over passions, and the gender-social organization of society, where a man is superior to a woman, a Greek is superior to a barbarian, and so on. Within the framework of this naturalistic paradigm Plato`s and Aristotle’s approving attitude towards slavery should be understood, because from their point of view the soul itself can be slavish and cowardly by nature or, conversely, brave and freedom-loving. In the medieval paradigm of philosophizing, the conceptual connection of jus-tice-inequality is preserved; however, philosophers appeal more to divine law and divine justice. It is noted that in this epoch did emerge the concept of a “just war” as a sacred moral duty to protect the innocent. This concept of a just war remains relevant to this day, in Ukrainian military realities. In the era of the Enlightenment, with the advent of the new European paradigm of philosophizing, where the emphasis is on the rational subject and his will to power, justice began to be understood precisely as equality, as evi-denced by the philosophical tradition begun by I. Kant and continued in the twentieth century in the theories of justice of J. Rawls and J. Habermas.

Abstract In this paper we consider the equality problem of generalized Bajraktarević means, i.e., we are going to solve the functional equation which holds for all $$x=(x_1,\dots ,x_n)\in I^n$$ x = ( x 1 , ⋯ , x n ) ∈ I n , where $$n\ge 2$$ n ≥ 2 , I is a nonempty open real interval, the unknown functions $$f,g:I\rightarrow \mathbb {R}$$ f , g : I → R are strictly monotone, $$f^{(-1)}$$ f ( - 1 ) and $$g^{(-1)}$$ g ( - 1 ) denote their generalized left inverses, respectively, and the vector-valued weight functions $$p=(p_1,\dots ,p_n):I\rightarrow \mathbb {R}_{+}^n$$ p = ( p 1 , ⋯ , p n ) : I → R + n and $$q=(q_1,\dots ,q_n):I\rightarrow \mathbb {R}_{+}^n$$ q = ( q 1 , ⋯ , q n ) : I → R + n are also unknown. This equality problem in the symmetric two-variable case (i.e., when $$n=2$$ n = 2 and $$p_1=p_2$$ p 1 = p 2 , $$q_1=q_2$$ q 1 = q 2 ) was solved under sixth-order regularity assumptions by Losonczi in 1999. The authors of this paper improved this result in 2023 by reaching the same conclusion assuming only first-order differentiability. In the nonsymmetric case, assuming the third-order differentiability of f, g and the first-order differentiability of at least three of the functions $$p_1,\dots ,p_n$$ p 1 , ⋯ , p n , Grünwald and Páles proved that (*) holds if and only if there exist four constants $$a,b,c,d\in \mathbb {R}$$ a , b , c , d ∈ R with $$ad\ne bc$$ a d ≠ b c such that $$\begin{aligned} cf+d>0,\qquad g=\frac{af+b}{cf+d},\qquad \text{ and }\qquad q_\ell =(cf+d)p_\ell \qquad (\ell \in \{1,\dots ,n\}). \end{aligned}$$ c f + d > 0 , g = a f + b c f + d , and q ℓ = ( c f + d ) p ℓ ( ℓ ∈ { 1 , ⋯ , n } ) . The main goal of this paper is to establish the same conclusion under first-order differentiability.

We establish a correspondence between Lorenz curves and Pickands dependence functions, thereby reframing the construction of any bivariate extreme-value copula as an inequality problem. We discuss the conditions under which a Lorenz curve generates a closed-form Pickands model, considerably expanding the small set of tractable parametrizations currently available. Furthermore, the Pickands measure-generating function M can be written explicitly in terms of the quantile function underlying the Lorenz curve, providing a constructive route to model specification. Finally, classical inequality indices like the Gini coincide with scale-free, rotation-invariant indices of global upper-tail dependence, thereby complementing local coefficients such as the upper tail dependence index λU.

One of problem discussed among scholars including orientalists is the difference in qira'at which has implications for interpretation in various aspects. This study aims to explain some opinions of orientalist scholars and Muslim scholars in response to the difference in qira'at. In addition, the study aims to see and analyze the implications of the difference in qira'at in several interpretations. The research method used is a qualitative method based on library research data with a descriptive-analytical approach. The findings of this study state that according to orientalists, the difference in qira'at will cause contradiction and chaos in determining the law. Meanwhile, according to Muslim scholars, differences in qira'at are a form of variation that will not alter the legal substance of the Quran. Besides that, there will be no conflict, change, or even chaos, because the Prophet conveyed qira'at according to the dialects of each tribe and nation. However, the difference in qira'at will have implications for four things, namely theological problems, fiqhiyah problems, gender equality problems, and miracle of the Qur’an itself.

The article is devoted to the problem of research of the axiological sphere of public relations in the concepts of modern political philosophy. In modern conditions, it should be noted the emergence of a new qualitative feature of sociality - the influence of metaphysical reflections on the state of social relations. The most acute problem in social research remains the persistent crisis of human existence, the trends of which reveal destructive realities that provoke a negative outlook for social development. This provokes the proliferation of subjectivist interpretations of the main categories of social and political philosophy. New forms of nihilism not only question the content of traditional values, but also attempt to eliminate values as such from the system of forms of social consciousness. In the fundamentals of the philosophical approach, the reason for this state of affairs can be stated as extreme forms of individualism. This suggests that the modern era can be considered as a stage of fulfillment of prophecies of metaphysical reflections on the inadmissibility of unification and depersonalization of man. In particular, the complexity of the category of justice has always been associated in philosophy with the need to solve the problem of the relationship between the general and the singular in being. This article substantiates the special importance of the principle of justice in revealing the current state of public relations. In modern conditions, the concepts of social and political philosophy maintain continuity with the previous analysis of this phenomenon in terms of revealing the problems of justice through the problems of equality and human dignity. That is why the relationship between two social principles remains debatable - the principle of justice and the principle of legitimacy. At the same time, due to significant changes in the social environment, special attention is needed to analyze the influence of philosophical reflections on the modern understanding of justice. In particular, this article highlights the importance in modern conditions of distinguishing the understanding of justice as the foundation of social institutions and justice as a virtue of an individual. This trend arises from the inevitability of recognizing the traditional consideration of the principle of justice in connection with the category of the common good. Due to the changing forms of social normativity in modern society, modern concepts of political philosophy pay attention to the destructive risks of attempts to formalize the norms of justice. The latter poses a threat to the stability of virtue in human life. At the same time, a certain epistemological bias in the analysis of the principle of justice becomes clear due to the influence of philosophical reflections. This is evidenced by the logic of the available research: from the analysis of everyone’s reasoned judgments about justice to the study of the real principles of justice, taking into account all relations of normativity. The principle of justice is derived from human needs, but it is still linked to the principles of equality, merit and neediness. There is a continuity with the thesis of previous concepts that justice in general is achievable only with an active human position in achieving the common Good. At the same time, in connection with the processes of digitalization of public relations today, it is necessary to take into account the anthropogenic impact on the principle of justice, but this is particularly indicated by the concepts of the political philosophy of technology. The complexity of social analysis actualizes the researchers’ appeal to the legacy of the Marxist school, in particular, to the principle of a materialistic understanding of history formulated in this school. The tendency to focus on the axiological consequences of Marxism is noteworthy. In particular, the article critically refuted the idea that Marx insisted on recognizing exploitation as fair. Attempts to interpret the Marxist school through the justification of some metaphysical Evil in it are fraught with a syncretic identification of the moral norm and the principle of justice. The reason for such trends is the ontological confusion of value and evaluation. Modern researchers recognize the effectiveness of applying the principle of a materialistic understanding of history in analyzing destructive phenomena in society. The analysis of the principle of justice states the need to turn to the principle of radical criticism, justified by Marx, which makes it possible to identify the dependence of the formation of political principles of society on the principle of justice.

ABSTRACTWomen participation in technology is one of the most important topics that leads to the problem of gender equality in a group where male presence clearly prevails. It is also a matter that appears in the metrics of ONU of Sustainable Development Goals (SDGs) proposed in 2015 proving it as a real society issue. The modern computation world was built through numerous important feminine efforts and discoveries throughout history. Even so, the majority of men in the field expose a strange phenomenon, where women are the minority in the area nowadays. One of the ways to mitigate that is to empower and encourage girls and women of all ages to enter and explore more subjects in technology and computer science and show them they’re capable of doing everything despite their gender.

By applying some techniques of set-valued and variational analysis, we study solution stability of nonhomogeneous split equality problems and nonhomogeneous split feasibility problems, where the constraint sets need not be convex. Necessary and sufficient conditions for the Lipschitz-likeness of the solution maps of the problems are given and illustrated by concrete examples. The obtained results complement those given in [Huong VT, Xu HK, Yen ND. Stability analysis of split equality and split feasibility problems. J Global Optim. https://doi.org/10.1007/s10898-025-01469-6.], where classical split equality problems and split feasibility problems have been considered.