This research addresses the contemporary global conflict surrounding transformations in social life through the lens of Critical Theory. The urgency of analyzing the thoughts of Herbert Marcuse and Jürgen Habermas lies in their critical engagement with the rational foundations of the modern social system. This study aims to conduct a comparative analysis of Marcuse’s and Habermas’s contributions to Critical Theory. The material object of this study is Critical Theory in social science, while the formal object focuses on the specific theories developed by Marcuse and Habermas. Employing a library research method and a comparative approach. Data processing in this study uses descriptive analysis, which means describing the data sources of Marcuse and Habermas’ Critical Theory, then analyzing the descriptive data sources from both Critical Theory thinkers. Marcuse’s key concept is the “one-dimensional man,” reflecting a critique of advanced industrial society, whereas Habermas introduces “communicative action” as a foundation for rational discourse in democratic societies. The differences in these concepts are shaped by their distinct philosophical and socio-historical contexts. The study concludes that Marcuse’s and Habermas’s theories represent a dialectical tension: Marcuse as a thesis with a monolithic representation of modern rationality (instrumental rationality that is adaptive with control, efficiency, and domination), Habermas as an antithesis with a typological representation of instrumental rationality and communicative rationality. Habermas does not reject instrumental rationality, but limits it only to non-human objects. When applied to humans, instrumental rationality causes social pathology. Their synthesis lies in recognizing the role of identity and intersubjective recognition in fostering communicative action. This study implies that the Islamic context in Marcuse and Habermas’ discourse leads to conceptual prospects for social cohesion and justice.

This study employs the sum of squares programming (SOSP) method to explore the maximum potential of rear-wheel steering (RWS) in enhancing vehicle stability by expanding the stability region. Firstly, an SOSP-based controller synthesis framework is developed, in which a shape function updating strategy is introduced to reduce the conservatism of stability region estimation. Secondly, to address the input-nonaffine nature of the RWS system, a state feedback control approach based on rear-wheel lateral force is proposed. This ensures an input-affine structure while minimising modelling error. In addition, a constraint reformulation technique is adopted to enhance the feasibility of the SOSP problem under rational system representations. Then, phase portraits and eigenvalue analyses based on SOSP solution reveal that the RWS input induces a dynamical bifurcation phenomenon, in which original saddle points are transformed into locally stable equilibria, thereby enhancing stability near the vehicle’s handling limits. The effectiveness of the synthesised control law is further evaluated under actuator constraints, demonstrating its feasibility within practical rear-wheel steering angle limits. Finally, the differential impact of RWS and active front steering (AFS) on stability region expansion is investigated, revealing fundamental differences in their stabilisation capabilities..

ABSTRACT In this paper, we develop a seven‐dimensional stochastic virus infection model incorporating two types of target cells at varying aggregation stages and a latent infection phase. By incorporating a general nonlinear incidence rate and accounting for the effects of white noise disturbances, this model provides a more rational and comprehensive representation of viral dynamics. Through rigorous analysis, we demonstrate the existence of a unique global solution for the stochastic system. By constructing appropriate Lyapunov functions, we establish the existence of an ergodic stationary distribution under a critical condition, indicating the long‐term persistence of target cells and virions. Additionally, spectral radius analysis is employed to determine the critical condition for viral eradication. Finally, we conduct numerical simulations to validate the theoretical findings and investigate the impact of key parameters such as noise intensity and infection rate, while exploring dynamical behaviors within the gap region to reveal novel characteristics of the model under diverse conditions.

Scholars have extolled the virtues of rationality for centuries while also debating what rationality is and who is rational. Advancing these debates, we used word embeddings trained on 840 billion words of internet text—and validated with Prolific workers in the United States—to uncover the representation, group stereotypes, and occupational correlates of rationality at scale in naturalistic language. Four results emerged. First, rather than being synonymous with competence, representations of rationality included both an analytic/logic component and an interpersonal/trust component. Second, irrationality was not merely the opposite of rationality but contained its own unique subcomponents (volatility and unfairness). Third, rationality was consistently ascribed to high-power targets across 66 social groups. Last, rationality (especially its analytic component) was consistently associated with both earnings and wage gaps across 101 occupations. Associations with demographic representation were less consistent. Complementing normative approaches, these descriptive findings advance canonical debates about rationality, extending understanding of its components, stereotypes, and correlates.

The article discusses the main features of the coverage of the topic of generations in academic and media discourse; it argues that there is a convergence between an academic and media discourse in texts concerning the theory of generations. A sample of texts from Rossiyskaya Gazeta, Moskovsky Komsomolets, Lenta.ru, Profil, Vedomosti, Kommersant for the period from 1.01.2024 to 18.02.2025 was analyzed. The process of convergence of different types of rationality is a natural and desirable phenomenon, unless the specific features of scientific and media styles of covering the theory of generations are ignored. Within the Russian academic research field there are studies of a proper level of theoretical and empirical validity. They provide the methodological foundations of the concept of generations, examine the conditions of formation and semantics of generational characteristics, discuss the problem of intergenerational boundaries, study the generational dynamics in the context of Russian history, etc. However, a simplified version of the generational theory is widespread in the media sphere. In media texts, as well as in many scientific publications, despite the existing criticism, the ‘generational theory’ by N. Howe and W. Strauss is dominated, which indicates the diffusion of academic and media discourse. This can be explained by the fact that this concept, in our opinion, contains signs of mass culture. The convergence of academic and media stylistics is expressed by the similarity of the texts in terms of the following characteristics: descriptiveness, schematism, lack of methodological foundations, lack of reflection on the heuristic possibilities of the theoretical model, consideration of the generation problem in a narrow theoretical context. This kind of interpenetration of discourse may decline the level of analysis of generational issues and distort the representation of scientific rationality in the media space. As a result, the convergence of styles requires constant studying and correction.

In order to model Nigerian crude oil prices, the study used Autoregressive Integrated Moving Average Intervention models. The rapid decline in the series was manifest in the time plot, necessitating an intervention process. The data were separated into pre-intervention and post-intervention series. At order one, the series was examined for stationarity. Four models were estimated based on AIC. There were pre- and post-intervention sections. To reduce the erroneous correlation effect between the pre- and post-intervention data, they were pre-whitened. The pre-whitened input series (pre-intervention series) and output series (post-intervention series) were both pre-whitened, and the cross-correlation between the two was investigated. The cross-correlation behaviors were used to generate a rational polynomial representation for the dynamic transfer function models. It was revealed that the calculated noise was autocorrelated. This filled up the gaps in the transfer function model, which was then used to fit the entire model. The resulting model was subjected to a diagnostic test and determined to be suitable.

Advances in the general capabilities of large language models (LLMs) have led to their use for information retrieval, and as components in automated decision systems. A faithful representation of probabilistic reasoning in these models may be essential to ensure trustworthy, explainable and effective performance in these tasks. Despite previous work suggesting that LLMs can perform complex reasoning and well-calibrated uncertainty quantification, we find that current versions of this class of model lack the ability to provide rational and coherent representations of probabilistic beliefs. To demonstrate this, we introduce a novel dataset of claims with indeterminate truth values and apply a number of well-established techniques for uncertainty quantification to measure the ability of LLM's to adhere to fundamental properties of probabilistic reasoning.

Abstract: A collection of (n×n) not-sole matrices on F domain this collection combine a group beneath process of matrix multiply invited the general linear group of measure on domain F, indicate . The kernel of a homomorphism of to F* is the special linear group and indicate by is the determinant of these matrices, and this homomorphism Thus contains all matrices of determinant one which is the subgroup of The objective of the study is to find the Artin directrix (A.d.) for the groups (2,23) and (2,29) from written the rational valued characters (r.v.ch.) of the rational representations (r.r.) as a linear combination of the induced characters (in.ch.) for these groups.

Criteria are given for the integral representation of a binary quartic form by certain integral ternary quadratic forms and its rational representation by some discriminant forms. These conditions depend on integral or rational solutions of a Weierstrass equation associated to the forms.

Irredundant Decomposition of the Radicals of Polynomial Ideals Based on Rational Univariate Representations

The present study aims to examine the status of Suhrawardi’s symbolic tales within his philosophical system from the standpoint of four major interpreters. Using a descriptive–analytical and critical approach, the research seeks to analyze the position of allegorical narratives in Suhrawardi’s intellectual framework based on fundamental concepts in Islamic philosophy and Illuminationist wisdom (ḥikmat al-ishrāq). The study explores the interpretive intent behind Suhrawardi’s adoption of an artistic form—namely the story—as a medium for expressing his philosophical and mystical ideas. Various views have been proposed regarding the role of the tale in Suhrawardi’s philosophy: some thinkers regard these tales as mere disguised expressions of his philosophical system; others interpret them as distinct mystical phenomena; while still others consider them purely artistic and independent of his philosophy. In this study, the views of four prominent Suhrawardi scholars—Dīnānī, Nasr, Corbin, and Pournamdarian—are philosophically analyzed and examined concerning the relationship between truth and story in Suhrawardi’s allegorical narratives. The findings indicate that each of these four interpreters, according to his own intellectual horizon, presents a unique explanation of the relationship between story and truth in Illuminationist wisdom. Dīnānī perceives the story as a symbolic and rational manifestation of Illuminationist philosophy; Nasr interprets it as a symbolic language for conveying mystical knowledge and sacred truth; Corbin views it as the epiphany and manifestation of truth in the imaginal (mithālī) level of existence; and Pournamdarian regards the tale as an artistic experience and literary expression of the philosopher’s inner journey. Ultimately, the perspective of this research aligns with Corbin’s interpretation—namely, that Suhrawardi’s symbolic stories are not rational representations of truth but rather its very manifestation within the realm of imagination and allegorical language. From this viewpoint, symbolism in Suhrawardi’s works is not merely a means of explanation but the very event of the manifestation of meaning itself.

In this work we find the cyclic decomposition for the groups SU(3,9) and SU(2,25) after we compute the conjugacy classes and the character table of rational representations for each group.

The collection of whole - account grade maps respecting a restricted group G of commutative group cf (G,Z) beneath spot wise addendum. Into these one group own - account generalized characters a subgroup indicate R(G). Whole invertible ´ model form a group on a field F indicate ( ,F). A homo. of GL(n,F) to F-{0} is the determinant of these model, ( ,F) indicate the kernel of it. Thus ( ,F) is a subgp. of ( ,F) include whole models of determinant 1 on F. Let vector void on F, indicate whole linear isomo. of V upon same, a representation of G for representation void is a homo. of to . A representation model of is a homo. of to , where is the degree of the representation model. From the rational representations character table (CTRR) we compute the cyclic decomposition (CD) for , and 7 to (2, ).

Abstract In this article, we study rational matrix representations of VZ p-groups (p is any prime). Using our findings on VZ p-groups, we explicitly obtain all inequivalent irreducible rational matrix representations of all p-groups of order $\leq p^4$ . Furthermore, we establish combinatorial formulae to determine the Wedderburn decompositions of rational group algebras for VZ p-groups and all p-groups of order $\leq p^4$ , ensuring simplicity in the process.

We describe a general procedure for mapping arbitrary n-qubit states to two-dimensional (2D) vector fields. The mappings use complex rational function representations of individual qubits, producing classical vector field configurations that can be interpreted in terms of 2D inviscid fluid flows or electric fields. Elementary qubits are identified with localized defects in 2D harmonic vector fields, and multiqubit states find natural field representations via complex superpositions of vector field products. In particular, separable states appear as highly symmetric flow configurations, making them both dynamically and visually distinct from entangled states. The resulting real-space representations of entangled qubit states enable an intuitive visualization of their transformations under quantum logic operations. We demonstrate this for the quantum Fourier transform and the period finding process underlying Shor's algorithm, along with other quantum algorithms. Due to its generic construction, the mapping procedure suggests the possibility of extending concepts such as entanglement or entanglement entropy to classical continuum systems, and thus may help guide new experimental approaches to information storage and nonstandard computation. Published by the American Physical Society 2024

Meta-collaboration-based semantic contrast for inductive knowledge representation learning

Structural mechanism of glass transition uncovered by unsupervised machine learning

Novel freeform optical design methods can be classified in two categories, depending on whether they focus on the generation of a starting point or the development of new optimization tools. In this paper, we design a freeform three-mirror anastigmat (TMA) and compare different surface representations using either a differential ray tracer as a new optimization tool or a commercial ray tracer (ANSYS-ZEMAX OpticStudio). For differential ray tracing, we used FORMIDABLE (Freeform Optics Raytracer with Manufacturable Imaging Design cApaBiLitiEs), an optical design library with differential ray tracing and Non-Uniform Rational B-Splines (NURBS) optimization capabilities, available under the European Software Community License (ESCL). NURBS allow a freeform surface to be represented without needing any prior knowledge of the surface, such as the polynomial degree in polynomial descriptions. OpticStudio and other commercial optical design software are designed to optimize polynomial surfaces but are not well-suited to optimize NURBS surfaces, requiring a custom optical design library. In order to demonstrate the interest in using NURBS representation, we designed and independently optimized two freeform telescopes over different iteration cycles; with NURBS using FORMIDABLE or with XY polynomials using OpticStudio. We then compared the resulting systems using their root mean square field maps to assess the optimization quality of each surface representation. We also provided a full-system comparison, including mirror freeform departures. This study shows that NURBS can be a relevant alternative to XY polynomials for the freeform optimization of reflective three-mirror telescopes as it achieves more a uniform imaging quality in the field of view.

Abstract Machine learning (ML)‐guided polymer design and synthesis will enable the next‐generation membrane material discovery for CO2 capture. Herein, ML is leveraged to establish a structure‐performance relationship for the eco‐friendly poly(ethylene oxide) (PEO) membrane and guide its design for high‐efficacy CO2/N2 separation. Through a rational fragment representation method and knowledge sharing across membranes fabricated by different methods, the precise prediction of CO2/N2 separation performance for PEO membranes with high Pearson correlation coefficients (0.973 for permeability and 0.875 for selectivity) despite data scarcity is demonstrated. Expertise knowledge and external monomer databases are then utilized in a human‐in‐the‐loop workflow to effectively explore high‐performance PEO membranes in the design space. Several discovered thermally crosslinked PEO membranes achieve CO2/N2 separation performances close to the 2019 Robeson upper bound, which are promising for practical large‐scale carbon capture applications. Model interpretation techniques are employed to provide data‐driven insights into the design of PEO membranes for high‐efficacy CO2/N2 separation. Further life cycle assessment results reveal the outstanding advantage of discovered PEO membranes in terms of environmental friendliness. The work highlights the enormous potential of ML in expediting the discovery of high‐performance carbon capture membrane materials.

In this paper we study the relationship between non-totally real number fields K and toroidal groups 𝒯, as well as meromorphic periodic functions, exploiting a representation of 𝒯 as the generalized Jacobian 𝔍 L (𝒞) of a suitable elliptic curve 𝒞. We consider in detail the cubic and quartic cases.In these cases, we write down the relations between the minimal polynomial of a suitable primitive element of K and the parameters defining the generalized Jacobian 𝔍 L (𝒞) corresponding to the toroidal group associated with the ring of integers. Furthermore, for such a toroidal group we explicitly show the analytic and rational representations of its ring of endomorphisms, the former giving in turn a new (complex) representation of the ring of integers of K.Moreover, for the cubic case, we give an explicit description of the m-torsion of 𝒯 in the geometric correspondence of 𝒯 with 𝔍 L (𝒞), as image of a fractional ideal of K.