As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent expressions with increasing problem size. We introduce quantum normal form reduction, a quantum computational framework designed to address this challenge. We construct an efficiently implementable quantum Hamiltonian whose ground state encodes all equivalent expressions in a quantum superposition. By preparing and manipulating these states, we tackle fundamental problems in equational reasoning, including verifying and counting equivalent expressions and identifying structural properties of equivalence classes. We demonstrate a quantum-inspired version of the algorithm using tensor networks to solve instances involving up to 1028 equivalent expressions, far beyond the reach of classical graph exploration. This framework opens the path for quantum symbolic computation in areas from circuit design to data compression, computational group theory, linguistics, and macromolecular modeling, unlocking previously inaccessible problems.

ABSTRACT This study described the structure and dielectric properties of Pb0.98-x Bax Ca 0.02 [(Zr0.52 Ti0.48)0.94 – (Zn1/3 Ta2/3)0.03 – (In1/3 Sb2/3)0.03] O3 (PBC–ZTZTIS) ceramics (where x = 0, 0.01, 0.02, 0.03, 0.04 and 0.05), were synthesized by a normal solid-state method and sintered at 1180°C. The crystal structure, microstructure and dielectric properties of the ceramics were investigated via X-ray diffraction, Raman analyses, scanning electron microscopy and dielectric spectroscopy. X-ray diffraction results demonstrate that all the samples lie within the morphotropic phase boundary (MPB) region. Raman-active modes in PBC–ZTZTIS were identified through group theory analysis. Scanning electron micrographs of the samples show a uniform distribution of grain and grain boundaries. The optimum dielectric properties of PBC–ZTZTIS such as dielectric constant ϵrmax = 653805, Curie temperature Tc = 507°C and the minimum dielectric loss (0.02%) were obtained at x = 0.03, which indicated that the PZT–BCZTIS ceramics are promising to lead to practical applications.

In this work, we introduce a new approach for constructing a renormalized and regularized Fock matrix for self-consistent field calculations. The scheme relies on second-order perturbation theory and is conceptually related to quasiparticle self-consistent second-order Green's function theory (GF2). The regularization is derived within the framework of perturbative similarity renormalization group (SRG) theory. By optimizing both the regularization and spin-scaling parameters, we introduce three SRG-qsGF2 variants that enable accurate predictions of quasiparticle energies and dipole moments. Lastly, we demonstrate that formulating second-order perturbation theory for the total electronic energy using the renormalized SRG-qsGF2 Fock matrix as the unperturbed Hamiltonian mitigates divergence problems commonly observed in conventional Møller-Plesset perturbation theory.

We prove the existence and multiplicity of solutions for a variable-exponent double-phase problem with parametric logistic reaction term. Combining variational and truncation methods with homological critical group theory, we prove the existence of at least one or two solutions with respect to a positive parameter, i.e., a bifurcation result. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2026/33/abstr.html

This article introduces Digital Connective Narratives (DCN) as a framework for explaining how large-scale meaning-making emerges in digital environments where group boundaries are fluid and participation is fragmented. Classic theories of groups, discourse communities, and collective narratives offer valuable insights into cohesion, identity, and shared cultural repertoires, but they presuppose forms of membership, continuity, and recognition that are often absent in networked publics. DCN refer to a meaning-making process whose product is the narrative field—an emergent discursive structure characterized by recurrent framing, shared semiotic nodes, patterned alignments, circulation trajectories, and temporal persistence. The article introduces the DCN model and distinguishes it from existing frameworks for analyzing collective meaning-making online, clarifying its distinctive contribution to the study of digital publics and providing a conceptual foundation for analyzing sense-making at scale in contemporary media ecosystems.

ABSTRACT Although defects are inevitable in materials and generally degrade their performance, they can also serve as a pathway to realize compatible functionalities. In the present work, the dense single‐phase Ho 2/3 Ta 2 O 6 ceramics with A ‐site‐deficient double‐perovskite structures were prepared, and the room‐temperature ferroelectricity with a remanent polarization of approximately 0.3 µC/cm 2 and a coercive field of 470 kV/cm was observed. A first‐order improper ferroelectric phase transition was identified near the Curie temperature of 762 K, as confirmed by the temperature‐dependent dielectric response and DSC measurement. Moreover, the temperature‐dependent in situ XRD verifies that the paraelectric phase above the Curie temperature belongs to the P 4/ mmm space group. Based on group theory analysis, the polar Pb 2 1 m phase is established by the coupling of the in‐phase oxygen octahedral rotation and the out‐of‐phase oxygen octahedral tilt in the prototype P 4/ mmm phase, while this tetragonal phase is derived from the ideal simple perovskite through the A ‐site layered ordering of Ho 3+ cations and vacancies; thus, the hybrid improper ferroelectricity originates from the synergistic interaction between the A ‐site layered ordering and oxygen octahedral tilting. This work unambiguously demonstrates the hybrid improper ferroelectricity in Ho 2/3 Ta 2 O 6 ceramics with A ‐site layered ordered double‐perovskite structures and significantly expands the research scope of hybrid improper ferroelectricity into double‐perovskite systems.

Object detection from unmanned aerial vehicle (UAV) imagery is essential for applications such as traffic monitoring, disaster response, and urban surveillance, yet most existing methods are developed and evaluated under clear-sky conditions. In real-world UAV operations, adverse weather including fog, rain, and snow introduces severe image degradation that simultaneously disrupts both the geometric and photometric properties of targets. This paper identifies two fundamental bottlenecks underlying this performance collapse: the lack of geometric invariance in standard convolutional operators and the inability of fixed receptive fields to reconstruct features corrupted by atmospheric interference. To address these bottlenecks, we propose SELPNet (Scene Exploration and Large Format Perception Network), a unified framework that integrates geometric alignment and multi-scale contextual perception into the YOLOv13 head. SELPNet consists of two key modules: (1) The Scene Exploration Convolution (SEC) leverages affine Lie group theory to construct a discrete manifold of rotation and scale transformations, actively probing multiple geometric views and selecting the most coherent response via a Maxout mechanism. (2) The Large Format Perception Module (LPM) introduces a dynamic dilation strategy with depthwise separable convolutions, progressively enlarging the receptive field from fine-grained edge preservation to scene-level contextual perception for semantic completion of degraded regions. We further construct and release AWU-OBB, a large-scale benchmark containing over 18,000 oriented bounding box-annotated UAV images across four representative scene categories. Ablation experiments demonstrate that SEC and LPM yield complementary gains, achieving a combined improvement of +4.26% mAP50 over the YOLOv13-n baseline with only 0.11 M additional parameters and 0.2 extra GFLOPs. The source code will be publicly released upon acceptance of this paper.

Study of the mechanical performance of multi-cell composite truss-like lightweight structures based on space group theory

Gendered communication inequality in low-income households is often obscured within domestic activities, despite its critical role in shaping household food habits. Women bear the primary responsibility for food provision; however, their voices and knowledge are frequently marginalized due to male dominance. Under conditions of economic constraint, food-related decisions tend to reflect power relations rather than nutritional considerations. This study aims to examine socio-economic conditions, forms of power relations in gendered communication, food decision-making processes, and food habits within low-income households in Banjar Regency, South Kalimantan. The research employs a qualitative approach with a multiple-case study design. Data were collected through in-depth interviews, observation, and documentation, and were analyzed thematically using NVivo 12 Pro. Muted Group Theory serves as the analytical lens to explore patterns of domination, subordination, acceptance, and negotiation that emerge in household food decision-making. The findings reveal that unequal food decisions are not solely a response to economic limitations, but are also shaped by communication practices embedded within gender-based power relations in low-income households. This study highlights the importance of gender-equitable interventions to promote healthier and more sustainable food practices.

A bstract We construct dimer graphs for relativistic Toda chains associated with classical untwisted Lie algebras of A, B, C 0 , C π , D types and twisted A, D types. We show that the Seiberg-Witten curve of 5d $$ \mathcal{N} $$ N = 1 pure supersymmetric gauge theory of gauge group G is a spectral curve of the relativistic Toda chain of the dual group G ∨ .

The aim of this short research note is to present some results about a conjecture of Barker and Gelvin [J. Group Theory 25 (2022), pp. 973–995, Conjecture 1.5 ] claiming that any source algebra of a p p -block ( p p is a prime) of a finite group has the unit group containing a basis stabilized by the left and right actions of the defect group. We obtain some reduction theorems for the existence of stable unital basis in source algebras of p p -block algebras. Along the way we investigate this problem for the p p -blocks of some finite simple groups.

Abstract End-spaces of infinite graphs naturally generalise the Freudenthal boundary and sit at the interface between graph theory, geometric group theory and topology. Our main result is that every end-space can be topologically represented by a special order tree. Our main proof ingredient is a structure theorem that we introduce, which carves out the order-tree-like structure of any graph in such a way that there is a natural bijection between the ends of the graph and the limit-type down-closed chains of the order-tree.

In our previous work, we introduced the concept of torsion angular bin strings (TABS), which is a discrete vector representation of a conformer's torsional angles. Through this discretization, conformational states can be counted, yielding an estimate of the upper limit of the expected conformational ensemble size (nTABS). Besides nTABS being used as a quantitative measure of molecular flexibility, TABS itself is a way of grouping the conformers of a molecule without picking thresholds. This feature of TABS is especially valuable, as selecting suitable thresholds for metrics such as heavy-atom root-mean-square deviation (RMSD) or shape Tanimoto is highly system-dependent and can thus be challenging when working with large sets of molecules. Here, we describe the update to the nTABS algorithm of the TABS package since the last release. In addition, we present a classification study of conformer ensembles by TABS and compare it to classifications by a shape Tanimoto metric. Scientific contribution In contrast to our previous implementation, which handled molecular topological symmetry by enumerating all possible combinations that were simply permutations of one another, the new implementation treats TABS as mathematical objects governed by group theory, specifically Burnside's Lemma. This approach requires substantially less code and delivers a notable improvement in computational speed. The study also builds upon our previously developed framework for categorization comparisons between TABS and heavy-atom RMSD. Here, we show the results of a similar comparison with a shape Tanimoto metric, which further support the hypothesis that TABS encode the shape of conformers in a meaningful way.

This study examines gender-based violence (GBV) against men in Uganda, with particular attention to its forms, causes, and consequences. Guided by hegemonic masculinity theory, muted group theory, plus power and control theory, the study explores how dominant gender norms, discursive exclusion, and non-physical strategies of domination shape men’s experiences of abuse and contribute to its underreporting in Uganda. Using a narrative inquiry approach, data were collected through semi-structured interviews with 15 Ugandan men aged 18 years and above who were married, divorced, or separated. Participants were selected using a combination of convenience and purposive sampling techniques. The data were analyzed thematically using MAXQDA 2020, resulting in three major themes: forms of GBV, causes of GBV, and consequences of GBV against men. Findings reveal that the primary causes of GBV against men include poverty, group pressure, adultery, family background, and female social support networks. The study further indicates that GBV against men manifests in multiple forms, including physical, sexual, verbal, psychological, and economic abuse. Consistent with power and control theory, many of these abuses were non-physical and aimed at exerting domination and control over male partners. The consequences of such violence included psychological trauma, financial losses, suicidal ideation, and marital separation. Hegemonic masculinity norms and muted group dynamics further emerged as key factors that silenced male victims, discouraged reporting, and limited institutional recognition of men as legitimate victims of GBV. These findings signify that GBV against men in Uganda is real, multifaceted, and underreported. It is driven by power dynamics and gender norms. A possible mitigation mechanism for GBV against men calls for inclusive policies, recognition, and responsive support systems nationally. The study recommends fair and inclusive hearings for all GBV victims, increased advocacy for men’s rights, expanded victim counseling services, and greater involvement of cultural and religious institutions in GBV prevention and response. To enhance awareness among policymakers and stakeholders, further research on GBV against men in Uganda and other global contexts is strongly recommended.

ABSTRACT Critiques of integration discourse highlight its top-down, state-driven nature and tendency to frame minorities as perpetual outsiders. This article examines how migrants construct racialised discourses of integration to position themselves as part of the white majority. Introducing discursive integration, it argues that through everyday talk, migrants actively perform belonging. This process operates via a dual strategy: Polish migrants construct the white English majority as a positive reference group, claiming racial similarity, while constructing non-white minorities as a negative reference group from whom they distance themselves. In doing so, they strategically subordinate Polishness to whiteness, discursively transforming from minority into majority members – they integrate through race. Drawing on qualitative research with Polish migrants in Bristol, England, the article uses reference group theory to show that participants compared themselves favourably to a normative white English majority while portraying non-white minorities as lazy, culturally incompatible, and threatening – embodying ‘failed integration’. Through this mechanism, Polish migrants discursively became part of the white majority. While situated in England, the findings offer a transferable model for understanding migrant integration in other racialised societies. The study argues that integration is a racialised project where claiming whiteness expands majority belonging – at the expense of more marginalised groups.

Abstract Paley-type partial difference sets and skew–Hadamard difference sets are classical objects in algebraic combinatorics, known for their rich connections with graph theory, coding theory, and group theory. In this paper, we explore new links between these combinatorial structures and group codes arising as ideals in finite group algebras. We construct such codes from difference sets and determine their dimensions in several cases. As an application of our links, we explicitly compute the full set of primitive central idempotents in certain abelian $$ p $$ p -group algebras, by employing the classical sets of quadratic residues and non-residues modulo $$ p $$ p , which are well-studied examples of difference and partial difference sets—we also obtain their dimensions and estimate their minimum weights.

Corrigendum to “Combined use of ‘‘two-step’’ and ‘‘field-theoretic’’ renormalization group theories for deterministic partial differential equations” [Phys. A 687 (2026) 131362

ABSTRACT Group theory has profoundly advanced physics and chemistry in systems with symmetries. Yet its use in structural engineering applications has not yet been fully explored beyond the aesthetics of symmetric designs. This work addresses two significant gaps that have limited the broader adoption of group‐theoretic methods in structural vibration analysis and clarifies their implications for structural design when multiple eigenvalues arise. First, a problem‐independent approach is presented with detailed derivations for constructing group representations for symmetric structures directly from the ‐invariance for structural vibration analysis. This method applies effectively to both dihedral groups and the higher‐order Platonic groups, including tetrahedral (), octahedral (), and icosahedral () symmetries. The method used in this work scales well with structural complexity and enables both explicit and canonical block diagonalizations. Second, this work provides a comprehensive guide to applying finite‐point‐group representations in structural vibration analysis and proves that the dimensions of irreducible representations determine eigenfrequency multiplicities. Although no optimization is performed in this work, this theoretical result has direct implications for structural optimization, resolving longstanding misconceptions about the coalescence of eigenvalues by showing that symmetry is the origin of repeated eigenfrequencies. The theoretical developments are validated on truss structures with dihedral and higher‐order symmetries, accurately predicting their eigenfrequency distributions.

Conventional molecular graphs are often unable to reliably encode stereochemistry, especially for symmetric molecules, nontetrahedral centers, and transition states. To overcome this, we present StereoMolGraph, an open-source Python library implementing a stereochemistry-aware graph representation for molecules and condensed graphs of reactions. Our method uses permutation-invariant local stereodescriptors, grounded in group theory, to provide an extensible representation of chirality. Based on this we introduce methods allowing for robust comparison of stereoisomers, including the identification of enantiomerism and diastereomerism, and support fleeting stereochemistry in transition states. We demonstrate the library's utility for complex organic molecules and metal complexes and analysis of distinct chiral reaction pathways. With RDKit interoperability and visualization features, StereoMolGraph offers a practical and transparent tool for advanced stereochemically aware chemoinformatics workflows.

Metal halide perovskites show exceptional potential for solar energy, thermoelectrics, catalysis, and other photochemical technologies, with performance rooted in electronic structure-driven properties. In ABX3 halide perovskites, localized and often aspherical local electron densities from B-site lone pairs or polarizable X- anions can distort the lattice. However, the links among electronic structure fluctuations and distortions like tilting of the BX6 octahedra and off-centering of the B-site from the center of its octahedron are not fully understood. Using group theory and ab initio molecular dynamics, we quantify how lone pairs, halide polarization, off-centering, and octahedral tilting interact in the cubic phase CsBBr3, with B = Pb, Sn, and Ge. We find that lone pair-induced off-centering and octahedral tilting are symmetry-decoupled. Instead, stereochemical lone pair expression of the B-site ion is correlated to octahedral tilting through the propensity of the B-site to form a transient, partial covalent bond with the surrounding halide ions that stiffens octahedral tilting modes. These results link local electronic asymmetry to structural fluctuations and suggest that dynamic modulation of electronic symmetry offers a pathway to control functional properties in halide perovskites.