Search Results (422)

In this paper, we study Hahn’s problem with respect to a Dunkl-perturbed raising operator. More precisely, we prove that, up to a dilation, the generalized Hermite polynomials are the only $T_{\mu ,\alpha }$-classical symmetric orthogonal polynomials, where $T_{\mu ,\alpha }=T_{\mu }+\alpha t\mathbb{I}$, $\alpha \in \mathbb{C}\setminus \left\{0\right\}$ and $\mathbb{I}$ denotes the identity operator on the space of polynomials with complex coefficients. The argument uses an operator product rule for $T_{\mu }$, duality for the associated functionals, and a symmetry-enforced identification together with matching three-term recurrences. The result provides an operator-theoretic Hahn-type characterization that complements semiclassical Pearson-equation descriptions and clarifies the effect of the raising perturbation $\alpha t\mathbb{I}$. Full article

A fundamental question when comparing Western and Chinese traditions is what if any similarities exist between the key metaphysical concepts Being and Non-Being and you 有 and wu 無. We find an inspired solution in the oldest preserved translation of the Laozi, the “Liber Sinicus Táo Tě Kīm inscriptus, in Latinum idioma Versus.” This 18th c. Latin translation by a Jesuit Figurist makes a particularly fascinating argument for the equation of Being and you 有 and Non-Being and wu 無. Essential to this is recognizing Non-Being as a type of Being that more closely matches the Laozi’s term wu 無. From this starting point, the translator fuses the three cosmogonies of chapters 1, 40, and 42 to reveal a Daoism-inflected trinitarian theology where Non-Being (wu) and Being (you) become terms to express the complex relationship of the three divine Persons. This effort to connect Daoism and Catholicism both has great historical value and also may serve as a resource for articulating East Asian forms of theology. Full article

In this paper we will be concerned with zeta-symmetry—the functional equation for the (Riemann) zeta-function (equivalents to which are called modular relations)—and reveal the reason why so many results are intrinsic to PFE (Partial Fraction Expansion) for the cotangent function. The hidden reason is that the cotangent function (as a function in the upper half-plane, say) is the polylogarithm function of order 0 (with complex exponential argument), and therefore it shares properties intrinsic to the Lerch zeta-function of order 0. Here we view the Lerch zeta-function defined in the unit circle as a zeta-function in a wider sense, as a function defined in the upper and lower half-planes. As evidence, we give a plausibly most natural proof of Ramanujan’s formula, including the eta transformation formula as a consequence of the modular relation via the cotangent function, speculating the reason why Ramanujan had been led to such a formula. Other evidence includes the pre-Poisson summation formula as the pick-up principle (which in turn is a generalization of the argument principle). Full article

The transition to a circular economy depends on the widespread adoption of sustainable products by consumers. However, the point-of-sale purchase decision is a complex process, influenced not only by ethical arguments but also by sensory cues. This study investigates how the aesthetics (visual design) and materiality (tactile sensation) of green products shape value perception and purchase intention. Using a qualitative methodology based on a focus group, the research directly compares consumer reactions to green products (e.g., a bamboo toothbrush) versus their conventional alternatives (e.g., plastic). Thematic analysis of the data reveals a fundamental dichotomy among consumers: while one segment associates high-tech aesthetics and perfect finishes with quality and hygiene, another segment values natural materials and their “imperfections” as signs of authenticity and responsibility. The results demonstrate that there is no single, universally accepted “sustainable aesthetic” and highlight the need for designers and marketers to align the visual and tactile language of products with the value system of the target consumer segment. The study provides a framework for understanding how design can act as either a barrier to or a catalyst for the adoption of sustainable products. Full article

The development of efficient and accurate numerical methods forms a crucial foundation for revealing complex dynamic evolution in nonlinear dynamical systems. Focusing on nonlinear inertia-coupled systems, this paper constructs a semi-analytical method that integrates the mathematical framework of real modal analysis with the piecewise constant arguments and Taylor series (P-T) method. This method first conducts symmetric preprocessing on the second-order term coefficient matrix of the system to construct the proportional damping decoupling form. Then, it realizes the linear term decoupling corresponding to this proportional damping form by using the mathematical framework of real modal analysis. Finally, the P-T method is applied to solve the dynamic response of the nonlinear system. Numerical validation using a two-dimensional aeroelastic system demonstrates that, under the premise of achieving the same computational accuracy as the time-domain minimum residual method (TMRM), the computational efficiency of the proposed method is significantly better than that of TMRM. Full article

Multifractality in time series analysis characterizes the presence of multiple scaling exponents, indicating heterogeneous temporal structures and complex dynamical behaviors beyond simple monofractal models. In the context of digital currency markets, multifractal properties arise due to the interplay of long-range temporal correlations and heavy-tailed distributions of returns, reflecting intricate market microstructure and trader interactions. Incorporating multifractal analysis into the modeling of cryptocurrency price dynamics enhances the understanding of market inefficiencies. It may also improve volatility forecasting and facilitate the detection of critical transitions or regime shifts. Based on the multifractal cross-correlation analysis (MFCCA) whose spacial case is the multifractal detrended fluctuation analysis (MFDFA), as the most commonly used practical tools for quantifying multifractality, we applied a recently proposed method of disentangling sources of multifractality in time series to the most representative instruments from the digital market. They include Bitcoin (BTC), Ethereum (ETH), decentralized exchanges (DEX) and non-fungible tokens (NFT). The results indicate the significant role of heavy tails in generating a broad multifractal spectrum. However, they also clearly demonstrate that the primary source of multifractality encompasses the temporal correlations in the series, and without them, multifractality fades out. It appears characteristic that these temporal correlations, to a large extent, do not depend on the thickness of the tails of the fluctuation distribution. These observations, made here in the context of the digital currency market, provide a further strong argument for the validity of the proposed methodology of disentangling sources of multifractality in time series. Full article

Fractional-order chaotic systems have emerged as powerful tools in secure communications and multimedia protection owing to their memory-dependent dynamics, large key spaces, and high sensitivity to initial conditions. However, most existing fractional-order image encryption schemes rely on fixed-order chaos and conventional solvers, which limit their complexity and reduce unpredictability, while also neglecting the potential of variable fractional-order (VFO) dynamics. Although similar phenomena have been reported in some fractional-order systems, the coexistence of hidden attractors and stable equilibria has not been extensively investigated within VFO frameworks. To address these gaps, this paper introduces a novel discrete variable fractional-order dark matter–dark energy (VFODM-DE) chaotic system. The system is discretized using the piecewise constant argument discretization (PWCAD) method, enabling chaos to emerge at significantly lower fractional orders than previously reported. A comprehensive dynamic analysis is performed, revealing rich behaviors such as multistability, symmetry properties, and hidden attractors coexisting with stable equilibria. Leveraging these enhanced chaotic features, a pseudorandom number generator (PRNG) is constructed from the VFODM-DE system and applied to grayscale image encryption through permutation–diffusion operations. Security evaluations demonstrate that the proposed scheme offers a substantially large key space (approximately $2^{249}$) and exceptional key sensitivity. The scheme generates ciphertexts with nearly uniform histograms, extremely low pixel correlation coefficients (less than 0.04), and high information entropy values (close to 8 bits). Moreover, it demonstrates strong resilience against differential attacks, achieving average NPCR and UACI values of about 99.6% and 33.46%, respectively, while maintaining robustness under data loss conditions. In addition, the proposed framework achieves a high encryption throughput, reaching an average speed of 647.56 Mbps. These results confirm that combining VFO dynamics with PWCAD enriches the chaotic complexity and provides a powerful framework for developing efficient and robust chaos-based image encryption algorithms. Full article

Phorusrhacids correspond to a group of birds considered to be apex predators, which are a common element of the American fossil Cenozoic avifauna, especially in Argentina, where it is not unusual to find at least two species of terror birds. Nevertheless, the presence of more than one species of terror bird outside Argentina is null. Here we report a second terror bird from the middle Miocene of La Venta locality. The new specimen could reach approximately 180 kg, being about 15% larger than the previous report of a terror bird for the locality. Although it is not possible to completely discard the possibility of these two specimens belonging to a dimorphic species, morphological differences may indicate so. Certainly, the presence of two gigantic terror birds coexisting in the La Venta locality represents an interesting scenario for further studies on their ecology and niche partitioning; this could be an argument for the presence of large open areas within the forests and wetlands of La Venta, further supporting the complex and diverse ecosystems in this region during the Middle Miocene period. Full article

This study examines the structure of student argumentation on artificial intelligence (AI) within the framework of the Toulmin model. We analyzed essays on AI written by 452 Hungarian secondary school students, coding for the presence of the six Toulmin components (claim, data, warrant, backing, qualifier, rebuttal). The results show that students frequently use fundamental argumentation components such as claim, data, and rebuttal. However, elements that provide deeper, more nuanced argumentation, such as backing and qualifiers, appear rarely. Using hierarchical cluster analysis, we identified three distinct argumentation profiles: Critical Arguers, who construct complex structures that also reflect on counterarguments; Minimal Arguers, who follow a simplified, primarily claim-based strategy; and Direct Rebutters, who employ a confrontational style of argumentation that omits the warrant but focuses on rebuttal. Based on our findings, we propose differentiated pedagogical strategies to foster the development of critical thinking in students with different argumentation styles. Full article

Little research has studied verb inflection and argument structure complexity effects in teenagers with developmental language disorders (DLDs). However, verb production and comprehension deficits that characterize younger children with DLD might persist over time. Seventeen French-speaking teenagers with DLD and seventeen controls (typical language, TL group) were tested with fLEX, an application designed to assess lexical and inflectional production and comprehension of three different verb types: intransitives, transitives and ditransitives, i.e., verbs that require none, one or two overt complements. Participants performed three tasks: action naming, sentence production and sentence comprehension involving third singular and plural present tense. Both groups performed similarly on action naming. Subject–verb agreement errors characterized participants with DLD both in sentence production and comprehension; however, verb–argument structure had no effect on any of the tasks. These results characterize verb deficits in teenagers with DLD as affecting inflectional processes rather than lexical ones: they are found in production and comprehension, persist until adolescence and are thus a target for evaluation and intervention in French-speaking teenagers. Results are discussed from a cross-linguistic perspective and in light of current theories on DLD. Full article

Background: Unlike medical training, science teacher training in Brazil does not include PBL as a curricular methodology. However, there is a Pedagogical Residency Program (PRP) that allows teaching experiences that are different from those provided in the undergraduate course. Thus, in this research, we propose a formative intervention in PBL for scholarship holders in the Pedagogical Residency Program (hereinafter Residents), aiming to answer the following question: “What are the perceptions of pre-service teachers about the planning, implementation, and evaluation of a PBL intervention in physics teaching?”. Methods: Five Residents taught an elective course specially designed for the application of PBL to teach secondary school physics. The training of the Residents in PBL occurred almost simultaneously with the offering of the elective subject. To reveal their perceptions, we collected Residents’ teaching plans, problem scenarios, and reflective analyses. Results: The results demonstrate that the Residents encountered several difficulties in developing and implementing the PBL methodology when teaching physics. Regarding development, the difficulties lie in coherently aligning the learning objectives with the highly complex active methodology of PBL. In addition, another clear difficulty is developing a problem situation appropriate to the knowledge that one wishes to develop. During the intervention, the Residents realized how difficult it is to implement PBL to allow students to develop skills and knowledge in a reflective way. Conclusions: The results indicate that PRP is necessary to develop methodologies such as PBL, as it allows supervision and reflection on practice. However, we also observed that the results point to the urgent need to introduce PBL in the initial training of science teachers; this process can be established in three stages: strategically studying lesson planning for the implementation of PBL, developing problem situations that align with the knowledge that one wishes to develop, and developing metacognitive regulation and argumentation skills to conduct interventions based on PBL. Full article

This study explores the interplay between environmental justice and energy democracy in the context of forest-based energy conflicts in Türkiye, focusing on the case of the Akbelen Forest. It draws on qualitative data from community-based actions and legal documents to examine how local communities engage in collective action against extractivist energy policies that threaten their ecological and social environments. The findings reveal a complex web of multilayered injustices, including procedural, distributional, and recognitional dimensions, experienced by the affected populations. In this regard, the Akbelen case demonstrates how these different dimensions intersect and constitute a framework of “multiple justice”. The central argument of this study, developed primarily through our visualised network graph, is that the Akbelen case demonstrates the limitations of current environmental governance frameworks in accommodating community-based ecological values and rights. This analysis demonstrates how energy democracy can function as both a normative and strategic instrument for rethinking participatory planning and forest governance. The present paper contributes to ongoing debates in the fields of political ecology and environmental governance by situating grassroots mobilisation within a broader discussion of just energy transitions. The study also emphasises the necessity of inclusive, multi-actor governance models that prioritise democratic participation, ecological integrity, and intergenerational equity. Full article

This article examines the rhetorical affordances of political claims to victimhood by US president Donald Trump during his first and second terms in office. By applying Critical Discourse Analysis to victimhood claims tactically deployed in the discursive performances of the US president, this analysis demonstrates the versatility and multi-functionality of victimhood claims as a political communication strategy in different contexts, which may account for, at least partly, the appeal of far-right populist leaders to national electorates. The analysis calls attention to a novel argumentative pattern, attested in Trump’s empowered victimhood rhetoric upon his inauguration as second-term president of the USA. This pattern consists of constructing prolonged economic injury inflicted on the nation and announcing retribution against the constructed victimizer(s). This emancipated performative style of claiming victimized nationhood is used to justify and forewarn the implementation of illiberal and coercive politics, in this case, the waging of a global trade war by the US president. Focusing on Trump as an original case study of the construction of ‘economic victimhood’ to justify aggressive economic policy, this paper aims to advance our understanding of the rhetorically complex and continuously evolving victimhood rhetoric of authoritarian populists, as well as the leverages accrued thereof, and adds to a growing body of the literature on the discursive–ideological shifts triggered by authoritarian populism. Full article

This paper aims to analyze adults’ responses to children’s argumentative contributions within children–adult dialogic interactions. More precisely, we focus on the phenomenon of children opening subdiscussions within argumentative interactions with peers and adults. This phenomenon occurs when a child problematizes and calls into question some proposition in the ongoing discussion, hence the opening of a subdiscussion is an initiative that comes as unexpected from the perspective of the adult. In this contribution, we examine what happens after a child opens a subdiscussion and how the adult’s reaction to such initiatives can shape the development of dialogue. This means that we observe adult behaviour in dialogic interactions with children, given the complexity of the adult’s role in such interactions. Drawing on the dialogical approach to argumentation, we present and discuss some excerpts of children–adult subdiscussions at a kindergarten. The data analysis uses concepts and tools from a linguistics-based approach to argumentation, i.e., the pragma-dialectical theory, and it highlights conversational dynamics of children–adult argumentative discourse. The study’s contribution is twofold: (1) it presents the important and delicate role of the adult in dialogic children–adult interactions; (2) it shows how the development of children’s arguments is intrinsically linked to the flexibility of the discussion space organized by the adult. Full article

We consider domain-type patterns in biological membranes that possess an in-plane membrane order. Domains are inseparably linked to topological defects, and many features related to them can be guessed based on universal topological arguments. However, much more complex membrane patterns are typically observed. As possible generators of such configurations, we analyze two relatively simple and universal phenomena. Both are based on continuous symmetry breaking (CSB), which manifests ubiquitously in all branches of physics. We present the Imry–Ma argument which, in addition to CSB, requests the presence of uncorrelated random-field-type disorder. Next, we discuss the Kibble–Zurek mechanism. In addition to CSB it considers dynamical slowing when a relevant phase transition is approached. These approaches were originally introduced in magnetism and cosmology, respectively. We adapt them to effectively two-dimensional membranes and discuss their potential role in membrane structure formation. Full article