A bstract This work, which accompanies [1], is about constructing smooth solutions in type II and eleven dimensional supergravity which describe supersymmetry preserving RG flows from four-dimensional SCFTs in the UV to three-dimensional SQFTs in the IR, through holography. We show that all the different UV fixed points flow to theories which confine external quarks and have a mass gap. We proceed by presenting extended calculations of a plethora of observables and analyse the dual field theories in great detail. This includes a boundary analysis and application of holographic renormalization methods in the simplest case of the type IIB solution. Many of the observables computed here have a universal behaviour: they factorize into two parts, one of which includes information about the UV SCFTs, and the other describing the dynamics of the RG flow, which is the same regardless of the UV fixed point.

This paper is devoted to the study of the relationship between the fundamental algebraic, analytic, and topological invariants of Artinian local algebras. Among other things, it is shown that the length of the modules of derivations and Kähler differentials of every local Artinian Gorenstein algebra is not greater than the length of the algebra reduced by one. The proof relies on the theory of duality in the cotangent complex of analytic algebras, the basic properties of faithful modules over Artinian rings, and the structure of annihilators and socles of the modules of derivations and Kähler differentials. As a result, it turns out that the Tyurina number of a smoothable zero-dimensional Gorenstein singularity cannot be less than its Milnor number, so the inequality τ ≥ μ \tau \geq \mu holds.

Quantum gravity effects are expected to resolve the black hole singularity and the effects may deform the region near but outside the horizon. Applying AdS/CFT correspondence, we see their signatures from the viewpoint of dual conformal field theory. As a regularized geometry, we consider AdS gravastar constructed by gluing AdS-Schwarzschild and de Sitter spacetime. The retarded Green's functions of dual conformal field theory have bulk-cone singularities associated with null trajectories in the bulk and we obtain the singularities specific to a horizonless geometry. We also observe echoes coming from waves reflected behind the photon sphere. The existence of echoes implies the modification of geometry inside the photon sphere.

With the high penetration of distributed photovoltaics (PV) in distribution areas, transformer capacity limits and source–load fluctuations have become key factors constraining PV accommodation. To accurately assess the PV hosting capacity under energy storage regulation, this paper proposes an assessment method based on operating region analysis. First, a coordinated operation model for the distribution area is established, incorporating the transformer capacity, energy storage constraints, and power balance. On this basis, the calculation boundaries for the PV hosting capacity are discussed in two scenarios: Model 1 ignores power curve uncertainty, characterizing the geometry of the conventional operating region to find the maximum deterministic hosting capacity (S1) that keeps the region non-empty. Model 2 introduces box-type uncertainty sets for the source and load, proposes the concept of a “Self-Balanced Operating Region”, and constructs a robust feasibility determination model (f3) based on a Min–Max–Min structure. To solve this multi-layer nested non-convex model, an iterative algorithm based on duality theory and Benders decomposition is employed to determine the robust hosting capacity under uncertainty (S2) at the critical point where f3 shifts from zero to non-zero. Case studies show that source–load uncertainty leads to a significant contraction of the operating region, and the robust hosting capacity under uncertainty requirements is strictly less than the deterministic hosting capacity (S1>S2). This method quantifies the reduction effect of uncertainty on the accommodation capability, providing a theoretical basis for planning high-renewable penetration distribution areas and energy storage configuration.

Due to the rise of cardinality minimization in optimization, sparse support vector machines (SSVMs) have attracted much attention lately and show certain empirical advantages over convex SVMs. A common way to derive an SSVM is to add a cardinality function such as ℓ0-norm to the dual problem of a convex SVM. However, this process lacks theoretical justification. This paper fills the gap by developing a local duality theory for such an SSVM formulation and exploring its relationship with the hinge-loss SVM (hSVM) and the ramp-loss SVM (rSVM). In particular, we prove that the derived SSVM is exactly the dual problem of the 0/1-loss SVM, and the linear representer theorem holds for their local solutions. The local solution of SSVM also provides guidelines on selecting hyperparameters of hSVM and rSVM. Under specific conditions, we show that a sequence of global solutions of hSVM converges to a local solution of 0/1-loss SVM. Moreover, a local minimizer of 0/1-loss SVM is a local minimizer of rSVM. This explains why a local solution induced by SSVM outperforms hSVM and rSVM in the prior empirical study. We further conduct numerical tests on real datasets and demonstrate potential advantages of SSVM by working with locally nice solutions proposed in this paper.

Aligning input and assessment: Pictorial measures in audiovisual vocabulary research

The dual modification strategy of nitrogen-doped carbon coating with MnO inter-layers helps enhance the stability of silicon anodes.

Abstract To address the motion safety challenges faced by quadrupedal robots when performing automated inspection tasks within the confined and structurally complex environment of space launch sites, this paper proposes a nonlinear model predictive control method incorporating precise obstacle avoidance constraints. To enhance the precision of motion control, the geometric shapes of the quadrupedal robot and environmental obstacles are represented as polytopes. Utilising the strong duality theory of convex optimization, the originally non-smooth and non-differentiable distance constraints between the robot and obstacles are transformed into smooth, differentiable constraints. These are then integrated into the NMPC motion control framework. To achieve comprehensive environmental adaptability, the proposed method extends obstacle avoidance movement from a two-dimensional plane to three-dimensional space. This paper conducts experimental validation across four typical obstacle scenarios. The results demonstrate that the proposed method effectively ensures the movement safety and passability of robots within complex, confined launch site environments, thereby providing a reliable technical solution for automated inspection at space launch facilities.

Mathematics education has long been influenced by diverse learning theories that are frequently applied in isolation, leading to theoretical fragmentation in instructional design. This study addresses that gap by proposing the DECADE learning model as a theoretically integrated framework that systematically synthesizes cognitivism, constructivism, information processing theory, dual coding theory, and cognitive load theory within a coherent instructional architecture. The study aims to establish the epistemological foundation and structural validity of this multi-theory integration in the context of mathematics education. Employing a mixed-method developmental design, qualitative thematic analysis was conducted to map the five theoretical foundations into a progressive six-phase instructional structure, followed by quantitative expert judgment to assess content and construct validity. The results demonstrate strong conceptual stability, with mean validity indices exceeding 90% of the ideal score, indicating high alignment between theoretical rationale, instructional syntax, and structural coherence. Rather than claiming empirical effectiveness, this study confirms the theoretical and structural feasibility of DECADE as an expert-validated framework. The findings contribute to mathematics education by offering a principled synthesis that bridges constructivist meaning construction and cognitive regulation, thereby providing a consolidated theoretical foundation for future empirical investigation and instructional innovation.

Dihydroquercetin (DHQ) is a flavonoid compound with notable pharmacological activities. Developing a green and efficient synthesis route for its sustainable production remains a considerable challenge. This study proposed a semisynthetic strategy based on a non-noble nickel catalyst for the selective catalytic hydrogenation of quercetin to produce DHQ. Under the conditions of 200 °C and 7 MPa H2 for 2 h, the Ni/CNT catalyst achieved a DHQ yield of 32.3% from quercetin, which is markedly higher than the commercial Pd/C catalyst (13.2%). This can be attributed to the synergistic effect between its unique structural characteristics and the underlying electronic effects. Based on the dual descriptor theory for predicting reaction sites and comparative experiments with different supports, this study clarified the inherent selectivity challenges in the hydrogenation of quercetin to DHQ and highlighted the key role of the unique tubular curved structure of carbon nanotubes. Furthermore, kinetic analysis in this study determined that the activation energy for the selective hydrogenation of quercetin to DHQ catalyzed by Ni/CNT is 76.15 kJ/mol. Further analysis revealed that the activation energy for the DHQ formation step is higher than that for its subsequent consumption step (E a1 > E a2), and the consumption rate constant is greater than the formation rate constant (k 2 > k 1). These results indicate that DHQ, as an intermediate, is difficult to accumulate, highlighting the necessity of precise control over reaction conditions to improve its yield, thereby providing a basis for the development of a green and efficient DHQ synthesis process.

This study is a theoretical review that examines, from a holistic perspective, the effects of background music used in classroom settings on students’ cognitive, affective, and social learning processes. Drawing on contemporary research in educational psychology, environmental structuring, learning theories, and special education, the contributions of background music to learning efficiency have been analyzed multidimensionally. The literature indicates that appropriately selected background music can increase attention span, support performance in cognitive tasks, and positively influence classroom interactions by facilitating students’ emotional regulation. In particular, instrumental and low-tempo genres such as lo-fi, classical, and ambient music have been reported to yield beneficial outcomes for both general student populations and individuals with special educational needs, including ADHD, autism, and learning disabilities. However, the effects of music emerge through complex interactions among multiple variables, including individual differences, task type, musical preference, and classroom atmosphere. On a theoretical level, the study is framed within Cognitive Load Theory (Sweller), Dual Coding Theory (Paivio), Multimedia Learning Theory (Mayer), and the Mood–Arousal Hypothesis (Thompson), demonstrating how music can be understood not merely as an aesthetic element but as a pedagogical tool capable of regulating and supporting learning processes. Methodologically, the research is structured as a review study and employs qualitative content analysis to examine selected empirical and theoretical works published at both national and international levels. Based on the findings, recommendations for music-based auditory arrangements applicable in classroom environments are supported by systematic tables that provide a concrete roadmap for instructional practice. Background music applications should therefore be considered a strategic resource that not only supports students’ attention but also balances the socio-psychological dynamics of the classroom, fostering an inclusive and multisensory learning environment.

The growing popularity of short-form video platforms has significantly transformed the landscape of digital advertising in India. In an era where audiences increasingly consume algorithm-curated content tailored to their interests, brands are rapidly shifting toward short-duration video formats to capture audience attention and enhance engagement. This study examines the effectiveness of short-form video advertising in enhancing brand popularity and compares the performance of Instagram Reels on Instagram and YouTube Shorts on YouTube. The research highlights the importance of short-form video as an emerging advertising strategy and explores the advantages of adopting such formats for brand communication. The study is theoretically grounded in key communication and cognitive frameworks, including the Uses and Gratifications Theory, Dual Coding Theory, and Cognitive Load Theory. These theoretical perspectives help explain short-form video as a multisensory, cognitively engaging, and persuasive format that operates within algorithm-driven digital environments. The study adopts a controlled experimental design, with data collected from 548 respondents aged between 18 and 35 years across three metropolitan cities in India. Participants were exposed to branded short-form video stimuli, after which both unaided and aided recall were measured. Statistical analysis reveals that exposure to short-form video significantly enhances brand recall outcomes (p < .001), indicating that short-form videos function as a highly effective branding tool. The findings further indicate that Instagram Reels demonstrate greater effectiveness than YouTube Shorts in terms of brand recall. This difference can be attributed to higher engagement intensity and stronger perceived social interactivity on the Instagram platform. Regression analysis also reveals that emotional storytelling and the first three seconds of a video play a crucial role in attracting audience attention and improving recall performance. These elements operate within algorithm-based feeds that amplify engaging content and increase repeated exposure. By integrating platform-specific video characteristics with audience behavior and cognitive theories, this research provides a deeper understanding of short-form video advertising within algorithm-driven media ecosystems. The study highlights the strategic importance of short-form video as a powerful tool for digital brand communication in an increasingly competitive media environment.

This study examines how a group of independent agricultural producers formulates a coalition to mitigate the mismatch risks arising from uncertain yield and demand by leveraging the risk pooling effect. A stochastic linear programming model is formulated to characterise the optimisation problem inherent to the coalitional game. By employing a stochastic duality approach, we demonstrate the nonemptiness of the core of the risk pooling game. Furthermore, a straightforward method is proposed for designing a fair cost allocation scheme applicable to all members of the coalition. Moreover, we establish the convexity of the risk pooling game with a linear investment cost, and this result guarantees the population monotonicity of the coalition. Subsequently, we investigate the risk pooling game involving nonlinear investment costs (i.e., concave and convex functions). The stochastic duality approach is further employed to develop a fair cost allocation scheme and ensure the nonemptiness of the core of the resulting game. Additionally, the risk pooling games involving two types of products (complementary and substitutable products) are explored based on stochastic duality theory. For these scenarios, we propose cost allocation schemes that lie in the core of the corresponding cooperative games. Finally, we conclude that innovative collaborative strategies can effectively mitigate uncertainty-induced risks, indicating that for agricultural producers confronting yield and demand uncertainties, collaboration outperforms individual action.

This paper develops a unified cohomological framework for analyzing n-derivations and their induced derivational automorphisms on nest algebras, extending classical Hochschild cohomology into the realm of higher-order operator algebraic structures. By constructing explicit n-cochain complexes adapted to the triangular nature of nest algebras, we classify n-derivations up to cohomological equivalence and provide precise criteria for their innerness. We demonstrate that the vanishing of higher-order cohomology groups corresponds to structural rigidity, while non-trivial cohomology classes reflect obstructions to decomposability and inner implementation. Moreover, we show that cohomologically trivial n-derivations preserve essential algebraic features, including the radical, center, invariant subspaces, and two-sided ideals. Through explicit computations of Hn(A,A) for low-dimensional examples, we verify the existence of non-trivial cohomological classes. Additionally, we introduce a dual cohomology theory for n-automorphisms via exponential mappings and establish a bidirectional correspondence between infinitesimal derivations and global automorphisms. This approach unifies derivational and automorphic symmetries under a single cohomological classification, offering new perspectives toward deformation theory, categorical dualities, and quantum operator structures.

We examined how emotional motivation of background stimuli and prospective memory (PM) targets, along with cognitive control, jointly influence the PM aftereffects using a repetitive PM cue paradigm. Experiment 1 revealed that high background avoidance motivation inhibited PM aftereffects, whereas the combination of background approach motivation and target avoidance motivation enhanced PM aftereffects—indicating that emotional motivation modulates PM aftereffects by regulating cue salience and cognitive resource consumption. Experiment 2 showed that focal cues exerted a stronger inhibitory effect on PM aftereffects, while focal cues paired with incongruent background-irrelevant stimuli enhanced PM aftereffects—demonstrating that cognitive control regulates PM aftereffects through cognitive resource availability. The above results indicate that: (1) The generation mechanism of PM aftereffects aligns with the modified dual mechanism theory, involving spontaneous retrieval and strategic monitoring processes that are dynamically shaped by emotional motivation and cognitive control. (2) The reactivation and deactivation of completed intentions constitute a dynamic continuum, jointly modulated by emotional and cognitive factors, with cognitive resource availability serving as a critical mediator.

IntroductionThis study aimed to evaluate the effectiveness of embedded picture mnemonics, specifically designed for the Turkish alphabet, in improving letter recognition skills among first-grade students. The research was grounded in two prominent cognitive frameworks: Cognitive Load Theory and Dual Coding Theory. While Cognitive Load Theory suggests that reducing unnecessary cognitive effort enhances learning, Coding Theory posits that combining verbal and visual information strengthens memory and comprehension.MethodsA quasi-experimental design was used, with participants divided into three groups: an experimental group (N=30) and two control groups (N=25 and N=30). Letter recognition accuracy and speed were assessed using a multiple-choice test administered via tablets, and data were analyzed using 2x3 doubly multivariate repeated measures analysis of variance (RM-MANOVA).ResultsMultivariate analysis revealed a significant main effect for the intervention group, with the experimental group significantly outperforming both control groups. Specifically, the mnemonic-based instruction yielded large effect sizes for both letter recognition accuracy (F(2, 82) = 11.68, p < 0.001, ηp2 = 0.222) and recognition speed (F(2, 82) = 22.59, p < 0.001, ηp2 = 0.355). Descriptive statistics also showed that students in the experimental group achieved higher letter recognition accuracy and faster recognition speed in both measurement points.ConclusionThe results are consistent with theoretical assumptions derived from Cognitive Load Theory, suggesting that embedded picture mnemonics may support more efficient processing of letter–sound correspondences. Moreover, the use of visual associations supported by dual coding enhanced students’ ability to recognize and recall letters. These findings align with prior research and highlight the potential of mnemonic-based strategies in early literacy instruction within similar linguistic and instructional contexts.

In this paper, we consider a class of three-composite nonconvex optimization problems, in which the nonsmooth function is further composed with a linear operator. This problem has many applications such as sparse signal recovery, image processing and machine learning. Based on the conjugate duality theory, we present an accelerated preconditioned primal-dual gradient algorithm for this problem. Compared with the existing algorithms, our algorithm only needs to calculate the proximal mapping of the conjugate function $h^∗$ which is always convex and lower semicontinuous and it does not need to calculate the proximal mapping of nonconvex functions. This may significantly reduce the computation load. We prove that the sequence generated by the proposed algorithm globally converges to a critical point when the function satisfies the Kurdyka- Lojasiewicz property. We also obtain the convergence rate of the proposed algorithm. Finally, numerical results on sparse signal recovery and image processing illustrate the efficiency and competitiveness of the proposed algorithm.

Statics and kinematics are often viewed as intertwined branches of mechanics. The principle of virtual work indicates this interconnection: For a system in static equilibrium, the total work performed by all forces during any virtual displacement must equal zero. In this work, we make the interplay between statics and kinematics more explicit by focusing on two engineering structures-tensegrity and origami. Specifically, we demonstrate a quantitative duality relationship between the states of self-stress of tensegrity and the infinitesimal mechanisms of origami. More importantly, we show that this duality remains invariant under nondegenerate linear transformations applied to the tensegrity and origami configurations. Furthermore, we establish that the stability property of tensegrity, particularly superstability, is preserved under such transformations. We apply the invariant duality theory to tensegrity and origami structures with prismatic and polyhedral geometries, illustrating its broad applicability. Such duality is also applicable to the fast generation of irregular, three-dimensional architected materials and structures.

In the era of digital communication, multimedia design has become a key tool for enhancing advertising, user interfaces, and brand communication. Dynamics, sound, and interaction—core elements of multimedia design—strongly influence visual impact and memory formation. However, current research mainly focuses on individual elements, lacking a systematic understanding of their synergistic effects. To address this gap, this study proposes a multimedia memory formation model based on multimodal memory theory, dual coding theory, and the working memory model. Case analysis and experiments have found that dynamic design boosts visual appeal and attention span, synchronized sound effects enhance emotional engagement and short-term memory, and interactive design strengthens long-term memory through active user participation. The study develops a dual evaluation index system, confirming the integrative power of multimedia elements. It not only advances theoretical understanding but also offers practical strategies for optimizing multimedia synergy in visual communication.

The digital economy has transformed how organisations communicate with stakeholders, creating demand for cross-media design strategies that deliver coherent, persuasive, and measurable messages across platforms. This article examines the theoretical foundations, design principles, and qualitative research methodology necessary to study cross-media design practices in contemporary business communication. Drawing on semiotics, media richness theory, dual coding theory, and affordance theory, the paper develops an integrated theoretical framework to analyse how cross-media strategies shape stakeholder perceptions, brand meaning, and engagement. The methodological section presents a robust qualitative design—constructivist grounded theory combined with multimodal discourse analysis and in-depth interviewing—suitable for exploring practitioner perspectives and organisational practices. The paper concludes with implications for practitioners, suggestions for pedagogical curricula, limitations, and directions for future research. Keywords: cross-media design, business communication, digital economy, multimodal discourse, qualitative methodology, theoretical framework.