Eigenvalue systems for integer orthogonal bases of multi-matrix invariants at finite N by Adrian Padellaro, Sanjaye Ramgoolam, Ryo Suzuki

“…While the restricted Schur basis relies on the Artin-Wedderburn decomposition of symmetric group algebras, the covariant basis relies on a variant which we refer to as the Kronecker decomposition. …”
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Change in Seasonality Pattern of EU Farmgate Milk Price by Jakub Olipra

“…Since 2007 farmgate milk prices in EU have become much more volatile and their seasonal pattern has stopped being so explicit. The purpose of this research is to test the hypothesis that seasonality still plays an important role in shaping farmgate milk prices in EU while its amplitude decreases together with the growing integration of the EU milk market with the global market. …”
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POD-DEIM Based Model Order Reduction for the Spherical Shallow Water Equations with Turkel-Zwas Finite Difference Discretization by Pengfei Zhao, Cai Liu, Xuan Feng

“…We consider the shallow water equations (SWE) in spherical coordinates solved by Turkel-Zwas (T-Z) explicit large time-step scheme. To reduce the dimension of the SWE model, we use a well-known model order reduction method, a proper orthogonal decomposition (POD). …”
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Numerical design of nonstationary wavelets: Enhanced filter design andapplications in image compression by A. Boussaad, Y. Fourar, K. Melkemi

“…This structured approach allows for explicit formulation of the dual filters while ensuring accurate decomposition and reconstruc-tion. …”
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Technical note: A comparative study of chemistry schemes for volcanic sulfur dioxide in Lagrangian transport simulations – a case study of the 2019 Raikoke eruption by M. Liu, M. Liu, L. Hoffmann, L. Hoffmann, J.-U. Grooß, J.-U. Grooß, Z. Cai, S. Grießbach, S. Grießbach, Y. Heng

“…By analyzing the dependence between the oxidants and <span class="inline-formula">SO₂</span> concentrations, correction formulas are derived to adjust the oxidant fields used in the explicit solution, leading to a good trade-off between computational efficiency and accuracy. …”
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Interference Analysis of Very Fast Transient Overvoltages in Gas-Insulated Substations Using a Hybrid Algorithm by Muhammad Bilal, Hafiz Muhammad Azib Khan, Abdul Mueed, Kamran Liaqat Bhatti, Syed Safdar Raza, Muhammad Siddique

“…The hybrid domain decomposition method-multilevel fast multi-pole algorithm (DDM-MLFMA) is presented herein. …”
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Note on warped compactification. Finite brane potentials and non-Hermiticity by Sudhakantha Girmohanta, Yuichiro Nakai, Motoo Suzuki, Yaoduo Wang, Junxuan Xu

“…It is accomplished by finding an explicit form of the general scalar product that re-establishes the orthogonality in the KK decomposition.…”
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Interpolation by Hankel Translates of a Basis Function: Inversion Formulas and Polynomial Bounds by Cristian Arteaga, Isabel Marrero

“…In this paper, we use the projection operators associated with an appropriate direct sum decomposition of the Zemanian space ℋμ in order to derive explicit representations of the derivatives SμmΦ and their Hankel transforms, the former ones being valid when m∈ℤ+ is restricted to a suitable interval for which SμmΦ is continuous. …”
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Protocol for exploring pathways to equitable outcomes in post-stroke aphasia and dysphagia. by Charles Ellis, Marcello Perraillon, Richard Lindrooth, Molly Jacobs, Karen Hegland, Anouk Grubaugh, Candice Adams-Mitchell

“…Evidence suggests that racial disparities may be partially explained by structural barriers that can arise from implicit and explicit provider biases, institutional practices, public policies, or characteristics of the community where patients reside and recover from their conditions. …”
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Jordanian deformation of the non-compact and s l 2 $$ \mathfrak{s}{\mathfrak{l}}_2 $$ -invariant XXX −1/2 spin-chain by Riccardo Borsato, Miguel García Fernández

“…We use explicit examples as well as the techniques of the coordinate and of the algebraic Bethe ansatz to discuss the construction of the (generalised) eigenvectors of the deformed model. …”
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Polynomial Approximation over Arbitrary Shape Domains by Mohammad J. Mahtabi, Arash Ghasemi, Amirehsan Ghasemi, James C. Newman

“…Furthermore, theorems are proved to show the convergence and accuracy of the proposed method, together with an explicit form of the Weierstrass theorem for polynomial approximation. …”
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The Higher Accuracy Fourth-Order IADE Algorithm by N. Abu Mansor, A. K. Zulkifle, N. Alias, M. K. Hasan, M. J. N. Boyce

“…This study develops the novel fourth-order iterative alternating decomposition explicit (IADE) method of Mitchell and Fairweather (IADEMF4) algorithm for the solution of the one-dimensional linear heat equation with Dirichlet boundary conditions. …”
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Contrastive Feature Disentanglement via Physical Priors for Underwater Image Enhancement by Fei Li, Li Wan, Jiangbin Zheng, Lu Wang, Yue Xi

“…Our framework employs a multi-stream decomposition architecture with three specialized decoders to disentangle the latent feature space into components associated with degradation and those representing high-quality features. …”
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FDAE: Lightweight Privacy Protection Based on Face Detection and Image Encryption by Li You, Qianqian Liu, Shuai Li, Tianyu Yang

“…Specifically, we developed a YOLOv7-based face detection algorithm, further enhanced with Explicit Visual Center (EVC) and Spatial Context Pyramid (SCP) modules, to accurately localize facial regions. …”
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Scaling limit of soliton lengths in a multicolor box-ball system by Joel Lewis, Hanbaek Lyu, Pavlo Pylyavskyy, Arnab Sen

“…We establish the sharp scaling of its ruin probabilities, Skorokhod decomposition, strong law of large numbers and weak diffusive scaling limit to a semimartingale reflecting Brownian motion with explicit parameters. …”
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MERGE: A Modal Equilibrium Relational Graph Framework for Multi-Modal Knowledge Graph Completion by Yuying Shang, Kun Fu, Zequn Zhang, Li Jin, Zinan Liu, Shensi Wang, Shuchao Li

“…Subsequently, a fusion approach based on low-rank tensor decomposition is adopted to align multiple modal features in both the explicit structural level and the implicit semantic level, utilizing the structural information inherent in the original knowledge graphs, which enhances the interpretability of the fused features. …”
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Assessing the Role of Energy Mix in Long-Term Air Pollution Trends: Initial Evidence from Poland by Mateusz Zareba

“…This study also investigates regional variations in pollution levels by analyzing correlations between geographic location, industrialization intensity, and the proportion of green areas across Poland’s administrative regions (Voivodeships). This spatially explicit approach provides deeper insights into the linkages between energy production and pollution distribution at a national scale. …”
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How much carbon is stored in the stem bark of Austrian trees? by Muhammed Sinan, Mathias Neumann, Hubert Hasenauer

“…It is currently common that the carbon stored in the bark is recorded as part of the total tree carbon stock (including the stump) and no explicit data is reported for bark carbon. Tree bark is an important, yet currently unknown, carbon storage, plays a vital role during the life of a tree and is important for the decomposition process following tree death. …”
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Spectral-spatial wave and frequency interactive transformer for hyperspectral image classification by Tahir Arshad, Bo peng, Ali Rahman, Rahim khan, Sajid Ullah khan, Sultan Alnazi, Nazik Alturki

“…While Convolutional Neural Networks (CNNs) and Transformers have shown strong capabilities in modeling local and global dependencies, most existing architectures operate directly on raw spectral-spatial inputs and lack explicit mechanisms for frequency-domain decomposition thereby overlooking potentially discriminative phase and frequency components. …”
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Vibration Signal Analysis for Intelligent Rotating Machinery Diagnosis and Prognosis: A Comprehensive Systematic Literature Review by Ikram Bagri, Karim Tahiry, Aziz Hraiba, Achraf Touil, Ahmed Mousrij

“…Articles that aligned with at least one of the targeted topics cited above and provided unique methods and explicit results qualified for retention, while those that were redundant or did not meet the established inclusion criteria were excluded. …”
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