An explicit solution of coupled viscous Burgers' equation by the decomposition method by Doğan Kaya

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Explicit evaluations of subfamilies of the hypergeometric function $ _3F_2(1) $ along with specific fractional integrals by Abdelhamid Zaidi, Saleh Almuthaybiri

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Pauli decomposition via the fast Walsh-Hadamard transform by Timothy N Georges, Bjorn K Berntson, Christoph Sünderhauf, Aleksei V Ivanov

“…Such a decomposition requires significant computational resources for large matrices. …”
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Decomposition of Idempotent Operators on Hilbert <i>C</i>*-Modules by Wei Luo

“…For arbitrary (not necessarily adjointable) idempotent operators that admit a decomposition into linear combinations or products of two idempotents, we derive explicit representations for all such decompositions. …”
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Posets arising from decompositions of objects in a monoidal category by Kevin Ivan Piterman, Volkmar Welker

“…When this poset has finite height, we define decompositions and partial decompositions of X which are coherent with $\sqcup $ , and order them by refinement. …”
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Interpretable Supervised Muscle Network Decomposition by Multifactorial ANOVA-ICA by Jun-Ichiro Hirayama

“…Existing muscle network decomposition methods do not explicitly disentangle the influence of experimental factors such as task parameters or subject groups, hindering meaningful interpretation. …”
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From Domain Decomposition to Model Reduction for Large Nonlinear Structures by Leturcq, Bertrand, Le Tallec, Patrick

“…With this loading reduction, the local solution can be explicitly obtained from a small set of precomputed elementary elastic solutions. …”
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THE LEVI DECOMPOSITION OF THE LIE ALGEBRA M_2 (R)⋊gl_2 (R) by Edi Kurniadi, Henti Henti, Ema Carnia

“…In this resulst, it has been given by direct computations and we obtained that the explicit formula of Levi decomposition of  the affine Lie algebra  whose basis is  is written by  with is  is the Levi sub-algebra of  .…”
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Transformer-Based Decomposition of Electrodermal Activity for Real-World Mental Health Applications by Charalampos Tsirmpas, Stasinos Konstantopoulos, Dimitris Andrikopoulos, Konstantina Kyriakouli, Panagiotis Fatouros

“…In particular, the authors introduce the Feel Transformer, a novel Transformer-based model adapted from the Autoformer architecture, designed to separate phasic and tonic components without explicit supervision. The model leverages pooling and trend-removal mechanisms to enforce physiologically meaningful decompositions. …”
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Sparse high-dimensional decomposition of non-primary auditory cortical receptive fields. by Shoutik Mukherjee, Behtash Babadi, Shihab Shamma

“…These results confirm with explicit details the presumed hierarchical organization of the auditory cortex.…”
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Decomposition of Automorphisms of Certain Solvable Subalgebra of Symplectic Lie Algebra over Commutative Rings by Xing Tao Wang, Lei Zhang

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Multi-Satellite Task Parallelism via Priority-Aware Decomposition and Dynamic Resource Mapping by Shangpeng Wang, Chenyuan Zhang, Zihan Su, Limin Liu, Jun Long

“…First, we introduce a graph theoretic model to represent the task dependency and priority relationships explicitly, combined with a novel algorithm for task decomposition. …”
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<i>H</i>_∞ Control for Systems with Mechanical Constraints Based on Orthogonal Decomposition by Ahmad Aldaher, Sergei Savin

“…Our method is based on the orthogonal decomposition of the state variables and the use of two linear controllers and a Luenberger observer, tuned to achieve the desired properties of the closed-loop system. …”
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Modelling the effect of climate–substrate interactions on soil organic matter decomposition with the Jena Soil Model by M. Pallandt, M. Pallandt, M. Pallandt, M. Schrumpf, H. Lange, M. Reichstein, L. Yu, B. Ahrens

“…We use a mechanistic, microbially explicit SOC decomposition model, the Jena Soil Model (JSM), and focus on the depolymerisation of litter and microbial residues by microbes at different soil depths as well as the sensitivities of the depolymerisation of litter and microbial residues to soil warming and different drought intensities. …”
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A voxel-based approach for simulating microbial decomposition in soil: Comparison with LBM and improvement of morphological models. by Mouad Klai, Olivier Monga, Mohamed Soufiane Jouini, Valérie Pot

“…We also tested several numerical strategies, including implicit, explicit, synchronous, and asynchronous schemes. To validate our VGA, we compare it with LBioS, a 3D model that integrates diffusion (via the Lattice Boltzmann method) with biodegradation, and Mosaic, a Pore Network Geometrical Modelling (PNGM) which represents the pore space using geometrical primitives. …”
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A synthesis of <i>Sphagnum</i> litterbag experiments: initial leaching losses bias decomposition rate estimates by H. Teickner, H. Teickner, E. Pebesma, K.-H. Knorr

“…<p>Our knowledge of the magnitude and controls of <i>Sphagnum</i> decomposition rates is derived to a large extent from litterbag experiments that do not explicitly consider initial leaching losses. …”
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Wave-turbulence decomposition and turbulence parameterization in aquatic wave environments using improved Synchrosqueezed Wavelet Transform (iSWT) by Xingxing Zhao, Daobin Ji, Lianghong Long, Zhongyong Yang, Zhengjian Yang, Defu Liu, Andreas Lorke

“…The methods include Ensemble Empirical Modal Decomposition (EEMD), Phase method (PH), Variational Mode Decomposition (VMD), Synchrosqueezed Wavelet Transform (SWT) and improved Synchrosqueezed Wavelet Transform (iSWT). …”
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Multi-dimensional water quality indicators forecasting from IoT sensors: A tensor decomposition and multi-head self-attention mechanism. by Li Bo, Lv Junrui, Luo Xuegang

“…To overcome these limitations, we propose TGMHA (Tensor Decomposition and Gated Neural Network with Multi-Head Self-Attention), a novel hybrid model that integrates three key innovations: 1) Tensor-based Feature Extraction: We combine Standard Delay Embedding Transformation (SDET) with Tucker tensor decomposition to reconstruct raw time series into low-rank tensor representations, capturing latent spatio-temporal patterns while suppressing sensor noise. 2) Multi-Head Self-Attention for Inter-Indicator Dependencies: A multi-head self-attention mechanism explicitly models complex inter-dependencies among diverse water quality indicators (e.g., pH, dissolved oxygen, conductivity) via parallel feature subspace learning. 3) Efficient Long-Term Dependency Modeling: An encoder-decoder architecture with gated recurrent units (GRUs), optimized by adaptive rank selection, ensures efficient modeling of long-term dependencies without compromising computational performance. …”
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A Hybrid LMD–ARIMA–Machine Learning Framework for Enhanced Forecasting of Financial Time Series: Evidence from the NASDAQ Composite Index by Jawaria Nasir, Hasnain Iftikhar, Muhammad Aamir, Hasnain Iftikhar, Paulo Canas Rodrigues, Mohd Ziaur Rehman

“…This study proposes a novel hybrid forecasting approach designed explicitly for long-horizon financial time series. It incorporates LMD (Local Mean Decomposition), SD (Signal Decomposition), and sophisticated machine learning methods. …”
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HDF-Net: Hierarchical Dual-Branch Feature Extraction Fusion Network for Infrared and Visible Image Fusion by Yanghang Zhu, Mingsheng Huang, Yaohua Zhu, Jingyu Jiang, Yong Zhang

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