A New Method for Evaluating the Stability of Retaining Walls by Shiqi Zhang, Yingfa Lu, Lier Lu

“…Assuming that the soil wedge and retaining wall satisfy the Duncan–Zhang model and the linear elastic Hooke constitutive model, respectively, the strain solutions of the soil wedge and retaining wall are obtained. …”
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Quantifying flexibility and optimizing energy communities’ participation in energy markets through dispatch strategies: A Finnish case study by Hussain Ahmed, Matti Vilkko

“…The problem is formulated as a mixed-integer linear programming model, integrating unit commitment and economic dispatch optimization concepts. …”
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Relationship between depression improvement and activities of daily living recovery in patients with fractures by Shunji Araki, Takahiro Ogawa, Yoshikazu Takaesu

“…Patients were classified into three groups based on change in depressive symptoms: remission, partial improvement, and no improvement. Multivariate linear regression analysis was used to evaluate factors associated with change in the FIM score. …”
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Improving resilience of networked multi-energy carrier microgrids through proactive scheduling by Ali Akbar Ghasemi, Mohsen Gitizadeh, Mohammadali Norouzi

“…The optimization problem is modeled as a two-stage mixed-integer linear programming. In the first stage, scheduling of the microgrids is programmed in normal mode. …”
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Advanced Mathematical Model for the Transport of Aggregating Nanoparticles in Water Saturated Porous Media: Nonlinear Attachment and Particle Size‐Dependent Dispersion by Vasileios E. Katzourakis, Constantinos V. Chrysikopoulos

“…Furthermore, an efficient and accurate solver for the PBE, and an iterative solver for the linear or nonlinear attachment equations were employed. …”
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How do tree- and stand-level factors influence belowground biomass and carbon storage in tanoak (Notholithocarpus densiflorus)? by Brandon H. Namm, John-Pascal Berrill

“…Tree size was the best linear predictor of belowground biomass and carbon, indicating that a 25-cm diameter tanoak, for example, stored 70 kg of biomass and 34 kg of carbon in its root system. …”
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Stable and inert manganese complexes for magnetic resonance imaging by Ndiaye, Daouda, Tóth, Éva

“…We specifically focus on the molecular ligand design, including linear, macrocyclic and bicyclic (bispidine) chelators that allowed for substantially enhanced kinetic inertness of the complexes, as well as for ligand selectivity for Mn$^{2+}$ versus the main biological competitor Zn$^{2+}$. …”
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Development of a wind-based storm surge model for the German Bight by L. Schaffer, L. Schaffer, A. Boesch, J. Baehr, T. Kruschke

“…In this study, we present a simple, effective storm surge model for the German Bight, utilizing a multiple linear regression approach based solely on 10 m effective wind speed as the predictor variable. …”
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A Capillary Model for Predicting Saturated Hydraulic Conductivity of Ion-Adsorption Rare Earth Ore Based on Improved Kozeny–Carman Equation by Liang Shi, Yun-zhang Rao, Dan Wang, Mei-dao Zhang, Tao Huang

“…According to the experimental results, the diameter of the capillary was calculated with Darcy's formula. Then we obtained a linear-fit relationship between capillary diameter and porosity to express the specific surface area variation with porosity. …”
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A fifth order block methods for solving second-order stiff ordinary differential equations using trigonometric functions and polynomial function as the basis function by Opoyemi O. Enoch, Catherine O. Alakofa

“…The numerical solution of second-order ordinary differential equations (ODEs) is examined in this work through a four-step linear multistep method. It employs a combination of trigonometric and polynomial functions as the approximate solution to the general second-order ordinary differential equations (ODEs). …”
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Nonlinear Decoupling Study of Six-Axis Acceleration Sensor Based on Improved BP Neural Network by Jialin Zhang, Chunzhan Yu, Chengxin Du, Zhe Hao, Zhibo Sun

“…Based on the mid-frequency standard vibration device APS 129 ELECTRO-SEIS (SPEKTRA, Stuttgart, Baden-Württemberg, Germany), the calibration data are obtained and the improved BP neural network decoupling model is trained to complete the nonlinear decoupling of the test set. Compared with the linear decoupling method, the decoupled six-axis accelerometers with the improved BP neural network model have acceleration measurement accuracies of 0.035%, 0.018% and 0.039% along the x, y and z axes, respectively, which indicates that the model has high decoupling accuracy, and it can significantly improve the measurement accuracy of the sensors. …”
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Feedback-Driven Dynamical Model for Axonal Extension on Parallel Micropatterns by Kyle Cheng, Udathari Kumarasinghe, Cristian Staii

“…Dynamical systems analysis reveals that a saddle–node bifurcation in the actin adhesion subsystem drives a transition to a high-traction motile state, while traction feedback shifts a pitchfork bifurcation in the signaling loop, promoting symmetry breaking and robust alignment. An exact linear solution in the tubulin transport subsystem functions as a built-in speed regulator, ensuring stable elongation rates. …”
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Some graph parameters of Indu-Bala product of graphs by Indulal Gopalapilla, John Joy Mulloor, Liju Alex, Deena Scaria

“…The Aα matrix associated with a graph is a convex linear combination of its adjacency matrix and degree diagonal matrix, offering deeper insights into the properties of both matrices. …”
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Enhanced Transformer Network With High-Dimensional Attention Mechanism for Diabetic Retinopathy Classification by M. Rizvana, Sathiya Narayanan

“…In addition, the classification head present in the ViT block incorporates sequential dropout layer in addition to the standard linear dropout layer. For experimentation, APTOS 2019 fundus image dataset containing 3662 images falling under 5 classes is used. …”
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Climate Change and Maize Yield in Iowa. by Hong Xu, Tracy E Twine, Evan Girvetz

“…Despite a wide range in the predicted amount of warming and change to summer precipitation, all simulations predict a decrease in maize yields from late 20th century to middle and late 21st century ranging from 15% to 50%. Linear regression of all models predicts a 6% state-averaged yield decrease for every 1°C increase in warm season average air temperature. …”
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Schema Understandability: A Comprehensive Empirical Study of Requirements Metrics by Tanu Singh, Vinod Patidar, Manu Singh, Álvaro Rocha

“…The study then employed six classification techniques—logistic regression, naive Bayes, linear discriminant analysis with decision tree, reinforcement learning, voting rule, and a hybrid approach—within both univariate and multivariate models to identify strong predictors of schema understandability. …”
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Development of Flow Injection Spectrophotometric Method for 1-Napthylthiourea Using Sodium Nitrite and Sulphanilic Acid Diazotization Reaction by Muhammad Asghar, Mohammad Yaqoob, Sami Ullah, Samar Ali, Nusrat Munawar, Abdul Nabi

“…The limit of detection (S/N = 3) is 0.01 mg/L with a sampling throughput of 45/h. The method is linear over the range of 0.05–120 mg/L (R2=0.9995,n=7), with calibration equation y = 0.031x−0.018 (y = absorbance; x = mg/L) and relative standard deviation (n=3) 1.8–3.6%. …”
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Desorption isotherms and isosteric heat of 'cajuzinho-do-cerrado' achenes by Karine F. Barbosa, Juliana de F. Sales, Osvaldo Resende, Daniel E. C. de Oliveira, Jacson Zuchi, Kelly A. de Sousa

“…Data of hygroscopic equilibrium moisture content were fitted to different mathematical models through non-linear regression analysis, using the Gauss-Newton method. …”
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In-Plane Stability of Circular Arch Under Uniform Vertical Load Based on the Asymptotic Method by Jing Jin, Mingzhou Su

“…The results show the following: (1) The parameter perturbation method is effective for the snap-buckling of a shallow arch, and the fifth-order solution is sufficiently accurate. (2) For shallow arches with a large modified slenderness ratio, the influence of the axial load component cannot be neglected. (3) Regardless of the rise-to-span ratio of the arch, the nonlinear bending moment is significantly larger than the linear bending moment. (4) In the anti-symmetric buckling analysis, the eigenvalue obtained using the second-order WKB method is smaller than that obtained using the third-order WKB method; therefore, the second-order solution can be used as the critical load. (5) For shallow arches with a small rise-to-span ratio, the critical load for anti-symmetric buckling closely matches the classical solution, and the results from arches subjected to a uniformly distributed radial load are reliable. …”
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The Impact of Urbanization on Greenhouse Gas Emissions: A Multidimensional Analysis by M. S. Bekturganova

“…The study is based on econometric analysis of panel data collected from 107 countries from 2004 to 2023 from the World Development Indicators (WDI) database, using linear regression models to examine the relationship between urbanization levels and CO₂ emissions. …”
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