The Theory and Applications of Hölder Widths by Man Lu, Peixin Ye

“…Then, we investigate the relationship between Hölder widths and other widths, showing that some Hölder widths are essentially smaller than <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi></mrow></semantics></math></inline-formula>-Kolmogorov widths and linear widths. …”
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On the Fractional Dynamics of Kinks in Sine-Gordon Models by Tassos Bountis, Julia Cantisán, Jesús Cuevas-Maraver, Jorge Eduardo Macías-Díaz, Panayotis G. Kevrekidis

“…In particular, we modified the order <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> of the temporal derivative to that of a Caputo fractional type and found that, for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>β</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula>, this imposes a dissipative dynamical behavior on the coherent structures. …”
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Incoherency Problems in a Combination of Description Logics and Rules by Shasha Huang, Jing Hao, Dang Luo

“…At last, we investigate the relationship between suspicious semantics and paraconsistent semantics.…”
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Solutions of Cauchy Problems for the Caudrey–Dodd–Gibbon–Kotera–Sawada Equation in Three Spatial and Two Temporal Dimensions by Yufeng Zhang, Linlin Gui

“…Finally, the solutions of Cauchy problems for the CDGKS equation in three spatial and two temporal dimensions are constructed by introducing a novel nonlocal <i>d</i>-bar formalism, in which several new long derivative operators, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>D</mi><mi>x</mi></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>D</mi><mi>y</mi></msub></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>D</mi><mi>t</mi></msub></semantics></math></inline-formula>, are constructed for the study of the initial value problem for the CDGKS equation. …”
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The Axiomatic Characterization of the Grey Shapley Value by Mehmet Gençtürk, Mahmut Sami Öztürk, Osman Palancı

“…In this study, the grey Shapley value is characterized by the following axioms: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-gain loss, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-null player, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">G</mi></semantics></math></inline-formula>-differential marginality. …”
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Seasonal Mathematical Model of Salmonellosis Transmission and the Role of Contaminated Environments and Food Products by Mohammed H. Alharbi, Fawaz K. Alalhareth, Mahmoud A. Ibrahim

“…Further simulations examined the dynamics of disease extinction and persistence based on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">R</mi><mn>0</mn></msub></semantics></math></inline-formula>. …”
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Prospects for the Use of Quasi-Mersen Numbers in the Design of Parallel-Serial Processors by Aruzhan Kadyrzhan, Kaisarali Kadyrzhan, Akhat Bakirov, Ibragim Suleimenov

“…Such a set of prime numbers satisfies the criterion <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><msub><mi>p</mi><mn>1</mn></msub><msub><mi>p</mi><mn>2</mn></msub><msub><mi>p</mi><mn>3</mn></msub><msub><mi>p</mi><mn>4</mn></msub><mo>+</mo><mn>1</mn><mo>=</mo><mi>P</mi></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>P</mi></semantics></math></inline-formula> is also a prime number. …”
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An Effective Iterative Process Utilizing Transcendental Sine Functions for the Generation of Julia and Mandelbrot Sets by Khairul Habib Alam, Yumnam Rohen, Anita Tomar, Naeem Saleem, Maggie Aphane, Asima Razzaque

“…Moreover, we apply <i>s</i>-convexity to the iteration procedure to construct orbits under convexity conditions, and we present a theorem that determines the condition when a sequence diverges to infinity, known as the escape criterion, for the transcendental sine function <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo form="prefix">sin</mo><mo>(</mo><msup><mi>u</mi><mi>m</mi></msup><mo>)</mo><mo>−</mo><mi>α</mi><mi>u</mi><mo>+</mo><mi>β</mi></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>u</mi><mo>,</mo><mi>α</mi><mo>,</mo></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>β</mi><mo>∈</mo><mi mathvariant="double-struck">C</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>≥</mo><mn>2</mn></mrow></semantics></math></inline-formula>. …”
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On the Evidence of Dynamical Dark Energy by Qing Gao, Zhiqian Peng, Shengqing Gao, Yungui Gong

“…While the DESI BAO data slightly tightens the constraints on model parameters and increases the tension between the Chevallier–Polarski–Linder (CPL) model and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Λ</mo></semantics></math></inline-formula>CDM model, we find that the influence of DESI BAO data on the constraint of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>w</mi><mn>0</mn></msub></semantics></math></inline-formula> is small in the SSLCPL model. …”
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Towards an Automated Design Evaluation Method for Wire Arc Additive Manufacturing by Johannes Pusicha, Henrik Stromberg, Markus Quanz, Armin Lohrengel

“…An angle of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mn>65</mn><mo>°</mo></msup></semantics></math></inline-formula> is identified as an effective separation limit. …”
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Impact of Key DMD Parameters on Modal Analysis of High-Reynolds-Number Flow Around an Idealized Ground Vehicle by Hamed Ahani, Mesbah Uddin

“…Key findings show that a 90% contribution to the pressure drag comes from modes with a frequency of less than 26 Hz (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>t</mi></mrow></semantics></math></inline-formula> = 0.187), while the friction drag requires 84 Hz (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>t</mi></mrow></semantics></math></inline-formula> = 0.604) for similar energy capture. …”
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Supervised vs. Self-Managed Exercise Therapy for Improving Shoulder Function After Traumatic Dislocation and Sprain: A Systematic Review and Meta-Analysis by Daniel Koska, Robert Zetzsche, Tobias A. Mayer, Christian Maiwald

“…Both treatment modes showed similar pooled effects (standardized mean difference, SMD_conservative: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>0.35</mn></mrow></semantics></math></inline-formula>, 95% CI [<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>1.39</mn></mrow></semantics></math></inline-formula>, 0.69]; SMD_{post-surgical}: <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>0.23</mn></mrow></semantics></math></inline-formula>, 95% CI [<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>−</mo><mn>1.21</mn></mrow></semantics></math></inline-formula>, 0.75]), with a marginal improvement in shoulder function favoring supervised therapy. …”
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Synthesis of Nanocrystalline Mn-Doped Bi₂Te₃ Thin Films via Magnetron Sputtering by Joshua Bibby, Angadjit Singh, Emily Heppell, Jack Bollard, Barat Achinuq, Sarah J. Haigh, Gerrit van der Laan, Thorsten Hesjedal

“…This study reports the structural and magnetic properties of Mn-doped <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>Bi</mi><mn>2</mn></msub><msub><mi>Te</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula> thin films grown by magnetron sputtering. …”
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Polynomial Identities for Binomial Sums of Harmonic Numbers of Higher Order by Takao Komatsu, B. Sury

“…</mo></mrow></semantics></math></inline-formula> Recently, Mneimneh proved that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">D</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>. …”
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Optimization of the Screw Conveyor Device Based on a GA-BP Neural Network by Qiang Guo, Yunpeng Zhuang, Houzhuo Xu, Wei Li, Haitao Li, Zhidong Wu

“…Specifically, when the outer diameter of the spiral for screw conveyance in the straw baler was <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mi mathvariant="normal">D</mi><mo>=</mo><mn>320</mn><mo> </mo><mi>mm</mi></mrow></mrow></semantics></math></inline-formula>, the pitch was <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mi mathvariant="normal">S</mi><mo>=</mo><mn>200</mn><mo> </mo><mi>mm</mi></mrow></mrow></semantics></math></inline-formula>, and the rotational speed of the pickup shaft was <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>138</mn><mo> </mo><mi>r</mi><mo>/</mo><mi>min</mi></mrow></semantics></math></inline-formula>, the straw baler could achieve the maximum conveying capacity and the minimum power consumption. …”
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Emergence of Self-Identity in Artificial Intelligence: A Mathematical Framework and Empirical Study with Generative Large Language Models by Minhyeok Lee

“…Our framework posits that self-identity emerges from two mathematically quantifiable conditions: the existence of a connected continuum of memories <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi><mo>⊆</mo><mi mathvariant="script">M</mi></mrow></semantics></math></inline-formula> in a metric space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="script">M</mi><mo>,</mo><msub><mi>d</mi><mi mathvariant="script">M</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula>, and a continuous mapping <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>I</mi><mo>:</mo><mi mathvariant="script">M</mi><mo>→</mo><mi mathvariant="script">S</mi></mrow></semantics></math></inline-formula> that maintains consistent self-recognition across this continuum, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi mathvariant="script">S</mi><mo>,</mo><msub><mi>d</mi><mi mathvariant="script">S</mi></msub><mo>)</mo></mrow></semantics></math></inline-formula> represents the metric space of possible self-identities. …”
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A Pilot Study on the Age-Dependent, Biomechanical Properties of Longitudinal Ligaments in the Human Cervical Spine by Narendra Singh, Ana Trajkovski, Jovan Trajkovski, Robert Kunc, Jose Felix Rodriguez Matas

“…The investigation concentrated on the effects of age on four mechanical parameters of the uniaxial stress–stretch curve: initial tangent stiffness (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>E</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></semantics></math></inline-formula>), maximum tangent stiffness (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>m</mi></mrow></msub></mrow></semantics></math></inline-formula>), ultimate stress (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>u</mi></mrow></msub></mrow></semantics></math></inline-formula>) and ultimate stretch (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mi>u</mi></mrow></msub></mrow></semantics></math></inline-formula>). …”
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Efficient Generative-Adversarial U-Net for Multi-Organ Medical Image Segmentation by Haoran Wang, Gengshen Wu, Yi Liu

“…For instance, in evaluations on the CHAOS T2SPIR dataset, EGAUNet achieves approximately <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mo>%</mo></mrow></semantics></math></inline-formula> higher performance on the Jaccard metric, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>%</mo></mrow></semantics></math></inline-formula> higher on the Dice metric, and nearly <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mo>%</mo></mrow></semantics></math></inline-formula> higher on the precision metric in comparison to advanced networks such as Swin-Unet and TransUnet.…”
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Effects of Thermodynamics on the Concurrent Accretion and Migration of Gas Giants in Protoplanetary Disks by Hening Wu, Ya-Ping Li

“…The thermodynamics effect is modeled with a thermal relaxation timescale using a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula>-cooling prescription. …”
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Optimization of Shear-Thickening Polishing Parameters for Optical Glass Based on Grey Relational Analysis by Yunxiao Han, Yangsi Yang, Binghai Lyu, Wei Hang, Xu Wang, Julong Yuan

“…Sixteen orthogonal experiments were conducted to assess the effects of polishing speed (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi></mrow></semantics></math></inline-formula>), angle (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>θ</mi></mrow></semantics></math></inline-formula>), and slurry concentration (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>C</mi></mrow></semantics></math></inline-formula>) on the material removal rate (MRR) and surface roughness (Ra). …”
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