Revisiting the Group Classification of the General Nonlinear Heat Equation <i>u_t</i> = (<i>K</i>(<i>u</i>)<i>u_x</i>)<i>_x</i> by Winter Sinkala

“…In this paper, we revisit the group classification of the general nonlinear heat (or diffusion) equation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>u</mi><mi>t</mi></msub><mo>=</mo><msub><mfenced separators="" open="(" close=")"><mi>K</mi><mrow><mo>(</mo><mi>u</mi><mo>)</mo></mrow><mspace width="0.166667em"></mspace><msub><mi>u</mi><mi>x</mi></msub></mfenced><mi>x</mi></msub><mo>,</mo></mrow></semantics></math></inline-formula> where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mo>(</mo><mi>u</mi><mo>)</mo></mrow></semantics></math></inline-formula> is a non-constant function of the dependent variable. We present the group classification framework, derive the determining equations for the coefficients of the infinitesimal generators of the admitted symmetry groups, and systematically solve for admissible forms of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mo>(</mo><mi>u</mi><mo>)</mo></mrow></semantics></math></inline-formula>. …”
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Mandibular reconstruction outcomes for in-house patient-specific solutions by Matthew D. Marquardt, Erin Cowen, Rachel Fenberg, Natalia von Windheim, Margaret Lashutka, Abigail E. Reid, Amit Agarwal, Enver K. Ozer, Ricardo L. Carrau, James W. Rocco, Catherine T. Haring, Stephen Y. Kang, Nolan B. Seim, Matthew O. Old, Kyle K. VanKoevering

“…Inter-rater reliability was assessed via intraclass correlation coefficient. Demographic, clinical, surgical, and radiographic variables were also collected to profile cohort characteristics and outcomes. …”
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Developing CGMap: Characterizing Continuous Glucose Monitoring Data in Patients with Type 2 Diabetes by Shuzhen Bai, Chu Lin, Xiaoling Cai, Suiyuan Hu, Jing Wu, Ling Chen, Wenjia Yang, Linong Ji

“…However, glucose variability decreased with increased BMI. Meanwhile, greater glycemic variability was associated with worse islet function, higher baseline glucose level, and higher hemoglobin.…”
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Approximate analytical solution of a class of highly nonlinear time–fractional-order partial differential equations by Richard Olu Awonusika

“…The method assumes a fractional power series in the time variable whose expansion coefficients are functions of the space variable. …”
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The Cerebellum Posterior Lobe Associates with the Exophthalmos of Primary Hyperthyroidism: A Resting-State fMRI Study by Wen-Feng Liu, Yong-Qiang Shu, Pei-Wen Zhu, Biao Li, Wen-Qing Shi, Qi Lin, Yu-Xin Liu, Meng-Yao Zhang, You-Lan Min, Qing Yuan, Yi Shao

“…The interrelationships between the DC values and clinical variables in the patients with EOPH were evaluated using Pearson’s correlation coefficient. …”
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Effect of Pre-Trip Information in a Traffic Network with Stochastic Travel Conditions: Role of Risk Attitude by Yun Yu, Shiteng Zheng, Yuankai Li, Huaqing Liu, Jianan Cao

“…User equilibrium states of the two regimes have been analyzed, based on the canonical BPR travel time function with power coefficient <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi></mrow></semantics></math></inline-formula>. …”
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Evaluation of ChatGPT-4 as an Online Outpatient Assistant in Puerperal Mastitis Management: Content Analysis of an Observational Study by Fatih Dolu, Oğuzhan Fatih Ay, Aydın Hakan Kupeli, Enes Karademir, Muhammed Huseyin Büyükavcı

“…However, evaluator variability and the subjective nature of assessments highlight the need for further optimization of AI tools. …”
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Modelación de la Solubilidad de Panela Granulada y Otros Edulcorantes en Agua by Nelly Lara, Alejandra Clavijo, Verónica Barrera

“…Se evaluó el efecto de las variables independientes (genotipo  de caña panelera, temperatura de la fuente de calentamiento y la condición higiénica  de la caña) sobre las constantes de solubilidad de las muestras experimentales de panela granulada. …”
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Modelación de la Solubilidad de Panela Granulada y Otros Edulcorantes en Agua by Nelly Lara, Alejandra Clavijo, Verónica Barrera

“…Se evaluó el efecto de las variables independientes (genotipo  de caña panelera, temperatura de la fuente de calentamiento y la condición higiénica  de la caña) sobre las constantes de solubilidad de las muestras experimentales de panela granulada. …”
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Modelación de la Solubilidad de Panela Granulada y Otros Edulcorantes en Agua by Nelly Lara, Alejandra Clavijo, Verónica Barrera

“…Se evaluó el efecto de las variables independientes (genotipo  de caña panelera, temperatura de la fuente de calentamiento y la condición higiénica  de la caña) sobre las constantes de solubilidad de las muestras experimentales de panela granulada. …”
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Reliability of the Cutting Alignment Scoring Tool (CAST) to Assess Trunk and Limb Alignment During a 45-Degree Side-Step Cut by Lauren S Butler, Eryn K Milian, Amie DeVerna, Kevin Latz, Henry B Ellis, Alexa R Martinez, Kristin Hayden, Christian Gerstenkorn, Sara C Carpenito, Charles W Wyatt, Dai Sugimoto

“…The hypotheses were: 1) there would be good–to-excellent inter-rater and intra-rater reliability among sports medicine providers, 2) there would be good to almost perfect agreement for cut width and trunk lean variables and moderate to good agreement for valgus variables of the CAST…”
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Strong Amplitude Modulation of Hard-band X-Ray Quasiperiodic Oscillation with Soft-band Flux in RE J1034+396 by Ruisong Xia, Hao Liu, Yongquan Xue

“…They are highly correlated, with an average cross-correlation function (CCF) peak coefficient of 0.61 and a lag of approximately 3 ks. …”
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Solving Linear Programming Problems by Reducing to the Form with an Obvious Answer by Gleb D. Stepanov

“…From the coefficients of the mentioned functionals, a matrix is formed, which is called the LPP matrix. …”
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Faktor-Faktor yang Mempengaruhi Auditor Switching dengan Financial Distress sebagai Pemoderasi by Herninda Pitaloka, Agung Guritno

“…The analysis included descriptive statistical tests, model feasibility tests, classification matrix tests, the formation of logistic regression functions, partial parameter significance tests, simultaneous parameter significance tests, coefficients of determination tests and MRA tests. …”
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Distinctive Gait Variations and Neuroimaging Correlates in Alzheimer's Disease and Cerebral Small Vessel Disease by Xia Zhou, Wen‐Wen Yin, Chao‐Juan Huang, Si‐Lu Sun, Zhi‐Wei Li, Ming‐Xu Li, Meng‐Meng Ren, Ya‐Ting Tang, Jia‐Bin Yin, Wen‐Hui Zheng, Chao Zhang, Yu Song, Ke Wan, Yue Sun, Xiao‐Qun Zhu, Zhong‐Wu Sun

“…Gait metrics included the timed up and go (TUG) test, dual‐task TUG (DTUG) test, Berg balance scale (BBS), dual‐task cost (DTC), step length, gait speed, cadence and coefficient of variation of gait. The relationships among structural and perfusion variations, gait metrics and cognitive function were examined. …”
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EVALUATION OF A DECRESE IN WORK PRODUCTIVITY IN PATIENTS WITH RHEUMATOID ARTHRITIS by Olga Yuryevna Vakulenko, D V Goryachev, O A Krichevskaya, Sh F Erdes

“…HAQ and RA duration (months) are the most significant variables for predicting work ability.…”
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Application of Post-Occupancy Evaluation in the Design of Collegiatae Educational Space: (Case study: Faculty of Arts and Architecture, Islamic Azad University-Tehran South Branch) by Reza Naghdbishi, Zeinab Gohari

“…This analysis identified the relationship between research variables and evaluated their impact on the design. …”
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Gender-specific assessment of lipid profiles correlation with serum uric acid in non-dialysis chronic kidney disease patients: Prospective observational cross-sectional study by Yousuf Abdulkarim Waheed, Yousuf Abdulkarim Waheed, Huanhuan Yin, Jie Liu, Shifaa Almayahe, Maryam Bishdary, Karthick Kumaran Munisamy Selvam, Syed Muhammad Farrukh, Shulin Li, Shulin Li, Yanping Wang, Yanping Wang, Disheng Wang, Disheng Wang, Disheng Wang, Xinglei Zhou, Dong Sun, Dong Sun, Dong Sun

“…Using a multistage stratified sampling method based on age and SUA to examine the differences among groups, Spearman’s correlation and linear regression analysis were utilized to study the association between SUA and lipid profiles, and multivariate analysis to determine the effect of SUA quartiles on multiple dependent variables collectively.ResultsLDL-c was positively correlated with SUA levels, with Spearman’s correlation coefficients of R=0.3553 in males and 0.5137 in females (both with P&lt;0.0001). …”
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Long-term conservation tillage breaks the plough pan and promotes the development of preferential flow by Jinze Han, Jianye Li, Qiang Chen, Xingyi Zhang

“…Macropores and preferential flow critically regulate soil hydrological functions and ecosystem services in agricultural systems. …”
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Network Analysis of Key Instrumental Activities of Daily Living and Cognitive Domains for Targeted Intervention in US Older Adults Without Dementia: Cross-Sectional Study by Jiaying Li, Rendong He, Erh-Chi Hsu, Junxin Li

“…Network analysis identified central and bridge variables. Nonparametric and case-dropping bootstrap methods checked network stability. …”
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