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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Creating Balance on Bandwidth Consumption using Network Coding in Wireless Sensor Networks by Ehsan Kharati

“…For this purpose, we need to calculate the derivative of the Lagrangian function relative to its variables, in order to determine the condition as a multi-excited multi-equation device. …”
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Multimodality Data Integration in Epilepsy by Otto Muzik, Diane C. Chugani, Guangyu Zou, Jing Hua, Yi Lu, Shiyong Lu, Eishi Asano, Harry T. Chugani

“…Moreover, an effort was made to derive quantitative variables (such as the spatial proximity index, SPI) characterizing the relationship between complementing modalities on a more generic level as a prerequisite for efficient data mining strategies. …”
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Diversity and interdomain networks of bacterial, pico-protist and nano-protist communities in a marine ranching by Xinyi Zheng, Xin Guo, Xin Guo, Xiaoqing Lin, Cheng Huang, Lingfeng Huang

“…Although seasonal fluctuations in environmental variables generally influence microbial community dynamics, our comprehension of interdomain microbial co-occurrence patterns remains incomplete. …”
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Optimal Design Method of Integrated Energy Systems Considering Staged Planning and Equipment Replacement by Lei ZOU, Yiming TANG, Zhuping LIU, Zhengyong WU, Chao FANG, Chaoqun WANG, Fushuan WEN

“…Then, with the whole project cycle as the optimization time scale, the relationship between the equipment installation year and the current remaining life is modeled by introducing the equipment selection and operation decision variables. Finally, considering the influence of economic factors such as nominal interest rates and inflation rates, an objective function, involving investment costs, operating costs, and equipment residual value income, is constructed, with the optimal economical performance as the goal. …”
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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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Multi-Scale Multi-Domain Hybrid Finite Element Modeling of Light Propagation by Jingwei Wang, Zhanwen Wang, Lida Liu, Yuntian Chen

“…We revisit finite element method of modeling multi-scale photonic/electromagnetic devices via the proposed beam basis function, in combination with domain decompositions. …”
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Interval Economic Dispatch for Commercial Campus Integrated Energy System with Demand Response Considering Multiple Uncertainties by Xuan Sheng, Shunjiang Lin, Weikun Liang, Yue Pan, Mingbo Liu

“…Test results from actual CCIES demonstrate that the DR can improve the economy and reduce the uncertain fluctuation range of both the objective function and state variables. The ED result can maintain an economical and secure operation under multiple uncertain fluctuations.…”
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Construction Concrete Price Prediction Based on a Double-Branch Physics-Informed Neural Network by Kaier Shi, Ruiqing Han, Zhipeng Li, Pan Guo

“…Traditional price prediction of construction material concrete often adopts macroeconomic indicators as independent variables. However, since there is often a closer relationship between the raw materials of construction concrete and the production of construction materials, the price prediction of construction concrete based on raw material prices can more directly ensure the prediction accuracy. …”
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Peak Arm Current Reduction of Modular Multilevel Converter Based on Particle Swarm Optimizer for Circulating Current Injections by Riyadh Toman Thahab, Tahani Hamodi Al-Mhana

“…The magnitude and phase of the injected components are treated as variables in the optimisation process, with the goal of minimising the peak arm current as the cost function. …”
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THE PROPOSAL MODEL OF RATIONAL WORKFORCE ASSIGNMENT IN DOKUZ EYLUL UNIVERSITY BY ANALYTIC HIERARCHY PROCESS BASED 0-1 INTEGER PROGRAMMING by Yılmaz GÖKŞEN, Hakan AŞAN, Onur DOĞAN, Mustafa ÜNLÜ, Osman PALA

“…The Assignment model of the type of linear programming models is a mathematical method used to match the right person for the right job. The coefficients of the variables in the objective function of the assignment model constitute potential contributions of employees. …”
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Large live biomass carbon losses from droughts in the northern temperate ecosystems during 2016-2022 by Xiaojun Li, Philippe Ciais, Rasmus Fensholt, Jérome Chave, Stephen Sitch, Josep G. Canadell, Martin Brandt, Lei Fan, Xiangming Xiao, Shengli Tao, Huan Wang, Clément Albergel, Hui Yang, Frédéric Frappart, Mengjia Wang, Ana Bastos, Philippe Maisongrande, Yuanwei Qin, Zanpin Xing, Tianxiang Cui, Ling Yu, Lei He, Yi Zheng, Xiangzhuo Liu, Yuqing Liu, Aurelien De Truchis, Jean-Pierre Wigneron

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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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Effects of shading on photosynthetic characteristics and shade-tolerance evaluation of three Ranunculaceae plants by HAN Ruiting, ZHAO Dandan, WANG Weiyi, ZHANG Gexiang*

“…The light saturation point(LSP), light compensation point(LCP)and dark respiration rate(Rd)of the three plants decreased gradually.(3)The original fluorescence(Fo)decreased first and then increased, while the maximum fluorescence(Fm), variable fluorescence(Fv), maximum photochemical efficiency of PS Ⅱ(Fv/Fm)and potential activity of PS Ⅱ(Fv/Fo)values increased first and then decreased; the quantum ratio of heat dissipation(φDo)and the energy dissipated per unit reaction center(DIo/RC)decreased first and then increased, while electron transport quantum yield(φEo), light energy absorbed per unit reaction center(ABS/RC), light energy captured per unit reaction center(TRo/RC), energy used to transfer electrons per unit reaction center(ETo/RC), photosynthetic performance index(PIabs)and comprehensive performance index(PItotal)increased first and then decreased.(4)Comprehensive analysis on 20 single indicators by using analysis methods such as principal component analysis and membership function method showed that the shade-tolerance of the three plants ranked as Thalictrum fortunei > Delphinium anthriscifolium var. savatieri > R. japonicus. …”
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A Predictive Model for Estimating Reservoir Impounding Time Based on the Net Inflow and Storage Volume by Harimukti Rosita R., Pitojo T. Juwono, Lily M. Limantara, Emma Yuliani

“…The methodology involves analysing existing conditions (based on observed data from initial impounding in several reservoirs), identifying influential variables, and developing a predictive model for reservoir impounding duration. …”
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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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Study on the Photosynthetic Physiological Responses of Greenhouse Young Chinese Cabbage (<i>Brassica rapa</i> L. <i>Chinensis Group</i>) Affected by Particulate Matter Based on Hyp... by Lijuan Kong, Siyao Gao, Jianlei Qiao, Lina Zhou, Shuang Liu, Yue Yu, Haiye Yu

“…Particulate matter affects both the light environment and air quality in greenhouses, obstructing normal gas exchange and hindering efficient physiological activities such as photosynthesis. …”
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