Homotopic Approximate Solutions for the Perturbed CKdV Equation with Variable Coefficients by Dianchen Lu, Tingting Chen, Baojian Hong

“…This work concerns how to find the double periodic form of approximate solutions of the perturbed combined KdV (CKdV) equation with variable coefficients by using the homotopic mapping method. …”
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Global Existence and Blow-Up for the Euler-Bernoulli Plate Equation with Variable Coefficients by Jianghao Hao, Jie Lan

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Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations by Xiaoxiao Zheng, Yadong Shang, Yong Huang

“…By the results of the equation, the first integral method and the extended hyperbolic function method are extended from the constant coefficient nonlinear evolution equations to the variable coefficients nonlinear partial differential equation.…”
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A New Random Coefficient Autoregressive Model Driven by an Unobservable State Variable by Yuxin Pang, Dehui Wang

“…The autoregressive coefficient is an unknown function with an unobservable state variable, which can be estimated by the local linear regression method. …”
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3D Variable Coefficient KdV Equation and Atmospheric Dipole Blocking by Juanjuan Ji, Yecai Guo, Lanfang Zhang, Lihua Zhang

“…A (2 + 1)-dimensional variable coefficient Korteweg-de Vries (3D VCKdV) equation is first derived in this paper by means of introducing 2-dimensional space and time slow-varying variables and the multiple-level approximation method from the well-known barotropic and quasi-geostrophic potential vorticity equation without dissipation. …”
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Two-point boundary value problem for a partial differential equation in spaces of periodic functions by V.S. Ilkiv, Z.M. Nytrebych, P.Y. Pukach, M.I. Vovk

“…We investigate the two-point in time boundary value problem for the partial differential equations of the second-order with one spatial variable and constant coefficients. The problem is considered in in the spaces of functions which Fourier coefficients are characterized by exponential behavior on the Cartesian product of the time interval and spatial domain $\mathbb{R}/2\pi\mathbb{Z}$. …”
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Periodic Oscillation of Fuzzy Cohen-Grossberg Neural Networks with Distributed Delay and Variable Coefficients by Hongjun Xiang, Jinde Cao

“…A class of fuzzy Cohen-Grossberg neural networks with distributed delay and variable coefficients is discussed. It is neither employing coincidence degree theory nor constructing Lyapunov functionals, instead, by applying matrix theory and inequality analysis, some sufficient conditions are obtained to ensure the existence, uniqueness, global attractivity and global exponential stability of the periodic solution for the fuzzy Cohen-Grossberg neural networks. …”
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Genetics of Physiological Variation Within and Between Larval Wild-Type AB and Backcrossed NHGRI-1 Zebrafish (<i>Danio rerio</i>) by Gil Martinez-Bautista, Moira Ryann Cartee, Dyuksha Kunder, Crystelle Lee, Karol Tang, Neha Nagarajan, Pamela Padilla, Warren Burggren

“…To explore the role of genetics in physiological variation, we assessed variation of cardiac function (heart rate, stroke volume, and cardiac output), oxygen consumption, yolk conversion efficiency, and cost of development in embryonic and larval AB wild-type and NHGRI-1 zebrafish (low heterozygosity line backcrossed from AB wild-type) exposed to different temperature and oxygen regimes. …”
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Experimental Characteristics of Mechanical Continuously Variable Transmission with Internal Force Functions by A. V. Yurkevich, A. V. Tereshin, V. A. Soldatkin

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Exact Soliton Solutions to the Variable-Coefficient Korteweg–de Vries System with Cubic–Quintic Nonlinearity by Hongcai Ma, Xinru Qi, Aiping Deng

“…Under the help of the wave ansatz method, we obtain the exact soliton solutions to the variable-coefficient KdV system, such as the dark and bright soliton solutions, Tangent function solution, Secant function solution, and Cosine function solution. …”
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Propagation Properties of Laguerre–Gaussian Beams with Three Variable Coefficient Modulations in the Fractional Schrödinger Equation by Xinru Hao, Yong Liang, Min Zou, Bin Zhong, Chao Tan

“…This article investigates the transmission characteristics of Laguerre–Gaussian (LG) beams under cosine modulation, power function modulation and linear modulation based on the variable coefficient fractional Schrödinger equation (FSE), respectively. …”
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Calculation of heating laminar fluid flow with variable heat transfer coefficient on the surface of circular channel by U. V. Vidin, V. S. Zlobin, R. V. Kazakov

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Variable step-size LMS algorithm with hybrid weight coefficients based on the Rayleigh distribution curve by CHEN Dongwei, LIU Weidong, ZHANG Mingyi, JIN Mengzhe, FANG Qingyuan

“…The impact of the new variable step function parameters <italic>α</italic>, <italic>β</italic>, <italic>γ</italic> and the hybrid filter weight coefficient <italic>W</italic>(<italic>n</italic>) on the proposed algorithm performance and interference suppression analysis were discussed in detail. …”
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Lie Group Classification of a Class of Variable Coefficient Boiti–Leon–Manna–Pempinelli Equations by Christodoulos Sophocleous

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Novel Nonlinear Dynamical Solutions to the (2 + 1)‐Dimensional Variable Coefficients Equation Arise in Oceanography by Hajar F. Ismael, Tukur Abdulkadir Sulaiman, Harivan R. Nabi, Shams Forruque Ahmed

“…The assistance of the Hirota bilinear method secures different forms of multiple solitons and M‐lump waves, such as one‐, two‐, and three‐soliton, by using different functions of variable coefficients. Moreover, the long‐wave technique is under consideration when analyzing hybrid solutions, namely mixed soliton‐lump, two‐soliton‐lump, and soliton‐two‐lump solutions. …”
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Interdecadal Variability of Summer Precipitation Efficiency in East Asia by Jian Wang, Shu Gui, Anqi Ma, Ruowen Yang, Qi Zhang

“…Two major modes of summertime precipitation efficiency are identified using Empirical Orthogonal Function (EOF) analysis. …”
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Research on Energy-Efficient Building Design Using Target Function Optimization and Genetic Neural Networks by Youxiang Huan

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Statistical Inference for the Heteroscedastic Partially Linear Varying-Coefficient Errors-in-Variables Model with Missing Censoring Indicators by Yuye Zou, Chengxin Wu

“…In this paper, we focus on heteroscedastic partially linear varying-coefficient errors-in-variables models under right-censored data with censoring indicators missing at random. …”
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Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients by Zhao Li, Peng Li, Tianyong Han

“…Finally, the periodic wave solutions, implicit analytical solutions, hyperbolic function solutions, and Jacobian elliptic function solutions of the coupled nonlinear Schrödinger equations with variable coefficients are constructed.…”
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Series Solution Method Used to Solve Linear Caputo Fractional Initial Value Problems with Variable Coefficients by Aghalaya S Vatsala, Govinda Pageni

“…Computing the solution of the linear Caputo fractional differential equation with variable coefficients cannot be obtained in closed form as in the integer-order case. …”
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