Growth-rate distributions of gut microbiota time series by E. Brigatti, S. Azaele

“…Here a neutral model based on a stochastic differential equation with demographic noise, which presents a closed form for these distributions, is used to describe the population dynamics of microbiota. …”
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Experimental Investigation and Analysis of Dynamic Buckling of Drill String in Horizontal Well by Fushen Ren, Baojin Wang, Lei Zhao, Anhe Zhu

“…This paper focuses on the rotational drill string in horizontal well. The differential equation of the dynamic buckling is established considering some various factors, including friction, the drill string-borehole interaction, and rotation, and the equations of the critical load of the sinusoidal buckling and the spiral buckling are derived. …”
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Analysis of Nonlinear Structural Dynamics and Resonance in Trees by H. Doumiri Ganji, S.S. Ganji, D.D. Ganji, F. Vaseghi

“…Many of such nonlinear differential equations are complicated to solve. Therefore, this paper focuses on an accurate and simple solution, Differential Transformation Method (DTM), to solve the derived equation. …”
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An innovative analytical method utilizing aboodh residual power series for solving the time-fractional newell-whitehead-segel equation by Seyed Edalatpanah, Eisa Abdolmaleki

“…One of the key advantages of our approach is that the Aboodh transformation operator converts the fractional differential equation into an algebraic equation, thereby significantly reducing the computational effort required in the subsequent algebraic steps. …”
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Network-level reproduction number and extinction threshold for vector-borne diseases by Ling Xue, Caterina Scoglio

“…Relationships between basic reproduction numbers of two deterministic network-based ordinary differential equation vector-host models, and extinction thresholds of corresponding stochastic continuous-time Markov chain models are derived under some assumptions. …”
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Dynamics of evolutionary competition between budding and lytic viral release strategies by Xiulan Lai, Xingfu Zou

“…In this paper, we consider the evolutionary competition between budding and lytic viral release strategies, using a delay differential equation model with distributed delay. When antibody is not established, the dynamics of competition depends on the respective basic reproductive ratios of the two viruses. …”
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A mathematical model of weight change with adaptation by Diana M. Thomas, Ashley Ciesla, James A. Levine, John G. Stevens, Corby K. Martin

“…Key factors are an adaptation of resting metabolic rate, non-exercise activity thermogenesis and dietary induced thermogenesis. We develop a differential equation model based on the first law of thermodynamics that incorporates all three adjustments along with natural age related reduction of the resting metabolic rate. …”
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HPM-Based Dynamic Sparse Grid Approach for Perona-Malik Equation by Shu-Li Mei, De-Hai Zhu

“…The Perona-Malik equation is a famous image edge-preserved denoising model, which is represented as a nonlinear 2-dimension partial differential equation. Based on the homotopy perturbation method (HPM) and the multiscale interpolation theory, a dynamic sparse grid method for Perona-Malik was constructed in this paper. …”
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Analysis and Study on Bending Vibration Frequency of New Corrugated Steel Web Composite Box Girder by Xiaomeng Zang, Genhui Wang, Zichen Zhang

“…In order to accurately analyze the bending vibration frequency of the new composite box girder, the effects of web folding effect, shear lag, and shear deformation are comprehensively considered in this paper, and the elastic control differential equation and natural boundary conditions of the composite box girder are established by using the Hamilton principle. …”
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A Strength Design Method of Cemented Backfill with a High Aspect Ratio by Zhi-zhihui Wang, Ai-xiang Wu, Hong-jiang Wang

“…Then, by the combination of the minor principal stress trajectory method and the horizontal slice method, an ordinary differential equation of stresses was established and then solved numerically. …”
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A weak invariance principle and asymptotic stability for evolution equations with bounded generators by E. N. Chukwu, P. Smoczynski

“…The theory is illustrated with an example of an integro-differential equation of interest in the theory of chemical processes. …”
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POSFUST RELIABILITY OF A NON-REPAIRABLE MULTI-STATE SYSTEM WITH POSFUST FAILURE RATE ESTIMATION by Harendra Yadav, Mukesh Kumar Sharma, Vishnu Narayan Mishra

“…In this approach, Markov process (multi-state system) is used for getting the governing differential equation for transition from one state to another state. …”
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A stochastic model for water-vegetation systems and the effect of decreasing precipitation on semi-arid environments by Shannon Dixon, Nancy Huntly, Priscilla E. Greenwood, Luis F. Gordillo

“…The model, a stochastic differential equation approximation derived from a Markov jump process, is used to generate extensive simulations that suggest a relationship between precipitation reduction and the desertification process, which might take several years in some instances.…”
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Aggregation and environmental transmission in chronic wasting disease by Olga Vasilyeva, Tamer Oraby, Frithjof Lutscher

“…Wedevelop a strategic differential equation model for ChronicWasting Disease and include direct and indirect transmission aswell as host aggregation into our model. …”
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Tensile Failure Mechanism of Antiseepage System for Slope with Solid Waste Underground Landfill by Liu Fei, Zhongxi Jiang

“…The analytical solutions of the tensile force and displacement of the antiseepage membrane was calculated through differential equation of equilibrium. With general slag and ardealite slag as the research objects, the major parameters affecting the internal tensile force of the antiseepage membrane were analyzed and studied by the combination of numerical and theoretical methods. …”
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Sandwich-Type Results and Existence Results of Analytic Functions Associated with the Fractional <i>q</i>-Calculus Operator by Sudhansu Palei, Madan Mohan Soren, Daniel Breaz, Luminiţa-Ioana Cotîrlǎ

“…Furthermore, we employ the existence of univalent solutions to a <i>q</i>-differential equation connected with a fractional <i>q</i>-integral operator of fractional order. …”
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Global dynamics of a simple model for wild and sterile mosquitoes by Yu Ichida, Yukihiko Nakata

“…Then, the global behavior of the solution of the two-dimensional ordinary differential equation system is classified in a two-parameter plane represented by the natural death rate of mosquitoes and the sterile mosquito release rate. …”
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Mathematical model of penetration of cylindrical electromagnetic fields with axial symmetry through the plane screen from permalloy by V. Т. Erofeenko

“…The boundary-value problem is based on the use of differential Maxwell equations and complementary nonlinear differential equation for the field of magnetization, characterizing the permalloy. …”
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Global dynamics of a vector-host epidemic model with age of infection by Yan-Xia Dang, Zhi-Peng Qiu, Xue-Zhi Li, Maia Martcheva

“…In this paper, a partial differential equation (PDE) model is proposed to explore the transmission dynamics of vector-borne diseases. …”
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Application of Laplace Transform For Solving Population Growth and Decay Models. by Natukunda, Pamellah

“…Laplace can be used to convert complex differential equations to a simpler form having polynomials, convert derivatives into multiple domain variables, and then convert the polynomials back to the differential equation using the Inverse Laplace transform, telecommunication field to send signals to both sides of the medium. …”
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