Superfluidity in the stochastic limit by L. Accardi, S. V. Kozyrev

“…Starting from the usual Hamiltonian describing the interaction between the Bose condensate and the normal phase, we prove the existence of superfluidity in the stochastic limit and deduce a nonlinear (quadratic) kinetic equation describing the evolution of the density of superfluid liquid.…”
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Input-to-State Stability for Dynamical Neural Networks with Time-Varying Delays by Weisong Zhou, Zhichun Yang

“…By employing the Lyapunov-Krasovskii functional method and linear matrix inequalities (LMIs) technique, some new sufficient conditions ensuring the input-to-state stability (ISS) property of the nonlinear network systems are obtained. Finally, numerical examples are provided to illustrate the efficiency of the derived results.…”
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Some Difference Inequalities for Iterated Sums with Applications by Wu-Sheng Wang, Shanhe Wu

“…The main objective of this paper is to establish two new nonlinear sum-difference inequalities with multiple iterated sums. …”
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Some results on boundary value problems for functional differential equations by P. Ch. Tsamatos, S. K. Ntouyas

“…The results are based on the nonlinear Alternative, of Leray-Schauder and rely on a priori bounds on solutions. …”
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On Multiple Positive Solutions for Singular Fractional Boundary Value Problems with Riemann-Stieltjes Integrals by Lufeng Gu, Qiuyan Zhong, Zhuyan Shao

“…The nonlinearity possesses singularities on both its time and space variables. …”
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Research of the Multi Parameter Edge of Chaos of Non- linear Simple Pendulum System by He Shanghong, Xie Jin, Cheng Jiefeng, Cui Qingyu

“…It is demonstrated that,by using the obtained results can provide a convenient means to design a nonlinear simple pendulum with periodic motion.…”
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Optimal Control of a Viscous Shallow Water Equation by Wenbin Zhang, Jiangbo Zhou

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Nontrivial Solution for a Nonlocal Elliptic Transmission Problem in Variable Exponent Sobolev Spaces by Bilal Cekic, Rabil A. Mashiyev

“…In this paper, by means of adequate variational techniques and the theory of the variable exponent Sobolev spaces, we show the existence of nontrivial solution for a transmission problem given by a system of two nonlinear elliptic equations of p(x)-Kirchhoff type with nonstandard growth condition.…”
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Mathematical Fundamentals of Modern Linear Optics by Andrey V. Gitin

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The association of visceral and subcutaneous fat areas with phenotypic age in non-elderly adults, mediated by HOMA-IR and HDL-C by Yuanhong Liu, Min Xu, Liqing Wang, Linyun Meng, Mengran Li, Shumin Mu

“…For abdominal subcutaneous fat area (SFA), this relationship was nonlinear in individuals aged 18–44 years and 45–59 years, with thresholds of 2.969 m² and 3.394 m², respectively. …”
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Study on the Creep Constitutive Model of a Sandstone Rock under the Water-Rock Interaction by Zuosen Luo, Zuoxiang Zhu, Jianlin Li, Lehua Wang, Qiao Jiang, Jingyu Zhang, Eleyas Assefa, Huafeng Deng

“…Combined with the author’s previous research on the triaxial creep characteristics of sandstone under water-rock interaction, a nonlinear creep constitutive model was established to capture the degradation behavior of a sandstone rock due to cyclic wetting and drying of the reservoir water. …”
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Catastrophic and violent tornadoes: a detailed review of physical-mathematical models by Sergey A. Arsen’yev, Lev V. Eppelbaum

“…First, gravity forces and hurricane winds in the upper troposphere form a long nonlinear wave in the lower troposphere. Second, the wind in the upper atmosphere and nonlinearity amplifies the resulting gravity nonlinear wave, which propagates at the speed of the initial tidal wave. …”
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Seismic Evaluation and Retrofit of Reinforced Concrete Buildings with Masonry Infills Based on Material Strain Limit Approach by Mangeshkumar R. Shendkar, Denise-Penelope N. Kontoni, Sasankasekhar Mandal, Pabitra Ranjan Maiti, Omid Tavasoli

“…A three-dimensional four-storey building with masonry infills has been analyzed with nonlinear static adaptive pushover analysis by using the SeismoStruct software. …”
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Accelerated pseudo-transient method for elastic, viscoelastic, and coupled hydromechanical problems with applications by Y. Alkhimenkov, Y. Y. Podladchikov

“…Recent advancements have demonstrated the APT method's computational efficiency, particularly when applied to quasi-static nonlinear problems using Graphical Processing Units (GPUs). …”
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Shallow-Water Wave Dynamics: Butterfly Waves, X-Waves, Multiple-Lump Waves, Rogue Waves, Stripe Soliton Interactions, Generalized Breathers, and Kuznetsov–Ma Breathers by Sarfaraz Ahmed, Ujala Rehman, Jianbo Fei, Muhammad Irslan Khalid, Xiangsheng Chen

“…A nonlinear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mn>3</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>-dimensional nonlinear Geng equation that can be utilized to explain the dynamics of shallow-water waves in fluids is given special attention. …”
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Study on an Intelligent Prediction Method of Ticket Price in a Subway System with Public-Private Partnership by Shengmin Wang, Jun Fang, Lanjun Liu, Han Wu

“…This model not only makes full use of the powerful nonlinear modeling ability of the BP algorithm, but also takes advantage of the strong optimization ability and fast convergence speed of the SSA. …”
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Groundwater Level Forecasting in the Jakarta Groundwater Basin by Andi Agus Nur, Dani Ruswandi

“…The main advantage of AI models is their ability to reproduce nonlinear and complex processes without a full understanding of the underlying physics. …”
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Analysis of a No Equilibrium Linear Resistive-Capacitive-Inductance Shunted Junction Model, Dynamics, Synchronization, and Application to Digital Cryptography in Its Fractional-Ord... by Sifeu Takougang Kingni, Gaetan Fautso Kuiate, Romanic Kengne, Robert Tchitnga, Paul Woafo

“…A linear resistive-capacitive-inductance shunted junction (LRCLSJ) model obtained by replacing the nonlinear piecewise resistance of a nonlinear resistive-capacitive-inductance shunted junction (NRCLSJ) model by a linear resistance is analyzed in this paper. …”
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An Updating Method for Finite Element Models of Flexible-Link Mechanisms Based on an Equivalent Rigid-Link System by R. Belotti, R. Caracciolo, I. Palomba, D. Richiedei, A. Trevisani

“…Model updating is not straightforward since the resulting model is nonlinear and its coordinates cannot be directly measured. …”
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A State-of-the-Art Fractional Order-Driven Differential Evolution for Wind Farm Layout Optimization by Sichen Tao, Sicheng Liu, Ruihan Zhao, Yifei Yang, Hiroyoshi Todo, Haichuan Yang

“…Meanwhile, the Differential Evolution algorithm (DE), known for its strong global optimization ability and excellent performance in handling complex nonlinear problems, is well recognized in continuous optimization issues. …”
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