THE OPTIMAL PRINCIPLE OF BELLMAN IN THE PROBLEM OF OPTIMAL MEANS DISTRIBUTION BETWEEN ENTERPRISES FOR THE EXPANSION OF PRODUCTION by A. Tarasenko, I. Egorova

“…The method of dynamic programming has been considered, which is used in solving multiple problems in economics, on the example of using Bellman’s optimality principle for solving nonlinear programming problems. On a specific numerical example, the features of the solution have been shown in detail with all the calculations. …”
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Nonexistence of Homoclinic Orbits for a Class of Hamiltonian Systems by Xiaoyan Lin, Qi-Ming Zhang, X. H. Tang

“…We give several sufficient conditions under which the first-order nonlinear Hamiltonian system x'(t)=α(t)x(t)+f(t,y(t)),  y'(t)=-g(t,x(t))-α(t)y(t) has no solution (x(t),y(t)) satisfying condition 0<∫-∞+∞[|x(t)|ν+(1+β(t))|y(t)|μ]dt<+∞‍, where μ,ν>1 and (1/μ)+(1/ν)=1, 0≤xf(t,x)≤β(t)|x|μ, xg(t,x)≤γ0(t)|x|ν, β(t),γ0(t)≥0, and α(t) are locally Lebesgue integrable real-valued functions defined on ℝ.…”
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Solution of the Falkner–Skan Equation Using the Chebyshev Series in Matrix Form by Abdelrady Okasha Elnady, M. Fayek Abd Rabbo, Hani M. Negm

“…A numerical method for the solution of the Falkner–Skan equation, which is a nonlinear differential equation, is presented. The method has been derived by truncating the semi-infinite domain of the problem to a finite domain and then expanding the required approximate solution as the elements of the Chebyshev series. …”
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Transient Interaction of a Spherical Shell with an Underwater Explosion Shock Wave and Subsequent Pulsating Bubble by H. Huang, K.C. Kiddy

“…The nonlinear interaction problem is analyzed by simultaneously solving the mass, momentum, and energy conservation equations together .with appropriate material constitutive equations governing the fluid dynamics of the explosion gaseous product and the water and the structural dynamics of the compliant shell. …”
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Consensus of Second-Order Multiagent Systems with Directed Signed Networks and Communication Delays by Huiqin Pei, Qiang Lai

“…First, under a strongly connected directed graph, some properties for signed digraph and the model of second-order MASs are provided. A distributed nonlinear consensus control protocol is proposed for implementing consensus of second-order MASs with signed digraph and communication delay. …”
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Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales by Yongkun Li, Chao Wang

“…Finally, as an application of our results, we study the existence of almost periodic solutions for an almost periodic nonlinear dynamic equations on time scales.…”
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A multi-base harmonic balance method applied to Hodgkin-Huxley model by Aymen Balti, Valentina Lanza, Moulay Aziz-Alaoui

“…Our aim is to propose a new robust and manageable technique, called multi-base harmonic balance method, to detect and characterize the periodic solutions of a nonlinear dynamical system. Our case test is the Hodgkin-Huxley model, one of the most realistic neuronal models in literature. …”
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Characterization of Lipschitz Spaces via Commutators of Fractional Maximal Function on the $p$-Adic Variable Exponent Lebesgue Spaces by Wu, Jianglong, Chang, Yunpeng

“…In this paper, the main aim is to give some characterizations of the boundedness of the maximal or nonlinear commutator of the $p$-adic fractional maximal operator $ \mathcal{M}_{\alpha }^{p}$ with the symbols belong to the $p$-adic Lipschitz spaces in the context of the $p$-adic version of variable Lebesgue spaces, by which some new characterizations of the Lipschitz spaces and nonnegative Lipschitz functions are obtained in the $p$-adic field context. …”
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Convergence of Monotone Generalized $\alpha$-nonexpansive Mappings in Ordered Hyperbolic Metric Spaces by Samir Dashputre, Kavita Sakure

“…Moreover, we provide an application of our results to nonlinear integral equations.…”
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A QP-Free Algorithm for Finite Minimax Problems by Daolan Han, Jinbao Jian, Qinfeng Zhang

“…The nonlinear minimax problems without constraints are discussed. …”
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Vector Bond Graph Method of Kineto- static Analysis for 3SPS + 1PS Paralell Robot by Wang Zhongshuang, Tao Yangyang, Liu Shang, Chen Ji

“…For the algebraic difficulties brought by differential causality and nonlinear junction structure in automatic modeling and kineto- static analysis of spatial robot mechanism,the effective bond graph augment method is proposed. …”
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Mathematical Formulation of Soft-Contact Problems for Various Rheological Models of Damper by Wiesław Grzesikiewicz, Artur Zbiciak

“…The main finding of the paper is a method of description of soft-contact phenomenon between rigid object and deformable rheological structure by the system of explicit nonlinear differential-algebraic equations easy for numerical implementation. …”
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An Index for Measuring Functional Diversity in Plant Communities Based on Neural Network Theory by Naiqi Song, Jin-Tun Zhang

“…The results showed that SOFM index was an effective method in the evaluation of functional diversity and its change in plant communities. Significant nonlinear correlations of SOFM index with the common used methods, FAD, MFAD, FDp, FDc, FRic, and FDiv indices, also proved that SOFM index is useful in the studies of functional diversity.…”
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Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate by Yongli Cai, Xixi Wang, Weiming Wang, Min Zhao

“…We investigate the complex dynamics of an epidemic model with nonlinear incidence rate of saturated mass action which depends on the ratio of the number of infectious individuals to that of susceptible individuals. …”
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Decoupling the Stationary Navier-Stokes-Darcy System with the Beavers-Joseph-Saffman Interface Condition by Yong Cao, Yuchuan Chu, Xiaoming He, Mingzhen Wei

“…Newton iteration will be used to deal with the nonlinear systems. Numerical results are presented to illustrate the features of the proposed method.…”
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A Verification and Evaluation Method for Top-down Design of Sprag Clutches by Yu Hao, Lu Min, Chen Liqiang, Li Zhengminqing

“…Based on this, a dynamic law of nonlinear positive correlation between load and the above indicators is obtained.…”
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Infinitely Many Eigenfunctions for Polynomial Problems: Exact Results by Yi-Chou Chen

“…For any polynomial yx, we assume that T:Rx→Rx is a nonlinear operator with Tyx=Fx, yx. In this paper, we will find an eigenfunction yx∈Rx to satisfy the following equation: Fx, yx=ayx for some eigenvalue a∈R and we call the problem Fx, yx=ayx a fixed point like problem. …”
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Effect of Variation of Hard Segment Content and Graphene-Based Nanofiller Concentration on Morphological, Thermal, and Mechanical Properties of Polyurethane Nanocomposites by Michał Strankowski

“…Both applied nanofillers influenced melting and crystallization of the PU matrix. The nonlinear viscoelastic behavior of the nanocomposites (Payne effect) was studied, and the results were compared with theoretical predictions.…”
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Adaptivity in Crashworthiness Calculations by Ted Belytschko, Sang-Ho Lee, I-Sheng Yeh, Jerry I. Lin, Chen-Shyh Tsay, James M. Kennedy

“…h-Adaptive finite element methods for nonlinear transient analysis by explicit time integration are described. …”
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ADAPTIVE FUZZY SLIDING MODE CONTROL FOR THE TURNTABLE SERVO SYSTEM by HUANG Pei, WANG XinYuan

“…The integral sliding mode surface is used to design the switching function and the fuzzy method is used to realize the high precision control of linear systems and nonlinear systems. The simulation results show that the adaptive fuzzy sliding mode control is not only robust and fast response speed,but also can greatly weaken the chattering phenomenon of sliding mode control under the similar control effect.…”
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