Opportunities for gas-phase science at short-wavelength free-electron lasers with undulator-based polarization control by Markus Ilchen, Enrico Allaria, Primož Rebernik Ribič, Heinz-Dieter Nuhn, Alberto Lutman, Evgeny Schneidmiller, Markus Tischer, Mikail Yurkov, Marco Calvi, Eduard Prat, Sven Reiche, Thomas Schmidt, Gianluca Aldo Geloni, Suren Karabekyan, Jiawei Yan, Svitozar Serkez, Zhangfeng Gao, Bangjie Deng, Chao Feng, Haixiao Deng, Wolfram Helml, Lars Funke, Mats Larsson, Vitali Zhaunerchyk, Michael Meyer, Tommaso Mazza, Till Jahnke, Reinhard Dörner, Francesca Calegari, Olga Smirnova, Caterina Vozzi, Giovanni De Ninno, Jonas Wätzel, Jamal Berakdar, Sadia Bari, Lucas Schwob, Jérémy R. Rouxel, Shaul Mukamel, Klaus Bartschat, Kathryn Hamilton, Luca Argenti, Nicolas Douguet, Nikolay M. Novikovskiy, Philipp V. Demekhin, Peter Walter

“…Their revolutionary and innovative developments have opened new fields of science regarding nonlinear light-matter interaction, the investigation of ultrafast processes from specific observer sites, and approaches to imaging matter with atomic resolution. …”
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Switch Reluctance Motor Control Based on Fuzzy Logic System by S. V. Aleksandrovsky, Yu. N. Petrenko

“…However, the SRM has the disadvantage of nonlinear characteristic and control. It is suggested to use controller based on fuzzy logic system. …”
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Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion by Yongchun Zhou, Xiaohui Ai, Minghao Lv, Boping Tian

“…Based on the norm in the Hilbert Space L2[0,1], the second order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion into the space spanned by nonlinear function subspace. Karhunen-Loève expansion for this process is obtained together with the relationship of that of a generalized Brownian bridge. …”
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Solving Fuzzy Volterra Integrodifferential Equations of Fractional Order by Bernoulli Wavelet Method by R. Mastani Shabestari, R. Ezzati, T. Allahviranloo

“…Using the collocation points, this method transforms the fuzzy fractional integrodifferential equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown coefficients. …”
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Triple Positive Solutions of a Nonlocal Boundary Value Problem for Singular Differential Equations with p-Laplacian by Jufang Wang, Changlong Yu, Yanping Guo

“…We establish the existence of triple positive solutions of an m-point boundary value problem for the nonlinear singular second-order differential equations of mixed type with a p-Laplacian operator by Leggett-William fixed point theorem. …”
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Higher-Order Equations of the KdV Type are Integrable by V. Marinakis

“…We show that a nonlinear equation that represents third-order approximation of long wavelength, small amplitude waves of inviscid and incompressible fluids is integrable for a particular choice of its parameters, since in this case it is equivalent with an integrable equation which has recently appeared in the literature. …”
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Exact Null Controllability for Fractional Nonlocal Integrodifferential Equations via Implicit Evolution System by Amar Debbouche, Dumitru Baleanu

“…We introduce a new concept called implicit evolution system to establish the existence results of mild and strong solutions of a class of fractional nonlocal nonlinear integrodifferential system, then we prove the exact null controllability result of a class of fractional evolution nonlocal integrodifferential control system in Banach space. …”
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Existence and Convergence of the Positive Solutions of a Discrete Epidemic Model by Zhijian Wei, Meitao Le

“…We consider a class of system of nonlinear difference equations arising from mathematical models describing a discrete epidemic model. …”
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Quasiperiodic Solutions of Completely Resonant Wave Equations with Quasiperiodic Forced Terms by Yixian Gao, Weipeng Zhang, Jing Chang

“…This paper is concerned with the existence of quasiperiodic solutions with two frequencies of completely resonant, quasiperiodically forced nonlinear wave equations subject to periodic spatial boundary conditions. …”
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Several Dynamic Properties of Solutions to a Generalized Camassa-Holm Equation by Zheng Yin

“…For a nonlinear generalization of the Camassa-Holm equation, we investigate the dynamic properties of solutions for the equation under the assumption that the initial value u0(x) lies in the space H1(R). …”
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The Convergence Ball and Error Analysis of the Relaxed Secant Method by Rongfei Lin, Qingbiao Wu, Minhong Chen, Lu Liu

“…Radius estimate of the convergence ball of the relaxed secant method is attained for the nonlinear equation systems with Lipschitz continuous divided differences of first order. …”
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Some Fixed Point Theorems for Boyd and Wong Type Contraction Mapping in Ordered Partial Metric Spaces with an Application by Santosh Kumar, Faustine Nziku

“…Finally, the existence of the solution of nonlinear integral equation is discussed as an application of the main result.…”
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Global stability for the prion equation with general incidence by Pierre Gabriel

“…We consider the so-called prion equation with the general incidence term introduced in [14], and we investigate the stability of the steady states.The method is based on the reduction technique introduced in [11].The argument combines a recent spectral gap result for the growth-fragmentation equation in weighted $L^1$ spaces and the analysis of a nonlinear system of three ordinary differential equations.…”
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On a general convergence for Broyden like update method by Rabindranath Sen, Rini Chattopadhyay, Tripti Saha

“…The role of Broyden's method as a powerful quasi-Newton method for solving unconstrained optimization problems or a system of nonlinear algebraic equations is well known. We offer here a general convergence criterion for a method akin to Broyden's method in Rn. …”
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Smooth Approximations of Global in Time Solutions to Scalar Conservation Laws by V. G. Danilov, D. Mitrovic

“…In order to solve the problem, we use and further develop the weak asymptotic method, recently introduced technique for investigating nonlinear waves interactions.…”
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Global Existence of Weak Solutions to a Fractional Model in Magnetoelastic Interactions by Idriss Ellahiani, EL-Hassan Essoufi, Mouhcine Tilioua

“…Some commutator estimates are used to prove the convergence of nonlinear terms.…”
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On the existence of a solution for some distributed optimal control hyperbolic system by Dariusz Idczak, Stanislaw Walczak

“…We consider a Bolza problem governed by a linear time-varying Darboux-Goursat system and a nonlinear cost functional, without the assumption of the convexity of an integrand with respect to the state variable. …”
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Bezier Curves Method for Fourth-Order Integrodifferential Equations by F. Ghomanjani, A. V. Kamyad, A. Kılıçman

“…The Bezier curves method is applied to solve both linear and nonlinear BVPs for fourth-order integrodifferential equations. …”
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Head Injury Reduction in Automobile Pedestrian Impact by David R. Lemmon, Ming-yi Wu, Ronald L. Huston

“…The procedures and analysis are conducted using a nonlinear dynamic finite element program for an Oldsmobile Ciera hood and a Ford Taurus hood/fender.…”
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Improved integrate-and-fire model for RSA by Michele Barbi, Angelo Di Garbo, Rita Balocchi

“…The model performance is evaluated using a test based on the nonlinear prediction approach. Moreover, a short comparative account of two similar models described in the literature is given.…”
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