Re-iterated approximation methods for nonlinear Volterra integral equations
Mathematical Modelling and AnalysisIn this article, the Newton-iteration scheme based upon iterated Galerkin operator is applied for solving non-linear Volterra Urysohn integral equations of the second kind for smooth and weakly singular kernels. A one step of improvement by iteration to
Samiran Chakraborty +3 more
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Advanced Science, EarlyView.A catalytic allosteric DNAzyme assay (SMART) is developed by engineering DNAzyme into a unimolecular biosensor, enabling highly sensitive and multiplex detection of small molecules and nucleic acids. SMART enables extraction‐free, one‐pot, one‐step, isothermal, and cost‐effective detection of biological markers, achieving >95% accuracy for rapid ...
Yanzhe Shen +12 more
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Polynomial Spline Collocation Methods for Volterra Integrodifferential Equations with Weakly Singular Kernels [PDF]
IMA Journal of Numerical Analysis, 1986 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Global dynamics of the Euler-alignment system with weakly singular kernel
, 2021 This letter studies the Euler-alignment system with weakly singular influence functions by introducing a novel technique to bound the density. Instead of resorting to a nonlinear maximum principle used in [C. Tan, Nonlinearity, 33: 1907--1924, 2020] to bound the interaction term $ \ast $ by $ ^s$ with $s\in (0, 1)$ for $ $ with an algebraic ...
Bhatnagar, Manas, Liu, Hailiang
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Smoothness of solutions of Volterra integral equations with weakly singular kernels [PDF]
Solution smoothness of Volterra integral equations with weakly singular ...
Feldstein, A., Miller, R. K.
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Hyperbolicity of varieties supporting a variation of Hodge structure [PDF]
, 2017 We generalize former results of Zuo and the first author showing some hyperbolicity properties of varieties supporting a variation of Hodge structure. Our proof only uses the special curvature properties of period domains.
Brunebarbe, Yohan, Cadorel, Benoit
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Smart Exploration of Perovskite Photovoltaics: From AI Driven Discovery to Autonomous Laboratories
Advanced Energy Materials, EarlyView.In this review, we summarize the fundamentals of AI in automated materials science, and review AI applications in perovskite solar cells. Then, we sum up recent progress in AI‐guided manufacturing optimization, and highlight AI‐driven high‐throughput and autonomous laboratories.
Wenning Chen +4 more
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An Efficient RBF-Based Collocation Approach for Second-Order Fractional Partial Integro-Differential Problems with Singular Kernel [PDF]
Journal of Applied and Computational MechanicsThis paper presents an efficient numerical method for solving second-order time-fractional partial integro-differential equations (PIDEs) with weakly singular kernels.
Arshed Ali, Imtiaz Ahmad
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A Quadrature Method for Cauchy Integral Equations with Weakly Singular Perturbation Kernel
Journal of Integral Equations and Applications, 1992 The authors study the singular integral equation \[ a(x)u(x)+\pi^{- 1}b(x)\int^{+1}_{-1}u(t)/(t-x)dt+\int^{+1}_{-1} k(x,t)u(t)dt=f(x) \] on \((-1,+1)\); the first integral is to be interpreted as the Cauchy principal value, \(a\), \(b\) and \(f\) are given Hölder continuous functions, and the perturbation kernel \(k\) is a given smooth or weakly ...
Mastroianni, Giuseppe +1 more
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Polynomial Spline Collocation Methods for Volterra Integrodifferential Equations with Weakly Singular Kernels [PDF]
, 2017 In this paper we investigate the attainable order of (global) convergence of collocation approximations in certain polynomial spline spaces for solution of Volterra integrodifferential equations with weakly singular kernels.
BRUNNER, HERMANN
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