Personally, I think "change of variable" is an important trick in computational math. If we can see the connection of two classes of problems using change of variables, then the algorithms designed for one class can be applied to another class. However, there are some problems. Firstly, if...
As first demonstrated by the characterization of the quantum Hall effect by the Chern number, topology provides a guiding principle to realize the robust properties of condensed-matter systems immune to the existence of disorder. The bulk–boundary corre
Ch 6.CSET Math: Functions Ch 7.CSET Math: Linear Algebra Vector in Math | Definition, Types & Examples6:27 Performing Operations on Vectors in the Plane5:28 How to Find Unit Vector & Normal Vector | Formula & Examples4:13 Linear Equations | Definition, Formula & Solution7:28 ...
Article MathSciNet MATH Google Scholar Abadi, A.: Nonlinear Dynamics of Self-excitation in Antoparametric Systems. Ph.D. Thesis, University of Utrecht, University of Utrecht (2003) Szabelski, K., Warminski, J.: Parametric self-excited nonlinear-system vibrations analysis with inertial excitation...
Next, we convert it to binary values (1 representing material and 0 representing void) by considering a threshold t sampled as \(t \sim {{{\mathcal{U}}}(0,{t}_{\max })\) with tmax = 3/5, which was chosen to increase the variance (in terms of sparsity) of the sampled st...
This result is the hyperbolic counterpart to seminal works on the parabolic Φ34-model by Hairer (Invent. Math. 198(2):269–504, 2014) and Hairer-Matetski (Ann. Probab. 46(3):1651–1709, 2018). The heart of the matter lies in establishing local in time existence and uniqueness of ...
Math. Anal. 6 (1), 1-10 (2012).Sidorov D.N., Sidorov N.A. Convex majorants method in the theory of nonlinear Volterra equations. Banach J. Math. Anal. 6, 1, 2012, 1 - 10.Sidorov D.N. Convex majorants method in the theory of nonlinear Volterra equations / D.N. Sidorov, N....
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A definition of a piecewise continuous unpredictable function is provided, and theoretical results on the existence, uniqueness, and stability of discontinuous unpredictable solutions for linear impulsive differential equations are given. The authors use randomly determined unpredictable sequences, where the ...