Implement a nonuniform quantizer as the following piecewise function: y = -3.5, x < -3 y = -1.5, -3 ≤ x < -1 y = -0.5, -1 ≤ x < 0 y = 0.5, 0 ≤ x < 1 y = 1.5, 1 ≤ x < 3 y = 3.5, 3 ≤ x Your function should ac
PIECEWISE-LINEAR PHASEMORREY SPACESNon-standard grand-Lebesgue and Morrey spaces are considered in this work, together with grand-Sobolev and Morrey-Sobolev spaces generated by them. Dirichlet problems for Laplace equation in different versions are considered in these spaces in a bounded domain of n-...
A very important point in spectral methods is the appropriate selection of basis functions. For example, if the functions in the problem and its solution are sufficiently smooth (differentiable), polynomial basis functions, such as Chebyshev, Legendre, Bernstein, etc., are suitable functions for ...
There are a few special cases of periodic structures that exhibit non-affine transformations. For example, uniform bending, where all of the unit cells deform with the same radius of curvature, can be thought of transforming a line into a circle segment, such as when the synclastic bending be...
of the kernel should allow to relax the smoothness requirements on the dataf(orc, if we are solving the convolution equation). In the present paper we address thea priorianalysis of the gCQ for this important class of problems. More precisely, as a first step in the development of this ...
General Regions of Integration An example of a general bounded region DD on a plane is shown in Figure 1. Since DD is bounded on the plane, there must exist a rectangular region RR on the same plane that encloses the region DD, that is, a rectangular region RR exists such that DD is...
In this paper, a versatile solver of a nonconformal volume integral equation based on the Schaubert-Wilton-Glisson (SWG) basis function is presented. Instead of using a piecewise constant function, the robust conventional SWG basis function is chosen and used directly for discontinuous boundaries. ...
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also poses new challenges as the distribution evolves over time. Characterizi...
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Response curves: (a) β = 0; (b) β > 0; and (c) β < 0 2.4.3 Van der Pol’s equation As another application example of the perturbation method, we consider a self-excited system described by van der Pol’s equation: [2.241]x¨−ε1−x2x˙+ω2x=0 where the ...