Exponential kernel

In the opposite case of slow flip limit, cojp co, the exponential kernel can be approximated by the delta function, exp( —cUj t ) ii 2S(r)/coj, thus renormalizing the kinetic energy and, consequently, multiplying the particle s effective mass by the factor M = 1 + X The rate constant equals the tunneling probability in the adiabatic barrier I d(Q) with the renormalized mass M, ... 

For exponential kernel (1.77) t2 = 2t2 = t2. Consequently d2g(o))/da>2 o becomes positive only at k > 1/2. For this condition, which is also seen from Eq. (1.94), Kj(t) changes sign at sufficiently large t and the spectrum g(co) is split into two lines with a minimum in between. In contrast, the second moment of the kernel (1.95) diverges and... 

In general it is fair to say that rheologists have been conservative in their use of non-exponential kernels. One particular form clearly stands out as a candidate for describing experimental data, at least for a limited range of relaxation times. This is the power law equation, often applied to... 

Figure 10.1 A Gaussian kernel is shown in (a), and an exponential kernel is shown in (b).

Figure 10.2 A Gaussian and an exponential kernel for an image of 256 pixels.

Instead of using a Gaussian as a kernel we can also use an exponential kernel with... 

Figure 10.3 The input images are shown in the first row, the result of a convolution with a Gaussian kernel is shown in the second row, and the result of a convolution with an exponential kernel is shown in the last row.

Figure 10.18 A comparison between the computed and the actual illuminant along a horizontal line of the image (marked by a white line in Figure 10.17). Local space average color is computed using an exponential kernel, a Gaussian kernel, or a resistive grid.

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