Sentence examples for by the delta function from inspiring English sources

In other words, (D_eG) is the space spanned by the delta function supported at (e) and all of its derivatives.

In the simulation a new moving mesh algorithm is designed to deal with the difficulty caused by the delta function in the traveling heat source.

Since the second term in Eq. (20) is represented by the delta function, the second term becomes the source time function χ (t) in Eq. (32).

The RWT result is obtained by applying the RWT to the LFM signal and then compute the line integral along the straight line with its direction specified by the delta function δ u−bmτ−w0).

As is known from Equation (21), the slope value of AFL is b times of chirp rate of LFM signal, it is therefore essentially to compute the line integral along a straight line with its direction specified by the delta function δ u−bmτ) in the ambiguity plane in order to realize energy accumulation.

Ward (unpublished document available at http://es.ucsc. edu/̃ward/papers/Basic_Tsunami_Theory.doc) obtained an equation for displacement (equation (5.3.10) in the document) for an instantaneous sea-bottom deformation, whereas we have derived an expression for velocity (Eqs. (20) and (21)) in this study with the source term given by the delta function.

The cancelling pulses can be thus generated by propagating the delta function train to this filter, and this principle is illustrated in Figure 8 and its hardware implementation is given in Figure 9. Figure 8 Principle of cancelling pulse generated by delta function trains.

The Frobenius norm of a matrix or vector is denoted by ||·|| and the delta function by δ.

As one of them, the LPIM is based on the local weak form of the partial differential equations and easily implements the boundary conditions due to the shape functions constructed by the PIM with the delta function properties.

\end{align} Point moments can thus be represented by the derivative of the delta function.

where,,, and denote the number of paths, the path gain between the terminal and relay at stage (=1,2), the th path time delay normalized by IFFT sampling period, and the delta function, respectively.