For example, if the radius of convergence is 1/N, then the interval of convergence includes (a – 1/N, a + 1/N); In order to find the interval of convergence, find the radius of convergence first then insert the result into (a–R,a+R). For the radius of convergence forcomplex-v...
Since you assume that the radius of ∑anxn∑anxn is RR, you know that lim sup|an|1/n=1Rlim sup|an|1/n=1R. Now you want to compute the radius of ∑nnn!anxn∑nnn!anxn, which is (by the above criterion) 1 over lim sup|nnn!an|1/nlim sup|...
to calculate f^(ω)f^(ω), by assuming ω≤0ω≤0 and with the real axis and the (infinite) semicircular arc in the upper half plane as contour of integration. How does the integrand behave on that arc, parametrised by ReiφReiφ with R≫0R≫0 and 0≤φ≤π0≤...
In general mathematics, a functional may refer to a function specifically produced from a set ofreal-valued functions.For example, a functional could be the maximum of a set of functions on theclosed interval[0, 1]. Abinary functionaltakes two sets of functions to create one function. For e...
We focused our analyses on 76 pairs of forest tree species. We used data from the French National Forest Inventory to calculate species dominant height in 1368 mixed stands. We then used previously developed models to estimate the expected dominant height in virtual monospecific stands with the sa...
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I want to calculate spectral radius of matrix A, which is in a two dimension array. as you know, for doing that, i need to calculate eigenvalues of this matrix, but i don't know how can i do that. does anybody have experience with this problem? i mean, how can i calculate eigenval...
It is straightforward to calculate the impulse vector as Δvi = Δviαi, where αi = p(ti)/∥p(ti)∥. All of the required values are retrievable from the extremal, which is the solution of the TPBVP for T \gg T_{{\min \limits }}. Note that it is possible to parameterize ...
To check for convergence and divergence of the series ∑n=1∞un, the series can be represented as un=(−1)n+1pnor un=(−1)npn, where pn⩾0,∀n,. Then for convergence of the series, the following conditions...
An undirected graph is a structure composed of vertices connected by edges. Edges are assigned weights corresponding to the distance between the connected points. Useful algorithms such as Dijkstra’s algorithm to calculate shortest paths [171], Minimum Spanning Tree [172], and graph-based clustering...