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Combinatorics
Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012
Another sequence of combinatorial import has a generating function that may be simply computed. Suppose βn = n, n ≥ 0. Then fβ(x)=∑1∞aixi=x/(1−x)2. This formula is easily derived by differentiating the ordinary infinite geometric series, and multiplying by x. Note that since a0 = 0 we begin the summation at i = 1; if we begin at i = 0, we get the same series. Differentiating again, with another multiplication by x, gives us another formula: ∑1∞i2xi=(1+x)/(1−x)3. With these formulas, we are able to find the generating function for any integer sequence produced by a quadratic polynomial.
CORDIC Algorithms and Architectures
Published in Keshab K. Parhi, Takao Nishitani, Digital Signal Processing for Multimedia Systems, 2018
For obvious reasons we restrict consideration to radix 2 number systems below: δm,i = 2sm,i. It will be shown later that the shift sequencesm,i is generally a nondecreasing integer sequence. Hence, a CORDIC iteration can be implemented using only shift and add/subtract operations.
The Structure of Trees
Published in Kenneth H. Rosen, Graphs, Algorithms, and Optimization, 2005
Let T be a tree with V(T) = {1, 2,...,n}. A Prüfer sequence for T is a special encoding of T as an integer sequence. For example, the tree of Figure 5.17 with n = 9 has Prüfer sequence t = (6, 9, 1, 4, 4, 1, 6).
A new iterative method for solving the multiple-set split variational inequality problem in Hilbert spaces
Published in Optimization, 2023
Nguyen Thi Thu Thuy, Nguyen Trung Nghia
Let be a real sequence which does not decrease at infinity in the sense that there exists a subsequence such that Define an integer sequence by Then as and for all , we have
Non-rigid rank-one infinite measures on the circle
Published in Dynamical Systems, 2023
Hindy Drillick, Alonso Espinosa-Dominguez, Jennifer N. Jones-Baro, James Leng, Yelena Mandelshtam, Cesar E. Silva
If is an integer sequence such that , and then for each k.