Domination polynomialdoubly connected setfriendship graphCactus chain graphM. H. AKHBARI, F. MOVAHEDI, and M. ARSLANOV, Asian-European J. Math. https://doi.org/10.1142/S1793557119500360doi:10.1142/S1793557119500360Akhbari, M. H.Movahedi, F....
In some situations, we may know two points on a graph but not the zeros. If those two points are on opposite sides of the x-axis, we can confirm that there is a zero between them. Consider a polynomial function f whose graph is smooth and continuous. The Intermediate Value Theorem ...
The exponent says that this is a degree-4 polynomial; 4 is even, so the graph will behave roughly like a quadratic; namely, its graph will either be up on both ends or else be down on both ends. Since the sign on the leading coefficient is negative, the graph will be down on both...
We observe that solutions to these polynomial graph filter models are also solutions to an overdetermined system of equations. It suggests that in some instances, the model needs to learn a reasonably high order polynomial. On investigation, we find the proposed models ineff...
Fig. 1.1b is a graph of the following polynomial equation: (1.13)x4+7x3+12x2−4x−16=0 which has two real and distinct roots at −4 and 1, and two real and repeated roots at −2. The point of tangency with the x-axis indicates the presence of the repeated roots. At this...
The security of cryptographic protocols is often based on the hardness of certain computational problems, e.g., inverting a given trapdoor one-way permutation. Breaking the protocol security then requires solving the underlying computational problem. To prove this, one generally considers reductions; i...
In local averaging, for each window Y¯ is computed on the basis of all the observations on X that are in the window. When the number of observed values on X is small, the resulting graph is jagged, as with binning. Windows that contain a fixed number of n+ 1 observations can be ...
Louise is still new and actively being worked on and so has not yet been used in large-scale real-world applications. Published work on Louise has so far focused on describing the working principles behind Louise's underlying TPC algorithm rather than demonstrating its full potential as a ...
On a graph, you find extreme values by looking to see where there’s a mountain top (“peak”) or valley floor. Mathematically, you find them by looking at thederivative. At an extreme point, where there is a direction change, the derivative of the function is zero. ...
Over the last decade, algorithms that extend the eigenvalue decomposition (EVD) to the realm of polynomial matrices have had a growing impact on signal processing theory and practice, mainly because they can be used to solve generalisations of narrowband problems typically addressed by the EVD, in...