A commutative ring, together with a function, ƒ, from the nonzero elements of the ring to the nonnegative integers, such that (1) ƒ(xy) ≥ ƒ(x) ifxy≠ 0, and (2) for any members of the ring,xandy, withx≠ 0, there are membersqandrsuch thaty=qx+rand eitherr=0 orf(r...
TheEuclideanReduction(a,b,z)command returns the last numerically well-conditioned basis accepted by the Coprime algorithm [2]. This corresponds to the smallest degree pair of polynomials in the sequence of numerically well-behaved polynomial remainders that can be obtained from(a,b)by unimodular re...
metric space- a set of points such that for every pair of points there is a nonnegative real number called their distance that is symmetric and satisfies the triangle inequality Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc. ...
Illustrate the above discussion with a few examples. Remark. You can apply the Euclidean algorithm to positive real numbers as well, but it is not guaranteed to stop. In fact, if the initial pair is (a, 1) then it stops if and only if a is rational (and the result will be 1/d ...
It does not add the security parameter to the proposed algorithm. Dipti Prasad Mukherjee et al. [5] work on a new algorithm in the spatial domain, which provides buyer authentication with the multimedia objects, it provides robust against the standard Stirmark attack. Image authentication scheme...
Bézout's identity (also called Bézout's lemma) is a theorem in the elementary theory of numbers: let a and b be nonzero integers and let d be their greatest common divisor. Then there exist integers x and y such that ax+by=d ...
The 5NN graphs were then plotted using the same force-based algorithm where connected nodes are attracted and non-connected nodes repelled from one another40, Fig. 4d,e. Remarkably, surface inversion of the hub-centric world city network produced a highly modular network with geometric qualities...
In the algorithm, considering that Ricci curvatures have negative values, they are not easy to deal with, so we use a sigmoid function to transform the Ricci curvatures. It is assumed that 𝐶𝑝𝑎𝑖𝑟𝑠Cpairs are node pairs sampled by a random walk based on the Ricci curvature. ...
This algorithm is very simple, but it can be used to give a new name to a regularity that is found and to discover higher-order regularities by regarding this regularity as a new attribute. For example, suppose we get the data 1-9 as shown in Table 9.3 by measuring the weight of the...
In this paper we present the definition of the Exact Euclidean Medial Axis on Higher Resolution which has the same properties as the MA but with a better thinness characteristic, against the price of rising resolution. We provide an efficient algorithm to compute it. 1 Introduction In 1961, ...