If the distance is less than zero, then the starting point of the line will be returned; if the distance is greater than the length of the line, then the end point of the line will be returned. Double use_percentage The distance may be specified as a fixed unit of measure or a rat...
or in other words, the set of feasible matrices of the relaxation is precisely G(F), where F is the original feasible set. In the previous example, consider the case where Q=−1 and q=0, so that the original quadratic problem is a nonconvex problem with optimal value given by −...
We find that our synthetic data generation can rediscover some fairly complex theorems and lemmas known to the geometry literature, as shown in Fig.4, despite starting from randomly sampled theorem premises. This can be attributed to the use of composite actions described in Extended Data Table1,...
Some of the modeling for lung geometry uses exponential models, starting with the premise that the lung is a dichotomous branch tree with a parental branch of greater length and diameter and an exponential decrease with every daughter branch due to maximizing entropy. Nevertheless, when this model...
In other words, on an infinite chess board, the fraction of squares you can cover with “friendly” Rooks, Bishops or Queens is vanishingly small. As a reminder, by “friendly” I mean that none of the pieces are threatening each other by standard chess rules. Also, if you were to thro...
With this key, any application can access all REST API. In other words, this key can be used as a master key in the account that they are issued in. For publicly exposed applications, our recommendation is to use the confidential client applications approach to access Azure Maps REST APIs ...
Some jargon is words plucked from the common language, such as “smooth”. The common meaning may guide you to what mathematicians want in it. A smooth function has a graph with no gaps, no discontinuities, no sharp corners; you can see smoothness in it. Sometimes the common meaning is ...
is the simple graph with the set \({\mathscr {t}}\) as its vertices and where a pair of vertices t , \(t'\) form an edge if and only if \(|s(t,t')|=1\) . in other words, \(g_{\mathscr {l}}\) is an induced subgraph of the hypercube \(q_e\) . note that (i)...
We could look at any number of geometric forms for examples of these two perspectives – two completely mutually exclusive thought systems – that reflect our journey back to source using symbol as a starting point, and returning us to our shared essence as the ultimate destination. “… the ...
In this work, we analyze theoretically and verify experimentally such geometry-independent features for radiation, thus presenting a novel class of radiating resonators, i.e., antennas, with an operating frequency irrelevant to the geometry shape while only determined by the host material’s ...