Definition 2 (Recurrence operator) A recurrence operator \(\mathcal {R}\) maps the program variables \({\text {Vars}}(\mathcal {P}) \) to the polynomial ring \(\mathbb {R}[{\text {Vars}}_n(\mathcal {P})]\). The set of equations $$\begin{aligned} \{ x(n{+}1) = \mat...
Now by explicit calculation using (17) and the definition of the energy operator (20) one can verify that: J2=E(E+1), (23) where J2=Jx2+Jy2+Jz2 is the su(2) Casimir with eigenvalue j(j+1) when acting on the state |j;m⟩. This tells us that we can identify the eigen...
As we will see in the following, this definition turns out to be useful when studying the dissipation in the presence of a single loop. Due to the presence of the loop, we have a new degree of freedom, the cycle flow strength f. According to the KCL Eq. (2), the flows in the ...
Definition 12 Let v and u be adjacent vertices of a graph. Vertex v is dominated by vertex u if every vertex adjacent to v is also adjacent to u. In an interval representation, if two intervals Iu and Iv of the real line intersect, then one contains the two endpoints of the other, ...
Broadcast is the fundamental collective communication routine in which the same message is delivered from a single source to all the nodes in a network. The most efficient way to implement broadcast is through the construction of a broadcast tree. We introduce a revised definition of optimality ...
There are two alternative approaches to the definition of bandwidth: (1) through the complementary sensitivity function, and (2) through the sensitivity function. We present the approach of (1) in the sequel; see also Further Readings. Conceptually, bandwidth is defined as the frequency range ...
In CRFs based on “local” connectivity, nodes connect adjacent pixels in x (Kumar & Hebert, 2006), whereas in the fully connected definition such as here (Figure 2f), each node is linked to every other (Krähenbühl & Koltun, 2011). Linking each node of the graph created from x ...
Therefore, it is not possible to reach a new set point for a plant in open-loop mode unless the input is changed manually. Furthermore, the disturbances drive the system away from its original operating point. In addition, some plants are unstable and cannot be operated without a controller...
How to deal with the simplicity constraint is still an open issue in small N cases. In fact, the general geometric operators with respect to D-polytopes can also be defined by the coherent states of spatial geometry such as the gauge invariant coherent intertwiners. Also, the definition of ...
Definition A shape made by bending material back on itself. A fastening made by tying pieces of material together. 5 Use in Physical World Often adjustable and temporary, e.g., loops in lace. Secure and permanent, e.g., knots in ropes. 10 Symbolism Simplicity and repetition, e.g., loop...