Sentence examples for any pair of action from inspiring English sources

Here, for any pair of action profiles p(n) and p(m), with ( n, m ) ∈ I 2 and n ≠ m, we have that ϕ(p(n)) ≠ ϕ(p(m)) with probability one.

Conservation of total angular momentum does not follow immediately from Newton's laws but demands the additional assumption that any pair of forces, action and reaction, are not only equal and opposite but act along the same line.

President Obama took a pair of actions on Tuesday aimed at exposing pay discrimination and improving wages for women.

By Jeff Shesol April 9, 2014 President Obama took a pair of actions on Tuesday aimed at exposing pay discrimination and improving wages for women.

Obama has been relegated to quietly signing modest proposals into law using his executive authority – his administration announced a pair of actions last year aimed at limiting firearm access for individuals with mental health issues.

Those will cap a year in which Mr. Spielberg will have shared producer credits on six films, including a pair of summer hits, "Super 8" and "Transformers: Dark of the Moon," and a pair of action-adventure pictures, "Cowboys & Aliens" and "Real Steel," that have yet to open.

We will use its solutions to construct a pair of action-angle variables.

Introducing a pair of action-angle variables ((J,vartheta)inmathbb {R}^{kappa}timesmathbb{T}^{kappa}) ((Bbb{T}^{kappa}:=Bbb {R}^{kappa}/2pi mathbb{Z}^{kappa})), one can obtain an equivalent Hamiltonian that does not depend on the time variable.

We introduce a pair of action-angle variables ((J,theta)inmathbb {R}^{m}timesmathbb{R}^{m}), (theta=omega t) with dot{theta}=omega,qquad dot{ J}=-frac{partial H}{partialtheta},qquad dot{z_{n}}=mathrm{i}frac{partial H}{partialbar{z}_{n}},qquad dot{bar{z}}_{n}=-mathrm{i}frac{partial H}{partial z_{n}},quad nin mathbb{Z}^{d}.

Thus, in general, the maximum number of different partitions we can have is |A|+(|A|×|X|), where |A| comes from the reward function of each action and |A|×|X| comes from the factored probabilistic transition functions considering each pair of action and state variable.

To refer to the partitions of an MDP, we use a special notation: for each action a∈A, we have a partition (mathcal {P}_{R}^{a}) with respect to the reward function; and for each pair of action a∈A and state variable X i ∈X that can be changed by a, we have a partition (mathcal {P}_{X_{i}}^{a}) with respect to the factored probabilistic transition function.