Sentence examples for a directed system from inspiring English sources

For β i = ( α i, t i ) ∈ I, i = 1, 2, we define β 1 ≤ β 2 if and only if α 1 ≤ α 2, t 1 ≤ t 2. In this case, I is also a directed system.

In this case, ( G, ≤ ) is a directed system when the binary relation ≤ on G is defined by s ≤ t if and only if { s } ∪ s G ¯ ⊇ { t } ∪ t G ¯, s, t ∈ G.

By Day [18], if D has a left invariant mean, then there exists a net { λ α : α ∈ A } of finite means on G such that lim α ∈ A ∥ λ α − l s ∗ λ α ∥ = 0. for every s ∈ G, where A is a directed system, and l s ∗ is the conjugate operator of l s.

Proof Since D has a left invariant mean, there exists a net { λ α : α ∈ A } of finite means on G such that lim α ∈ A ∥ λ α − l s ∗ λ α ∥ = 0 for every s ∈ G, where A is a directed system.

A net { λ α : α ∈ I } of finite means on G is said to be strongly left regular if lim α ∈ I ∥ λ α − l s ∗ λ α ∥ = 0. for all s ∈ G, where A is a directed system and l s ∗ is the conjugate operator of l s.

If S is left (respectively, right) reversible, ( S, ⪯ ) is a directed system when the binary relation ⪯ on S is defined by a ⪯ b if and only if { a } ∪ a S ¯ ⊃ { b } ∪ b S ¯ (respectively, { a } ∪ S a ¯ ⊃ { b } ∪ S b ¯ ), a, b ∈ S. Let S be a semitopological semigroup and C a closed convex subset of a metric space ( X, d ).

Because managers needed to be able to give rewards and bonuses at their own discretion, sticking to a centrally directed system of wages was very difficult.

Take an element 0 ≤ f ∈ Y. Then there is an upwards directed system ( f τ ) ⊂ L p with 0 ≤ f τ ↑ f ν-a.e.

If the United States had a direct system of voting, Clinton would have been the one at the White House on Thursday meeting with President Obama.

It will give carmakers a choice of two systems to install: either a "direct" system, which calculates pressure by using a battery-operated measuring device on each of the four tires, or an "indirect" system, which infers pressure by calculating the difference in rotational speeds between wheels, using a computer in the vehicle's antilock braking system.

The procedure outlined improves the detection limit of a direct system, decreasing it from 1×10−4 to 3×10−6 M by use of a pre-concentration volume of 40.0 ml and 200 μl of 75% acetonitrile in water as the eluent.