Sentence examples for is again valid from inspiring English sources
Vice versa, if u i = 1, constraint (4) reduces to ∑ j ∈ V : j ∈ Z ∑ s ∈ Ŝ z ij s ≥ 2 which is again valid for the above arguments.
If z ij s 1 = 1 then constraint (5) (respectively constraint (6)) reduces to + x i s 2 − x j s 2 ≤ 0 (respectively − x i s 2 + x j s 2 ≤ 0 ), which is again valid.
If u i = 0, constraint (3) reduces to u i + 1 ≤ 0 which is trivially valid for Formulation 2. If u i = 1, constraint (3) reduces to u i + 1 ≤ 1 which is again valid.
Vice versa, If ∑ j ∈ V : j ∈ Z ∑ s ∈ Ŝ z (i + 1 ) j s = 1, constraint (11) reduces to ∑ j ∈ V : j ∈ Z ∑ s ∈ Ŝ z ij s ≥ 1 which is again valid due to Propositions 1 and 2. □ Proposition 6 forces vertices in V H ′ to be sorted according to a decreasing degree order.
Being in a vocational school or being out-of-school again significantly raised the odds of having had intercourse compared to being in a general school or university, and the socio-cultural interpretation advanced for males is again valid.
This is also the case for segmented quadratic or cubic phase signals for which Equation (6) is again not valid for the whole signal duration.
where (mathbf {C}_{A}^{b}oplus mathbf {C}_{B}^{b}) itself is again a valid codeword and hence the WNC function (fleft (mathbf {d}_{A}^{b},mathbf {d}_{B}^{b}right)) can be decoded directly from the relay observation (using a conventional single user decoder (mathcal {C}_{b}^{-1})).
The sufficient conditions for this approach to be valid is again the causal assumptions of positivity, exchangeability and consistency.
Other concerns, such as the selection of 'well behaved' users, the expectations of users, time delays and the focus on short-term concerns are again not valid criticisms of user involvement.
This again is a valid concern.
The following are also valid, again where α is any wff:(∀x)(∀y)α ≡ (∀y)(∀x)α (∃x)(∃y)α ≡ (∃y)(∃x)α The extensions of these lead to the following rule: 2. If a wff contains an unbroken sequence either of universal or of existential quantifiers, these quantifiers may be rearranged in any order and the resulting wff will be equivalent to the original wff.
