Sentence examples for only if corresponding from inspiring English sources

So, via Remark 2.7, we obtain that equilibrium points and can be stable concurrently only if corresponding and are negative concurrently.

For example, it was proven by Brands [2] that for every nonnegative p ( t ) and bounded delay τ ( t ), (1.7) is oscillatory if and only if corresponding ordinary differential equation (1.10) is oscillatory.

Conservative House Majority Leader Eric Cantor made similarly bewildering comments after the Virginia earthquake earlier this week, declaring that government response to that event would only occur if corresponding cuts were made in other spending.

The similarity theorem may be reformulated as the AAA (angle-angle-angle) similarity theorem: two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.

In the network graph there exists an edge between an intermediate node and a species node if and only if the corresponding reaction involves, as reactant or product, a complex of the corresponding species.

We use following notations to denote vertices and edges in G and L(G): let i,j∈V denote two vertices in the original graph G, we use (i,j) to represent the edge in G and the corresponding vertex in L(G) two vertices of L(G) are adjacent if and only if their corresponding edges share a common endpoint ('are incident') in G and they form a length two directed path.

It was shown that such a group is stable if and only if the corresponding graph is stable and Baudisch generalized this fact to the simple theory context.

We will conclude by presenting and proving the key theorem of this talk: The free action on an $L^\infty $ space is ergodic if and only if the corresponding cross product von Neumann algebra is a factor.

Another main result of this paper is the following: Ifμis a canonical Gibbs measure, then it is extreme (or a "pure phase") if and only if the corresponding weak Sobolev spaceW1, 2 onΓis irreducible.

To address this extremal problem, we introduce Hankel-type operators on spaces of matrix functions and prove that this problem has a solution if and only if the corresponding Hankel-type operator has a maximizing vector.

By establishing a theorem of function theory over the bidisk, it is shown that a Beurling type quotient module is essentially normal if and only if the corresponding inner function is a rational inner function having degree at most (1,1).