Sentence examples for exists and unique from inspiring English sources

if such pair exists and unique.

Property 1: When the power price of the source node and other cooperative jamming nodes are fixed, the equilibrium point of utility function ( {U}_{J_m} ) of every cooperative jamming node exists and unique.

Since a solution of the system (11)–(12) exists and is unique, then the process described in Eq. (9) exists and is unique.

Every solution (x t) ) of (1.2) with initial value condition (1.4) exists and is unique on ([0, +infty)). Let us show initially that (x (t )) exists and is unique on ([0, r]).

We show that the solution exists, and is unique, bounded, nonnegative, and globally defined.

It is proven in [Lee87a] that such a solution exists and is unique for every SDF graph that is "consistent," as defined below.

Such z ∈ C always exists and is unique.

The next assertion shows that (resp., ) exists and is unique.

The solution of Algorithm 1 exists and is unique.

Therefore, the inverse NDFT exists and is unique, and x can be calculated by.

Since Δ is nonempty, closed and convex, (P_{Delta}(x)) exists and is unique.