Sentence examples for defined by the equality from inspiring English sources

All three were defined by the equality of opposition.

The spectral radius of the operator defined by the equality.

The rearrangement can be defined by the equality (2.1).

and the operator is defined by the equality where for and for We have.

The spectral radius of the operator defined by the equality (3.26). is zero for every positive number [4].

Finally, general equilibrium is defined by the equality (in each period) between supply and demand of goods and factors, and the savings-investment identity.

where the operator and the function are defined by the equalities (2.6).

For example, if we assume that given source nodes have to transmit messages of sizes to destinations in a given time, the polyhedral set is defined by the equalities and inequalities.

Therefore, we can extract from the sequence ({{eta}_{t_{n}}}) a subsequence ({{eta}_{k}}), which is defined by the equalities ({eta}_{k}={eta}_{t_{n_{k}}}), (kinmathbf{N}) (henceforth, we define a sequence ({t_{k}}) by the equality (t_{k}=t_{n_{k}})), and ({{eta}_{k}}) weakly converges to some function η̃ in (H(Omega)).

Process (1.1) has a unique stationary ergodic distribution p0,..., p N defined by the equalities d p i (t)/d t = 0 for 0 ≤ i ≤ N. Let J i, t) = δ i p i (t) - λ i -1 p i -1 t) be the current through the state i in t time moment, J i) = δ i p i - λ i -1 p i -1 be the current in the stationary state.

It is shown that, if a mapping satisfies the following functional equation for all with, which is defined by the above equality, then the mapping is realized as the sum of an additive mapping and a quadratic mapping.