Sentence examples for problems can be established from inspiring English sources

The relationship between density distributions and various routing costs may be further analyzed, and the equivalence between geodesic problems and optimum routing vector field problems can be established.

A specific diagnosis of a liver problem can be established by performing a needle biopsy.

The approximation of the truncation and accumulated errors in the numerical solution of a linear initial-valued partial differential equation problem can be established by using a semidiscretized scheme.

By maximizing the achievable rate (12), the joint power allocation problem can be established as (13).

By [25], an important and new equivalent mixed type integral equation for our problem can be established.

According to the above fundamental result, a new and important equivalent mixed type integral equation for the problem can be established.

The convergence of Algorithm 1 to the global optimal solution of problem P1 (i.e., problem (4)) can be established by using proposition[34], Proposition 4.2.

Different environments, testing protocols, scopes and problem domains can be established to develop limited versions or variants of the original Turing test.

Now, we are in a position to state the local existence result to problem (1.1), which can be established by using arguments similar to those in [14].

end{aligned} (2.20) We now state the local existence result of problem (2.13 - 2.20), which can be established by combining with the argument of [6].

For instance, the membership of a propositional formula \ \phi\) with atomic letters among \(P_0,\ldots, P_{n-1}\) in the problem \(\sc{SAT}\) can be established by searching through the set \(S_{\phi}\) of possible valuation functions of type \ v:\{0,\ldots,n-1\} \rightarrow \{0,1\}\), to determine if there exists \ v \in S_{\phi}\) such that \(\llbracket \phi \rrbracket_v = 1\).