Sentence examples for a minimal solutions from inspiring English sources

Further iterations are possible and this gives a convergent sequence of upper and lower bounds under the conditions of Theorems 5 and 6 and provided that Perron-Kreuser theorem holds (which implies that the recurrence admits a minimal solutions).

A minimal solution is the one that minimizes the summed changes of the 5 variables.

Although mathematical solutions for specific boundaries had been obtained through the years, it was not until 1931 that Douglas (and independently the Hungarian American mathematician Tibor Radó) first proved the existence of a minimal solution for any given "simple" boundary.

Although mathematical solutions for specific boundaries had been obtained through the years, it was not until 1931 that the American mathematician Jesse Douglas (and independently the Hungarian American mathematician Tibor Radó) first proved the existence of a minimal solution for any given "simple" boundary.

It is guaranteed that a minimal solution exist, consisting of prime compatibles only.

We define a minimal solution Y min ∈ [ Y L, Y U ] as a function satisfying the reverse inequalities.

Only the element x ¯ = 0 is a minimal solution of ( SP − ⪯ C l ).

A minimal solution may be defined similarly by reversing the last inequality.

Furthermore, (alpha^) and (beta^) are a minimal solution and a maximal solution of (1.1) in Ω, respectively.

A second independent solution of (51) which is a minimal solution of (52) as ν → +∞ follows from [[25], Theorem 2].

In this paper, we investigate the existence of a minimal solution of general dual fuzzy linear equation systems.