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"A minimal existence means you don't buy things you don't need," Mr. Rogers said.
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A third of one's contemporaries are dead, and many more, with profound mental or physical damage, are trapped in a tragic and minimal existence.
The resulting method can be applied under some necessary and sufficient, and thus minimal, existence conditions for causal state observers.
For example, just as the principles in (P.12ξ,i) assert the existence of a minimal underlapper for any pair of suitably related entities, one may at this point want to assert the existence of a maximal overlapper, i.e., not a "sum" but a "product" of those entities.
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.
Analogously, we can prove the existence of a minimal element.
The existence of a minimal map is sensitive to small perturbations of the norm.
Then Theorem 3.8 ensures the existence of a minimal compact subset of such that (3.15).
The proof for the existence of a minimal element of S is analogous.
In this section, we establish the existence of a minimal nonnegative solution for problem (1.5).
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