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A series of direct shear box tests were conducted on samples of dune sand- waste crumb rubber mixture in loose and slightly compacted condition for comparison purposes.
The manure's compacted condition, in addition to decreased gas diffusion (which limited O2 diffusion), also retained anoxic conditions longer because of the trapped water.
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If is compact, condition (i) is satisfied trivially.
Cerami [23] presented a weaker compact condition than the above classical ( PS ) c condition.
That is, the proof of our compact condition is more simple than that in [8].
In this paper, assuming a natural sequentially compact condition we establish new fixed point theorems for Urysohn type maps between Fréchet spaces.
To obtain a homoclinic solution of (5), some compact condition is needed, so weighted sequence spaces (l_{eta}^{p}) are also introduced in this section.
Remark 2.6 In fact, the function satisfying Condition ( C ∗ ) implies the dissipative property in some sense, and Condition ( C ∗ ) is very natural in view of the compact condition, and the uniform Condition (C).
In the course of proving existence of positive solution and negative solution, our conditions are general, but the proof of our compact condition is more simple than that in [8].
end{aligned} (61 Because the set of feasible allocations (mathbf {Z}) is compact, Condition F means that the solution path ((x,y_{i})) is bounded for any (iin mathbf {N}. ) Hence, by continuity of the utility functions L is also bounded.
However, to the best of our knowledge, the existence and uniqueness of mild solution of the initial value problem (1.1)–(1.2) under compact condition have not been deeply investigated yet.
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