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K-Tech Tree was established as a strategy for finding necessary technologies and developing the technologies to implement SWMI.
We also extend a classic result of Colbourn and Rosa on quadratic leaves, finding necessary and sufficient conditions for the existence of a K3-decomposition of λKn−E(Q), where Q is any 2-regular subgraph of Kn.
Also solved is the more general problem of finding necessary and sufficient conditions for the embedding of a partial 3-path design of order n into a 3-path design of order k≥n+2.
Ohno in [39] devoted most of the paper to finding necessary and sufficient conditions for (C_{varphi}D) to be bounded as well as for (C_{varphi}D) to be compact on the Hardy space (H^{2}).
In this paper we consider resolvable decompositions, finding necessary and sufficient conditions for a 4-cycle factorization of K a,p λ1,λ2) (when λ1 is even) or of K a,p λ1,λ2) minus a 1-factor (when λ1 is odd) whenever a is even.
Here the algorithms of finding necessary conditions are all linear and readily done using computer algebra system such as Mathematica or Maple, and these play an important role in solving completely the integrability and linearizability for the 3 : − q resonant case.
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Should the Act pass, individual jurisdictions, many of them cash-strapped, will ultimately be responsible for finding the necessary funding to make mandated improvements.
The Nets, prone to not finding the necessary intensity until the second half, again fell into an early hole.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com