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This allows a well-posed problem to be formulated.
The Irwin relationship for the crack tip energy release rate in terms of the crack tip intensity factors then allows the intensity factors for the unsolved problem to be formulated, thereby giving the desired weight function.
The method allowed the problem to be formulated as a two-dimensional Helmholtz eigenvalue problem, which could be solved with general purpose software rather than custom written codes, but appeared to be limited to ducts without flow.
As noted in [27], the DS theory allows the problem to be formulated to reflect the state of knowledge, rather than physics, which is particularly applicable in this work, as there are too many unknowns (emitter power, pathloss and locations) to be able to define precisely the actual state.
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This paper develops a GCD theory-based approach that allows challenging problems to be formulated in a robust fashion.
In this paper, we develop a GCD-based theoretical approach that allows challenging problems to be formulated in a robust fashion.
For two spatial dimensions the problem needs to be formulated into either ODE nodes or PDEs in one spatial dimension linked by ODEs in the other spatial dimension.
Solid mechanics problems use to be formulated in tensor notation in three-dimensional (3D) Euclidean space.
In Section 2, some concepts in graph theory are described, and the problem to be investigated is formulated.
The analysis of the results is difficult through statistical techniques, and needs restrictive assumptions for the problem to be analytically formulated, or a prohibitively large computational endeavor.
In the next section, the problem to be dealt with is formulated and the necessary preliminaries are presented.
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