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Customer preferences for different function solution principles are obtained from multiple customers using fuzzy pairwise comparison (FPC).
By simply dropping out selected field functions, several reduced variational principles are obtained as special forms for piezoelectricity, elastodynamics, and electromagnetics, respectively.
The strongest versions of all these composition principles are obtained by asserting them as axiom schemas holding for every condition ψ, i.e., effectively, by foregoing any reference to ψ altogether.
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The product CAD data that is used within these principles is obtained from a neutral STEP file format, ensuring its compatibility amongst existing CAD programs.
The second-order variational equation for the BSDE (3) and the maximum principle are obtained.
For example, the concepts of Ćirić contraction [5], quasi-contraction [6], JS-contraction [7], and JS-Ćirić contraction [8] have been introduced, and many interesting generalizations of the Banach contraction principle are obtained.
The optimal flow distribution principle is obtained by calculating the minimum value of the total entransy dissipation.
Then, a unified variational principle is obtained for the regular region, with one or more fixed internal surface of discontinuity.
On the other hand, the temperature map can in principle be obtained using non-invasive imaging modalities such as optical methods14, 15, infrared thermometry16, ultrasound17, x-ray computed tomography (CT 18, or magnetic resonance imaging (MRI 19.
Thus shorter information travel times between two points on the CME leading edge could, in principle, be obtained using a non-linear ray path taking advantage of the increased Alfvén speed deep within the CME.
Hamilton's principle is stated for the regular region and a three-field variational principle is obtained under some constraint conditions.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com